United States
Environmental Protection
Agency
Office of Research and
Development
Washington DC 20460
EPA/600/R-99/011
February 1999
v>EPA
Three-Dimensional NAPL
Fate and Transport Model
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EPA/600/R-99/011
February 1999
THREE-DIMENSIONAL NAPL FATE AND TRANSPORT MODEL
by
Gary A. Pope, Kamy Sepehrnoori, Mukul M. Sharma,
Daene C. McKinney, Gerald E. Speitel, Jr., and Richard E. Jackson*
Center for Petroleum and Geosystems Engineering
The University of Texas at Austin
Austin, Texas 78712
and
*Duke Engineering and Services, Inc.
9111 Research Blvd.
Austin, Texas 78758
Cooperative Agreement CR-821897
Project Officer
Jong Soo Cho
Subsurface Protection and Remediation Division
National Risk Management Research Laboratory
Ada, Oklahoma 74820
NATIONAL RISK MANAGEMENT RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OH 45268
Printed on Recycled Paper
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Notice
The U. S. Environmental Protection Agency through its Office of Research and Development partially
funded and collaborated in the research described here under assistance agreement number CR-821897 to
The University of Texas at Austin. It has been subjected to the Agency's peer and administrative review and
has been approved for publication as an EPA document. Mention of trade names or commercial products
does not constitute endorsement or recommendation for use.
When available, the software described in this document is supplied on "as-is" basis without guarantee or
warranty of any kind, express or implied. Neither the United States Government (United States
Environmental Protection Agency, Office of Research and Development, National Risk Management
Research Laboratory), The University of Texas at Austin, nor any of the authors accept any liability
resulting from use of this software.
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Foreword
The U. S. Environmental Protection Agency is charged by Congress with protecting the Nation's land, air,
and water resources. Under a mandate of national environmental laws, the Agency strives to formulate and
implement actions leading to a compatible balance between activities and the ability of natural systems to
support and nurture life. To meet these mandates, EPA's research program is providing data and technical
support for solving environmental problems today and building a science knowledge base necessary to
manage our ecological resources wisely, understand how pollutants affect our health, and prevent or reduce
environmental risks in the future.
The National Risk Management Research Laboratory is the Agency's center for investigation of
technological and management approaches for reducing risks from threats to human health and the
environment. The focus of the Laboratory's research program is on methods for the prevention and control
of pollution to air, land, water, and subsurface resources; protection of water quality in public water
systems; remediation of contaminated sites and ground water; and prevention and control of indoor air
pollution. The goal of this research effort is to catalyze development and implementation of innovative,
cost-effective environmental technologies; develop scientific and engineering information needed by EPA
to support regulatory and policy'decisions; and provide technical support and information transfer to ensure
effective implementation of environmental regulations and strategies.
Simulation models are needed for analyzing and predicting the fate and transport of nonaqueous phase
liquids (NAPLs) in the subsurface environment and to assess the effectiveness of remedial actions at NAPL
contaminated sites. There are a number of crucial questions concerning the physical, chemical, and
biological processes affecting the fate and transport of NAPLs that can only be addressed by modeling the
processes under realistic conditions taking into account aquifer heterogeneities, compositional phenomena,
geochemistry, microbiology, and other complications. This report describes the development, testing and
validation of a comprehensive flow and transport simulator (UTCHEM) that can model fate and transport of
NAPLs as well as processes for their remediation. Illustrations of both surfactant remediation and
bioremediation of contaminated aquifers are given.
Clinton W. Hall, Director
Subsurface Protection and Remediation Division
National Risk Management Research Laboratory
111
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Abstract
We have added several new and significant capabilities to UTCHEM to make it into a general-purpose
NAPL simulator. The simulator is now capable of modeling transient and steady-state three-dimensional
flow and mass transport in the groundwater (saturated) and vadose (unsaturated) zones of aquifers. The
model allows for: changes in fluid properties as a site is remediated; heterogeneous aquifer properties; the
flow and transport of remedial fluids whose density, viscosity and temperature are variable, including
surfactants, cosolvents and other enhancement agents; the dissolution and/or mobilization of NAPLs by
nondilute remedial fluids; and chemical and microbiological transformations. Appropriate physical,
chemical and biological process models important in describing the fate and transport of NAPLs in
contaminated aquifers have been incorporated into the simulator, such as multiple organic NAPL phase,
nonequilibrium interphase mass transfer, sorption, microbiological and geochemical reactions, and the
temperature dependence of pertinent chemical and physical properties. The biodegradation model includes
inhibition, sequential use of electron acceptors, and cometabolism and can be used to model a very general
class of bioremediation processes. The model can be used to simulate the actual field operation of
remediation activities such as surfactant remediation or bioremediation as well as laboratory experiments
with large-scale aquifer models.
A systematic evaluation was undertaken to assess the applicability and accuracy of all physical and chemical
models of the various pertinent phenomena such as capillary pressure, relative permeability, adsorption,
nonequilibrium mass transfer, dispersion, and phase behavior. The microbiological model suitable for very
general bioremediation simulations was added to UTCHEM and tested with data from the literature with
good agreement. Comparisons to analytical solutions were made and numerical dispersion control and
accuracy testing were performed. The model was tested against experimental and field data. The
FORTRAN source code has been delivered to EPA along with sample input and output files.
This report contains 12 sections. Section 1 gives an overview of the project objectives and
accomplishments. Sections 2 through 12 describe the formulation of UTCHEM. Appendix A contains the
user's guide for UTCHEM, Appendix B contains the user's guide for UTCHEM local grid refinement.
Appendix C presents the discretized flow equations.
This report was submitted hi fulfillment of CR-821897 by The University of Texas at Austin under partial
sponsorship of the U.S. Environmental Protection Agency. This report covers a period from September
1994 to September 1996 and work was completed as of September 1996.
IV
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Contents
Notice •. ii
Foreword iii
Abstract iy
Figures viii
Tables ix
Section 1 Project Summary 1
1.1 Introduction 1
. 1.2 Model Development 2
1.2.1 Microbiological Population Modeling 3
1.2.2 Numerical Enhancements to the Model 4
1.2.3 New Relative-Permeability and Capillary-Pressure Models 5
1.2.4 New Organic and Tracer Components 6
1.3 Model Evaluation 8
1.4 Conclusions 9
Section 2 UTCHEM Model Formulation 15
2.1 Introduction 15
2.2 Model Formulation •. 17
2.2.1 General Description 17
2.2.2 Mass Conservation Equations . 18
2.2.3 Energy Conservation Equation 19
2.2.4 Pressure Equation 19
2.2.5 Non Equilibrium Dissolution of Nonaqueous Phase Liquids 20
2.2.6 Well Models .„ .?. 21
2.2.7 Fluid and Soil Properties 21
2.2.8 Adsorption 21
2.2.9 Cation Exchange 23
2.2.10 Phase Behavior 24
2.2.11 Phase Saturations 27
2.2.12 Interfacial Tension 27
2.2.13Density 28
2.2.14 Capillary Pressure 28
2.2.15 Relative Permeability 31
2.2.16 Trapping Number 32
2.2.17 Viscosity 34
2.2.18 Polymer Permeability Reduction 35
2.2.19 Polymer Inaccessible Pore Volume 36
2.3 Numerical Methods 36
2.3.1 Temporal Discretization 36
2.3.2 Spatial Discretization 36
2.4 Model Verification and. Validation 37
2.5 Summary and Conclusions 38
2.6 Nomenclature 38
Section 3 Hysteretic Relative Permeability aind Capillary Pressure Models 46
3.1 Introduction 1 46
3.2 Oil Phase Entrapment ,....46
3.2.1 Kalurachchi and Parker 47
3.2.2 Parker and Lenhard 47
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3.3 Capillary Pressure 48
3.3:1 Two-Phase Flow 48
3.3.2 Three Phase Oil/Water/Air Flow 48
3.4 Relative Permeability :-;-yy; AQ
3.5 Capillary Number Dependent Hysteretic Model 48
Section 4 UTCHEM Tracer Options 51
4.1 Introduction £{
4.2 Non-Partitioning Tracer ^j
4.3 Partitioning Tracer 5{
4.3.1 Water/Oil 51
4.3.2 Gas/Oil 52
4.4 Radioactive Decay $6
4.5 Adsorption •>•*
4.6 Reaction ^
4.7 Capacitance D4
Sections Dual Porosity Model 56
5.1 Introduction £°
5.2 Capacitance Model • •>%
5.3 Subgridding,. £g
5.4 Implementation 2X
5.5 Results 60
5.6 Conclusions gi
5.7 Nomenclature Oi
Section 6 UTCHEM Model of Gel Treatment 69
6.1 Introduction 2^
6.2 Gel Conformance Treatments °y
6.3 Gel Viscosity /{
6.4 Gel Adsorption /}
6.5 Gel Permeability Reduction '\
6.5.1 Chromium Retention l\
6.5.2 Cation Exchange /^
6.5.3 Adsorption /^
6.5.4 Precipitation 4o
6.5.5 Polymer/Chromium Chloride Gel /^
6.5.6 Polymer/Chromium malonate Gel /•}
6.5.7 Silicate Gel 7,4
6.6 Temperature Effects /->
Section 7 Multiple Organic Components 76
7.1 Introduction 40
7.2 Mass Transfer for Nonaqueous Phase Liquid /o
7.2.1 No Surfactant or Surfactant Concentration Below CMC /o
7.2.2 Surfactant Concentration Above CMC 77
7.3 Physical Properties for NAPL Mixture 79
7.4 NAPL Mixture Viscosity g|
7.5 Density of NAPL Mixtures gl
7.6 Adsorption of Organic Species gj
7.7 Nomenclature 81
Section 8 EQBATCH Program Description .' 83
8.1 Introduction g^
8.2 User's Guide S3
Section 9 Microbiological Population Modeling 105
9.1 Introduction
9.2 Model Description and Features
9.3 Biodegradation Equations and Solution Procedure
9.4 Example Simulations«
9.4.1 LNAPL Simulation Example 110
9.4.2 DNAPL Simulation Example 110
VI
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Section 10 Well Models 117
10.1 Introduction 117
10.2 Vertical Wells with Cartesian or Curvilinear Grid Options 117
10.2.1 Well Constraints for Injection Wells „ 118
10.2.2 Well Constraints for Production Wells 119
10.3 Vertical Wells with Radial Grid Option 120
10.3.1 Rate Constraint Injector 120
10.3.2Rate Constraint Producer 120
10.3.3 External Boundary 120
10.4 Horizontal Well with Cartesian or Curvilinear Grid Options 121
10.4.1 Productivity Index for Horizontal Wells 121
Section 11 Effect of Alcohol on Phase Behavior 124
11.1 Introduction -. 124
11.2 Alcohol Partitionaing 124
11.3 Effective Salinity ....„ 127
114 Flash Calculations 128
11.4.1 For Type II(-) Phase Bahavior 131
11.4.2 For Type II(+) Phase Bahavior 131
11.4.3 For Type III Phase Behavior 135
Section 12 Organic Dissolution Model in UTCHEM 139
12.1 Introduction 139
12.2 Saturated Zone (Gas Phase Is Not Present) 139
12.2.1 Organic Solubility 140
12.2.2 Phase Saturations 141
12.3 VadoseZone .143
12.4 Nomenclature 144
Appendix A UTCHEM 6.1 User's Guide 146
A.I Introduction 146
A.2 Operation of the Simulator 147
A.3 Input Data Description 152
A.4 Output Files 225
A.5 Geochemistry Option (IREACIM) 229
A.6 Main Program Flow Outline 232
A.7 Phases and Species in UTCHEM 234
A.8 Time-Step Selection 236
A.9 Description of work.job File 238
Appendix B UTCHEM Local Grid Refinement User's Guide 239
B.I Introduction 239
B.2 Local Grid Refinement Specifications 240
B.3 Operation of the Simulator 244
B.4 Input Data Description 245
B.5 Nomenclature 299
B.6 Output Files and Reactions 303
Appendix C Discretized Flow Equations 318
References.
.322
VII
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Figures
1.1 Comparison of substrate profiles calculated by UTCHEM simulator to those predicted by
the model of Molzefar/. (1986) 9
1.2 a) Definition of zone and interlace and b) coarse-fine and fine-fine interfaces 10
1.3 Comparison between analytical solutions and third-order finite-difference solutions in
UTCHEM 11
1.4 Simulated and laboratory PCE recovery from the 2-D column 12
1.5 Tracer concentrations produced at extraction well SB-1 during Hill AFB Phase I test 12
1.6 Surfactant concentrations produced at extraction well SB-1 during Hill AFB Phase I test 13
2.1 Schematic representation of Type II(-) 43
2.2 Schematic representation of high-salinity Type II(+) 43
2.3 Schematic representation of Type III 43
2.4 Correspondence between (a) ternary diagram and (b) hand plot 43
2.5 Coordinate transformation for the two-phase calculations in Type III 44
2.6 Measured and simulated PCE saturation at the location of Core 3 prior to surfactant
flooding (after Freeze etal, 1994) 44
2.7 Measured and simulated PCE saturation at the location of Core 6 at the end of surfactant
flooding (after Freeze et al, 1994) 45
3.1 Capillary pressure curves as a function of effective water saturation 50
5.1 Comparison of capacitance model (UTCHEM) to equivalent dual porosity model
fUTDUAL) results 63
5.2 Schematic of matrix block subgrids 63
5.3 Comparison of capacitance model vs. subgrid model in UTCHEM 64
5.4 Subgrid refinement studies with UTCHEM, Km = 3.243x10-2 ftS/day 64
5.5 Comparison of UTCHEM and UTDUAL subgridding 65
5.6 2D subgrid refinement studies with UTCHEM 65
5.7 Comparison of execution time with different numbers of subgrids, ID ease 66
5.8 Comparison of execution time with different numbers of subgrids, 2D case 66
5.9 Comparison of simulated results vs. analytical solution (Tang et al, 1981) for radionuclide
concentration in the fracture 67
5.10 Comparison of simulated results vs. analytical solution (Tang et al., 1981) and SWIFT II
(Reeves et al., 1986) for radionuclide concentration in the matrix 67
9.1 Modeling domain size and discretization 112
9.2 NAPL saturation history in the vicinity of a hypothetical gasoline spill 112
9.3 Comparison of benzene and toluene concentrations in the aqueous phase 500 days after a
gasoline spill 113
9.4 Concentrations of benzene without biodegradation, benzene with biodegradation, toluene,
oxygen, and nitrate in upper 1.2 m of aquifer along aquifer center line at 500 days 114
9.5 Plan view of TCE, a hypothetical TCE tracer, methane and oxygen concentrations in the
upper 1.2m of a confined aquifer 170 days after a TCE spill 114
11.1 Schematic representations of a) Type II(-), b) Type II(+), and c) Type III 137
11.2 Effect of alcohol on the maximum height of binodal curve 138
11.3 Coordinate transformation for Type III. 138
vin
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Tables
1.1 List of Elements and Reactive Species 14
1.2 Physical Property Data Used in the 2-D Simulations 14
2.1 Physical Property Input Parameters for the Test Cell Simulation 45
i
3.1 Notation Used in Section 3 50
5.1 Equivalence Between Capacitance and Dual Porosity Models 68
5.2 Input Data for the Comparisons of Capacitance Model in UTCHEM to Dual Porosity
Model in UTDUAL 68
8.1 Water Analysis for Makeup and Formation Water 88
8.2 Example List of Elements and Reactive Species 88
8.3 List of Reactions for the Example Run ~. 89
8.4 Stoichiometric Coefficient of I™ Element in J™- Fluid Species (for the AR Array) 91
8.5 Stoichiometric Coefficient of I™ Element in J^} Solid Species (for the BR Array) 91
8.6 Stoichiometric Coefficient of I™ Element in Ith- Sorbed Species (for the DR Array) 91
8.7 Stoichiometric Coefficient of Im Element in J"1 Surfactant Associated Cation (for the ER
Array) „. 92
8.8 Exponent of fa Independent Fluid Species (for BB Array). 92
8.9 Exponent of fa Independent Species in the Ith Solid (for EXSLD Array) 93
8.10 Charge of I«i Fluid Species (for CHARGE Array) 93
8.11 EquifibriurnConstants for Ith Fluid Species (for EQK Array) 93
8.12 Charge of fa Sorbed Species (for SCHARG Array) 93
8.13 Exchange Equilibrium Constants for fa Exchange (for EXK Array)...., 93
8.14 Exponent of Ktn Independent Species in fa Equilibrium Relation (for EXEX Array) 94
8.15 Valence Difference Between Cation Involved In Exchange (for REDU Array) 94
8.16 Solubility Product of I™ Solid (for SPK Array) 94
8.17 Charge of Ith Surfactant Associated Cation (for CHACAT Array) 94
8.18 Equilibrium Constant for fa Exchange (for ACATK Array) 94
8.19 Exponent of fa Independent Species in Im Cation Exchange on Surfactant (for EXACAT
Array) 94
8.20 Sample Input Data for EQBATCH Program 95
8.21 Sample Output of EQBATCH Program 97
8.22 Sample UTCHEM Input File Generated From EQBATCH Program 102
9.1 Flow Parameters for All Simulations , 115
9.2 Parameters for LNAPL Simulation Example 115
9.3 Parameters for DNAPL Simulation Example 116
IX
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Section 1
Project Summary
1.1 Introduction
Pioneering research conducted at The University of Texas at Austin has provided a scientific and engineering
basis for modeling the enhanced recovery of oil and the enhanced remediation of aquifers through the
development and application of compositional simulators. This research has resulted in the development and
application of a, 3-D, multicomponent, multiphase, compositional model of chemical flooding processes,
UTCHEM, which accounts for complex phase behavior, chemical and physical transformations and
heterogeneous porous media properties, and uses advanced concepts in high-order numerical accuracy and
dispersion control and vector and parallel processing. The simulator was originally developed by Pope and
Nelson in 1978 to simulate the enhanced recovery of oil using surfactant and polymer processes. Thus, the
complex phase behavior of micellar fluids as a function of surfactant, alcohol, oil, and aqueous components
was developed early and has been extensively verified against enhanced oil recovery experiments.
Generalizations by Bhuyan et al. in 1990 have extended the model to include other chemical processes and a
variety of geochemical reactions between the aqueous and solid phases. The nonequilibrium dissolution of
organic components from anonaqueous phase liquid (NAPL) into a flowing aqueous or microemulsion phase
is modeled using a linear mass-transfer model. In this simulator, the flow and mass-transport equations are
solved for any number of user-specified chemical components (water, organic contaminants, surfactant, alcohols,
polymer, chloride, calcium, other electrolytes, microbiological species, electron acceptors, etc.). These
components can form up to four fluid phases (air, water, oil, microemulsion) and any number of solid minerals
depending on the overall composition. The microemulsion forms only above the critical micelle concentration
(CMC) of the surfactant and is a thermodynamically stable mixture of water, surfactant and one or more organic
components. All of these features taken together; but especially the transport and flow of multiple phases with
multiple species and multiple chemical and biological reactions make UTCHEM unique. A description of
UTCHEM model formulation is given in Delshad et al. [1996].
The objective of this research was to develop, validate and apply a three-dimensional, multiphase,
multicomponent model capable of simulating the fate and transport of NAPLs in the saturated and unsaturated
zones of confined and unconfmed aquifers undergoing enhanced remediation. The model is capable of simulating
multiple solids and fluid phases (water/air/NAPL) under realistic aquifer conditions and transformations of both
inorganic and microbiological species. The specific objectives of this research were:
• Develop a three-dimensional simulation model capable of evaluating aquifer remediation methods using
enhanced dissolution and/or mobilization of NAPLs trapped at residual saturation in aquifers. The
simulator is capable of modeling transient and steady-state, three-dimensional flow and mass transport in
the groundwater (saturated) and vadose (unsaturated) zones of aquifers. The simulator allows for:
changes in fluid properties as a site is remediated; heterogeneous aquifer properties; the flow and transport
of remedial fluids whose density, viscosity and temperature are variable, including surfactants, cosolvents,
microbes, and other enhancement agents; the dissolution of NAPLs by nondilute remedial fluids; and
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Section 1 - Project Summary
chemical and microbiological transformations. Nondilute components such as surfactant can and typically
do cause large changes in phase volumes, phase velocities, and phase properties that cannot be accurately
modeled by assuming these components are at very low concentrations so that they follow the
conventional advection-reaction-dispersion equation used in almost all groundwater models. Rather,
more general mass-balance equations and constitutive equations such as those used here must be solved.
The resulting set of equations are highly nonlinear and more difficult to solve than those in conventional
models, but provide a vastly more general and accurate description of the processes that actually occur
in aquifers undergoing remediation, the migration ofNAPLs in the subsurface, and the natural attenuation
processes ofNAPLs in the subsurface. Many of these processes such as the migration of the NAPLs
during and after a spill or disposal operation involve the flow of two or more phases, which requires the
modeling of relative permeability and other effects related to multiphase flow.
• Incorporate appropriate physical, chemical, and biological process models important in describing the fate
and transport of contaminants in aquifers, such as nonequilibrium interphase mass transfer, sorption, decay
processes, microbiological and geochemical reactions, capillary pressure and relative permeability.
• Incorporate numerical-dispersion-minimization techniques and efficient solution algorithms into the model.
• Evaluate the model through a series of tests including comparison with analytical solutions, experimental
data, and results from other models. Present a theoretical analysis and demonstration of the numerical
dispersion control and minimization techniques employed in the model.
• Demonstrate the stability and robustness of the model with sensitivity analysis simulations using various
aquifer conditions (surface spill conditions, initial saturation distributions) and heterogeneities (spatial
variations of permeability and porosity).
• Evaluate this new model by comparison with data from actual field operations of remediation, in
particular, surfactant-enhanced remediation at the Canadian Forces Borden site and other large-scale
model aquifer or field operations such as the one recently completed at the Air Force Base in Utah.
• Provide copies of the UTCHEM source code and the user's guide to U.S. EPA personnel.
1.2 Model Development
During the past three years, we have added several new and significant capabilities to UTCHEM to make it into
a general-purpose NAPL simulator. These new features are discussed below. The simulator is now capable of
modeling transient and steady-state three-dimensional flow and mass transport in the groundwater (saturated)
and vadose (unsaturated) zones of aquifers. The model allows for changes in fluid properties as a site is
remediated; heterogeneous aquifer properties; the flow and transport of remedial fluids whose density, viscosity
and temperature are variable, including surfactants, cosolvents and other enhancement agents; the dissolution
and/or mobilization ofNAPLs by nondilute remedial fluids; and chemical and microbiological transformations.
Appropriate physical, chemical and biological process models important in describing the fate and transport of
NAPLs in contaminated aquifers have been incorporated into the simulator, such as multiple organic NAPL
phase, nonequilibrium interphase mass transfer, sorption, microbiological and geochemical reactions, and the
temperature dependence of pertinent chemical and physical properties. The biodegradation model includes
inhibition, sequential use of electron acceptors, and cometabolism and can be used to model a very general class
of bioremediation processes. The model can be used to simulate the actual field operation of remediation
activities such as surfactant remediation or bioremediation as well as laboratory experiments with large-scale
aquifer models.
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Section 1 - Project Summary
1.2.1 Microbiological Population Modeling
Biodegradation capabilities have been added to a three-dimensional, multiphase, multicomponent porous
media flow model. The model simulates the transport and biodegradation of light nonaqueous phase liquids
(LNAPLs) and dense nonaqueous phase liquids (DNAPLs). The biodegradation model describes biological
transformation of the organic contaminants originating from NAPL sources and can accommodate multiple
substrates, electron acceptors, and biological species.
Here we give a brief description of the model assumptions and the capabilities. For more detailed information
on model formulation, method of solution, and example simulations to demonstrate its capability, please refer
to de Blanc etal. [1996a,b]. UTCHEM simulates the biodegradation of chemical compounds that can serve
as substrates (carbon and/or energy sources) for microorganisms. The model simulates the destruction of
substrates, the consumption of electron acceptors (e.g., oxygen, nitrate, etc.), and the growth of biomass.
Substrates can be biodegraded by free-floating microorganisms in the aqueous phase or by attached biomass
present as microcolonies in the manner of Molz et al. [1986]. Multiple substrates, electron acceptors and
biological species are accommodated by the model. Important assumptions for the biodegradation model are:
i
1. Biodegradation reactions occur only in the aqueous phase.
2. Microcolonies are fully penetrated; i.e., there is no internal resistance to mass transport within the
attached biomass.
3. Biomass is initially uniformly distributed throughout the porous medium.
4. Biomass is prevented from decaying below a lower limit by metabolism of naturally occurring
organic matter unless cometabolic reactions act to reduce the active biomass concentrations below
natural levels.
5. The area available for transport of organic constituents into attached biomass is directly proportional to
the quantity of biomass present.
6. The number of cells per microcolony, biomass density, and microcolony volume are constant, so that
mass per microcolony is also constant.
The biodegradation model includes the following features:
• Monod, first-order, or instantaneous biodegradation kinetics.
« Formation of biodegradation by-products.
• External mass-transfer resistances to microcolonies (mass-transfer resistances can be ignored by the
user if desired).
• Inhibition of biodegradation by electron acceptors and/or toxic substrates.
• Nutrient limitations to biodegradation reactions.
• First-order abiotic decay reactions.
• Enzyme competition between multiple substrates.
• Modeling of cometabolism with transformation capacities and reducing power limitations using the
model of Chang and Alvarez-Cohen [1995].
• Biodegradation reactions in both the vadose and saturated zones.
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Section 1 - Project Summary
The biodegradation model equations describe the transport of substrate and electron acceptor from the
aqueous phase into attached biomass, the loss of substrate and electron acceptor through biodegradation
reactions, and the resulting growth of the free-floating or attached biomass. The flow and biodegradation
system is solved through operator splitting, in which the solution to the flow equations is used as the initial
conditions for the biodegradation reactions. This approach is convenient because modifications can be made
to the system of biodegradation equations without having to reformulate the partial differential equations that
describe advection and dispersion.
The biodegradation equations comprise a system of ordinary differential equations that must be solved at each
gridblock and each timestep after the advection and dispersion terms are calculated. Because the mass transfer
terms can make the system of equations stiff, the system is solved using a Gear's method routine published
by Kahaner et al. [1989]. The characteristics and numerical solution of this system of equations are discussed
by de Blanc et al [1996b].
To validate the model, one-dimensional, single-phase simulation based on the example given in Molz et al.
[1986] has been run. The UTCHEM simulation results have been compared to biodegradation model
solutions published by Molz et al. In this simulation, a single substrate is biodegraded by attached biomass
using oxygen as the electron acceptor. The reactor is 100 cm long with initial colony density of l.OxlO5
colonies per cm3 of porous medium. Pore velocity is 25 cm/day. The initial substrate and oxygen
concentrations are constant throughout the reactor at 5 mg/L. At the boundary x = 0 and time zero, the
substrate concentration is increased instantaneously to 15 mg/L. At the same boundary, the oxygen
concentration is maintained at 5 mg/L. Substrate profiles generated by the two models are shown in Fig. 1.1.
The simulation results are very similar to the data of Molz et al., indicating that the UTCHEM biodegradation
model is functioning properly. The model predictions are not exactly the same because of slightly different
assumptions about endogenous decay and slightly different flow conditions.
1.2.2 Numerical Enhancements to the Model
We present a summary of the local grid-refinement method and implementation in
formulation and simulation examples are given in UTCHEM-LGR User's manual.
UTCHEM. The
The aquifer is initially defined by a coarse grid (called a base grid) with NXCxNYCxNZC standard cells
(gridblocks). Subject to memory limitations, any number and any combination of the base grid cells can be
refined by a single local-level NXFxNYFxNZF that is of fixed resolution for all refined cells. The refined
base grid cells are called zones. The resulting grid is comprised of coarse base cells and fine-zone regions.
When a coarse base cell or a fine zone is adjacent to a refined base cell or zone, this gives rise to a coarse-fine
interface or fine-fine interface, respectively. With respect to a given zone, the interfaces act as interior domain
boundaries. An example is presented in Fig. 1.2, where the definition of zone and interface are illustrated in
Fig. 1.2a.
The implementation strategy attempts to treat each zone as a separate domain subject to interior domain
boundary conditions and is in that sense based on domain decomposition, pictorially illustrated in Fig. 1.2b.
Computations in the interior of each local fine zone are effectively performed in isolation from other regions
of the flow domain (giving rise to an inner loop) subject to appropriate interface and exterior boundary
conditions that are imposed in an outer loop over the local domains and serve to connect the various local
domains together.
Local grid refinement (LGR) has been implemented for the Cartesian option with a higher-order scheme or
two-point upstream weighting for the concentration equations, although single-point upstream weighting is
also maintained as an option. While the current code allows static (fixed) local cell refinement, where each
coarse cell selected for refinement remains refined and the grid does not change throughout the computation,
the implementation will allow future extension to dynamic local refinement.
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Section 1 - Project Summary
Some recent examples of use of this kind of local refinement in reservoir simulation can be found in Espedal
etal. [1990] and Deimbacher and Heinemann [1993]. However, with the exception of Edwards [1992a,b]
and Edwards and Christie [1993] where a higher-order (in space and time) total-variation-diminishing type
scheme is employed, all other adaptive methods in reservoir simulation to date have employed first-order
upstream differencing for discretization of the advective terms in the flow equations. The new method and
development reported here have led to the first simulator to include local grid refinement with a higher-order
scheme and a full tensor diffusion operator in three dimensions.
Most of the current code development, in terms of new subroutines, is concerned with treatment of the
domain interface conditions for the concentration equations and pressure equation, which enable the zones to
link together and complete the global flow-domain solution definition. Aspects that have critical impact on
this logic deal with identification of the junction type at an interface. For example, a coarse cell that has been
refined can have a neighboring cell that is either refined or coarse or a physical boundary, and appropriate
internal or external boundary conditions (Neumann/Dirichlet) must be imposed. In addition, the coarse-fine
and/or fine-fine zone configurations that underlie the higher-order scheme for concentrations must be
identified. While the pressure equation involves nearest-neighbor and nearest-interface-neighbor information,
the higher-order scheme stencil support relies on neighbor and neighbor-of-neighbor information. In addition
the full tensor diffusion operator relies on nearest neighbor and diagonal neighbor information, adding another
level of complexity to the implementation.
Zone interior calculations can be performed in isolation and, subject to appropriate boundary interface
conditions, the solution procedure can simplistically be visualized as a sequence of calls to the simulator for
each domain, followed by calls to boundary-coupling routines that "seal" the isolated local zones together,
forming the global domain. However, in practice, the implementation is far more involved.
In addition to the nontrivial interface routines directly concerned with solving the flow equations, further
interface logic is required for the calculation of any nonlocal variable that is a function of more than a single
cell. The code has to be sifted for such cases. Examples include determination of the maximum flow rate
required for calculating the maximum timestep, testing for negative saturations and pressures, and material-
balance calculations, and all involve tests and/or calculations over all domain cells; more complex examples
arise with physical models such as capillary number, which involves further interface routines to handle the
spatial derivatives. Definition of physical boundary conditions such as injection/production wells and
inflow/outflow boundaries both involve summations over a range of cells, and appropriate interface tests and
calculations must be built into the code to ensure that a given boundary condition extends over the desired
region of the flow domain.
A cell-centered finite-volume formulation is employed in constructing discretizations of the flow equations
applicable on grids with embedded local refinement. In a cell-centered formulation, the flow domain is
represented by a grid of quadrilateral cells. All flow variables including saturations, concentrations and
pressures are defined at the cell centers, and the flow equations are integrated over each cell using the Gauss
flux theorem.
This is the first simulator to offer LGR with a higher-order scheme and full tensor diffusion in three
dimensions applicable to a variety of problems of practical importance. The initial three-dimensional results
were very encouraging. Successful adaptivity requires that the key coarse grid cells (containing flow
variables with steep gradients) be refined. Static refinement is best suited to problems where crucial flow
gradients are known a priori to be contained in certain regions of the domain.
1.2.3 New Relative-Permeability and Capillary-Pressure Models
A new multiphase capillary-pressure and relative-permeability function has been implemented in UTCHEM.
As the result of this task, UTCHEM has now the option of either Brooks-Corey or van Genuchten capillary-
pressure functions. The two-phase gas-water, water-oil, or microemulsion-oil and three-phase oil-water-gas
5
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Section 1 - Project Summary
capillary pressure-saturation functions are determined using the generalization of Parker et al, [1987] to the
two-phase flow model of van Genuchten [1980]. The new two- and three-phase relative permeabilities are
also based on the generalization of Parker and Lenhard to the two-phase flow model of van Genuchten.
Both capillary-pressure and relative-permeability functions account for hysteresis due to arbitrary changes- in
saturation path by incorporating an oil-phase-entrapment model. The hysteresis modeling in UTCHEM is
based on the work by Kalurachchi and Parker [1992]. The assumptions made in developing and applying this
model are;
• The model applies only to strongly water-wet media where the wettability in descending order is for
water (or microemulsion), oil, and gas phases. Oil will be used in this report to mean any nonaqueous
phase liquid (NAPL).
• The model applies to three-phase air-water-oil flow in the vadose zone and two-phase oil-water or oil-
microemulsion flow in the saturated zone.
» To avoid numerical oscillations with changes from two phases (air-water) to three phases (air-water-
oil), once a location is classified as a three-phase node, it will not revert back to two phases (air-water),
• Gas entrapment is neglected for the three-phase case. Therefore, oil entrapment in three-phase air-
water-oil flow can be inferred directly from that in a two-phase oil-water system.
• Water relative permeability is unaffected by oil entrapment.
• There is no oil entrapment on the main drainage curve,
• There is no oil entrapment when water saturation is at its residual value in the vadose zone.
A detailed description on the formulation of the new hysteretic capillary-pressure and relative-permeability
models is given in Section 2,2 of this report.
1,2.4 New Organic and Tracer Components
New organic and tracer components were added to UTCHEM. We have added multiple organic components
so that we can model NAPL mixtures. Adding this capability to UTCHEM required developing a phase-
behavior model for NAPL mixtures and the physical property models such as density and viscosity for each
phase. We have also added additional water tracer components and gas phase tracers.
New organic components
Nonaqueous phase liquids (NAPLs) usually consist of more than one organic species that mix and form a
single liquid. Common examples of such miscible species include TCE, TCA and PCE among many others.
When NAPLs leak to the subsurface, they can dissolve and migrate into groundwater. To model the fate and
transport of these soluble organics during remediation processes such as pump-and-treat, bioremediation and
surfactant remediation, it is important to determine the migration of the individual soluble organics. The
dissolution can be either a local equilibrium or a rate-limited (nonequih'brium) mass-transfer process. We
have added the capability of multiple organic components to UTCHEM to model these NAPL mixtures. The
multiple organic dissolution can be either local-equilibrium partitioning or a rate-limited mass transfer. We
also developed and incorporated in UTCHEM a phase-behavior model for a mixture of NAPL mixtures,
surfactant, and water. The physical-property models developed and implemented for a NAPL mixtures in
UTCHEM were density, viscosity, and adsorption. A more detailed description of the model is given in
Section 2.6 of this report.
Three recent papers by Baran et al. [1994a,b,c] show that the phase behavior of surfactants with both pure
chlorocarbons and mixtures of chlorocarbons is similar to classical phase behavior with hydrocarbons. The
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Section 1 - Project Summary
phase behavior changes from microemulsiori in equilibrium with excess oil (Winsor Type I or Type II(-)) to
microemulsion in equilibrium with excess aqueous and organic phase (Winsor Type III), and to
microemulsion in equilibrium with excess water (Winsor Type II or Type !!(+)) as salinity increases. The
lower and upper limits of effective salinity are the effective salinities at which three phases form or disappear.
The optimal salinity is defined as the midpoint of these two salinity limits .
Hand's equation (Pope and Nelson, 1978) is used in UTCHEM to describe the phase envelope and binodal
curve. For organic mixtures, the upper and lower limits of effective salinity, the height of binodal curve at
lower, optimal, and upper salinities are functions of organic species concentrations. These parameters are
modeled as functions of the equivalent alkane carbon number (EACN) of the mixture, which is a function of
organic species concentrations. EACN for an alkane is the number of carbons in the alkane chain of the
hydrocarbon; for example, it is equal to 6 for hexane. EACN for a nonalkane is obtained by measuring the
optimal salinity for a binary mixture of an alkane and a nonalkane with known molar fractions. The measured
optimal salinity is used to determine EACN for the binary mixture. For example, the EACN data listed in the
Baran et al. papers are built into the UTCHEM database: PCE (EACN = 2.90), COU (EACN = -0.06), TCE
(EACN = -3.81), p-xylene (EACN = 2), toluene (EACN=1), 1,2-C6H4C12 (EACN = -4.89), 1,2-C2H4C12
(EACN = -12.10), CHC13 (EACN =-13.67), CH2C12 (EACN = -13.79), and 1,1,2,2-C2H2C14
(EACN = -22.15).
New tracer components
The number of oil/water tracers in UTCHEM was previously limited to three. Modifications to the model
have been completed to allow the simulation of any number of tracer components.
Gas tracers have been added to UTCHEM. The gas-phase tracers are either chemical nonreacting or
radioactive components. The gas tracer can partition only between gas and organic phases with a constant
partition coefficient. Radioactive decay is applied to radioactive tracers with a constant decay coefficient. The
gas tracers can also adsorb on the soil surface using a linear adsorption model and a constant retardation
factor.
Enhancements of Geochemical Option
The geochemical option in UTCHEM has been extended to allow the modeling of any aqueous and solid
reactive species. In the original UTCHEM model, the component numbering in the transport calculations was
fixed in the source code and each reaction option had specific geochemical components and species. Thus, the
geochemical option in UTCHEM was limited only to those specific species and reactions. This restriction
was removed by implementing a dynamic component-numbering scheme for geochemical components. The
component numbers are increased according to the user-specified elements. Component partitioning between
phases and the adsorbed and solid concentrations in the mass-balance calculations are not, however, included
for all the new species.
To test and illustrate the UTCHEM capability in modeling a complex geochemical process, an application to
an acid mine-tailing contamination problem was simulated. A total of 51 aqueous species and 7 solid species
were simulated (Table 1.1). New components such as chromium, lead, and sulfate were included that were
not available in the original UTCHEM model. The aquifer and site conditions for this example were similar
to the conditions at the Nordic site near Elliot Lake, northern Ontario (Walter et al, 1994). The initial and
injected component concentrations were similar to those used in the simulation by Walter et al. Initial
concentrations for UTCHEM simulation were determined by equilibrating the water and mineral phases using
batch equilibrium calculations. The UTCHEM results showed a very similar trend to those presented by
Walter et al. The results were not expected to be identical since the conditions were different; i.e., species
such as K, Mn, and Fe were not included in the UTCHEM simulation.
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Section 1 - Project Summary
1.3 Model Evaluation
The numerical accuracy of the UTCHEM model has been evaluated through a series of tests including
comparisons with analytical solutions and experimental data.
The numerical accuracy of UTCHEM model was evaluated by comparison with analytical solutions for
problems such as the 1-D water tracer, 2-D tracer, and polymerflood examples given in Fig. 1.3 (Liu et a/.,
1994) and by comparison with 2-D laboratory column data of Pennell et al. [1996]. The experiment involved
a 2-D horizontal sandpack contaminated with tetrachloroethylene (PCE). A mixture of surfactant solution
was injected under both mobilization and solubilization conditions for PCE removal from the column. The
UTCHEM model with the recently added trapping number (Jin, 1995; Delshad et al, 1996) was used to
model this experiment.
The column was packed with 40-270 mesh Ottawa sand with a permeability of 16.3 darcies and porosity of
0.3509. Table 1.2 gives the physical properties. The surfactant solution was a 4% 1:1 mixture of sodium
dihexyl sulfosuccinate and sodium dioctyl sulfosuccinate (Aerosol AY/OT) in 500 mg/L CaCl2- The
measured phase behavior and fluid properties such as viscosity, density, and desaturation data were used to
obtain the UTCHEM input parameters. The injection rate was at 4.95 cc/min (0.0488 ft3/day). Pennell et al.
observed that the injected surfactant solution appeared to preferentially flow along the top of the soil column,
while mobilized PCE migrated downward through the soil column because of buoyancy forces. It took about
3 pore volumes of surfactant solution to completely displace the mobilized bank of PCE formed near the
column outlet. To model the results of the laboratory data, 2-D simulations with 22 gridblocks in the
horizontal direction and 10 gridblocks in the vertical direction were performed. Figure 1.4 compares the
laboratory and simulated free-product PCE recovery as a function of surfactant solution throughput. This
favorable comparison indicates that UTCHEM can successfully model the vertical migration and mobilization
of PCE.
The model was also evaluated by comparison with data from actual field operations of remediation, in
particular, surfactant enhanced aquifer remediation (SEAR) at the Canadian Forces Borden site and a field-
scale tracer and SEAR tests at the Operational Unit 2 site at Hill Air Force Base in Utah. The UTCHEM
simulator was used to model the surfactant-enhanced remediation of PCE in a test cell at the Borden site in
Allison, Ontario (Freeze et al., 1994). UTCHEM was able to closely reproduce the PCE recovery and the
PCE distribution. The second sets of simulations were performed to design pre- and post-surfactant flushing
partitioning interwell tracer tests and to design the surfactant flood for the Operational Unit 2 (OU2) site at
Hill AFB, Utah. A multitude of simulation cases were performed to develop the recommended designs for
the tests. These simulations have also allowed us to study the effect of design variables such as injection and
extraction wells, number of wells, and well pattern. Figures 1.5 and 1.6 show a favorable comparison of the
field and UTCHEM predictions of effluent tracer and surfactant concentrations. The field design, results, and
UTCHEM predictions are given in Brown et al. [1996] and Brown [1999]. The stability and robustness of
the simulation results were evaluated with sensitivity analysis to various aquifer conditions, for example,
initial saturation distribution, permeability and porosity distributions, and injection/extraction strategies
(Brown, 1999).
More examples of UTCHEM large-scale simulations are given in a report prepared by INTERA (Butler and
Jin, 1996). INTERA's particular role in this project was to apply UTCHEM to typical NAPL problems that
INTERA encountered during its work at various hazardous waste sites in North America. UTCHEM was
used to study the distribution, volume, and remediation of DNAPL in an alluvial aquifer. The model was
used to design both a partitioning interwell tracer test (PITT) and a subsequent surfactant flood at the
Portsmouth Gaseous Diffusion Plant in southern Ohio. The analysis of an actual PITT conducted at
Portsmouth in July 1996 is also included in the report.
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Section 1 - Project Summary
1.4 Conclusions
As the result of this three-year research contract, we have developed a mathematical model capable of
simulating the performance of three-dimensional, multicomponent, multiphase flow of NAPLs in subsurface
environments including saturated and unsaturated conditions. A systematic evaluation was undertaken to
assess the applicability and accuracy of all physical and chemical models of the various pertinent phenomena
such as capillary pressure, relative permeability, adsorption, nonequilibrium mass transfer, dispersion, and
phase behavior. A biological component was added to UTCHEM. Comparisons to analytical solutions were
made and numerical dispersion control and accuracy testing were performed. The model was tested against
experimental and field data. The model will be delivered to U.S. EPA along with user manuals and sample
outputs. The model is in the form of a FORTRAN source code that has been optimized for a vector
computer.
1
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0.014 4- "^^ tracer after 4 days
0.000
Solid lines - UTCHEM model
Symbols - Data from Molz et al. (1986)
0
20
40 60
distance in column (cm)
80
100
Figure 1.1. Comparison of substrate profiles calculated by UTCHEM simulator to those predicted
by the model of Molz et al. [1986].
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Section 1 - Project Summary
Adaptive Grid Refinement Notation
Composite Grid
h-Adaptive Grid
Patch
Window
ZONE
Coarse-Fine Interface
Figure 1.2a. Definition of zone and interface.
Decomposition of Domain
Figure 1.2b. Coarse-fine and fine-fine interfaces.
10
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Section 1 - Project Summary
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11
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Section 1 - Project Summary
Free product PCE
(column experiment)
ft—•••"•"••?•
Free product PCE
(simulated)
Solubilized PCE
(simulated)
0.5 1.0 1.5
Pore volumes injected
Figure 1.4. Simulated and laboratory PCE recovery from the 2-D column.
400
300
o
£ 200
0)
§
O
100
UTCHEM 2-propanol
A Field 2-propanol, K=0
UTCHEM 1-pentanol
o Field 1-pentanol, K=3.9
Figure 1.5. Tracer concentrations produced at extraction well SB-1 during
Hill AFB Phase I test.
12
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Section 1 - Project Summary
1.0
0.0
40 60 80 100 120 140
Time (hrs)
Figure 1.6. Surfactant concentrations produced at extraction well SB-1
during Hill AFB Phase I test.
13
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Section 1 - Project Summary
Table 1.1. List of Elements and Reactive Species
ELEMENTS
AQUEOUS SPECIES
SOLID SPECIES
Cr
H
Pb
Mg
Ca
Na
Al
Si
Cl
C03
SO4
o
Cr(OH)2+, H+, Pb2+, Mg2+,
Ca2+, Na+ A13+, H4SiO4,
cr, co32-, so42-, H2o, OH",
H3SiO4", MgOH+, MgCO3 (Aq.),
MgHCO3+, MgSO4 (Aq.), CaOH+,
CaHCO3+, CaCO3 (Aq.), CaSO4 (Aq.),
NaC03", NaHCO3 (Aq.), NaSO4",
A1OH 2+, A1(OH)2+, A1SO4+,
A1(S04)2", PbCl+, PbCl2 (Aq.),
PbCl3", PbCl42", Pb(CO3)22",
PbOH"1", Pb2OH3+, PbSO4 (Aq.),
PbCO3 (Aq.), Pb(S04)22", PbHCO3+,
HC03", H2C03 (Aq.), HSO4", Cr3+,
Cr(OH)2+, CrCl2+, CrCl2+, CrSO4+,
CrOHSO4 (Aq.), Cr2(OH)2SO4
Cr2(OH)2(S04)2(Aq.)
2+
CALCITE (CaCO3)
GIBBSITE (A1(OH)3)
GYPSUM (CaS04)
SiO2
CERRUSITE (PbCO3)
ANGLESITE (PbSO4)
Cr(OH)3
Table 1.2. Physical Property Data Used in the 2-D Simulations
Permeability, darcies
Porosity, fraction
Residual water saturation
Residual PCE saturation
Initial water saturation
Water viscosity, cp
PCE viscosity, cp
Water density, g/cc
PCE density, g/cc
Surfactant density, g/cc
Initial/injected chloride cone., meq/L
Initial/injected calcium cone., meq/mL
16.3
0.3509
0.30
0.1242
0.8758
1.0
0.89
1.0
1.63
1.15
0.009
0.009
14
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Section 2
UTCHEM Model Formulation
This chapter is an expanded version of the paper by Delshad et al. [1996] where we describe a three-
dimensional, multicomponent, multiphase compositional finite difference simulator for application to the
analysis of contaminant transport and surfactant enhanced aquifer remediation (SEAR) of nonaqueous phase
liquid (NAPL) pollutants. The simulator can model capillary pressures, three-phase relative permeabilities
(water/gas/organic phases or water/organic/microemulsion phases), dispersion, diffusion, adsorption,
chemical reactions, nonequilibrium mass transfer between phases and other related phenomena. The finite-
difference method uses second- and third-order approximations for all of the time and space derivatives and a
flux limiter that makes the method total variation diminishing (TVD). Mixtures of surfactant, alcohol, water
and NAPL can form many types of micellar and microemulsion phases with a complex and important
dependence on many variables of which the dilute aqueous solution typically assumed in SEAR models is
just one example. The phase behavior model is central to our approach and allows for the full range of the
commonly observed micellar and microemulsion behavior pertinent to SEAR. The other surfactant related
properties such as adsorption, interfacial tension, capillary pressure, capillary number and microemulsion
viscosity are all dependent on an accurate phase behavior model. This has proven to be a highly successful
approach for surfactant enhanced oil recovery modeling, so it was adapted to SEAR modeling. However,
there are many significant differences between petroleum and environmental applications of surfactants, so
many new features have been added to model contaminant transport and remediation and these are described
and illustrated for the first time here.
2.1 Introduction
Many nonaqueous phase liquids (NAPLs) are used.in large quantities by many industries throughout the
world. Due to their wide usage, organic liquids are among the most common type of soil and groundwater
pollutants. Of the organic chemical contaminants which have been detected in groundwaters, dense
nonaqueous phase liquids (DNAPLs) such as chlorinated solvents are among the most frequently and serious
types encountered. DNAPLs are heavier than water, typically volatile, and only slightly soluble in water.
Many conventional remediation techniques such as pump-and-treat, vapor extraction, and in-situ
biorestoration have proven to be unsuccessful or of limited success in remediating soil and groundwater
contaminated by DNAPL due to low solubility, high interfacial tension, and the sinking tendency below the
water table of most DNAPLs. Surfactant enhanced aquifer remediation is actively under research and
development as a promising technology that avoids at least some of the problems and limitations of many
other remediation methods.
Surfactants have been studied and evaluated for many years in the petroleum industry for enhanced oil
recovery from petroleum reservoirs (Nelson and Pope, 1978). Surfactants are injected to create low interfacial
tension to reduce capillary forces and thus mobilize trapped oil. Solubilization and mobilization are the two
mechanisms by which surfactants can enhance the removal of NAPLs from saturated zones. Surfactants can
also be used to increase the solubility without generating ultra-low interfacial tension or mobilizing the trapped
oil. Enhanced solubility is the main mechanism for recovery of entrapped organic residuals in surfactant
15
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Section 2 - UTCHEM Model Formulation
enhanced aquifer remediation (Fountain, 1992; Fountain and Hodge, 1992; Powers et al., 1991; West and
Harwell, 1992; Wunderlichef a/., 1992; Brown etal, 1994; Pennell etal., 1994). For example, the solubility
of perchloroethylene (PCE) is increased 300 fold by the addition of a 4% blend of sodium diamyl and dioctyl
sulfosuccinates (Abriola et al., 1993). SEAR can also be based on mobilization of the residual DNAPL,
which has a greater potential to increase the remediation but is riskier because of the movement of free-phase
DNAPL.
The objective of SEAR modeling is to aid in the scaleup and optimization of the design of SEAR, to assess
the performance of the method at both the laboratory and field scales with respect to both risk and
effectiveness, to improve our understanding of process mechanisms, and to explore alternative strategies and
approaches to remediation. To the extent that these modeling objectives are met, risk will be reduced and
fewer mistakes will be made, the performance and cost effectiveness of the method will be improved, and the
number of field trials will be minimized. The model should have the capability of modeling advection,
dispersion, and the mass transfer of species (surfactant, water, organic contaminants, air) in the aquifer under
various pumping and injection strategies. Most multiphase compositional models reported in the
environmental engineering literature (Abriola and Finder, 1985a,b; Baehr and Corapcioglu, 1987; Faust et al.,
1989; Letniowski and Forsyth, 1990; Sleep and Sykes, 1990; Mayer and Miller; 1990; Kalurachchi and
Parker, 1990; Sleep and Sykes, 1993) are limited in their applicability in one way or another (1-or 2-
dimensional modeling, single species, equilibrium mass transfer, inadequate numerical accuracy, and lack of
modeling miscibility which occurs during surfactant flooding). The only SEAR models reported in the
literature are for single phase flow and are those of Wilson [1989], Wilson and Clarke [1991] and Abriola et
al. [1993] with simplified surfactant phase behavior and properties. None of these models account for the
effects of surfactant on interfacial tension (IFT), surfactant phase behavior, capillary number, or surfactant
adsorption. This paper describes the formulation and application of a general purpose chemical compositional
simulator, The University of Texas Chemical Flooding simulator (UTCHEM), for use in SEAR studies, that
does not have these common limitations.
Enhanced oil recovery processes such as polymer flooding or surfactant/polymer flooding have utilized
polymer to reduce fluid mobility to improve the sweep efficiency of the reservoir, i.e., to increase the volume
of the permeable medium contacted at any given time (Lake, 1989; Sorbie, 1991). Sweep efficiency is
reduced by streamline pattern effects, gravity effects, viscous fingering, channeling (caused by contrasts in the
permeability) and flow barriers. Polymers could be used in the SEAR process to improve the sweep
efficiency just as they have been in enhanced oil recovery and this may reduce the cost, risk and time required
to remediate the aquifer. Under some conditions, polymers can also reduce the dispersion and adsorption of
the surfactant and this is another potential benefit of using them. Polymer concentrations on the order of 500
mg/L are likely to be adequate for SEAR applications, so the additional cost of the polymer is small compared
to the potential reduction in surfactant costs assuming that fewer pore volumes of surfactant will be needed as
a result of the polymer.
UTCHEM can be used to simulate a wide range of displacement processes at both the field and laboratory
scales. The model is a multiphase, multicomponent, three-dimensional finite-difference simulator. The
model was originally developed to model surfactant enhanced oil recovery but modified for applications
involving the use of surfactant for enhanced remediation of aquifers contaminated by NAPLs. The balance
equations are the mass conservation equations, an overall balance that determines the pressure for up to four
fluid phases, and an energy balance equation to determine the temperature. The number of components is
variable depending on the application, but would include at least surfactant, oil and water for SEAR modeling.
When electrolytes, tracers, co-solvents, polymer, and other commonly needed components are included, the
number of components may be on the order of twenty or more. When the geochemical option is used, a large
number of additional aqueous components and solid phases may be used.
A significant portion of the research effort on chemical flooding simulation at The University of Texas at
Austin has been directed toward the development and implementation of accurate physical and chemical
16
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Section 2 - UTCHEM Model Formulation
property models in UTCHEM. Heterogeneity and variation in relative permeability and capillary pressure are
allowed throughout the porous medium, since for example each gridblock can have a different permeability
and porosity.
Surfactant phase behavior modeling is based in part on the Hand representation of the ternary phase diagram
(Hand, 1939). A pseudophase theory (Prouvost et al, 1984b; Prouvost et al., 1985) reduces the water, oil,
surfactant, and co-surfactant fluid mixtures to a pseudoternary composition space. The major physical
phenomena modeled are density, viscosity, velocity-dependent dispersion, molecular diffusion, adsorption,
interfacial tension, relative permeability, capillary pressure, capillary trapping, cation exchange, and polymer
and gel properties such as permeability reduction, inaccessible pore volume, and non-Newtonian rheology.
The phase mobilization is modeled through entrapped phase saturation and relative permeability dependence
on trapping number.
The reaction chemistry includes aqueous electrolyte chemistry, precipitation/dissolution of minerals, ion
exchange reactions with the matrix (the geochemical option), reactions of acidic components of oil with the
bases in the aqueous solution (Bhuyan, 1989; Bhuyan et al., 1990 and 1991) and polymer reactions with
crosslinking agents to form gel (Garver et al,, 1989; Kim, 1995).
Nonequilibrium mass transfer of an organic component from the oleic phase to the surfactant-rich
microemulsion phase is modeled using a linear mass transfer model similar to that given by Powers et al.
[1991]. Even in the absence of surfactant, the model allows for a small dissolution of oil in the aqueous
phase. Nonequilibrium mass transfer of tracer components is modeled by a generalized Coats-Smith model
(Smith etal, 1988).
The model includes options for multiple wells completed either horizontally or vertically. Aquifer boundaries
are modeled as constant-potential surfaces or as closed surfaces.
A dual-porosity formulation to model transport in fractured media has recently been added to the simulator
(Liang, 1997). We have recently incorporated a biodegradation model in UTCHEM. Multiple organic
compounds can be degraded by multiple microbial species using multiple electron acceptors (de Blanc, 1998;
Delshadetal., 1994).
The resulting flow equations are solved using a block-centered finite-difference scheme. The solution method
is implicit in pressure and explicit in concentration (IMPES type). One- and two-point upstream and third-
order spatial discretization are available as options in the code. To increase the stability and robustness of the
second-and third-order methods, a flux limiter that is total-variation-diminishing (TVD) has been added (Liu,
1993; Liu et al., 1994). The third-order method gives the most accurate solution.
2.2 Model Formulation
2.2.1 General Description
In this section, a brief description of the model formulation is given. Additional features needed only for
enhanced oil recovery can be found in Datta Gupta et al, [1986], Bhuyan et al, [1990], and Saad [1989]. The
balance equations are as follows:
1. The mass balance equation for each species.
2. The aqueous phase pressure is obtained by an overall mass balance on volume-occupying components
(water, oil, surfactant, co-solvent, and air). The other phase pressures are computed by adding the
capillary pressure between phases.
3. The energy balance equation.
17
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Section 2 - UTCHEM Model Formulation
Four phases are modeled. The phases are a single component gas phase (1=4) and up to three liquid phases:
aqueous (£=1), oleic (£=2), and microemulsion (£=3), depending on the relative amounts and effective
electrolyte concentration (salinity) of the phase environment. Any number of water, oil, or gas tracers can be
modeled. The tracers can partition, adsorb, and decay if they are radioactive. UTCHEM can model
partitioning interwell tracer tests (PITT) for the detection and estimation of contaminants and for the
remediation performance assessment in both saturated and vadose zones (Jin etal, 1995).
The flow equations allow for compressibility of soil and fluids, dispersion and molecular diffusion, chemical
reactions, and phase behavior and are complemented by constitutive relations.
2.2.2 Mass Conservation Equations
The assumptions imposed when developing the flow equations are local thermodynamic equilibrium except
for tracers and dissolution of organic component, immobile solid phases, slightly compressible soil and
fluids, Fickian dispersion, ideal mixing, and Darcy's law. The boundary conditions are no flow and no
dispersive flux across the impermeable boundaries.
The continuity of mass for component K in association with Darcy's law is expressed in terms of overall
volume of component K per unit pore volume (CK) as
-(CKpK)
at
£=1
(2.1)
where the overall volume of component K per unit pore volume is the sum over all phases including the
adsorbed phases:
for K= 1,..., nc
(2.2)
ncv is the total number of volume-occupying components. These components are water, oil, surfactant, and
air. np is the number of phases; CK is the adsorbed concentration of species K; and pK is the density of pure
component K at a reference phase pressure PR relative to its density at reference pressure PRO, usually taken at
the surface condition of 1 atm. We assume ideal mixing and small and constant compressibilities C£.
pK = l + C°(PR-PRO)
The dispersive flux is assumed to have a Fickian form:
(2.3)
(2.4)
The dispersion tensor KK^ including molecular diffusion (D^) are calculated as follows (Bear, 1979):
K
(2.5)
where (XL^ and (XTY are phase £ longitudinal and transverse dispersivities; i is the tortuosity factor with the
definition of being a value greater than one; ug[ and u^j are the components of Darcy flux of phase I in
18
-------
Section 2 - UTCHEM Model Formulation
directions i and j; and 8y is the Kronecker delta function. The magnitude of vector flux for each phase is
computed as
+(uze}2
The phase flux from Darcy's law is
(2.6)
(2.7)
where k is the intrinsic permeability tensor and h is the vertical depth. Relative permeability (kr^), viscosity
(\i.£), and specific weight (y^) for phase I are defined in the following sections.
The source terms RK are a combination of all rate terms for a particular component and may be expressed as
(2.8)
where QK is the injection/production rate for component K per bulk volume.
for component K in phase I and solid phase s respectively.
Analogous equations apply for the fluxes in the y- and z-directions.
and rKs are the reaction rates
2.2.3 Energy Conservation Equation
The energy balance equation is derived by assuming that energy is a function of temperature only and energy
flux in the aquifer or reservoir occurs by advection and heat conduction only.
(l-)psC
vs
T + V-
(2.9)
where T is the reservoir temperature; Cvs and Cv^ are the soil and phase I heat capacities at constant volume;
Cp£ is the phase £ heat capacity at constant pressure; and XT is the thermal conductivity (all assumed constant).
qH is the enthalpy source term per bulk volume. QL is the heat loss to overburden and underburden
formations or soil computed using the Vinsome and Westerveld [1980] heat loss method.
2.2.4 Pressure Equation
The pressure equation is developed by summing the mass balance equations over all volume-occupying
components, substituting Darcy's law for the phase flux terms, using the definition of capillary pressure, and
ncv
noting that ^ CK^ = 1. The pressure equati.cn in terms of the reference phase pressure (phase 1) is
K=l
P -
P -
(2.10).
K=l
19
-------
Section 2 - UTCHEM Model Formulation
where
total relative mobility with the correction for fluid compressibility is
K=I
The total compressibility, Ct, is the volume-weighted sum of the rock or soil matrix (Cr) and component
compressibilities (C£):
Ct — Cr
>cv
K
(2.11)
K=l
where <|> = <|>R[l + Cr (PR -PRO)].
2.2.5 Nonequilibrium Dissolution of Nonaqueous Phase Liquids
Mathematical models of multiphase flow in subsurface environments generally employ a local equilibrium
assumption; that is, it is assumed that the concentration of water leaving a region of residual NAPL has
dissolved concentrations of the organic phase at the solubility level. However, field data frequently indicate
that contaminant concentrations in groundwater are lower than their corresponding equilibrium values
(Mackay et al, 1985; Mercer and Cohen, 1990). Experimental investigations indicate that the dissolution
process is mass-transfer limited when (1) NAPL is distributed nonuniformly due to aquifer heterogeneity, (2)
water velocity is high and (3) NAPL saturation is low (Powers et al., 1991; Guarnaccia et al, 1992; Powers et
al., 1992). UTCHEM has the capability of modeling a nonequilibrium mass transfer relationship between
NAPL and water or microemulsion phases. The NAPL dissolution rate is assumed to be represented by a
linear driving force model similar to the one proposed by Abriola et al., [1992], Powers et al, [1991], Mayer
and Miller, [1990], and Powers et al, [1992]. The species mass transfer rate at the interface between the two
phases (R^f) is modeled as
for / = lor3
(2.12)
where MK is the mass transfer coefficient for species K across the boundary layer and CK^ and C^| are the
mass concentrations of K in the bulk aqueous solution and at equilibrium, respectively. Equation 2.12 can be
written in terms of volumetric concentration of organic species (K=2) as
3(S) -
+ M-
-C'
for I = 1 or 3
(2.13)
where C2^ is the volumetric concentration of organic species in the aqueous phase and C^ is the equilibrium
concentration. The time derivative was discretized using a backward finite difference approximation.
The equilibrium concentration for pure NAPL in water or aqueous phase with surfactant concentration below
the critical micelle concentration (CMC) is an input solubility limit which is small for many of the NAPLs of
interest to contaminant hydrogeologists. In the presence of surfactant, however, the equilibrium
concentrations are calculated for surfactant/NAPL/water phase behavior using Hand's equation. The
nonequilibrium concentration of NAPL in water and phase saturations are then computed using the previous
time step saturations and concentrations and the new time step equilibrium concentrations. The mass transfer
20
-------
Section 2 - UTCHEM Model Formulation
coefficient is assumed to be a constant although it may be a function of groundwater velocity, composition,
saturation, and porous medium properties (Pennell et al, 1993).
2.2.6 Well Models
Injection and production wells are considered source and sink terms in the flow equations. Wells can be
completed vertically in several layers of the aquifer or horizontally with any length and can be controlled
according to pressure or rate constraints. The well models used are based on formulations by Peaceman
[1983] and Babu and Odeh [1989]. The aquifer boundaries are treated as either constant-potential or closed
surfaces.
2.2.7 Fluid and Soil Properties
Geologic heterogeneities are probably the key factor which reduce the effectiveness of chemical enhanced
recovery processes because'their success depends on the delivery of injected chemical and water into the
subsurface to contact the organic liquids. Heterogeneities result in a complex distribution of DNAPL in
residual zones and pools. To capture some of the geologic features, reservoir properties such as formation
permeability, porosity, residual phase saturation, phase relative permeability, and phase capillary pressure are
allowed to vary spatially in UTCHEM. Phase trapping functions and adsorption of both surfactant and
polymer are modeled as a function of permeability.
Many of the properties of anionic surfactants and polymers depend on the electrolyte concentrations in the
water. Divalent cations such as calcium and magnesium ions are particularly important and can make
significant differences in adsorption and other properties even at the low concentrations typically found in
ground water. Furthermore, it cannot be assumed that these concentrations do not change since processes
such as cation exchange and mineral dissolution occur during surfactant remediation. In this paper, we
describe these electrolyte effects in terms of salinity or effective salinity (defined below) and these terms as
used in this context refer to any electrolyte concentrations of interest, but especially to those of interest to
surfactant remediation of aquifers containing ground water at low electrolyte concentrations. The same term
and the same models are used to describe high salinities typical of oil reservoirs, but it should not be inferred
that these electrolyte effects are only significant at high salinities. In fact, cation exchange between the water
and clays and between the water and micelles (when anionic surfactant above its critical micellar concentration
is present) is more important at low salinities typical of potable water than it is at high salinities such as sea
water or high salinity oil reservoirs.
The description of properties in this paper assumes that alcohols, polymer/cross-linker, and components for
high-pH flooding are absent. These property models are described in Saad [1989], Bhuyan et al. [1990], and
Kim [1995].
2.2.8 Adsorption
Surfactant
Surfactant adsorption can be an important mechanism for a SEAR process since it causes retardation and
consumption of surfactant. The remaining adsorbed surfactant after flushing with water at the end of the
remediation process may also be important even for food grade surfactants and even though the mass
concentration in the porous media at this time is likely to be very low on the order of the CMC. Some
additional time will be required for this remaining surfactant to biodegrade and this will depend on the
surfactant concentration among other variables. Surfactant adsorption has been the subject of extensive study
for many decades and is now very well understood, especially for the types of surfactants and porous media
of interest to SEAR. Rouse et al. [1993] and Adeel and Luthy [1994] are examples of recent studies done to
compare the adsorption of different types of surfactant on soils. Somasundaran and Hanna [1977] and
Scamehorn et al. [1982] are examples among the hundreds of studies done to evaluate the adsorption of
surfactants on porous media in the context of surfactant enhanced oil recovery. These studies show that
surfactant adsorption isotherms are very complex in general. This is especially true when the surfactant is not
21
-------
Section 2 - UTCHEM Model Formulation
isomerically pure and the substrate is not a pure mineral. However, we and others have found that for many
if not most conditions of interest to us the general tendency is for the surfactant isotherm to reach a plateau at
some sufficiently large surfactant concentration. For pure surfactants, this concentration is in fact the CMC,
which is often 100 times or more below the injected surfactant concentration. Thus, the complex detailed
shape of the isotherm below the CMC has little practical impact on the transport and effectiveness of the
surfactant and for this reason it has been found that a Langmuir-type isotherm can be used to capture the
essential features of the adsorption isotherm for this purpose. Camilleri et al. [1987a] illustrate this by
simulating an oil recovery experiment and Saad et al [1989] by successfully simulating a surfactant field
project using this approach. We also used a Langmuir-type adsorption isotherm for the simulation of the
surfactant remediation of the Borden cell test illustrated below.
UTCHEM uses a Langmuir-type isotherm to describe the adsorption level of surfactant which takes into
account the salinity, surfactant concentration, and soil permeability (Hirasaki and Pope, 1974). The adsorption
is irreversible with concentration and reversible with salinity. The adsorbed concentration of surfactant (K =
3) is given by
= nun
CK,-
(~ /*
CK ~CK
+ bK(CK-CK)
K = 3 or 4
(2.14)
The concentrations are normalized by the water concentration in the adsorption calculations. The minimum is
taken to guarantee that the adsorption is no greater than the total surfactant concentration. Adsorption
increases linearly with effective salinity and decreases as the permeability increases as follows:
-0.5
(2.15)
where CSE is the effective salinity described later. The value of a.j/b^ represents the maximum level of
adsorbed surfactant and bs controls the curvature of the isotherm. The adsorption model parameters &$i, aj2,
and bs are found by matching laboratory surfactant adsorption data.
Polymer
The retention of polymer molecules in permeable media is due to both adsorption onto solid surfaces and
trapping within small pores. The polymer retention similar to that of surfactant slows down the polymer
velocity and depletes the polymer slug. Polymer adsorption is modeled as a function of permeability, salinity,
and polymer concentration (Eq. 2.14 for K = 4). The parameter 34 is defined as
,-0.5
The effective salinity for polymer (CSEP) is
r C51+(pP-l)C61
CSEP =
Ml
(2.16)
(2.17)
where GSI, Cei, and Cn are the anion, calcium, and water concentrations in the aqueous phase and (5p is
measured in the laboratory and is an input parameter to the model.
Organic
Organic sorption can be an important parameter in assessments of the fate and transport of DNAPLs in soils.
The magnitude of sorbed organics is described in terms of a partition coefficient with respect to the organic
fraction, KQC (Karickhoff, 1984). The higher KQC, the greater is its tendency to sorb into organic carbon in the
subsurface. A linear sorption isotherm is used to model the organic sorption:
22
-------
is .e
B
the initial fluids saturating the soil. Cation exchange attec ts ^
have a significant effect on the optimum ^^^^^^ invol^ in the exchange
Fountain, 1992) and surfactant t^°^J^y^^D^^A cation exchange model based on
(<&f
(2.19)
(2.20)
where the superscripts f, c, and s denote free cation, adsorbed cation on clay, and adsorbed cation on micelles,
7etprcS The simulate input parameters are Qv, the cation exchange capacity of the mineral, P and P*,
the ion exchange constants for clay and surfactant, and Cf, the concentration of surfactant in meq/ml. The
decScal neutrality and mass balances needed to close the system of ion exchange equations are
(2.21)
(2.22)
(2.23)
(2.24)
r r f^ +CS +CC (2'25)
C5 - C6 = C12 + ^12 + <~i2
computed as
C6=cf6+cs6+cc6
C3 =C6+C12
1000 C3
(2.26)
where M3 is the equivalent weight of the surfactant.
23
-------
Section 2 - UTCHEM Model Formulation
The cation exchange equations are solved for the six unknowns Cg,Cj2»C6,Ci2,Cg,andCj2 using
Newton-Raphson method.
2.2.10 Phase Behavior
The surfactant/oil/water phase behavior is based on Winsor [1954], Reed and Healy [1977], Nelson and Pope
[1978], Prouvost et al. [1985], and others. Surfactant phase behavior considers up to five volumetric
components (oil, water, surfactant, and two alcohols) which form three pseudocomponents in a solution. In
the absence of alcohols (the formulation described in this paper), only three components are modeled. The
volumetric concentrations of these three components are used as the coordinates on a ternary diagram.
Salinity and divalent cation concentrations have a strong influence on phase behavior. At low salinity, an
excess oil phase that is essentially pure oil and a microemulsion phase that contains water plus electrolytes,
surfactant, and some solubilized oil exist. The tie lines (distribution curves) at low salinity have negative slope
(Fig. 2.1). This type of phase environment is called Winsor Type I, or alternatively Type II(-) in some of the
literature. If the surfactant concentration is below CMC, the two phases are an aqueous phase containing all
the surfactant, electrolytes, and dissolved oil at the water solubility limit and a pure excess oil phase. For high
salinity, an excess water phase and a microemulsion phase containing most of the surfactant and oil, and
some solubilized water exist. This type of phase environment is called Winsor Type E, or alternatively Type
II(+) (Fig. 2.2). An overall composition at intermediate salinity separates into three phases. These phases are
excess oil and water phases and a microemulsion phase whose composition is represented by an invariant
point. This phase environment is called Winsor Type in, or just Type III (Fig. 2.3).
Other variables besides electrolyte concentrations, e.g. alcohol type and concentration, the equivalent alkane
carbon number of the oil or solvent and changes in temperature or pressure also cause a phase environment
shift from one type of phase behavior to another type. Three papers by Baran et al. [1994 a,b,c] show that the
phase behavior of surfactants with both pure chlorocarbons such as trichloroethylene (TCE) and mixtures of
chlorocarbons such as TCE and carbon tetrachloride is essentially identical in form to the classical behavior
with hydrocarbons, so we are justified in using the same approach for these contaminants as we have used for
hydrocarbons.
The surfactant/oil/water phase behavior can be represented as a function of effective salinity once the binodal
curve and tie lines are described. The phase behavior model in UTCHEM uses Hand's rule (Hand, 1939) and
is based on the work by Pope and Nelson [1978], Prouvost et al. [1984b; 1985; 1986], Satoh [1984], and
Camilleriefa/. [1987a,b,c].
Effective Salinity
The effective salinity increases with the divalent cations bound to micelles (Glover et al., 1979; Hirasaki,
1982; Camilleri et al., 1987a,b,c) and decreases as the temperature increases for anionic surfactants and
increases as the temperature increases for nonionic surfactants.
(2.27)
where Csi is the aqueous phase anion concentration; 06 is a positive constant; fg is the fraction of the total
Cs
divalent cations bound to surfactant micelles as fj = —^-; and pjis the temperature coefficient.
The effective salinities at which the three equilibrium phases form or disappear are called lower and
upper limits of effective salinity (CSEL and CSEU)-
24
-------
Section 2 - UTCHEM Model Formulation
Binodal Curve
The formulation of the binodal curve using Hand's rule (Hand, 1939) is assumed to be the same in all phase
environments. Hand's rule is based on the empirical observation that equilibrium phase concentration ratios
are straight lines on a log-log scale. Figures 2.4a and 2.4b show the ternary diagram for a Type II(-)
environment with equilibrium phases numbered 2 and 3 and the corresponding Hand plot. The binodal curve
is computed from
• = A
I = 1,2, or 3
(2.28)
where A and B are empirical parameters. For a symmetric binodal curve where B = — 1, which is the current
formulation used in UTCHEM, all phase concentrations are calculated explicitly in terms of oil concentration
3
C2t (recalling CK^ = 1).
(2.29)
K=l
AC2, + A/(AC2£)2+4AC2£(l-C2^)j for I = 1, 2, or 3
Parameter A is related to the height of the binodal curve as follows
2C
3max,m
1-C
m = 0, I,and2
(2.30a)
3max,m
where m = 0, 1, and 2 are corresponding to low, optimal, and high salinities. The height of binodal curve is
specified as a linear function of temperature:
C3max,m = HBNC,m + HBNT,m(T ~ Tref ) m = 0, 1, and 2
where HBNC,m and HeNT,m are input parameters. Am is linearly interpolated as
(2.30b)
SEOP
forC ^SEOP
(2.31)
where CSEOP is the optimum effective salinity and the arithmetic average of CSEL and CSEU- The heights of
the binodal curve at three reference salinities are input to the simulator and are estimated based on phase
behavior laboratory experiments.
Tie lines for two-phases
For both Type II(-) and Type II(+) phase behavior, there are only two phases below the binodal curve. Tie
lines are the lines joining the composition of the equilibrium phases and are given by
3l
-33
:13
(2.32)
25
-------
Section 2 - UTCHEM Model Formulation
where £=1 for Type n(+) and £=2 for Type n(-). In the absence of available data for tie lines, F is calculated
from F = -1/B. For a symmetric binodal curve (B=-l), F is equal to 1. Since the plait point is on both the
binodal curve and tie line, we have
1~C2P~C3P
C2P
(2.33)
Applying the binodal curve equation to the plait point and substituting Cw (Eq. 2.29) in Eq. 2.33, we have
l_C2p -|[-AC2P +^(AC2p)2+4AC2p(l-C2P)J
E =
(2.34)
-2P
where Cap is the oil concentration at the plait point and is an input parameter for Type II(-) and Type II(+)
phase environments.
Tie lines for Type III
The phase composition calculation for the three-phase region of Type in is simple due to the assumption that
the excess oleic and aqueous phases are pure. The microemulsion phase composition is defined by the
coordinates of the invariant point. The coordinates of the invariant point (M) are calculated as a function of
effective salinity:
C2M
_ CSE~CCSEL
CSEU ~ CCSEL
is computed by substituting C2M in Eq. 2.29 and noting that CIM = 1- C2M -'
(2.35)
The phase composition calculations for lobes II(-) and II(+) are analogous. The plait point must vary from
zero to the n(+) value, C2PL or zero to II(-) value, C2PR. Here, we only consider the II(-) lobe. The plait
point is calculated by interpolation on effective salinity:
C2PR ~C2PR+'
-SEL
-SEU
-c
SEL
(2.36)
In order to apply Hand's equation, we transform the concentrations as shown in Fig. 2.5. The transformed
concentrations are
C\( =
secG
for 1 = 2 or 3
(2.37)
Cf i f-\t
2( -l-(~i(
The angle 6 is
.C3M
C1M
sec9 =
C1M +C3M
C1M
(2.38)
26
-------
Section 2 - UTCHEM Model Formulation
Parameter E of the tie line equation is now calculated in terms of untransformed coordinates of the plait point
as
E =
C1P
~ tane)C2PR - C3PR
C2P C2PRsece
where CSPR is given by Eq. 2.29 and CIPR = 1— C2PR —
(2.39)
2.2.11 Phase Saturations
The phase saturations in the saturated zone in the presence of surfactant are calculated from the phase
concentrations, overall component concentration, and saturation constraints once the phase environment and
phase compositions are known. The overall component concentration and saturation constraints are
' = 1,2, or 3
(2.40)
K=l
(2.41)
The phase saturations in the vadose zone (phase 3 is absent) are computed from the overall component
concentration and the saturation constraint by
So =
-2 ~C21 o _ Cl c _i c c
,01 — ,04 —1 —01 — 09
1-C21 l 1-CU' 4 X 2
(2.42)
where C2i is the concentration of dissolved organic species in the water phase.
2.2.12 Interfacial Tension
The two models for calculating microemulsion/oil (023) and microemulsion/water (ais) interfacial tension
(IFT) are based on Healy and Reed [1974] and Huh [1979]. The IFTs for water and oil (crow) and water and
air (<5aw) are assumed to be known constants.
Healy et al.
The first IFT model is based on Hirasaki's modification (Hirasaki, 1981) of the model of Healy and Reed
[1974]. Once the phase compositions have been determined, the interfacial tensions between microemulsion
and the excess phases (ais, 023) are calculated as functions of solubilization parameters:
= logio
'tt
for R/3 > 1
Gt
for 1=1,2
(2.43)
1 + G,
where
, G^2, and G^3 are input parameters. R ^ ls the solubilization ratio (——). The correction factor
C33
introduced by Hirasaki, F^, ensures that the IFT at the plait point is zero and is
27
-------
Section 2 - UTCHEM Model Formulation
1-e
-V2
for 1 = 1,
(2.44)
where
(2.45)
K=l
and in the absence of surfactant or the surfactant concentration below CMC, the IFTs equal a0w
Chun-Huh
The interfacial tension is related to solubilization ratio in Chun-Huh's equation as
0(3=
for t = 1 or 2
(2.46)
where c is typically equal to about 0.3. We introduced Hirasaki's correction factor F£ (Eq. 2.44) and modified
Huh's equation so that it reduces to the water-oil IFT (crow) as the surfactant concentration approaches zero.
R?3
for^=lor2
(2.47)
where a is a constant equal to about 10.
2.2.13 Density
Phase specific weights (y^ = gp^) are modeled as a function of pressure and composition as follows:
y( = Cieju+C2ej2e+C3ej3£+0.02533C5e-0.001299C6e+CBejBe for t = 1,..., np
where
(2.48)
- PRO) I- TkR is the component K specific weight at a reference pressure and is
an input parameter. The numerical constants account for the weight of dissolved ions and have units of psi/ft
per meq/ml of ions.
We have recently modified the density calculation for the microemulsion phase (I = 3) to use an apparent oil
component specific weight in the microemulsion phase (72 3 R) instead of the oil component specific weight
CY2R).
2.2.14 Capillary Pressure
Both the Parker et al. [1987] generalization of the van Genuchten [1980] model and the Brooks and Corey
[1966] model are options used to calculate the capillary pressure. Hysteresis in capillary pressure is taken into
account in a very simplistic fashion discussed below, but a full hysteretic and trapping number dependent
model that is more complete is also available (Delshad et al, 1994).
Brooks-Corey
Capillary pressure in Brooks and Corey capillary pressure-saturation relationship (Brooks and Corey, 1966) is
scaled for interfacial tension, permeability, and porosity (Leverett, 1941). The organic spill event in the
unsaturated (vadose) zone is assumed to be in the imbibition direction (total liquid saturation increasing). The
organic spill event in the saturated zone is taken to be in the first drainage direction (wetting phase, water,
28
-------
Section 2 - UTCHEM Model Formulation
saturation decreasing) for the entire spill process. The water flushing or surfactant injection process is
assumed to be in the imbibition direction for the entire injection period.
Vadose Zone
Implicit assumptions in the capillary pressure formulation in the vadose zone where up to three phases exist
are that the direction of descending wettability is water, organic, and air and that the water phase is always
present.
= l-S
nl
(2.49)
where the maximum capillary pressure Pfe is scaled by soil permeability and porosity and is equal to
_ (Ji/ /4> ,. , .
Cpcj — J 3 which then gives
a12vk
(2.50)
where Cpci and EPQ = -1/Aj are positive input parameters. The normalized saturations are defined as
e _ $e ~ Sir
1-S
(2.51)
lr
>4r
The entrapped organic saturation for three-phase (air/organic/water) flow (S2r) is based on a function by
Payers and Matthews [1982] which uses the two-phase entrapped saturation values:
S2r = S2rl 1~
l-Slr-S2r4
>2r4
S4
(2.52)
where S2ri and S2r4 are the entrapped organic saturations to flowing water and air phases, respectively.
Saturated Zone
The capillary pressure in the saturated zone where up to three phases (water, organic, microemulsion) exist
according to the surfactant phase behavior is calculated as follows.
Two-phase organic-water
The drainage capillary pressure is modeled using the Brooks-Corey function:
(2.53)
where Ad is a measure of pore size distribution of the medium, the entry pressure Pb equals Cpccj „ /— and the
normalized water saturation is defined as
= Sl ~ Slr
l-Sir
(2.54)
29
-------
Section 2 - UTCHEM Model Formulation
where Cpcd and EPCd = -1/A-d arQ mPut parameters. The UTCHEM input parameter EPCd must be a
negative value.
Two-phase water/microemulsion or organic/microemulsion
The imbibition capillary pressure using a Corey-type function is
(2.55)
For £=!,£'=! while for i - 2,1 = 3. P|^ equals CDCJ ——, I—. The normalized saturations are defined as
<5yi V k
(2.56)
S, -S
1 -alr
S ~ S
3r
1 - S2r - S3r
Three-phase water/organic/microemulsion
= 1-Snl
So —
>2r
(2.57)
(2.58)
(2.59)
where
The residual saturations (S^r) in Brooks and Corey's model are either a constant and input to the simulator or
computed as a function of trapping number discussed later.
van Genuchten
The three-phase capillary pressure-saturation function determined using the generalization of Parker et al.
[1987] to the two-phase flow model of van Genuchten [1980] is represented by
~Slr
1 - s
lr - S2r - S3r and Pw equals
—m
S, =1
h* >0
h*<0
— p Q
where Sf = — ^ — — ^ is the effective saturation, h* =
1 —
(2.60)
is the
PC££' is the scaled capillary pressure;
~n
scaling coefficient for fluid pair of i and £';a (UTCHEM parameter of CPC) and n (UTCHEM parameter
of EPC) are the model parameters, and m = 1-1/n. A significant difference between the van Genuchten and
Brooks Corey models is the discontinuity in the slope of the capillary pressure curve at the entry pressure in
the latter model whereas Eq. 2.60 is both continuous and has a continuous slope. The implementation of this
30
-------
Section 2 - UTCHEM Model Formulation
model in the simulator includes scaling a with soil permeability and porosity similar to that described in
Brooks-Corey model.
2.2.15 Relative Permeability
Multiphase relative permeabilities are modeled based on either Corey-type functions (Brooks and Corey,
1966; Delshad and Pope, 1989) or Parker et ol. [1987] extension of van Genuchten two-phase flow equation
to three-phase flow. Hysteresis in the Corey-type relative permeability model discussed below is accounted
for by assuming the flow in the saturated zone is on the drainage curve for the spill event and the remediation
of the saturated zone is an imbibition process. However, a full hysteretic relative permeability model that is
trapping number dependent is also available (Delshad et al., 1994).
Corey-Type
Multiphase imbibition and drainage relative permeabilities in both the vadose and saturated zones are modeled
using Corey-type functions that are a function of trapping number.
Vadose Zone
The organic phase movement hi a three-phase porous medium consisting of water/organic/air is assumed to
be in the imbibition direction during the organic spill hi the vadose zone. We also assume that water and air
relative permeabilities are unique functions of their respective saturations only. Organic phase relative
permeability, however, is assumed to be a function of two saturations (Delshad and Pope, 1989). These
assumptions are consistent with relative permeability measurements (Corey et al., 1956; Saraf and Fatt, 1967;
Schneider and Owens, 1970; Saraf et al, 1982; Payers and Matthews, 1982; Oak, 1990; Oak, et al, 1990).
k» — Ir0,,!1? ,Y" fnrf — 1 9 nr A
T@ — Y£ \ n£ ) JLUI •£ — i, £, ui H-
where the normalized saturations are defined as
S o — S or
- Slr - S2r£ - S4r
S2 ~ S2r
- Slr - S2r - S4r
for ^ = 1, or 4
(2.61)
(2.62)
(2.63)
where k°^, n^, and Sfy are the relative permeability endpoint, exponent, and entrapped saturation for phase i.
The trapped organic saturation for three-phase flow (S2r) is calculated from Eq. 2.52. These equations reduce
to two-phase flow relative permeabilities in the absence of the third phase.
Saturated Zone
The organic phase movement during the spill event in the saturated zone where up to two fluid phases (water
and organic) exist is assumed to be in the drainage direction. The organic movement during the remediation
process, e.g., water flushing or surfactant injection, however, is assumed to be in the imbibition direction for
the entire injection period.
Organic spill process
The relative permeabilities for water and organic fluid phases are
= k?2(i-snl)n2
(2.64)
(2.65)
31
-------
Section 2 - UTCHEM Model Formulation
where the normalized water saturation is Snl =
1-S
lr
Remediation process
There are up to three liquid phases present according to the surfactant/water/ organic phase behavior during a
SEAR process in the saturated zone. The relative permeabilities are assumed to be unique functions of their
respective saturations only. The latter assumption is supported by experimental data measured at The
University of Texas at Austin for a mixture of petroleum sulfonate, n-decane, isobutyl alcohol, and water
(Delshad et al., 1987; Delshad, 1990). The relative permeability is defined by
for 1=1,2, or 3
where the normalized saturations are defined as
for £=1,2, or 3
(2.66)
(2.67)
The relative permeabilities reduce to water/organic, water/microemulsion, or organic/microemulsion two
phase flow functions. The residual saturations, relative permeability endpoints, and exponents are either
constants and input parameters or functions of trapping number as discussed in the next section.
Parker et al.
Parker et al. [1987] extended the two-phase relative permeability-saturation expression derived by van
Genuchten to three-phase water/oil/air flow using scaled variables as follows:
(2.68)
u _
kr2=St-S1
kr4=(s4)1/2(l-St
(2.69)
(2.70)
where St is the total liquid saturation. The assumptions in deriving the above relative permeability functions
are that water or gas relative permeability is a function of its own saturation only whereas oil relative
permeability is a function of both water and oil saturations.
2.2.16 Trapping Number
One of the possible mechanisms for SEAR is the mobilization of trapped organic phase due to reduced
interfacial tension resulting from the injection of surfactants into the aquifer (Tuck et a/., 1988; Cherry et al.,
1990; Pennell et al., 1994; Brown et al., 1994). Buoyancy forces can also affect the mobilization of a trapped
organic phase and can be expressed by the Bond number (Morrow and Songkran, 1982). The Bond and
capillary numbers for the trapping and mobilization of a nonwetting phase are usually treated as two separate
dimensionless groups, one to represent gravity/capillary forces (Bond number) and the other to represent
viscous/capillary forces (capillary number). One of several classical definitions of capillary number
(Brownell and Katz, 1949; Stegemeier, 1977; Chatzis and Morrow, 1981; Lake, 1989) is as follows
32
-------
Section 2 - UTCHEM Model Formulation
Nr. =
for £=!,..., Dp
(2.71)
where £ and £' are the displaced and displacing fluids and the gradient of the flow potential is given by
=VP,-gp Vh.
Bond number can be defined as
NB, =
= 1,..., n
(2.72)
where k is the permeability and g is the gravitational force constant.
We have recently developed a new dimensionless number called the trapping number which includes both
gravity and viscous forces. The dependence of residual saturations on interfacial tension is modeled in
UTCHEM as a function of the trapping number. This is a new formulation that we found necessary to
adequately model the combined effect of viscous and buoyancy forces in three dimensions. Buoyancy forces
are much less important under enhanced oil recovery conditions than under typical SEAR conditions and so
had not until now been carefully considered under three-dimensional surfactant flooding field conditions as a
result.
The trapping number is derived by applying a force balance on the trapped NAPL globule. The forces
controlling the movement of the blob are the viscous force due to the hydraulic gradient, the trapping force
due to capillary pressure and the gravity force, which can act as either a driving or trapping force depending on
the direction of the flow. The condition for mobilizing a trapped blob of length L is as follows
Hydraulic force + Buoyancy force > Capillary force
Substituting the definition for each of these forces we have
AL|VAPc
The trapping number is defined by the left-hand side of Eq. 2.72b as
r-P/)Vhll
(2.72a)
(2.72b)
o,
(2.72c)
For one-dimensional vertical flow, the viscous and buoyancy forces add directly and a trapping number can
be defined as
Nc + Ng , For two-dimensional flow a trapping number is defined as
for i = 1,..., n
(2.73)
where 9 is the angle between the local flow vector and the horizontal (counter clockwise). The derivation of
trapping number for three-dimensional heterogeneous, anisotropic porous media is given by Jin [1995].
Residual saturations are then computed as a function of trapping number as
33
-------
Section 2 - UTCHEM Model Formulation
-------
Section 2 - UTCHEM Model Formulation
The viscosity of a polymer solution depends on the concentration of polymer and on salinity. The Flory-
Huggins equation (Flory, 1953) was modified to account for variation in salinity as
= lor3 (2.80)
where C^ is the polymer concentration in the water or microemulsion phase, \Jiw is the water viscosity, API,
Ap2, and APS are constants. The factor Csjgp allows for dependence of polymer viscosity on salinity and
,0
hardness. The effective salinity for polymer is given by Eq. 2.17 and Sp is the slope of
on a log-log plot.
lw
vs. CSEP
The reduction in polymer solution viscosity as a function of shear rate (y) is modeled by Meter's equation
(Meter and Bird, 1964):
M-o = IV +
uw
\Pct-l
(2.81)
Y
1/2
where Jin is the shear rate at which viscosity is the average of |J,p and |iw and Pa is an empirical
coefficient. When the above equation is applied to flow in permeable media, jip is usually called apparent
viscosity and the shear rate is an equivalent shear rate yeq. The in-situ shear rate for phase I is modeled by
the modified Blake-Kozeny capillary bundle equation for multiphase flow (Lin, 1981; Sorbie, 1991) as
-
ieq ~ p
(2.82)
where yc is equal to 3.97C sec'1 and C is the shear rate coefficient used to account for non-ideal effects such
as slip at the pore walls (Wreath et al, 1990; Sorbie, 1991). The appropriate average permeability k is given
by
k =
-1
(2.83)
2.2.18 Polymer Permeability Reduction
Polymer solutions reduce both the mobility of the displacing fluid and the effective permeability of the porous
medium. The permeability reduction is measured by a permeability reduction factor, R^, defined as
effective permeability of water
=
effective permeability of polymer
(2.84)
The change in mobility due to the combined effect of increased viscosity and reduced permeability is called
resistance factor, Rp, calculated by
35
-------
Section 2 - UTCHEM Model Formulation
(2.85)
The effect of permeability reduction lasts even after the polymer solution has passed through the porous
medium and is called the residual resistance factor, RRF, defined as
mobility before polymer solution
JXDI7 — •
mobility after polymer solutio
The permeability reduction factor in UTCHEM is modeled as
ft?, _ I^T-I , p. „
_ * y^k max L) urk *-*4l
1 4* bru C/i a
(2.86)
where
R
kmax "~
1-4
crk
^kxky
"T~
\K
(2.87)
and i refers to the phase with the highest polymer concentration, brk and Qk are the input parameters.
The effect of permeability reduction is assumed to be irreversible i.e., it does not decrease as polymer
concentration decreases and thus RRF = Rk- The viscosity of the phase that contains the polymer is multiplied
by the value of the Rk to account for the mobility reduction in the simulator.
2.2.19 Polymer Inaccessible Pore Volume
The reduction in porosity due to inaccessible or excluded pores to the large size polymer molecules is
called inaccessible pore volume. The resulting effect is a faster polymer velocity than the velocity of water.
This effect is modeled by multiplying the porosity in the conservation equation for polymer by the input
parameter of effective pore volume.
2.3 Numerical Methods
The pressure equation and species conservation equations are discretized spatially and temporally as described
below. The discretized equations are given in Appendix C.
2.3.1 Temporal Discretization
The temporal discretization in UTCHEM is implicit in pressure, explicit in concentration (IMPES-like). The
solution of the pressure equation using the Jacobi conjugate gradient method is then followed by a back
substitution into the explicit mass conservation equation for each component. The temporal accuracy for the
conservation equation is increased by using a time-correction technique that is second-order in time (Liu,
1993; Liu etol., 1994).
2.3.2 Spatial Discretization
Either one-point upstream, two-point upstream, or a third-order spatial discretization of the advective
terms is used (see Appendix C). It is well-known that lower-order upwind schemes cause smearing of the
36
-------
Section 2 - UTCHEM Model Formulation
saturation and concentration profiles by increasing numerical dispersion. There have been a number of
discretization methods developed to minimize these effects associated with multiphase flow and transport
simulation (Todd et al, 1972; Leonard, 1979; Taggart and Pinczewski, 1987; Bell et al, 1989; Le Veque,
1990; Datta Gupta et al, 1991; Blunt and Rubin, 1992; Dawson, 1993; Arbogast and Wheeler, 1995). We
use a scheme that is approximately third-order in space to minimize numerical dispersion and grid-orientation
effects. In order to obtain oscillation-free, high-resolution, high-order results, Harten [1983] developed the
total-variation-diminishing scheme (TVD) that includes a limiting procedure. The limiter is a flux limiter with
constraints on the gradient of the flux function (Sweby, 1984; Datta Gupta etal, 1991; Liu et al, 1994). The
limiter function developed by Liu [1993], v/hich varies as a function of timestep and gridblock size, was
implemented in the simulator.
2.4 Model Verification and Validation
UTCHEM has extensively been verified by comparing problems such as one-dimensional two-phase flow
with the Buckley-Leverett solution (Buckley and Leverett, 1942), one-dimensional miscible water/tracer flow
against the analytical solution of the convection-diffusion equation, two-dimensional ideal tracer flow with the
analytical solution given by Abbaszadeh-Dehghani and Brigham [1984], and two-dimensional nonlinear
Burgers equation (Schiesser, 1991) by Liu [1993]. Excellent agreement between the numerical and analytical
solutions were obtained when the TVD third-order scheme was used. The model has also been validated by
comparisons with laboratory surfactant floods (Camilleri et al, 1987a), field data from the Big Muddy
surfactant pilot (Saad et al, 1989), and a multiwell waterflood tracer field project (Allison et al, 1991).
Pickens et al [1993] have compared UTCHEM results with a tetrachloroethylene (PCE) infiltration
experiment in a sandpack with four types of sands performed by Kueper [1989] and Kueper and Frind
[1991]. They concluded that the simulator can accurately predict the vertical and lateral distribution of
DNAPL in a heterogeneous medium.
The model has recently been used to model the surfactant-enhanced remediation of PCE in a test cell at
Canadian Forces Base Borden in Allison, Ontario (Freeze et al, 1994). The model was 3 m by 3 m by 4 m
deep test cell described as layered with soil properties estimated from the field data. The detailed description
of the test cell is given by Kueper et al [1993]. PCE in the amount of 231 L was first injected to the center of
the test cell. The remediation process involved the following steps:
1. Direct pumping of free-phase for about two weeks where 47 L of PCE was recovered,
2. Pump and treat for about two months where additional 12 L of free-phase and dissolved PCE was
removed, and
3. Surfactant flushing to solubilize additional PCE for about seven months. The surfactant solution was
1 wt% nonyl phenol ethoxylate (NP 100) and 1 wt% phosphate ester of the nonyl phenol ethoxylate
(Rexophos 25-97). A total of 130,000 L of surfactant solution was recirculated through the test cell.
Additional 62 L of PCE was recovered as a result of enhanced solubility by the surfactant solution.
The surfactant-enhanced solubility of PCE was measured to be about 11,700 mg/L as compared to an
aqueous solubility of about 200 mg/L,.
The measured and simulated vertical distributions of PCE before and after the surfactant injection are shown
in Figs. 2.6 and 2.7 and show good agreement. Here we discuss the features of UTCHEM model that were
used in this application and the input parameters for the physical property models since Freeze et al. did not
discuss these in their paper. The assumptions made based on the test cell conditions were 1) isothermal
simulations, 2) insignificant electrolyte concentration, incompressible fluids and soil, equilibrium PCE
dissolution, and no mobilization of PCE. The species considered in the simulation were water, PCE, and
surfactant and the resulting phases were water, PCE, and microemulsion. The phase behavior parameters
were chosen such that either residual PCE/microemulsion, residual PCE/water, or single phase
microemulsion are present. Due to lack of any phase behavior measurements for this surfactant mixture, the
37
-------
Section 2 - UTCHEM Model Formulation
phase behavior parameters (C2p, Hbnc70 in Eq. 2.30b) were adjusted such that the simulated solubility is
similar to the measured value of 11700 mg/L. Table 2.1 gives the input parameters for the physical
properties. The test cell was simulated using 12 and 9 gridblocks in the x and y directions and 14 vertical
layers. The porosity was constant equal to 0.39 and the hydraulic conductivity in the range of 0.003 to 0.01
cm/s. The ratio of vertical to horizontal permeability was 1. Longitudinal and transverse dispersivities for all
three phases were assumed to be 0.03 and 0.01 m, respectively. The 201-day simulation of surfactant
flooding took 22 minutes on a DEC 3000/500 alpha workstation.
UTCHEM was able to closely reproduce both the PCE recovery and the vertical distribution of PCE over the
period of 201 days. The favorable comparison of UTCHEM results with the field test results demonstrates
the utility of the model in predicting SEAR processes at the field scale.
2.5 Summary and Conclusions
We have presented the description of a three-dimensional, multicomponent, multiphase compositional model,
UTCHEM, for simulating the contamination of aquifers by organic species and the remediation of aquifers by
surfactant injection. UTCHEM has the capability of simulating both enhanced dissolution and separate phase
removal of NAPLs from both saturated and vadose zones. The simulator has been verified with several
analytical solutions and validated by comparisons with both laboratory and field experiments.
The model uses a block-centered finite-difference discretization. The solution method is analogous to the
implicit in pressure and explicit in concentration method. Either one-, two-point upstream, or third-order
spatial weighting schemes is used. A flux limiter that is total-variation-diminishing has also been added to the
third-order scheme to increase stability and robustness.
UTCHEM accounts for effects of surfactants on interfacial tension, surfactant phase behavior, capillary
trapping, and surfactant adsorption. Multiphase capillary pressures, relative permeabilities, physical
dispersion, molecular diffusion, cation exchange, and partitioning of NAPLs to the aqueous phase which
accounts for nonequilibrium effects are some of the important physical properties features in the simulator.
UTCHEM can be used to design the most efficient surfactant remediation strategies taking into account
realistic soil and fluid properties. Due to its capability, several important variables that can significantly affect
the outcome of any SEAR program such as mobilization vs. solubilization, mobility control by adding
polymer, nonequilibrium interphase mass transfer, temperature gradient, and electrolyte concentrations where
the soil/water interactions are important; e.g., fresh water in the presence of clay can be studied before
implementing a field project.
2.6 Nomenclature
&3 Surfactant adsorption parameter
33 j Surfactant adsorption parameter, (L2)0-5
aj2 Surfactant adsorption parameter, (L2)0-5 (Eq/L3)-1
b3 Surfactant adsorption parameter
34 Polymer adsorption parameter
341 Polymer adsorption parameter, (L2)0-5
a42 Polymer adsorption parameter, (L2)0-5 (Eq/L3)-1
b4 Polymer adsorption parameter, L3/wt% polymer
brk Permeability reduction factor parameter, L3/wt% polymer
Ci)K Total concentration of species K in gridblock i, L3/L3 PV
CSE Effective salinity for phase behavior and surfactant adsorption, Eq/L3
38
-------
Section 2 - UTCHEM Model Formulation
CSEL
CSEP
CSEU
r<°
C6
K
req
Cr
CT
Cv^
Cys
Crk
Da
DK^
foe
fs
ZK
g
h
K
k
K
k
ka
y, kz
L
MK
n.
pc
Salinity for Type II(-)/ni phase boundary or lower effective salinity limit, Eq/L3
Effective salinity for polymer, Eq/L3
Salinity for Type ni/n(+) phase boundary or upper effective salinity limit, Eq/L3
Concentration of free calcium cations, L3/L3
Concentration of free sodium cations, L3/L3
Overall concentration of species K in the mobile phases, L3/L3
Equilibrium concentration of species K, L3/L3
Compressibility of species K, (mL-1!'2)"1
Adsorbed .concentration of species K, L3/L3 PV
Overall concentration of species K in the mobile and stationary phases, L3/L3 PV
Concentration of species K in phase £, L3/L3
Constant pressure heat capacity of phase I,
Rock compressibility,
Total compressibility,
Volumetric heat capacity of phase £,
Volumetric heat capacity of soil, QT^nr1
Permeability reduction factor parameter, L(wt%)1/3
Damkohler number
Diffusion coefficient of species K in phase I, L2!'1
Organic carbon fraction in soil
Amount of species K associated with surfactant, L3/L3
Gravitational constant, Ltr2
Depth, L
Dispersion coefficient, L2H
Average permeability, L2
Permeability tensor, L2
Soil permeability, L2
Apparent permeability used in capillary pressure calculations, L2
Amount of organic adsorbed per unit weight of organic carbon in soil, (mL'3)'1
Relative permeability of phase i
Endpoint relative permeability of phase i
Endpoint relative permeability of phase I at high and low capillary numbers
Absolute permeability in the x, y and z directions, L2
Length of the core, or reservoir length, L
Mass transfer coefficient for species K, t'1
Capillary pressure exponent
Relative permeability exponent for phase I (dimensionless)
39
-------
Section 2 - UTCHEM Model Formulation
nk>w
PR
QK
QL
Qv
QH
RF
Rk
RRF
RK
clow
^ti
t
At", Atn+1
T
i, Ay;, AZJ
Relative permeability exponent for phase £ at high and low capillary numbers
Bond number of phase £
Capillary number of phase t
Trapping number of phase £
Capillary pressure between phases £ and £', mL'1!'2
Pressure of phase £, mL'h'2
Reference pressure, mL'1!'2
Source/sink for species K, L3/T
Heat loss, Of1!/2
Cation exchange capacity of clay, Eq./L3
Enthalpy source per bulk volume, QHL"3
Polymer resistance factor
Polymer permeability reduction factor
Polymer residual resistance factor
Solubilization ratio for phase £, L3/L3
Total source/sink for species K, mL"3^1
Mass exchange rate at interface for species K in phase £, mL^f1
Reaction rate for species K in phase I, mL"3!'1
Reaction rate for species K in solid phase, mLr3!"1
Normalized mobile saturation of phase I used in relative permeability and capillary pressure
calculations
Saturation of phase I, L3/L3 PV
Residual saturation of phase I, L3/L3 PV
Residual saturation of phase £ at high and low capillary numbers L3/L3 PV
Time, t
Time-step size at nth and n+lth time level, t
Temperature, T
Trapping parameter for phase £
Darcy flux, Lr1
Size of gridblock i in the x, y, and z directions, L
Greek Symbols
a i -0:5 Microemulsion phase viscosity parameters
(XL, (XT Longitudinal and Transverse dispersivity, L
Pc Cation exchange constant for clay
Ps Cation exchange constant for surfactant
Pg Effective salinity parameter for calcium
40
-------
Section 2 - UTCHEM Model Formulation
Y
YKR
|0,0
|ip
M-a,ref
(ia>s
A,T
pg
ps
p£
aaw
awo
<))
(j> i
<&
T
Subscripts
Specific weight of species K, mL"2t'2
Shear rate, f1
Specific weight of species K at reference pressure, mL'2!'2
Oil viscosity, ML^T'1
Polymer viscosity, ML'1!'1
Polymer viscosity at zero shear rate, mL- h~ 1
Water viscosity, mL"1!'1
Viscosity of phase £, mL"1!'1
Viscosity of air at reference pressure,
Slope of air viscosity function
Drainage Capillary pressure exponent
Imbibition Capillary pressure exponent
Relative mobility of phase I, (mL- h~ *)- 1
Total relative mobility,
Thermal conductivity,
Rock density, m/L3
Soil density, m/L3
Density of phase I, m/L3
Interfacial tension between air and water, mt2
Interfacial tension between oil and water, mt2
Interfacial tension between phases i and i\ mt2
Porosity, fraction
Porosity of gridblock i, fraction
Potential, mL'1!'2
Tortuosity factor
K species number
1 - Water
2-Oil
3 - Surfactant
4 - Polymer
5 - Chloride
6 - Calcium
7 - Alcohol
8-air
9-K - Tracer components
i Phase number
1 - Aqueous
2 - Oleic
3 - Microemulsion
41
-------
Section 2 - UTCHEM Model Formulation
4-Air
r Residual
s solid
Superscripts
C Cation
f Free
S Surfactant
42
-------
Section 2 - UTCHEM Model Formulation
Surfactant
Surfactant
wai
Figure 2.1. Schematic representation
ofTypell(-).;
Surfactant
water
invariant point
two-phase
Figure 2.3. Schematic representation
of Type III.
water
Figure 2.2. Schematic representation
of high-salinity Type II (+).
Ternary dianram
Hand plot
Surfactant
log scale
water
- vs. _±_
"22 °12
VS.
°23 C13
B
log scale
Figure 2.4. Correspondence between (a) ternary diagram and (b) Hand plot.
43
-------
Section 2 - UTCHEM Model Formulation
Right lobe
Figure 2.5. Coordinate transformation for the
two-phase calculations in Type III.
198.75
5.0 10.0 15.0 20.0
PCE saturation, percent
25.0
Figure 2.6. Measured and simulated PCE saturation at the
location of Core 3 prior to surfactant flooding (after Freeze
etat., 1994).
44
-------
Section 2 - UTCHEM Model Formulation
198.75
198.25 ,
g 197.75
v\
•2 197.25
196.75
196.25
Simulated
• Measured
0.0
"2."0 4.0 6.0 8.0
PCE saturation, percent
10.0
Figure 2.7. Measured and simulated PCE saturation at the
location of Core 6 at the end of surfactant flooding (after
Freeze et al., 1994).
Table 2.1. Physical Property Input Parameters for the Test Cell Simulation
Property
Density
Pure water, g/cc
Pure PCE, g/cc
Surfactant, g/cc
Viscosity
Pure water (|iwX cp
Pure PCE (|0,0), cp
Microemulsion (max. value)
cci - as parameter values
Interfacial tension
PCE/water (aow)> dyne/cm
PCE/microemulsion (minimum value),
dyne/cm
G2i, G-22. 023 (Healy and Reed 1974)
PCE solubility
Max. in water, mg/L
Max. in surfactant, mg/L
Surfactant adsorption
Max. value, mg/g soil
Parameter values: aai, as2, 03
Capillary pressure (Corey function)
Imbibition: Cpci, A,
Relative permeability (Corey function)
Water (Imbibition):Sir, ni, k^
PCE: S2r, n2, k?2
Microemulsion: S3r, n$, k°3
Value
1
1.6249
1.15
1
0.89
4
3.4, 1.0,3.0,1.0,1.0
45
0.02
13, -14.5, 0.01
200
11,700
0.311
1.1,0.0, 1000
2.7, -0.454
0.306, 2.2, 0.556
0.0, 2.2, 0.309
0.306, 2.2, 0.556
References and Comments
Eq. 2.77; Parameters were estimated based
on the measured data for a different
surfactant mixture (Pennell et al, 1994)
Eq. 2.43; parameters are based on the
measured data for a different surfactant
mixture (Pennell etal, 1994)
West and Harwell [1992]
Fountain [1992]
Eq. 2.15; but assuming surfactant
adsorption is independent of
permeability
Eq. 2.55; based on Kueper [1989]
Eq. 2.66; based on Kueper [1989]
45
-------
Section 3
Hysteretic Relative Permeability and
Capillary Pressure Models
3.1 Introduction
A new multiphase capillary pressure and relative permeability function has been implemented in UTCHEM.
Both capillary pressure and relative permeability functions account for hysteresis due to arbitrary changes in
saturation path by incorporating an oil phase entrapment model. The hysteresis modeling in UTCHEM is
based on the work by Kalurachchi and Parker [1992]. The assumptions made in developing and applying this
model are
• The model applies only to strongly water-wet media where the wettability in descending order is for
water (or microemulsion), oil, and gas phases. Oil will be used in this report to mean any non-
aqueous phase liquid (NAPL).
• The model applies to three-phase air-water-oil flow in the vadose zone and two-phase oil-water or oil-
microemulsion flow in the saturated zone
• To avoid numerical oscillations with changes from two phases (air-water) to three phases (air-water-
oil), once a location is classified as a three-phase node, it will not revert back to two phases (air-
water).
* Gas entrapment is neglected for the three-phase case. Therefore, oil entrapment in a three-phase air-
water-oil can be inferred directly from that in a two-phase oil-water system.
• Water relative permeability is unaffected by oil entrapment e.g. krw = f (S\y).
• There is no oil entrapment on the main drainage curve.
• There is no oil entrapment when water saturation is at its residual value in the vadose zone.
We use the notation adapted from Parker et al. [1987] shown in Table 3.1.
3.2 Oil Phase Entrapment
On any scanning curve (e.g. point A on Fig. 3.1), effective residual oil saturation is estimated from Land's
equation (Land, 1968), where the residual nonwetting phase saturation after imbibition is related empirically to
the initial nonwetting saturation (1 - S™m) as
46
-------
Section 3 - Hysteretic Relative Permeability and Capillary Pressure Models
1-S
mm
R(l-S™n)
1
(3.1)
The trapped oil saturation at nonzero capillary pressure is calculated from the following relationships.
3.2.1 Kalurachchi and Parker
To estimate trapped oil saturation at nonzero capillary pressure, Kalurachchi and Parker estimated the trapped
oil saturation as the difference between residual oil saturation for the actual scanning curve and that for a curve
with a reversal point equal to the free (continuous) oil saturation on the actual path. This is exactly the same
idea as proposed by Stegemeier in 1977 and described in Lake_[1989]. For example, consider point B on the
scanning curve on Fig. 3.1 with apparent water saturation of S^, = Sw + Sot. Points B and C have the same
capillary pressure, therefore the difference between the x coordinates of points B and C is the disconnected
nonwetting phase saturation ( Sot). Using Land's relation for the residual oil saturation for the scanning path
— A f~*
starting from point A ( S<£) and that starting from point 0(8^) we have
1-S.
mm
w
+ R(l-S™n)
(3.2)
(3.3)
1 + R1-
and
sot=:
mm
0.0
1-S
mm
w
1-Sw
,sr
when S«, > S
mm
'w
(3.4)
otherwise
Equation 3.4 is a conditional quadratic equation that can be solved for Sot since S^, = Sw + Sot. Once Sot is
computed, capillary pressures and relative permeabilities are computed from the equations discussed below.
3.2.2 Parker and Lenhard
The trapped oil saturation is calculated by linear interpolation since the effective trapped oil saturation along
any scanning curve (e.g., the curve with reversal point of A in Fig. 3.1) varies from zero at the reversal point
of S^m to S™ at &„= 1 as
Sot = min
mm
(3.5)
47
-------
Section 3 - Hysteretic Relative Permeability and Capillary Pressure Models
where S^: is calculated from Eq. 3.2.
3.3 Capillary Pressure
The two-phase air-water, water-oil or microemulsion-oil and three-phase oil-water-air capillary pressure-
saturation function determined using the generalization of Parker et al. [1987] to the two-phase flow model of
van Genuchten [1980] is represented as follows.
3.3.1 Two-Phase Flow
(3.6)
where (3^ is the scaling coefficient for fluid pair i and i'\ a and n are the adjustable parameters, and
m = 1-1/n. The implementation of this model in the simulator includes scaling with intrinsic permeability (k)
fk"
and porosity () where a is replaced by a I— . P is approximated by the ratio of water-air interfacial tension
V*
(
-------
Section 3 - Hysteretic Relative Permeability and Capillary Pressure Models
= mm
high
+
glow _ shigh A
1 + T/ N.
T*
where I = w (or microemulsion), oil
(3.12)
where the S^gh and s]£w are the phase I residual saturations at high and low trapping numbers, T£ is the
adjustable parameter. This correlation was derived based on the experimental data for n-decane (Delshad,
1990) and have recently been successfully applied to residual PCE as a function of trapping number measured
by Pennell et al. [1996]. The trapping number NT^ is computed as
, -p/)Vh}
(3.13)
where h is the vertical depth (positive downward), pi and pf> are the displaced and displacing fluid densities,
and the gradient of the flow potential is given by V<3>^ = VP^> - g p p Vh.
We then substitute the water (or microemulsion) and oil residual saturations calculated from Eq. 3.13 for SWr
and S™ax in the calculations of entrapped oil phase saturations (Sot), capillary pressure, and relative
permeabilities described above. This extension makes the hysteretic model suitable for remediation processes
that involve changes in interfacial tension; e.g., co-solvent, surfactant, etc. (Delshad et a/., 1996). The
reduction in interfacial tension due to the presence of surfactant or co-solvent in the above equations is
calculated from a modified Huh's equation (Huh, 1979) where the interfacial tension is related to the
solubilization ratio (Delshad et al, 1996). The interfacial tension for oil-water in the absence of surfactant or
co-solvent or water-air fluid pairs is assumed to be a constant.
49
-------
Section 3 - Hysteretic Relative Permeability and Capillary Pressure Models
7mm
V
Effective water saturation
Figure 3.1. Capillary pressure curves as a function of effective water saturation.
Table 3.1. Notation Used in Section 3
Water and oil saturations:
Residual water saturation:
Effective water saturation :
Effective total liquid saturation:
Effective oil saturation:
Apparent water saturation:
Residual and trapped oil saturation:
Minimum effective water saturation
(corresponds to the reversal from drainage
to imbibition):
Maximum effective residual oil saturation
(corresponds to main imbibition curve):
S\v> SQ
S\vr
F Sw - Swr
"w 1-S
1 ^wr
-------
Section 4
UTCHEM Tracer Options
4.1 Introduction
Any number of tracers can be modeled in UTCHEM. These tracers can be water tracer, oil tracer, partitioning
oil/water tracer, gas tracer, and partitioning gas/oil tracer. There are up to two reacting tracers allowed.
Reacting tracers are considered only for water/oil tracers and tracer components 2 and 3 are reacting and
product tracers for the first reacting tracer. Tracer components 4 and 5 are reacting and product tracers for the
second reacting tracer. The assumptions made in the modeling of tracers are:
1. Tracers do not occupy volume
2. Tracers have no effect on the physical properties
The overall tracer concentrations are computed from the species conservation equations which include a
reaction term for the reacting tracer. The tracer phase concentrations are calculated according to the tracer type:
water, oil, gas, or partitioning.
UTCHEM can model single-well tracer test (Descant, 1989), partitioning interwell tracer tests (Allison et al.,
1991; Jin et al, 1995), and single-well wettability tracer test (Ferreira et al., 1992).
4.2 Non-Partitioning Tracer
The tracer phase composition for a non-partitioning tracer is proportional to the ratio of the total tracer
concentration to the total concentration of water, oil, or gas depending on the tracer type as
T = water, oil, or gas tracer
(4.1)
-K
4.3 Partitioning Tracer
4.3.1 Water/Oil
The tracer partitioning coefficient for a water/oil tracer is defined on the basis of water or oil
pseudocomponent concentration as
KT = ^ (4-2)
where C^ and C^2 are the tracer concentrations in the water and oil pseudocomponents. The tracer phase
compositions are then computed from the tracer material balance equation as
51
-------
Section 4 - UTCHEM Tracer Options
=C1ICT1
CT
(4.3)
where
cTl=.
CT2 = KT'
where Ci, C2 are the overall concentrations for water and oil species.
The partitioning coefficient of tracer i as a function of reservoir salinity is modeled using a linear relationship
as
where GSI is the concentration of anions in aqueous phase and C5i>ref is the electrolytes concentration in
chloride equivalent (eq/1) at a reference condition (initial electrolyte concentrations). TKSj is a constant input
parameter in (eq/1)"1 and K-i^sref i§ me partitioning coefficient at the reference salinity of C5i)ref in eq/1.
UTCHEM also has the capability of modeling tracer partitioning coefficients as a function of reservoir
temperature. Partitioning coefficient for tracer i as a function of temperature is given by a linear function as:
KTi = KTi)Tref t1 + TKi (T ~ Tref )) for tracer *
(4.5)
where the temperatures are in °F and Kri.Tref 1S me partitioning coefficient of tracer i at reference
temperature, Tref. TKi is a constant input parameter in ("F)'1.
4.3.2 Gas/Oil
The partitioning coefficient for a gas/oil tracer is defined as
KT =
(4.6)
and the phase concentration for the tracer is computed using the tracer material balance equation as
where
CT =
CT
8 C8+C2KT
CT
I = 2 and 4
(4.7)
= K.
C8+C2KT
where Cg, C2 are the overall concentrations for gas and oil species.
UTCHEM has the capability of modeling gas/oil tracer partitioning coefficients as a function of reservoir
temperature. Partitioning coefficient for tracers as a function of temperature is given by a linear function as:
52
-------
Section 4 - UTCHEM Tracer Options
KT. = KT. > ref [ 1 + TKj (T - Tref)] for tracer i (4.8)
where the temperatures are in °F and KT. >ref is the partitioning coefficient of tracer i at reference temperature
(Tref) and TKj is a constant input parameter in OF)'1.
4.4 Radioactive Decay
Radioactive decay can be used for any type of tracer (oil, water, gas) as
dC
dt
T _
(4.9)
where A, is a constant input radioactive decay coefficient in (days)'1. The above equation is solved for decayed
tracer concentration once the overall tracer concentration (C^) is solved for as
(4.10)
where At is the time step size in days.
4.5 Adsorption
The tracer adsorption for any type of tracer is assumed to be linear and can be modeled using an input
retardation factor parameter (Ds) as
(4.11)
where ax is the mass of adsorbed tracer divided by the mass of rock. pr and p^ are the rock and water (i = 1)
or gas phase (I = 4) densities. C-j- is the adsorbed tracer concentration. The adsorption is applied to total
tracer flux (convective and dispersive) and modeled as
U
(V
1 l
where u is the Darcy flux in ft/d and
-------
Section 4 - UTCHEM Tracer Options
and
_
~ ~hl°
_
~ hl°
(4.13)
where KH is an input reaction rate in day1. UTCHEM has the capability of modeling the tracer reaction rate
as a function of reservoir temperature. The rate of hydrolysis of tracer as a function of reservoir temperature
is given by:
=Kh.)refexp
for tracer i
(4.14)
where the temperature is in °K and K^. >ref is the rate of tracer hydrolysis at reference temperature (Tref) and
HKj is a constant input parameter in ("K)"1.
4.7 Capacitance
The capacitance model is based on a generalized Coats-Smith model (Smith et al, 1988) and is applied to
water/oil tracer components and gas tracer components (K). The model is unsteady state, therefore the
flowing and dendritic saturations can change in each time step. The phase saturations and phase composition
from the overall species concentration and phase flash are the flowing saturation (S^) and phase
concentrations (C^) in the capacitance model in UTCHEM. The mass transfer between the flowing and
dendritic fraction is given by
1
at
The dendritic saturation is calculated from:
(4.15)
(4.16)
where Fg is the flowing fraction for phase £ defined as
(4.17)
where the flowing fraction (F^) is assumed to be a linear function of fractional flow (fy). The intercepts of the
flowing fraction line versus fractional flow at the residual saturation of nonwetting phase (fi = 0.0) and
wetting phase (fi = 1.0) are F^Q and F^i and are input parameters. The product of dendritic saturation
and dendritic phase composition (C^) is
)
_ (rd
\n
)
,
+
(4.18)
where MK is the input mass transfer coefficient in (day)'1 and the dendritic phase composition
calculated from
is
54
-------
Section 4 - UTCHEM Tracer Options
The flowing phase saturations are then determined from
S^ — F^S^
and the total flowing tracer concentrations are computed as
CK -
~ CK ~
(4.19)
(4.20)
(4.21)
55
-------
Section 5
Dual Porosity Model
5.1 Introduction
In most naturally fractured reservoirs, fractures tend to be developed in a way that makes the fractures
interconnected and the bulk reservoir rock isolated into blocks. Fractured reservoirs can thus be considered as
blocks of porous rock matrix surrounded by a network of communicating channels (fractures). The rock
matrix generally has high bulk volume and high porosity, but very low permeability. In contrast, the fractures
occupy very small volume, but have high permeability. The dual porosity model assumes that there are two
flow systems coexisting in a fractured reservoir - an interconnected fracture system and a disjoint matrix
system. In the dual porosity model, continuity equations are solved for the two systems using conventional
methods, while the mass transfer between the two systems is calculated by so-called transfer functions that
characterize flow between matrix blocks and fractures. By dividing the matrix system into subgrids at each
fracture node, transient flow of fluid in the matrix and between matrix and fractures can be studied. For
simplicity, matrix blocks are often assumed to be regularly shaped. In this implementation, we Use
parallelepiped matrix blocks to handle vertical fractures and slabs for horizontal fractures.
This section presents results of a project to implement dual porosity behavior for tracer studies in UTCHEM,
a chemical flood simulator developed at the University of Texas at Austin. Two approaches were
implemented. In the first, a capacitance model already existing in UTCHEM was made to mimic dual
porosity behavior by setting capacitance parameters to equivalent dual porosity parameters. This approach is
equivalent to a dual porosity model with no subgridding. The second approach involved adapting a
subgridding approach developed by J. Chen [1993] for counter current imbibition in fractured reservoirs.
Test runs and comparisons with the SWIFT II simulator (Reeves et al, 1986) are also made.
5.2 Capacitance Model
Dispersion into matrix blocks from surrounding fractures is typically calculated by assuming that the tracer
concentration in the fractures is uniform within a given volume of reservoir rock. This assumption results in
the following equation for diffusion of a single tracer in a single fluid phase:
a(mCm)
<|>mKmS,
3C
m
(5.1)
where
(j>m = matrix porosity, fraction
C = average tracer concentration in matrix block, m/L3
Km = tracer diffusion coefficient in matrix, L2/t
56
-------
Section 5 - Dual Porosity Model
S A = matrix block surface area per unit bulk volume of reservoir, L"l
•.m
8n
f = tracer concentration gradient normal to matrix block surface, m/L4
If transient behavior is ignored, Eq. 5.1 may be approximated by
a(cm) , . ,
-± UaKm(cf-Cm)
(5.2)
where a is a shape factor to account for matrix block geometry and number of matrix blocks per unit
reservoir volume, and Cf is the tracer concentration in the fracture. Note that the shape factor has units of L'2.
Kazemi et al. [1976] recommended a shape factor for cubic matrix blocks of
4nN
(5.3)
where n is the number of matrix blocks per unit bulk volume of reservoir and N is the "dimensionality" of the
fracture set. A good discussion of shape factors can be found in M. M. Chen [1993].
UTCHEM includes a "capacitance" model that treats diffusive transfer in a similar manner. In the capacitance
model a fluid phase is divided into two fractions: a flowing fraction (which is analogous to the fracture system
in a dual porosity model) and a dendritic fraction (which is analogous to the matrix system). Since matrix
and fracture porosities are both based on total, reservoir bulk volume, the flowing fraction, F, and the dendritic
fraction, 1-F, are equivalent to:
Af of
^T (5-4)
<>»+«»
(5.5)
For single phase flow, of course, S = 1. Total porosity is simply
In the capacitance model, mass transfer from the flowing to dendritic fractions is calculated by
at
= M(Cf-Cd)
v '
(5.6)
(5.7)
or for a fixed dendritic fraction:
a(cd)_ M
at
c
(5.8)
57
-------
Section 5 - Dual Porosity Model
where Cd is the tracer concentration in the dendritic fraction, C is the tracer concentration in the flowing
fraction, and M is the capacitance mass transfer coefficient. The capacitance model can thus be made to
calculate dual porosity behavior using the equivalents given in Table 5.1.
Figure 5.1 shows comparisons of capacitance runs in UTCHEM compared to UTDUAL, a dual porosity
simulator developed at the University of Texas at Austin. Although UTDUAL has the capability of
subgridding matrix blocks (which would yield more accurate results), these comparisons were made with no
subgridding. For these comparisons, UTDUAL was modified slightly to account for tracer diffusion in a
manner similar to counter current water imbibition. Data used to generate Fig. 5.1 are given in Table 5.2.
Note the high degree of agreement. In fact, for a mass transfer coefficient of 10~5 sec'1, the two curves are
indistinguishable on the graph.
5.3 Subgridding
Due to the relatively low permeability in matrix blocks, viscous convection of phases is very slow and is
ignored in this formulation. Molecular diffusion of tracer becomes the dominant process flow within the
matrix. The equation for tracer diffusion into the matrix can be simplified into the following equation:
= v
• vc
m
(5.9)
where X is the radioactive decay constant of the tracer.
Parallelepiped matrix blocks are assumed for the subgridding. In the horizontal direction (j -index) the matrix
is subdivided into Nsub concentric grids. In the vertical direction (k-index), the matrix is sliced into Msub
slabs. Figure 5.2 shows the discretization of a single matrix block. The advantage of subgridding the matrix
this way is that many types of fracture systems can be described. By setting Msub=l and the vertical
diffusion coefficient to zero, a vertical fracture network can be simulated. If Nsub=l and the horizontal
diffusion coefficient is equal to zero, then horizontal fractures can be simulated. A combination of
subgridding in these two directions can be used to simulate a 3D fracture system. When Msub=l and
Nsub=l, the system reduces to the capacitance (no subgridding) model.
(5.10)
The volume fraction of each subgrid is an input value with the property:
/ *tt *""* JL t" ~~" 1 TV^
Jtmut J •"• ""* "^ > * * * )-^* ^-Cl 1 h
The volume fraction of the j* ring and kth layer subgrid is:
f _ (LxjkLyjk ~Lxj-lkLyj-lk)nk
Jjk — ~^ (5.11)
where V^ is the bulk volume of the kth layer of the matrix, Lxjk and Lyjkare the outer dimensions of the
subgrid, hk is the thickness of the kth layer, and Nsub is the number of the subgrids in the horizontal direction
(Fig. 5.2).
From Eqs. 5.10 and 5.11, the outer dimensions for each subgrid are calculated by:
58
-------
Section 5 - Dual Porosity Model
1=1
T T
yjk ~ y
= l,...,Nsub; k= l,...,Msub
= l,...,Nsub; k= l,...,Msub
(5.12)
(5.13)
where Lx and Ly are the dimensions of the matrix block.
The dimensions of a matrix block can be different than the dimensions of a gridblock. The mass transfer rate
is simply calculated by multiplying the mass transfer rate of one representative matrix block by the number of
matrix blocks per gridblock.
Using one-point upstream weighting, the finite-difference form of Eq. 5.9 becomes
At
+TH . (Cm)n +TV
i+i-kV /i+lk k+4-
j+lk
jk+1
Jk
(5.14)
where AVj™ is the volume of the jth ring arid the kth layer, and TV and TH are the transmissibilities in the
vertical and horizontal directions, respectively:
_TT
In.
i ,
m
_ fjkLxLyKz
hjk+l+hjk
and TC is calculated by:
TCjk=-(TV.k_1+TH.
The boundary condition is
Cjk = c j = Nsub; k = l,...,Msub (sides)
j = l,...,Nsub; k = 1 and k = Msub (top and bottom)
+TH. i +TV
(5.15)
(5.16)
(5.17)
(5.18)
5.4 Implementation
In this implementation the original 3D compositional code, UTCHEM, solves the pressure distributions and
tracer concentrations in the fracture system. After solving the fracture system equations, the tracer
concentration at each node is used as the boundary condition for the matrix at the same node. Only a single
tracer in single phase flow is handled.
59
-------
Section 5 - Dual Porosity Model
An additional subroutine, TDIFFU, is added to UTCHEM to do the matrix calculations. The methodology
used for this implementation is described by J. Chen [1993] and Chen et al. [1994]. In this routine, the
equations developed above are used to solve the tracer concentration distribution in the subgridded matrix
system. Concentrations in the fracture are modified to account for mass transfer between the matrix and
fracture.
Several other subroutines are also modified. Subroutine INOUT is extended to read in the parameters used to
describe the subgridding system. The initial values of the matrix tracer concentration are also read in this
routine. Subroutine TIMED is modified to set the initial tracer concentrations in the matrix system.
Calculations of the horizontal and vertical transmissibilities of the subgrids are added to the TRAN1 routine.
Some output commands are added to subroutine OUTDT1. And, of course, the MAIN program is also
modified to handle the new calculations. The distribution of tracer concentrations within the matrix are written
to output file CAPP.
In order to minimize the code changes to the whole system, the control flag for the dual porosity option is the
variable ICAP, which is also used to flag use of the capacitance model. A value of 2 is used to represent that
the dual porosity model with subgridding is used.
5.5 Results
Several test runs were made with this implementation. The first test is a comparison of the capacitance model
with the case of only one subgrid. A ID linear reservoir 1000 ft long with 10 ft width and depth is simulated.
Gridblock size is 10x10x10 ft3. Matrix blocks are also 10x10x10 ft3. There are thus 100 gridblocks in the
x-direction. Fracture and matrix porosities are 0.01 and 0.19, respectively. Permeability in the fractures is
1000 md and longitudinal dispersivity is 1.0 ft. Fluid injection rate is 0.5 ftVday. Figure 5.3 shows results
for mass transfer coefficients of 10'5,10"8 and 10~9 sec"1. Results show that the dual porosity model reduces
to the capacitance model when there is no subgridding.
The second comparison is between UTCHEM and UTDUAL (J. Chen, 1993). The reservoir and fluid
conditions are the same as the first set of runs, except that a diffusion coefficient (Km) of 4.32xlO'3 ft2/day
was used. The subgrid numbers compared are 1,2, 4, and 8. One more run with 16 subgrids was run on
UTDUAL which showed that the curve converges with only 8 subgrids. Figure 5.4 shows the results.
Figure 5.5 shows agreement between UTCHEM and UTDUAL. The pore volumes reported in these figures
refer to the total (fracture + matrix) pore volumes. The UTCHEM output files, however, give the fracture
pore volumes only.
The third case run was a 2D case. The reservoir is 100x100x10 ft3 and with grid number of 10x10x1. Each
grid size is 10x10x10 ft3. Fluid is injected in one corner and produced from an opposite corner, simulating a
quarter of a five-spot pattern. All other properties are the same as the second set of runs. The number of
matrix subgrids ranges from 1 to 8. Figure 5.6 shows the result. Note that the solid line is the overlap of the
two curves of the capacitance model and the dual porosity model with one subgrid.
It is expected that increasing the number of subgrids will increase computing time. However, the amount of
additional time required for additional subgridding is very small in this implementation. Figures 5.7 and 5.8
show CPU times for the runs made above. Note that only slightly more time was needed, even with 8
subgrids.
The last comparison is with SWIFT II (Reeves et al., 1986), a code developed for contaminant transport
studies. The case simulated is the transport of a decaying radionuclide in a fractured porous medium. A thin
fracture is situated within a saturated porous rock matrix. Both the fracture and matrix are semi-infinite in
extent. The radionuclide is convected and dispersed through the fracture with constant velocity and is diffused
into the rock matrix. The fracture aperture is 10'4 m, matrix porosity is 0.01, matrix tortuosity is 0.1, fracture
60
-------
Section 5 - Dual Porosity Model
dispersivity is 0.5 m, molecular diffusion coefficient in water is 1.6xlO~5 cm2/sec, radionuclide decay constant
is 0.0561 yr1, and fracture velocity is 0.01 m/day. Note that the value of the dispersivity in UTCHEM (Km)
is equivalent to the product of tortuosity times the molecular diffusion coefficient in water used by SWIFT II.
A constant tracer concentration boundary condition on the source side of the system is required to match an
analytical solution to this problem (Tang et al., 1981). UTCHEM was modified slightly to handle this
boundary condition. Variable gridblocks are used in both fracture and matrix. A 10,000-day period was
simulated. Figure 5.9 shows the radionuclide concentration in the fracture. Note that the simulated results
and the analytical solution by Tang et al. match very well. Figure 5.10 shows the radionuclide concentration
in the matrix 1.5 m from the injection point at 10,000 days. The result also matches the analytical solution.
This problem is described in detail in the SWIFT II manual (Reeves et al., 1986).
5.6 Conclusions
From the above test runs and comparisons with other simulators, the following conclusions are made:
1. A dual porosity formulation to model tracer flow in fractured reservoirs has been implemented in the
UTCHEM chemical flooding simulator. Good matches are obtained compared with other simulators.
2. Different fracture systems can be modeled by the simulator. These include vertical fractures,
horizontal fractures, and combinations of the two.
3. Computer time required to refine the matrix system does not appreciably increase for reasonable
numbers of subgrids.
4. The dual porosity model reduces to the capacitance model when the number of subgrids is equal to
one.
5.7 Nomenclature
O* = tracer concentration in dendritic fraction, m/L3
Cf = tracer concentration in flowing fraction or fracture system, m/L3
Cm = matrix block tracer concentration, m/L3
Cm = average tracer concentration in matrix block, m/L3
fjk = volume fraction of subgrid j, k, dimensionless
fsn
F = flowing fraction ~ , dimensionless
1—F = dendritic fraction ~r~ , dimensionless
{b )
hk = thickness of kth layer, L
Km = tracer diffusion coefficient in matrix, L2/t
Km
xy =
Km
z =
*Ly =
tracer diffusion coefficient in matrix in horizontal direction, L2/t
tracer diffusion coefficient in matrix in vertical direction, L2/t
matrix dimensions, L
= subgrid dimensions in x and y directions, L
61
-------
Section 5 - Dual Porosity Model
M = capacitance mass transfer coefficient, f1
Msub = number of subgrids in vertical dkection (layers)
n = number of matrix blocks per unit bulk volume of reservoir
N = dimensionality of fracture set
NSU5 = number of subgrids in horizontal dkection (rings)
SA = matrix block surface area per unit bulk volume of reservok, L"l
S^ = dendritic saturation, dimensionless
Sf = flowing saturation, dimensionless
TC = sum of transmissibilities in the vertical and horizontal dkections, L3/t
TH = transmissibility in the horizontal dkection, L3/t
TV = transmissibility in the vertical dkection, L3/t
t = time, t
^bk = bulk volume of layer k of the matrix, L~3
volume of the jth ring and the k* layer of matrix subgrids, L'3
= total porosity, fraction
(j> = fracture porosity, fraction
im = matrix porosity, fraction
A, = radioactive decay constant, f1
a = shape factor, L~2
AVJk
3Cm
3n
= tracer concentration gradient normal to matrix block surface, m/L4
62
-------
Section 5 - Dual Porosity Model
O
I
o>
o
o
-------
Section 5 - Dual Porosity Model
Capacitance
1 Subgrid
M=10"9 sec"1
Q
0
0.2
Pore volumes injected
Figure 5.3. Comparison of capacitance model vs. subgrid model in UTCHEM.
LO-
1
c °-8-
(O
Ia7^
fg °-5^
£ 0.4-i
CO
1 °-:
tn
S °-2Jl
I o.M
0.0
0
0.2
1.2
1.4
0.4 0.6 0.8 1
Pore volumes injected
Figure 5.4. Subgrid refinement studies with UTCHEM, Km = 3.243x10'2 ft2/day.
64
-------
Section 5 - Dual Porosity Model
1.0-
o 0.9-3
•£3
g°'M
g 0.7^1
o
o
8 subgrids UTDUAL
8 subgrids UTCHEM
Figure 5.5.
1.0-
o 0.9^
I a6^
3 A ^
£g 0.4-
1 0.3^
1 0.2^
•J o.i-
0.4 0.6 0.8 1
Pore volumes injected
Comparison of UTCHEM and UTDUAL subgridding.
0.0-
Capacitance
1subgrid
2 subgrids
4 subgrids
8 subgrids
0
I
0.2
0.4 0.6 0.8 1
Pore volumes injected
Figure 5.6. 2D subgrid refinement studies with UTCHEM.
i
1.2
1.4
65
-------
Section 5 - Dual Porosity Model
130-
^ 120~
*
S 110-
|D 100-
90-
80
O
Eg Capacitance
O Subgrids
0123456789
Number of subgrids
Figure 5.7. Comparison of execution time with different numbers of
subgrids, 1D case.
230-
220-
l90-
D 180-
Pu
°170-
160-
150-
0
El Capacitance
O Subgrids
T-
2
3 4
Number of subgrids
i i i i i i i i i i i i i i i i i i i i
56789
Figure 5.8. Comparison of execution time with different numbers of
subgrids, 2D case.
66
-------
Section 5 - Dual Porosity Model
UTCHEM 100 days
UTCHEM 1,000 days
UTCHEM 10,000 days
Analytical 100 days
Analytical 1,000 days
Analytical 10,000 days
Q
i •« i '"» i
34567
Distance down fracture
8
rQ-| rQ-
9
10
Figure 5.9. Comparison of simulated results vs. analytical solution (Tang et al.,
1981) for radionuclide concentration in the fracture.
SWIFT II
UTCHEM
Analytical
t = 10,000 days
= 1.5 m
0
0.4 0.6 0.8
Distance into matrix (m)
Figure 5.10. Comparison of simulated results vs. analytical solution (Tang et
al., 1981) and SWIFT II (Reeves et al., 1986) for radionuclide concentration in
the matrix.
67
-------
Section 5 - Dual Porosity Model
Table 5.1. Equivalence Between Capacitance and Dual Porosity Models
Capacitance Model
Porosity (<())
Flowing fraction (F)
Dendritic fraction (1— F)
Flowing fraction tracer concentration ( C )
Dendritic fraction tracer concentration ( C )
Mass transfer coefficient (M)
Dual Porosity Model
f
*f
f
f
Table 5.2. Input Data for the Comparisons of Capacitance
Model in UTCHEM to Dual Porosity Model in UTDUAL
System size
Fluid injection rate
Capacitance Model
Total porosity
Flowing fraction
Dendritic fraction
Mass transfer
coefficient
Dual Porosity Model
Fracture porosity
Matrix porosity
Shape factor
Matrix block size
Diffusion coefficient
100x10x10
0.5
0.20
0.05
0.95
10-5
10-8
10-9
0.01
0.19
0.08
10x10x10
10.8
l.OSxlO-2
1.08x10-3
ft
ft3/day
sec"1
sec"1
sec"1
ft-2
ft
ft2/day
ft2/day
ft2/day
68
-------
Section 6
UTCHEM Mode! of Gel Treatment
6.1 Introduction
This section is;based on the dissertation entitled "A Simulation Study of Gel Conformance Treatments" by H.
Kim, The University of Texas at Austin, Ph.D., May 1995.
6.2 Gel Conformance Treatments
The operational aspect of a gel treatment includes the following :
• Zonal isolation
• Types of gel treatments
• Shut-in time
• Gel injection rate
• Amount of gelant
The types of gel treatments are 1) simultaneous injection of polymer and crosslinker into the reservoir,
2) alternate injection of polymer and crosslinker slugs, and 3) injection of pre-gelled fluid into the reservoir.
The type of gel treatment selected influences the placement of the gel in the reservoir. In this study, the
simultaneous mode of injection of polymer and crosslinker was modeled.
The shut-in time allowed after injection, before the well is put back on production, is critical to the success of a
gel job. If the gel does not reach most of its strength, its efficacy in plugging the high-permeability layer will
suffer.
The injection rate determines the rate of shearing of the polymer and gel as well as the injection pressure. The
injection rate should be such that the wellbore pressure does not exceed the fracture pressure of the rock
matrix.
The amount of gelants injected determines the depth of penetration of the gel into the formation. The amount
injected must ensure adequate plugging of the high-permeability, watered-out zone.
Zonal isolation is used to selectively treat the problem zone. In some wells, improper well completion or
casing damage may lead to mechanical difficulties in achieving zonal isolation. In this work, gel treatments
were simulated with and without zonal isolation to demonstrate the effectiveness of zonal isolation.
The polymer-gel system chosen for a particular treatment will depend on its compatibility with the reservoir
and operational conditions. The properties considered when choosing a particular system are
69
-------
Section 6 - UTCHEM Model of Gel Treatment
• Viscosity
• Gelation time
• Permeability reduction
• Thermal and mechanical stability
• Mechanical strength
• Safety
Viscosity of the gel and polymer determines the wellbore pressure during injection. Very high viscosities
may cause the wellbore pressure to exceed the fracture pressure of the reservoir.
Gelation time depends on the kinetics of gel formation and influences the injection rate and shut-in time used
during the treatment. Ideally, the gelation time should allow proper placement of the gel before full gel
strength develops.
The permeability reduction caused by the gel in the porous medium is an indicator of its ability to modify the
flow patterns in the reservoir. In near-wellbore treatments, the gel should be able to plug the high water-cut
zones.
The ultimate mechanical strength developed by a gel is a measure of the pressure it can withstand before
breaking down. The gel should have enough mechanical strength to remain in place when subjected to
normal drawdown during production.
Safety of the gel, polymer and crosslinker may ultimately determine its usage. Gel components need to be
safe for handling and storage and should pose no risk to the environment. The application of some toxic gels
may be limited or restricted by the environmental concerns in certain locations. Studies of environmentally
benign gels that do not use any toxic materials as a gel component are active.
It is important to characterize the reservoir in which the gel is ultimately going to be placed. Some reservoir
characteristics that have a significant impact on gel treatment success are
• Permeability contrast
• Vertical communication
• Rock properties such as clay content
• Salinity
• Temperature
The permeability contrast between the layers influences the relative depth of penetration in the layers. A high
permeability contrast mitigates the damage done to the oil-producing low-permeability zone.
Crossflow between the layers leads to mixing of fluids between the.layers. This can cause some penetration
of low-permeability layers even during selective treatments. During post-gel treatment production, crossflow
may cause the water to bypass the plugged zone and be produced.
The clay content and the cation exchange capacity of the clays can have a significant impact on crosslinker
propagation. Experiments indicate that a significant portion of injected cations like chromium may be retained
on the clays and hence are not available for gelation. Salinity influences polymer and gel viscosities, while the
70
-------
Section 6 - UTCHEM Model of Gel Treatment
temperature of the reservoir affects the rate of gelation and the stability of the gel for an extended period of
time.
The gel properties modeled in UTCHEM include
• effect of gel on aqueous-phase viscosity,
• gel retention on matrix, and
• aqueous phase permeability reduction.
6.3 Gel Viscosity
The viscosity of an aqueous solution containing gel is modeled using the Flory-Huggins equation with
additional terms for gel (Thurston et al., 1987).
= Hw[l+(ApiC45l+Ap2C4)12+Ap3C4)13)c^p+AglC15)1+Ag2C15jl2]
(6.1)
6.4 Gel Adsorption
Gel retention modeling is done using a "Langmuir-type" isotherm to correlate adsorbed concentration with the
aqueous-phase concentrations.
C15 =
a!5 C15,l
+ b15c!5,l
(6.2)
6.5 Gel Permeability Reduction
The effect of gel on aqueous-phase permeability reduction is taken into account through a residual resistance
factor commonly used for polymer flooding.
RRF =
R
RFmax
Agk C15,l
Bgk C15,l
where the maximum residual resistance factor is calculated by
-1-4
1/
.Sr
(6.3a)
R
RFmax -
1
p
Crg I Apl CSEp
4>
(6.3b)
The parameter crg is an input parameter which depends on the gel type. The permeability reduction for silicate
gel (KGOPT=3) is independent of the silicate viscosity and the maximum residual resistance factor (RRFmax)
is equal to 10.
6.5.1 Chromium Retention
The following equilibria have been implemented in UTCHEM to simulate the exchange between chromium,
sodium and hydrogen on the clays.
71
-------
Section 6 - UTCHEM Model of Gel Treatment
6.5.2 Cation Exchange
6.5.2.1 Chromium-Sodium Exchange
3N? + Cr3* = 3Na+ + Cr3+
K
14,9 =
^ O
C14 C9.1
CQ3C
14,1
(6.4)
6.5.2.2 Hydrogen-Sodium Exchange
Na+ + H+ = Na+ + H+
K16,9
s\
C16 C9,l
/*
C9 C16,l
(6.5)
6.5.3 Adsorption
As an alternative to cation exchange, the retention of chromium has also been modeled as a "Langmuir-type"
isotherm in UTCHEM.
-14
_ a!4C14,l
1 + b14C14)1
(6.6)
6.5.4 Precipitation
Chromium precipitation is modeled using geochemical reaction equilibria in UTCHEM. Cr(III) precipitates
in the form of chromium hydroxide complex.
Cr3++ H2O = Cr(OH)2+ + H+ . (6.7)
Cr3++ 2H2O = Cr(OH)+ + 2H+ (6.8)
Cr(OH)3 1 = Cr3* + 3 Off (6.9)
Gel reactions are implemented in the source term as gel kinetic equations and the mass-conservation equation
is solved with reacted amount of each gel component.
Polymer molecules are crosslinked by Cr(III), which is known to be one of the most widely used
crosslinkers. Three types of gel reactions and kinetics are implemented in UTCHEM. The kinetics of
polymer/chromium chloride gel were modified, and gel reactions of polymer/chromium malonate gel and
silicate were modeled.
6.5.5 Polymer/Chromium Chloride Gel
Two sets of reactions and kinetics for polymer/chromium chloride gel are implemented in UTCHEM. The
first is in-situ gelation of polymer with sodium dichromate with reducing agent thiourea, and the second is the
gelation of Cr(III) with polymer to form gel.
The kinetics for the reaction between polymer and chromium have been generalized to allow for any exponent
(Hunt, 1987). The gel is formed by fast reaction of trivalent chromium (Cr(HI)) and polymer. There is an
option for the slow delaying reaction between Cr(VI) and thiourea. The sodium dichromate (Na2Cr2O7) and
thiourea (CS(NH2))2 are treated like tracers in the sense that they do not occupy any volume. The Cr(III) for
the gelation process can be generated in situ by redox reaction between Cr(VI) and thiourea.
72
-------
Section 6 - UTCHEM Model of Gel Treatment
Cr2O72- + 6CS(NH2 )2 + 8H+ ^—> 2Cr3+ + 3[CS(NH2 )2 ]2 + 7H2O
The gel reaction is highly dependent on pH (Lockhart, 1992; Seright and Martin, 1991). For more realistic
simulations of gel reactions, pH was implemented in the gel kinetic equation as hydrogen ion concentration.
6.5.6 Polymer/Chromium Malonate Gel
The components of polymer/chromium chloride gel are as follows:
1. Polymer - Hydrolyzed polyacrylamide (HPAM) and HE-100 (acrylamido-3-propane sulfonic acid
co-polymer) were used. HE-100/chromium malonate is reported to have a longer gelation time than
HPAM/chromium malonate (Lockhart, 1992).
2. Crosslinker - Chromium malonate, Cr ( HOOC - CH2 - COOH )•}. Among various complexes of
chromium, chromium malonate has the longest gelation time and stability at high temperature
(Lockhart, 1992).
3. Ligand (delaying) - Malonate ion (uncomplexed), ( HOOC - CH - COOH )". The uncomplexed
malonate ion as a delaying ligand is an optional component that gives a longer gelation time.
6.5.6.1 Kinetics
Case / (polymer and crosslinker only)
The kinetics for this gel are the same as the kinetics of chromium chloride gel except with different exponents:
[polymer] + n[Cr(HI)] =
[Cr
d[Cr(ni)] _
dt
= - k
[gel] ,
]X14[ polymer ]X4
X16
d [ gel ] = L d[Cr(ffl)]
dt " n dt
where the possible values for exponents from Lockhart [1992] are
X4 2.6
X14 0.6
X16 1.0
Case // (polymer, crosslinker, and malonate ion )
When the malonate ion is used as a delaying ligand, the gelation kinetics are different, with zero-order reaction
for chromium:
d[Cr(ni)]
dt
= - k
[ polymer ]
X4
d[gel] = L
dt n
[ malonate ]X13[H+]X16
d[Cr(IH)]
where some possible values for exponents from Lockhart [19912] are
73
-------
Section 6 - UTCHEM Model of Gel Treatment
X4
X13
X16
2.6
0.3
1.0
The uncomplexed malonate ion slowly decomposes to acetate and carbon dioxide, and this is a first-order
reaction:
( HOOC - CH - COOH )- > CHsCOO- + CO2
First-order reaction:
d[malonate] = _0037347 [malonate]
6.5.7 Silicate Gel
UTCHEM was modified to simulate the gel reaction of the silicate gel. Polymer and chromium were
replaced with silicate (SiC>2) and hydroxyl ion (OH-), respectively. The gelation was limited to occur only for
pH > 7 (Bennett et al., 1988; Her, 1979) to eliminate complex behavior of gel reaction rate at pH < 7, and the
aqueous-phase permeability-reduction factor was independent of silicate viscosity.
Silicate gel is formed by polymerization when appropriate conditions are established. The exact mechanism
of gelation is not clear yet; several authors (Her, 1979; Jurinak et al, 1989) explain the general mechanism of
gelations of various types of gels.
The general process of gelation is as follows (Jurinak et al., 1989):
• condensation of monomer and dimer silicate species to form higher-order oligomers,
• intramolecular condensation of silanol groups within polymers leading to ring closure and eventual
particle formation, and
• aggregation of individual particles to form chains and microgel.
The rate of gelation (Kristensen et al., 1993) is a function of
• silicate concentration
• pH
• ionic strength
• temperature
The basic equations that govern polymerization of silicate (Iler, 1979) are as follows:
SiQi + 2H2O = Si(OH)4 (6.10)
-SiOH + HOSi- = -SiOSi- + H2O (6.11)
In general form,
+ zOHT = SinOy(OH)^x.z) + (y-2)H20 , (6.12)
74
-------
Section 6 - UTCHEM Model of Gel Treatment
where
n = degree of polymerization
x = ratio of OH:Si
x = 4.85 n-1/3 - 7.8 n'2/3 + 4.2 n~1
y = ^JIX + z
z = number of charges on polymer
Equation 6.12 can be written in simplified form as
[SiO2] + m[OH-] = [silicate gel] ,
where m is the stoichiometric ratio.
From Eq. 6.13, the gelation kinetics equation can be derived.
(6.13)
(6.14)
where
X4 = gelation kinetics exponent for silicate
X14 = gelation kinetics exponent for hydroxyl ion
d [ gel ] _ d [ SiQz ]
dt " dt
where some possible values for exponents (Kristensen et al, 1993) are
X4 3.8
X14 -2.5
6.6 Temperature Effects
The reaction constants for gel (k) and the delaying reaction of sodium dichromate and thiourea (k,) are
calculated as a function of temperature if the temperature variation is modeled in the simulations as below.
kl = kiref
1 1
T T
ref
where the temperature T and Tref are in °R. The input parameters are Tref, KTi, and kiref for the dichromate
reaction. .
k = kref exp
, 1 1
kT<7
ref
where the input parameters are Tref, Kx2, and kref for the gel reaction.
75
-------
Section 7
Multiple Organic Components
We have added multiple organic components so that we can model NAPL mixtures. Adding this capability
to UTCHEM required developing a phase behavior model for NAPL mixtures and the physical property
models such as density and viscosity for each phase.
7.1 Introduction
Nonaqueous phase liquids (NAPLs) usually consist of more than one organic species that mix and form a
single liquid. Common examples of such miscible species include TCE, TCA and PCE among many others.
When NAPLs leak to the subsurface, they can dissolve and migrate into groundwater. To model the fate and
transport of these soluble organics during remediation processes such as pump-and-treat, bioremediation and
surfactant remediation, it is important to determine the migration of the individual soluble organics. The
dissolution can be either a local equilibrium or a rate-limited (non-equilibrium) mass transfer process. We
have added the capability of multiple organic components to UTCHEM to model these NAPL mixtures. The
multiple organic dissolution can be either at local equilibrium partitioning or a rate-limited mass transfer. We
also present the phase behavior model developed for a mixture of NAPL mixtures, surfactant, and water. The
physical property models to calculate the density, viscosity, and adsorption of the organic species and NAPL
mixtures are also included.
7.2 Mass Transfer for Nonaqueous Phase Liquid
When a NAPL component dissolves in water, its concentration in ground water can reach its solubility
(equilibrium mass transfer) but often is much lower than the solubility due to a rate-limited mass transfer.
UTCHEM allows for both equilibrium and nonequilibrium mass transfer for a multiple organic NAPL. The
mass transfer is modeled for the cases with or without surfactant.
7.2.1 No Surfactant or Surfactant Concentration Below CMC
7.2.1.1 Equilibrium Mass Transfer
For the equilibrium case, a constant partition coefficient between water and NAPL is assumed for each
organic species:
k=l,2,3,...,n0 (7.1)
The overall fluid concentrations for water (Ci), surfactant (Cs), and each organic components (C£) are solved
from the species mass conservation equation. The overall fluid phase concentration is the summation of
phase concentrations over all the phases:
Ck=CklS1 k=l,3
(7.2)
76
-------
Section 7 - Multiple Organic Components
and
Ck = CklSl + Ck2S2 k=l,2,3,-.., n0 (7.3)
The definitions of overall phase concentrations (Eqs. 7.2 and 7.3), the constraints that phase concentrations
sum up to one (C31 + XCkl +CH = 1 md SCk2 = ^' ^ me known partition coefficients for organic
k=l k=l
components (Eq. 7.1) are used to solve the phase concentrations and saturations. These equations are solved
by reformulating C31 and C£ in terms of Cn and using Newton's method to solve
no
f(Cn) = C31 + ]T,Ckl +CU -1 = 0. A phase stability rule is used to determine the number of phases. If
k=l
n o
> 1, the fluid is two phases. Otherwise, it is a single phase.
^-/v-O
k=lKk
7.2.1.2 Nonequilibrium Mass Transfer
For nonequilibrium mass transfer, a Linear driving force rate, as proposed by Powers et al. [1992] is used.
The mass transfer rate between NAPL and water interface for each NAPL component is a mass transfer
coefficient times the driving force that is the difference between the equilibrium and phase concentrations.
The mass transfer coefficient is currently modeled as a constant. The computational procedure for non-
equilibrium mass transfer requires the calculation of the equilibrium organic concentrations, C^q, first. Then
we solve for the phase concentrations and saturations for the nonequilibrium case. It is similar to the
equilibrium case, except that the mass balance equation for the organic in the water phase is used instead of
constant partition coefficient of the equilibrium case. The organic species mass balance equations in the water
phase are given by: •
(7.4)
+ Q°
kl
;(c°keiq-c°kl)
7.2.2 Surfactant Concentration Above CMC
7.2.2.1 Equilibrium Mass Transfer
When the surfactant concentration is greater than the CMC, micelles form. When organic species are
solubilized into these micelles under certain conditions, a microemulsion forms. Organic species dissolve by
two mechanisms: (1) organic components dissolve into water according to their equilibrium solubilities in
water and (2) the organic mixture solubilized by the micelles has the same composition as the NAPL. To
model both mechanisms, each organic component is divided into two parts, one associated with water, C^w,
and the other associated with the micelles,
iOO
The organic dispersed into water follows the constant partition coefficient as described above. The remainder
of the organic is assumed to follow the same microemulsion as used for a single component (as given in
Appendix C and based upon Hand's equation). The calculations of phase compositions are divided into two
parts. First, assume the surfactant is not present and calculate phase equilibrium concentrations as before.
77
-------
Section 7 - Multiple Organic Components
This calculation gives the overall concentration of each organic components associated with water,
-ow
COW /-i
k -Cl n
0
_ V
2-t
k=l
ow
Hand's equation is then used to calculate the phase concentrations and saturations using the normalized total
concentrations as
ci
CIN=—jr
(7.5)
k=l
no no
Ec°k-I<
/-i _ k=l k=l
C2N-—;r
C3N =1
1-£C°W-CMC
k=l
C3-CMC
(7.6)
(7.7)
k=l
Tlie phase concentrations and saturations for the normalized concentrations are calculated from Hand's
equations.
CkN -
k= 1,2,3
(7.8)
For the Type II(-) phase envkonment with corner plait point, Ci2N=0> C22N=1> <-'32N=05 and SIN=O. The
phase concentrations hi terms of the original concentrations are calculated from the following equations:
C1£=Cim l
n° "l
-£c°w-CMC
(7.9)
k=l
(7.10)
k=l
~CMC +CMC
)
(7.11)
and the saturation is unaffected by the normalization.
78
-------
Section 7 - Multiple Organic Components
7.2.2.2 Nonequilibrium Mass Transfer
Once the equilibrium saturations and concentrations are known, the organic species mass balance equations in
the aqueous phase (Eq. 7.12) are used to calculate the nonequilibrium saturations and concentrations. A
single mass transfer coefficient is assumed for all organic components.
11=1
(7.12)
k==l,2,3,...,n
where the equilibrium concentrations and saturations are already known from the phase behavior calculations.
7.3 Physical Properties for NAPL Mixture
Phase behavior, adsorption, viscosity, and density are the physical property relations modeled for the NAPL
mixtures.
7.3. 1 Phase behavior
Three recent papers by Baran et al. [1994a,b,c] show that the phase behavior of surfactants with both pure
chlorocarbons and mixtures of chlorocarbons is similar to classical phase behavior with hydrocarbons. The
phase behavior changes from microemulsion in equilibrium with excess oil (Winsor Type I or Type II(-)) to
microemulsion in equilibrium with excess aqueous and organic phase (Winsor Type III), and to
microemulsion in equilibrium with excess water (Winsor Type II or Type !!(+)) as salinity increases. The
lower (CSEL) and upper (CSEU) limits of effective salinity are the effective salinity which three phases form
or disappear. The optimal salinity (CSEOP) is defined as the midpoint of these two salinity limits (Salager et
al. 1979).
Hand's equation (Pope and Nelson, 1978) is used in UTCHEM to describe the phase envelope, binodal curve.
The concentrations at binodal curve are described by the following equation:
= 1,2,3
(7.13)
where parameter A and B are empirical parameters. Parameter A is related to the height of the binodal curve
and B is assumed to be -1 in UTCHEM for a symmetric binodal curve. Parameter A is a function of salinity
and is linearly interpolated with the values of A at low (m=0), optimal (m=l) and high (m=2) salinities as
following:
C
CSE CSEOP
CSEOP )
Parameter A in terms of the height of binodal curve is described as
(7.15)
79
-------
Section 7 - Multiple Organic Components
2C3
max.m
1-C
m=0,l,2
(7.16)
3max,m
For organic mixtures, the upper and lower limits of effective salinity for Type IE region, the height of binodal
curve at lower, optimal, and upper salinities are functions of organic species concentrations. These parameters
are modeled as functions of the equivalent alkane carbon number (EACN) of the mixture, which is a function
of organic species concentrations.
EACN =
(7.17)
k=l
where x£ is the molar fraction for organic components only,
= 1. EACN for an alkane is the number
k=l
of carbons in the alkane chain of the hydrocarbon, for example it is equal to 6 for hexane. EACN for a
nonalkane is obtained by measuring the optimal salinity for a binary mixture of an alkane and a nonalkane
with known molar fractions. The measured optimal salinity is used to determine EACN for the binary mixture
from Salager's equation. Then EACN for the nonalkane is calculated from Equation (7.17). The EACN data
listed in the Baran et al. papers are built into the UTCHEM database: C2Cl4 (PCE, EACN = 2.90), CCU
(EACN = -0.06), C2HC13 (TCE, EACN = -3.81), p-xylene (EACN = 2), toluene (EACN=1), 1,2-C6H4C12
(DCB, EACN = -4.89), l,2-C2H4Cl2 (EACN = -12.10), CHC13 (EACN = -13.67), CH2C12 (DCE,
EACN = -13.79), and 1,1,2,2-C2H2C14 (EACN = -22.15). *
The natural log of the optimal salinity is a linear function of EACN (Salager et al, 1979; Baran et al,
1994a,b.c)
In CSEOP = SSS(EACN - Emjn)
(7.18)
The slope sse is about 0.16 for the optimal salinity with the unit of wt.% per liter. The difference of the upper
and lower effective salinities for the three-phase region is assumed as a linear function of EACN
CSEU ~ CSEL _
CSEOP
where
CSEOP =
sdsEACN+bds
(7.19)
(7.20)
CsEOP> CSEL. and CSEU can be solved using Eqs. 7.18-7.20.
The solubilization parameter is usually reported by experimentalists doing surfactant phase behavior
measurements rather than the height of the binodal curve. The solubilization parameter is defined as the oil
/-<
concentration divided by the surfactant concentration in the microemulsion phase as a = 2>max . Thus,
^3, max
parameter A can be expressed in terms of the solubilization parameter:
Am= (c?m)~2 m = 0,l,2
(7.21)
80
-------
Section 7 - Multiple Organic Components
The solubilization parameter is a linear function of EACN as
= 0,l,2
(7.22)
In UTCHEM, coefficients sse, Emin, Sds, bds, sa>m, and b
-------
Section 7 - Multiple Organic Components
II, C°.^j = Concentration of species k and organic species k in phase £
Ck, C£ = Adsorbed concentration of species k and organic species k
CSE = Effective salinity
CSEL = Lower effective salinity
CSEOP = Optimal effective salinity
CSEU = Upper effective saUnity
Bk£ = Dispersion flux of species k in phase £
foc = Organic carbon fraction in soil
Adsorption of organic species k per unit weight of organic carbon in soil
Total number of organic species
Reference pressure
2^ = Source/sink term for species k and organic species k
Rk = Reaction rates for species
t = Time
Q^ = Darcy flux of phased
= Porosity
•fir0
Koc,k
no
PR
82
-------
Section 8
EQBATCH Program Description
8.1 Introduction
EQBATCH is a preprocessor batch program to calculate the equilibrium concentrations for all the flow and
solid species based on the chemical reactions considered in UTCHEM simulations. In this program, it is
assumed that all the flow species dissolve in a single phase, water. The initial pH of the formation or makeup
water can be matched by using EQBATCH with suitable input data. Also, the output of EQBATCH can be
used as the input data of UTCHEM for the geochemical options (IREACT = 2-4). In this section, a detailed
description for preparation of input data for EQBATCH is presented. To specify the reactions considered in
the simulations, elements and chemical species need to be identified. Based on the information of the
formation and makeup water analyses and the rock constituents, the key elements and chemical species can be
decided. The example shown in this section is based on the water analysis results listed in Table 8.1. The
elements such as hydrogen, sodium, calcium, magnesium, carbonate, and chlorine, are considered since these
chemicals are the primary ions contained in the formation and makeup water. The pseudo-element (oleic acid,
A) is taken into account as an element when the mechanism of in situ generated surfactant is considered.
From these elements, the expected chemical species involved in fluid reactions, clay adsorptions, cation
exchange, and solid dissolution/precipitation reactions can be specified (Table 8.2). There are 7 elements, 18
fluid species, 4 solid species, 4 clay adsorbed cations, and 3 surfactant cation exchangers considered in this
example. To represent the interactions among these chemical species, the reaction equilibrium relations are
required (Table 8.3). Tables 8.4-8.19 give the example input data for different sections of the input file. A
sample input file for EQBATCH is given in Table 8.20 and the output file for this example is given in Table
8.21. The EQBATCH program also writes the output data in a format similar to the geochemistry input data
of UTCHEM (Section 3.5 of the UTCHEM user's guide, lines 3.5.4 through 3.5.41) so it can be directly
pasted into the UTCHEM input file (Table 8.22).
8.2 User's Guide
A detailed user's guide for the EQBATCH program is presented as follows:
1. TITLE
A title line is required.
2. IREACT, ICHARGE, IMG
IREACT - Flag indicating the components to be considered
Possible values:
2 - Without acidic crude
3 - With acidic crude (insitu surfactant generation)
4- Gel option without acidic crude
ICHRGE - Flag indicating whether an oxygen mass balance or a charge balance will be used.
Possible Values:
0 - Oxygen balance used
83
-------
Section 8 - EQBATCH Program Description
1 - Charge balance in solution used
Note: If solid SiO2 is considered, the oxygen balance must be used
IMG - Flag indicating whether magnesium ions participate in cation exchange reactions or not.
Possible Values:
0 - Magnesium ions are considered.
1 - Magnesium ions are not considered.
3. NELET, NFLD, NSLD, NSORB, NACAT
NELET - Total number of elements less non reacting element.
NFLD - Total number of fluid species.
NSLD - Total number of solid species.
NSORB - Total number of sorbed species.
NACAT - Total number of surfactant associated cations.
4. NIAQ, NEX, NSLEL, NSURF1 (This line is read only if IMODE > 2)
NIAQ - Total number of independent fluid species.
NEX - Total number of insoluble exchangers.
NSLEL - Total number of elements comprising the solid species.
NSURF1 - Position number corresponding to the in situ generated surfactant anion in the fluid species
array FLDSPS.
Note: NSURF1 is automatically set to 0 by the program if IMODE = 2 or 4.
5. NH, NNA, NCA, NMG, NCARB
NH - Position number corresponding to the hydrogen element in the element array ELEMNT.
NNA - Position number corresponding to the sodium element in the element array ELEMNT.
NCA - Position number corresponding to the calcium element in the element array ELEMNT.
NMG - Position number corresponding to the magnesium element in the element array ELEMNT.
NCARB - Position number corresponding to the carbonate pseudo-element in the element array
ELEMNT.
Note: If any of these elements is not considered, the position no. must be set equal to 0.
6. NALU, NSILI, NOXY
NALU - Position number corresponding to the aluminum element in the element array ELEMNT.
NSDLI - Position number corresponding to the silicon element in the element array ELEMNT.
NOXY - Position number corresponding to the oxygen element in the element array ELEMNT.
7. NACD (This line is read only if IREACT = 3)
NACD - Position number corresponding to the petroleum acid pseudo-element in the element array
ELEMNT.
8a. NCR, NHFD, NCRFD (This line is read only if IREACT = 4)
NCR - Position number corresponding to the chromium in the element array ELEMNT.
NHFD - Position number corresponding to the hydrogen ion element in the fluid species array
FLDSPS.
NCRFD - Position number corresponding to CR(III) ion in the fluid species array FLDSPS.
8b. ELEMNTd), ELCRG(I), for 1 = 1, NELET
ELEMNT(I) - Name of the Ith element.
ELCRG(I) - Charge for the Ith element.
Note: The name of each element may not exceed 32 characters and each name must be on a
separate line of the input file.
84
-------
Section 8 - EQBATCH Program Description
9. FLDSPS(I), for 1 = 1, NFLD
FLDSPS(I) - Name of the Ith fluid species.
Note: The name of each fluid species may not exceed 32 characters and each name must be on a
separate line of the input file. If IREA.CT=3, the last fluid species must be HAW (petroleum acid in
water).
10. SLDSPS(I), for I = 1, NSLD (This line is read only if NSLD > 0)
SLDSPS(I) - Name of the Ith solid species.
Note: The name of each solid may not exceed 32 characters and each name must be on a separate
line of the input file.
11. SORBSP(I), for 1 = 1, NSORB (This line is read only if NSORB > 0)
SORBSP(I) - Name of the Ith adsorbed cation.
Note: The name of each adsorbed cation may not exceed 32 characters and each name must be
on a separate line of the input file.
12. ACATSP(I), for I = 1, NACAT (This line is read only if NACAT > 0)
ACATSP(I) - Name of the Ith surfactant adsorbed cation.
Note: The name of each surfactant adsorbed cation may not exceed 32 characters and each name
must be on a separate line of the input file.
13. NSORBX(I), for 1 = 1, NEX (This line is read only if NSORB > 0)
NSORBX(I) - Number of cations for Ith exchanger.
14. AR(IJ), for J = 1, NFLD, for 1 = 1, NELET « or »
AR(I,J), for J = 1, NFLD, for 1 = 1, NELET-1
AR(I,J) - Stoichiometric coefficient of Ith element in Ith fluid species.
Note: If ICHRGE = 0, then NFLD x NELET values are required by the program. If ICHRGE = 1,
then NFLD x (NELET-1) values are required by the program.
15. BR(I,J), for J = 1, NSLD, for 1 = 1, NELET « or »
BR(LJ), for J = 1, NSLD, for 1 = 1, NELET-1 (This line is read only if NSLD > 0)
BR(I,J) - Stoichiometric coefficient of Ith element in Ith solid species.
Note: If ICHRGE = 0, then NSLD x NELET values are required by the program. If ICHRGE = 1,
then NSLD x (NELET-1) values are required by the program.
16. DR(I,J), for J = 1, NSORB, for 1 = 1, NELET « or »
DR(I,J), for J = 1, NSORB, for 1 = 1, NELET-1 (This line is read only if NSORB > 1)
DR(LJ) - Stoichiometric coefficient of Ith element in Ith sorbed species.
Note: If ICHRGE = 0, then NSORB x NELET values are required by the program. If
ICHRGE = 1, then NSORB x (NELET-1) values are required by the program.
17. ER(I,J), for J = 1, NACAT, for 1 = 1, NELET « or »
ER(I,J), for J = 1, NACAT, for 1 = 1, NELET-1 (This line is read only if NACAT > 1)
ER(I,J) - Stoichiometric coefficient of Ith element in Jth surfactant associated cation.
Note: If ICHRGE = 0, then NACAT x NELET values are required by the program. If
ICHRGE = 1, then NACAT x (NELET-1) values are required by the program.
18. BB(I,J), for J = 1, NIAQ+NSORB+NACAT, for 1 = 1, NFLD+NSORB+NACAT
85
-------
Section 8 - EQBATCH Program Description
BB(I,J) - Exponent of the Ith independent fluid species concentration when the Ith fluid species is
expressed hi terms of independent species concentrations.
19. EXSLD(I,J), for J = 1, NIAQ, for 1 = 1, NSLD (This line is read only if NSLD > 0)
EXSLD(I,J) - Exponent of the Jth independent fluid species concentration in the solubility product
definition of the Ith solid.
20. CHARGE(I), for 1 = 1, NFLD
CHARGE® - Charge of the Ith fluid species.
21. EQK(I), for I = 1, NFLD
EQK(I) - Equilibrium constant for Ith fluid species when expressed in independent species
concentrations only.
22. SCHARG(I,J), for J = 1, NSORBX(I), for 1 = 1, NEX (This line is read only if NSORB > 0)
SCHARG(I,J) - Charge of the Jth sorbed species on the Ith exchanger.
23. EXK(IJ), for J = 1, NSORBX(I)-!, for 1 = 1, NEX (This line is read only if NEX > 0)
EXK(I, J) - Exchange equilibrium constant for Ith exchange equilibrium of the Ith insoluble
exchanger.
24. EXEX(I,J,K), for K = 1, NIAQ+NSORB+NACAT, for J = 1, NSORBX(I)-1, for 1 = 1, NEX
(This line is read only if and NEX > 0)
EXEX(I, J,K) - Exponent of Kth independent species in Jth equilibrium relation of the Ith exchanger
25. REDUC(IJ), for J = 1, NSORBX(I)-!, for 1 = 1, NEX (This line is read only if NEX > 0)
REDUC(I,J) - Valence difference of the two cations involved in the exchange reaction J on exchanger
I.
Note: This value is positive if the higher valence cation bulk concentration has a positive
exponent in EXEX(I, J) definition and is negative otherwise.
26. EXCAI(I), for 1 = 1, NEX (This line is read only if NEX >0)
EXCAI(I) - Exchange capacity of Ith insoluble exchanger.
Units: meq/ml pore volume
27. SPK(I), for 1 = 1, NSLD (This line is read only if NSLD > 0)
SPK(I) - Solubility product of Ith solid defined in terms of independent fluid species concentrations
only.
28. CHACAT(I), for 1 = 1, NACAT (This line is read only if NACAT > 0)
CHACAT(I) - Charge of Ith surfactant associated cation.
29. ACATK(I), for I = 1, NACAT-1 (This line is read only if NACAT > 0)
ACATK(I) - Equilibrium constant for Ith exchange equilibrium for cation exchanges on surfactant.
30. EXACAT(I,J) for J = 1, NIAQ+NSORB+NACAT, for I = 1, NACAT-1 (This line is read only
if NAG AT >0)
EXACAT(IJ) - Exponent of Jth independent species in Ith equilibrium for cation exchange on
surfactant.
86
-------
Section 8 - EQBATCH Program Description
31. C5I, CSURF
C5I - Initial concentration of chloride ion.
Units: meq/ml
CSURF- Initial concentration of surfactant.
Units: vol. fraction
32. CELAQI(J), for J = 1, NELET-1
CELAQI(J) - Initial concentrations of NELET-1 elements.
Units: equivalents/liter
33. CSLDI(I), for 1 = 1, NSLD (This line is read only if NSLD > 0)
CSLDI(I) - Initial concentration of Ith solid.
Units: moles/liter pore volume
34. CSORBI(I), for I = 1, NSORB (This line is readonly if NSORB >0)
CSORBI(I) - Initial concentration of Ith adsorbed cation.
Units: moles/liter pore volume
35. CAQI(J), for J = 1, NIND
CAQI(J) - Initial guesses for Ith independent species concentration, adsorbed species, and surfactant
associated species.
Units: moles/liter water
36. S
S - Initial water saturation in core flooding or reservoir condition.
Units: fraction
37. EQWPS (This line is read only if IREACT= 3)
EQWPS - Equivalent weight of petroleum acid.
87
-------
Section 8 - EQBATCH Program Description
Table 8.1. Water Analysis for Makeup and Formation Water
Ions
Na+> mg/1
Mg2+> mg/1
Ca2+. mg/1
C1-. mg/1
HCO3-, mg/1
CO23" , mg/1
SO2" , mg/1
pH
Formation water
2,398.90
36.46
54.2
2091
2623
240
—
8.1
Makeup water
52.9
11.54
67.13
39.00
152.55
6.00
134.56
7.95
Table 8.2. Example List of Elements and Reactive Species
Elements or pseudo-element:
Independent aqueous or oleic species:
Dependent aqueous or oleic species:
Solid species:
Adsorbed cations:
Adsorbed cations on micelles:
Hydrogen (reactive), Sodium, Calcium, Magnesium,
Carbonate, A (from acid HA), Chlorine,
H+, Na+,Ca2+, Mg2+CO23~ , HA0, H2O
Ca(OH)+, Mg(OH)+, Ca(HCO3)+, HAW, Mg(HCO3)+, OH-,
HCOg , A-, H2CO3, CaCOg , MgCOg
CaCO3 (Calcite), Ca(OH)2 (Calcium hydroxide), MgCO3
(Magnesite), Mg(OH)2 (Magnesium hydroxide)
H" + , Na + , Ca 2+, Mg 2+
Na + , C\ 2+, Mg 2+
88
-------
Section 8 - EQBATCH Program Description
Table 8.3. List of Reactions for the Example Run
Partitioning of HA
HA0 ^ HAW
Aqueous Reactions
H2O ^ H+ + OH"
HAW + OH" ^ A" + H2o
H+ + CO23' ^ HCO3
Ca2+ + H2O £> Ca(OH)+ + H+
Keq
Mg2+ + H2O ^> Mg(OH)+ + H+
Ke1
c*n j. TUT _L. r*c\ P /~io/'u/~io \
v_-a + ti + \^u 3 — > ^a^JtiL-u3-)
eq
Mg2+ + H+ + CO 3~ ^J Mg(HCO3)+
T^eQ
, O K Q
our _L c*c~\ ~~ ? tr (~*t~\
Zrl + l^-LJ o —» Jtl2^^J'2
Ca + + CO a" 7! CaCO?
j ^-'" o
2+ 2- KlO o
Mg + CO 3 ^ MgCO3
Partition Coefficient
[ w ] water
"°" [HAo]oil
Equilibrium Constant
K^ = [ H+] [ OH"]
eq [A'] [H+]
[HAw]
^eq [HCO^J
[H+] CO|"
eq [Ca(OH)+l [H+]
F" — _m..
ii-4 -
[Ca2+3
eq [Mg(OH)+] [H+]
[Mg2+l
^eq [ca(HC03)+]
[Ca2+] CO2' [H+]
e [Mg(HC03)+
-,r I U _l
1 ~ r 2+i 2
LMg ] CO 3 [H+]
eq [H2C°3]
8 ~ 0,0
CO| [H+]2
,eq [CaC03]
^ [Ca2+3 CO|
T,eq LMgC°?J
Kiu - 9 • 0 •
I Mg ] CO 3
89
-------
Section 8 - EQBATCH Program Description
Table 8.3. List of Reactions for the Example Run (cont.)
Dissolution Reactions
KSP
CaC03 p Ca2+ + COg'
sp
MgCO3 § Mg2+ + CO 3-
K?
Ca(OH)2 J| Ca2+ + 2OH"
KSP
Mg(OH)2 ^ Mg2+ + 20H'
Exchange Reactions (On Matrix)
ex
2Na"I" + Ca2+ ^ 2Na+ + Ca2+
K6X
2Na + + Mg2+ •£ 2Na+ + Mg2+
Kex
H + + Na+ + OH"^f Na+ + H2O
Exchange Reactions (On Micelle)
•^exm
^ A- Oa. "-1 + = 9-t-
2Na + + Ca2+ ^ 2Na + Ca
jrexm
2Na + + Mg2+ ^ 2Na+ + Mg 2+
Solubility Product
K^^ECa'lfcO2-]
KS2P = [Mg2+] [CO2']
KS3P =[Ca2+][H+] '2
KS4P =[Mg2+][H+]-2
Exchange Equilibrium Constant
r^2+
ex LCa J
Kl -
[Ca2+]
rex LMg2+.
K2 -
[Mg2+]
T,ex [Na+] _
K3 -
LNa+J[
[Na+]2
2
_Na+J
[Na+]2
2
_Na+J
H"+J
H+]
Exchange Equilibrium Constant
r<^2+
exm L*"a
_[Na+]2
X1 L^a+J2[Ca2+] '
where Ke™ = tf™ { [A-] +[S-] }
Kexm L^g2
^][Na+]2
L^a+J2[Mg2+3
where Kex,m = tf ™ { [A-] +[S-] }
90
-------
Section 8 - EQBATCH Program Description
Table 8.4. Stoichiometric Coefficient of Ith Element in
Jth Fluid Species (for the AR Array)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
H+
Na+
Ca2+
Ms2+
CCh2'
HA0
H2O
cacom+
Me(0m+
Ca(HCO^+
M2fHCCM+
A'
OR-
HCO*-
H2C03
CaCO3
MgCC>3
HAW
Ca
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
Mg
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
co^
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
Na
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
H
1
0
0
0
0
1
2
1
1
1
1
0
1
1
2
0
0
1
A
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
Note: The transposition of this table is the form required for
EQBATCH Program
Table 8.5. Stoichiometric Coefficient of Ith
Element in Jth Solid Species (for the BR
Array)
Table 8.6. Stoichiometric Coefficient of Ith
Element in Jth Sorbed Species (for the DR
Array)
Ca
Mg
CO3
Na
H
A
CaCOs
1
0
1
0
0
0
MgCOs
0
1
1
0
0
0
Ca(OH)2
1
0
0
0
2
0
Mg(OH)2
0
1
0
0
2
0
Ca
Mg
C03
Na
H
A
H+
0
0
0
0
1
0
Na+
0
0
0
1
0
0
Ca2+
1
0
0
0
0
0
Mg2+
0
1
0
0
0
0
91
-------
Section 8 - EQBATCH Program Description
Table. 8.7. Stoichiometric Coefficient of Ith
Element in Jth Surfactant Associated Cation
(for the ER Array)
Ca
Mg
C03
Na
H
; A
Na+
0
0
0
1
0
0
Ca2+
1
0
0
0
0
0
Mg2+
0
1
0
0
0
0
Table 8.8. Exponent of Jth Independent Fluid Species (for BB Array)
BH+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
H+
Na+
Ca2*
Mg2+
CO,2'
HA0
H?O
Ca(OH)+
Jtfg(OH)+
Ca(HCO,)+
Mg(HCO,)+
A"
OH-
HCXV
JHjCO^
CaCO-?
MgCO^
HAW
H+s
Na+s
Ca2+s
M£*S
Na+
Ca2-1-
Mg2+sa
1
-1
-1
1
1
-1
-1
1
2
Na+
1
Ca2+
1
1
1
1
MR2+
1
1
I
1
CO?2'
1
1
1
1
1
1
1
HA,,
1
1
1
HoO
1
H+
1
Nfote: The blank cells in the above table need to be filled with zero for the
Na+
1
Ca2+
1
Me2+
1
Sorbed Species
input data for EQBA
Na+ 1 Ca2+
1
1
M22 +
1
Surfactant Assoc. Cation
TCH program.
92
-------
Section 8 - EQBATCH Program Description
Table 8.9. Exponent of Jth Independent Species in the Ith Solid (for EXSLD Array)
CaCO3
MgC03
Ca(OH)2
Mg(OH)9
H+
0
0
-2
-2
Na+
0
0
0
0
Ca2+
1
0
1
0
Ms2+
0
1
0
1
CCh2'
1
1
0
0
HA0
0
0
0
0
H2O
0
0
0
0
Table 8.10. Charge of Ith Fluid Species
(for CHARGE Array)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Fluid species
H+
; Na+
Ca2+
Mg2+
co32-
HA0
H20
Ca(OH)+
Mg(OH)+
Ca(HCO3)+
Mg(HC03)+
A-
OH-
HCO3-
H2C03
CaCO3
MgCO3
HAW
Charge
1
1
2
2
-2
0
0
1
1
1
1
-1
-1
-1
0
0
0
0
Table 8.12. Charge of Jth Sorbed Species
(for SCHARG Array)
Adsorbed species
H+(sorbed)
Na+(sorbed)
Ca2+(sorbed)
Mg2+(sorbed)
Charge
1
1
2
2
Table 8.11. Equilibrium Constants for Ith
Fluid Species (for EQK Array)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Fluid species
H+
Na+ .
Ca2+
Mg2+
CO32'
HA0
H20
Ca(OH)+
Mg(OH)+
Ca(HCO3)+
Mg(HCO3)+
A'
OH-
HCO3-
H2C03
CaCO3
MgC03
HAW
Equilibrium Constants
1
1
1
1
1
1
1
0.12050E-12
0.38871E-11
0.14124E+12
0.58345E+12
0.85480E-14
0.10093E-13
0.21380E+11
0.3981 1E+17
0.15849E+04
0.47863E+04
0.85480E-04
Table 8.13. Exchange Equilibrium
Constants for Jth Exchange (for EXK Array)
Adsorbed
Kexl
Kex2
Kex3
Equilibrium Constants
0.2623E+03
0.1509E+03
0.1460E+08
93
-------
Section 8 - EQBATCH Program Description
Table8.14. Exponent of Ktn Independent Species in Jtn Equilibrium Relation (for EXEX Array)
H+
0
0
-1
Na+
2
2
1
Ca2+
-1
0
0
Mg2+
0
-1
0
co'^~
0
0
0
HA0
0
0
0
H2O
0
0
0
H+
0
0
1
Na+
-2
-2
-1
Ca2+
1
0
0
Mg2+"
0
1
0
Na+
0
0
0
Ca2+
0
0
0
Mg2+
0
0
0
Sorbed Species
Surfactant Assoc. Cation
Table 8.15. Valence Difference Between
Cation Involved In Exchange (for REDU
Array)
|Na+
Na+
H+
Ca2+
-1
Mg2+
-1
Na+
0
Table 8.16. Solubility Product of Ith Solid (for SPK Array)
CaCO3 | MgCO3 | Ca(OH)2
Mg(OH)
I 0.4953E-09 I 0.00007 I 4.7315E+22 | 5.6104E+16 I
Table 8.17. Charge of Ith Surfactant
Associated Cation (for CHACAT Array)
Na+ Ca2+
Table 8.18. Equilibrium Constant for Ith
Exchange (for ACATK Array)
I Na+
ll 2.5
Ca2+
2.94 |
Table 8.19. Exponent of Jth Independent Species in Ith Cation Exchange on Surfactant (for
EXACAT Array)
H*
0
0
Na+
2
2
Ca2+
-1
0
Mg2+
0
-1
CO2"
0
0
HA0
0
0
H2O
0
0
H+
0
0
Na+
0
0
Ca2+
0
0
Mg2+
0
0
Na+
-2
-2
Ca2+
1
0
Mg2+
0
1
Sorbed Species
Surfactant Assoc. Cation
94
-------
Section 8 - EQBATCH Program Description
Table 8.20. Sample Input Data for EQBATCH Program
Rl
3
7
7
5
0
6
1
18
1
4
0
4
4
1
0
1
4
12
2
CALCIUM
MAGNESIUM
CARBON (AS CARBOBATES)
SODIUM
HYDROGEN (REACTIVE)
ACID (PETROLEUM)
CHLORINE
HYDROGEN ION
SODIUM ION
CALCIUM ION
MAGENSIUM ION
CARBONATE ION
PETROLEUM ACID IN OIL
WATER
CALCIUM MONOHYDROXIDE ION
MAGNESIUM MONOHYROXIDE ION
CA (HC03) +
MG (HCO3) +
PETRLEUM ACID ANION
HYDROXIDE ION
BICARBONATE ION
DISSOLVED CARBON MONOHYDROXIDE
AQUEOUS CALCIUM CARBONATE
AQUEOUS MAGNESIUM CARBONATE
PETROLEUM ACID IN OIL
CALCIUM CARBONATE(SOLID)
MAGNESIUM CARBONATE (SOLID)
CALCIUM HYDROXIDE (SOLID)
MAGNESIUM HYDROXIDE(SOLID)
SORBED HYDROGEN ION
SOKBED SODIUM ION
SORBED CALCIUM ION
SORBED MAGNESIUM ION
SURF. ASSOCIATED SODIUM ION
SURF. ASSOCIATED CALCIUM ION
SURF. ASSOCIATED MAGNESIUM ION
2
2
-2
1
1
_i
-1
(* TITLE *)
(* IREACT ICHARGE IMG *)
(* NNELET NFLD NSLD NSORB NACAT *)
(* NIAQ HEX NSLWL NSURF1 *)
(* NH NNA NCA NMG NCARB *)
(* NALU NSILI NOXYG *)
(* NACD *)
4
0.
0.
0.
0.
1.
0.
1.0
0.0
1.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.0
0.0
0.0
0.0
0.0
1.0
0.0
0.0
1.
0.
0. 1. 0.
0. 0. 1.
0. 0. 0.
1. 0. 0.
0. 0. 0.
0. 0. 0.
0.0 1.0
1.0 0.0
1.0 0.0
0.0 0.0
0.0 2.0
0.0 0.0
0.0 1.0
0.0 0.0
0.0 0.0
1.0 0.0
0.0 0.0
0.0 0.0
1.0 0.0
0.0 1.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0. 0. 0.
1. 0. 0.
0.
0.
1.
0.
0.
0.
0.0
1.0
0.0
0.0
2.0
0.0
0.0
1.0
0.0
0.0
0.0
0.0
0.
0.
0.
0.
0.
0.
1.
1.
0.
0.
0.
0.
0.
0.
2.
0.
0.
0.
1.
0.
0.
0.
1.
0.
0.
0.
0.
1.
0.
0.
1.
0.
0.
0.
1.
0.
1.
0.
1.
0.
0.
0.
0.
1.
1.
0.
1.
0.
0.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0. 0. 1. 0. 0.
0. 0. 0. 1. 0.
1. 1. 1. 1. 0.
0. 0. 0. 0. 0.
1. 2. 0. 0. 1.
0. 0. 0. 0. 1.
0.
0.
(* FLDSPS *)
(* SLDSPS *)
(* SORBSPS *)
(* ACATSPC *)
(* NSORBX *)
(* AR *)
(* BR *)
(* DR *)
(* ER *)
95
-------
Section 8 - EQBATCH Program Description
Table
0.
0.
0.
0.
0.
-1
-1
1.
1.
-1
-1
1
2
0
0.
0
0.
0.
0.
0.
0.
0.
0.
0.
0.
-2
-2
1.
1.
0.
0.
1.
0.
0.
0.
••tl
-1
0.
0.
1.
2.
0.
0.
0.
0.
2.
0
8.20. Sample Input Data
0. 1.
0. 0.
0. 0.
0. 0.
0. 0.
. 0. 1.
. 0. 0.
0. 1.
0. 0.
. 0. 0.
. 0. 0.
0. 0.
0. 0.
0. 1.
0. 0.
0. 0.
0. 0.
0. 0.
0. 0.
0. 0.
0. 0.
0. 0.
0. 0.
0. 1.
0. 0.
. 0. 1.
. 0. 0.
1. 2.
1. 1.
58345e+12
15849e+04
1 . 2 .
793+01 0.
2. -1.
2. 0.
. 1. 0.
. -1. 0.
3403
474851e-09
2. 2.
5 2.94
2. -1.
2. 0.
059 0.0
0.
1.
0.
0.
0.
0.
1.
0.
1.
0.
0
n
n
n
i.
n
0.
0.
0.
0.
0.
0.
0.
0.
i.
0.
i.
2.
1.
0
0
2.
0. 0.
0. 0.
1. 0.
0. 1.
0. 0.
0. 0.
0. 0.
1. 0.
1. 0.
0. 1.
0. 0.
1. 0.
1. 0.
1. 0.
1. 0.
0. 1.
0. 0.
0. 0.
0. 0.
0. 0.
0. 0.
0. 0.
0. 0.
1. 0.
1. 0.
0. 0.
0. 0.
-2. 0.
1. 1.
.959e-12
0
0
0
0
1
0
0
0
0
0
n
n
n
n
0
n
0
0
0
0
0
0
0
0
0
0
0
0
i.
0.
.47863e+04
. 0
. 0
. 0
. 0
. 0
. 0
. 0
. 0
. 0
. 0
. 0
. 0
. 0
. 0
. 0
. 0
. 1
. 0
. 0
. 0
. 0
. 0
. 0
.
.
.
.
. 1.
0.
for EQBATCH Program (cont.)
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 0.
. 1.
. 0.
. 0.
. 0.
. 0.
. 0.
1. 1.
0
0
0
0
0
0
0
0
0
0
n
n
n
n
0
n
0
0
i
0
0
0
0
i
1205e-12
10093e-13
0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 0. 0.
. 1. 0.
. 0. 1.
. 0. 0.
. 0. 0.
. -1. -1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
n
0
n
0
0.
n
0.
0.
0.
0.
0.
i.
0.
-i.
0.38871e-ll
2138e+ll 0
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
n
n
n
n
0.
n
0.
0.
0.
0.
0.
0.
i.
0. 0. 0. 0.
0.14125e+12
(* BB *)
(* EXSLD *)
(* CHAEGE *)
.3981e+17
0.959-04
52+01 0.27+07
0
-1
0
0
-1
. 0. 0.
. 0. 0.
. 0. 0.
0.00007 0
. 0. 0.
. 0. 0.
00135 0.0015 0.047
00 0.0
.05 0.25
0.
0.
0000 0.0
01 0.002
0.
0.
0.
0. -2
0. -2
1. -1
.47315e+23 0
0.
0.
0.
1043
0. 0.
0. 0.
111.
.
.
.
1. 0. 0
0. 1. 0
0. 0. 0
.
.
.
0. 0.
0. 0.
0. 0.
.56045e+17
0. 0. -2
0. 0. -2
1. 0.0
0. 1.
043 0.019
(* KEQ *)
(* SCHARGE *)
(* KEX *)
(* EXEX *)
(* REDUC *)
(* EXCAI *)
(* KSP *)
(* CHACAT *)
(* KACAT *)
(* EXACAT *)
(*C50, Csurf*)
(*CELFLT 1,NELEMENT-1*)
( *CSLD ( I ) , 1=1 , NSLD* )
(* CSORBI *)
0.1200077231590e-05 0.01 O.le-04
0.4616423363603e-05 0.3092684582095e-08 0.5399766653843e-03
55.49999314650 l.Oe-06 l.Oe-02 l.Oe-03 l.Oe-04
l.Oe-06 l.Oe-08 l.Oe-08
0.602
500
(*CIND*)
(*S1*)
(*EQW*)
96
-------
Section 8 - EQBATCH Program Description
Table 8.21. Sample Output of EQBATCH Program
Rl
REACTIVE SYSTEM DESCRIPTION
TOTAL NO. OF ELEMENTS LESS ONE =
TOTAL NO. OF FLUID SPECIES
TOTAL NO. OF SOLID SPECIES
TOTAL NO. OF ADSORBED SPECIES =
NO. OF CATIONS ASSOC. WITH SURF.=
TOTAL NO. OF IND. FLUID SPECIES =
TOTAL NO. OF EXCHANGER
7
18'
4
4
3
7
1
ELEMENT NO.
1
2
3
4
5
6
7
FLUID SPECIES NO.
(INDEPENDENT)
1
2
3
4
5
6
7
(DEPENDENT)
8
9
10
11
12
13
14
15
16
17
18
SOLID SPECIES NO.
1
2
3
4
SORBED SPECIES NO.
1
2
3
4
ASSOC. CATION NO.
1
2
3
NAME
CALCIUM
MAGNESIUM
CARBON (AS CARBOBATES)
SODIUM
HYDROGEN (REACTIVE)
ACID (PETROLEUM)
CHLORINE
NAME
HYDROGEN ION
SODIUM ION
CALCIUM ION
MAGENSIUM ION
CARBONATE ION
PETROLEUM ACID'IN OIL
WATER
CALCIUM MONOHYDROXIDE ION
MAGNESIUM MONOHYROXIDE ION.
CA (HC03) +
MG (HCO3) +
PETRLEUM ACID ANION
HYDROXIDE ION
BICARBONATE ION
DISSOLVED CARBON MONOHYDROXIDE
AQUEOUS CALCIUM CARBONATE
AQUEOUS MAGNESIUM CARBONATE
PETROLEUM ACID IN OIL
NAME
CALCIUM CARBONATE(SOLID)
MAGNESIUM CARBONATE (SOLID)
CALCIUM HYDROXIDE (SOLID)
MAGNESIUM HYDROXIDE(SOLID)
NAME
SORBED HYDROGEN ION
SORBED SODIUM ION
SORBED CALCIUM ION
SORBED MAGNESIUM ION
NAME
SURF. ASSOCIATED SODIUM ION
SURF. ASSOCIATED CALCIUM ION
SURF. ASSOCIATED MAGNESIUM ION
CHARGE
2
2
_o
1
1
-1
-1
97
-------
Section 8 - EQBATCH Program Description
Table 8.21. Sample Output of EQBATCH Program (cont.)
NO. OF MOLES OF ELEMENT I IN ONE MOLE OF
FLUID SPECIES J
24 25
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
1= 1
1= 2
1= 3
I- 4
1= 5
1= 6
0.
0.
0.
0.
1.
0.
0.
0.
0.
1.
0.
0.
1.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
0.
1.
1.
0.
0.
0.
0.
2.
0.
1.
0.
0.
0.
1.
0.
0.
1.
0.
0.
1.
0.
1.
0.
1.
0.
1.
0.
0.
1.
1.
0.
1.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
1.
0.
0.
0.
1.
0.
1.
0.
0.
0.
1.
0.
2.
0.
1.
0.
1.
0.
0.
0.
0.
1.
1.
0.
0.
0.
0
0
0
0
1
1
NO. OF MOLES OF ELEMENT I IN ONE MOLE OF
SOLID SPECIES K
12345678
1= 1
1= 2
1= 3
1= 4
1= 5
1= 6
1.
0.
1.
0.
0.
0.
0.
1.
1.
0.
0.
0.
1.
0.
0.
0.
2.
0.
0
1
0
0
2
0
NO. OF MOLES OF ELEMENT I IN ONE MOLE OF
ADSORBED SPECIES K
r= i
1= 2
1= 3
1= 4
1= 5
1= 6
0.
0.
0.
0.
1.
0.
0.
0.
0.
1.
0.
0.
1.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
10
NO. OF MOLES OF ELEMENT I IN ONE MOLE OF
SURF. ASS. SPECIES K
K=
1= 1
1= 2
r= 3
1= 4
1= 5
1= 6
0.
0.
0.
1.
0.
0.
1.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
EXPONENT OF THE IND. SPECIES CONC. J
FOR FLUID SPECIES I
1= 1
1= 2
1= 3
1= 4
1= 5
1= 6
1= 7
1= 8
Is 9
1=10
1=11
1=12
1=13
1=14
1,
0.
0.
0.
0.
0.
0.
-1.
-1-.
1.
1.
-1.
-1.
1.
0.
1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
1.
0.
1.
0.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
1.
0.
1.
0.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
1.
1.
0.
0.
1.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
0.
1.
0.
0.
0
0
0
0
0
0
1
0
0
0
0
0
0
0
10
98
-------
Section 8 - EQBATCH Program Description
Table 8.21. Sample Output of EQBATCH Program (cont.)
1=15 2.
1=16 0.
1=17 o.
1=18 0.
0.
0.
o.
0.
0.
1.
o.
0.
0.
0.
i.
0.
1.
1.
i.
0.
0.
0.
o:
1.
0.
0.
o.
0.
FLUID SPECIES NO.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
CHARGE
1.
1,
2.
2,
-2.
0.0
0.0
0.0
1.0
1.0
1.0
-1.0
-1.0
-1.0
0.0
0.0
0.0
0.0
ADSORBED SPECIES NO. CHARGE
2.0
ASSOC. CATION(SURF) CHARGE
1.0
2.0
2.0
EXPONENT OF IND. FLUID SPECIES J IN THE
SOLUBILITY PRODUCT DEFINITION OF SOLID I
J=
1= 1 0.
1= 2 0.
1= 3 -2.
1= 4 -2.
0.
0.
0.
0.
1.
0.
1.
0.
0.
1.
0.
1.
5 6
1. 0.
1. 0.
0. 0.
0. 0.
0.
0.
0.
0.
10 11 12 13 14 15
FLUID SPECIES NO.
1 '"
2
3'.
4
5
6
7
8
9
10
11
12
13
14
15
EQUILM. CQNSATNT
0.10000E+01
0.10000E+01
0.10000E+01
0.10000E+01
0.10000E+01
0.10000E+01
0.10000E+01
0.12050E-12
0.38871E-11
0.14125E+12
0.58345E+12
0.95900E-12
0.10093E-13
0.21380E+11
0.39810E+17
99
-------
Section 8 - EQBATCH Program Description
Table 8.21. Sample Output of EQBATCH Program (cont.)
16
17
18
0.15849E+04
0.47863E+04
0.95900E-04
EXCHANGE EQUILIBRIUM CONSTANT FOR EQUILM. J
OF THE EXCHANGER I
0.7930E+01 0.5200E+01
3 4
0.2700E+07
EXCHANGER NO.
1
EXCHANGE CAPACITY
0.34030E+00
EXPONENT OF THE IND. SPECIES CONC. K IN
THE EXCHANGE EQUILIBRIUM J ON EXCHANGER I
16 17
18
J=2
J=3
0
0
-1
o o o
SOLID
2
2
1
o o o
-1.
0.
0.
0
0
0
NUMBER
1
2
3
4
0
-1
0
.0
.0
.0
0.0 0.0 0
0.0 0.0 0
0.0 0.0 0
.0
.0
.0
SOLUBILITY PRODUCT
0
0
0
0
.47485E-09
.70000E-04
-47315E+23
.56045E+17
0.0
0.0
1.0
-2.0
-2.0
-1.0
EXCHANGE EQLM. (I) ON SURF. BETAS(I)
0.25000E+01
0.29400E+01
EXPONENT OF THE IND. SPECIES CONC. K IN
THE EXCHANGE EQUILIBRIUM J ON SURFACTANT
10
11
12
1.0
0.0
0.0
0.0
1.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
13
0.0
0.0
0.0
14
15
K- 1 2
16 17 18
J=l
J-2
0.0
0.0
2.0
2.0
3
-1.0
0.0
4
0.0
-1.0
5
0.0
0.0
6
0.0
0.0
7
0.0
0.0
8
0.0
0.0
9
0.0
0.0
10 11
0.0
0.0
0.0
0.0
-2.0
-2.0
12
1.0
0.0
13
0.0
1.0
14
15
INITIAL AQ. ELEMENTAL CONCS.(MOLES/L)
234
9 10
.13500E-02 .15000E-02
.47000E-01 .10430E+00 .11104E+03 .19000E-01
INITIAL CHLORIDE CONC.(EQ/LITER)
INITIAL SURFACTANT CONC.(EQ/LITER) =
INITIAL SOLID CONCS.(MOLES/LITRE PV)
1234
5 10
.20000E+01 .OOOOOE+00 .OOOOOE+00 .OOOOOE+00
INITIAL ADSORED IONS(MOLES/LITRE PV)
1234
> 10
0.5900E-01
O.OOOOE+00
100
-------
Section 8 - EQBATCH Program Description
Table 8.21. Sample Output of EQBATCH Program (cont.)
.50000E-01 .25000E+00 .10000E-01 .20000E-02
INITIAL GUESSES OF INDEPENDENT CONCENTRATIONS
1.200077231590000E-006
4.616423363603000E-006
55.4999931465000
1.OOOOOOOOOOOOOOOE-003
1.OOOOOOOOOOOOOOOE-008
1.OOOOOOOOOOOOOOOE-002
3.092684582095000E-009
l.OOOOOOOOOOOOOOOE-006
1.OOOOOOOOOOOOOOOE-004
1.OOOOOOOOOOOOOOOE-008
1.OOOOOOOOOOOOOOOE-005
5.399766653843000E-004
1.OOOOOOOOOOOOOOOE-002
1.OOOOOOOOOOOOOOOE-006
END OF REACTION MODULE INPUT DATA
RESIDUALS AT THE END OF 18 ITERATIONS IDAMP = 1
O.OOOE+00 O.OOOE+00 -.555E-16 0.142E-13 O.OOOE+00 O.OOOE+00 O.OOOE+00 0.999E-15
0.666E-15 O.OOOE+00 O.OOOE+00 -.486E-16 -.245E-12 O.OOOE+00
FLUID SPECIES CONCENTRATIONS
0.7849769316806E-08 0.7529549105585E-01 0.2274287723632E-05 0.5387616767727E-04
0.2087910843759E-03 0.1899585758862E-01 0.5548234868752E+02 0.3491206679296E-10
0.2667875232078E-07 0.5265052518920E-06 0.5151920872179E-04 0.2320708633881E-05
0.1285770268228E-05 0.3504100430504E-01 0.5121744571970E-03 0.7525913499000E-06
0.5384043523296E-04 0.1821702742749E-05
SOLID SPECIES CONCENTRATIONS
0.2011131391413E+01 O.OOOOOOOOOOOOOE+00 O.OOOOOOOOOOOOOE+00 O.OOOOOOOOOOOOOE+00
SORBED SPECIES CONCENTRATIONS
0.7318622640939E-01 0.2600025853849E+00 0.2150482869699E-03 0.3340545815905E-02
SURF. ASSOCIATED CATION CONCS.
0.1900192355929E-01 0.6880963477427E-08 0.1916937102421E-06
ELEMENT NO. OLD TOTAL NEW TOTAL
1
2
3 •
4
5
6
ISOLN= 14
0.2011350000000E+01
0.3500000000000E-02
0.2047000000000E+01
0.3543000000000E+00
0.1110930000000E+03
0.1900000000000E-01
0.2011350000000E+01
0.3500000000000E-02
0.2047000000000E+01
0.3543000000000E+00
0.1110930000000E+03
0.1900000000000E-01
ERROR
O.OOOOOOOOOOOOOE+00
O.OOOOOOOOOOOOOE+00
O.OOOOOOOOOOOOOE+00
0.2220446049250E-15
-0.1110223024625E-15
O-.OOOOOOOOOOOOOE+OO
5.900000000000000E-002
111.019813773591
2.915115922082504E-002
COMPUTATION TIME= O.OOOOOE+00
INITIAL CONDITIONS FOR UTCHEM
011,021,050,060,0121,0.31,0141,0151
0.999997928798602 0.985633815850358
7.120600401936443E-006 9.429741461513917E-002
3.189083681891565E-004 7.173721717434252E-002
A- + HA(WATER) = 4.142411376630453E-006 HA(OIL) =
VOLUMES FRACTIONS OF WATER,OIL AND ACID
0.601998753136758 0.392282258708443 5.718988154799202E-003
EQUIV. OF ACID/LITRE TOTAL VOL 1.143797630959840E-002
EQK( 12) EQK( 18) 6.249160552927827E-013
6.249160552927826E-005
CSLDI(I),I=1,NSLD UNIT=MOLES/LITER PV
1.21069859002472 0.OOOOOOOOOOOOOOOE+000
0.OOOOOOOOOOOOOOOE+000
CSORBI(I),I=1,NSORB UNIT=MOLES/LITER PV
4.405801704523635E-002 0.156521232214020
2.011004415971278E-003
EXCHANGE CAPACITY(MEQ/ML PV)= 0.204860175692439
0.OOOOOOOOOOOOOOOE+000
1.294588006200680E-004
101
-------
Section 8 - EQBATCH Program Description
Table 8.22. Sample UTCHEM Input File Generated From EQBATCH Program
2
2
-2
1
-1
-1
FOLLOWING LINES OF DATA FORMATED FOR UTCHEM
7 18 4 4 3 1
7 1 4 12
54123
6
CALCIUM
MAGNESIUM
CARBON (AS CARBOBATES)
SODIUM
HYDROGEN (REACTIVE}
ACID (PETROLEUM)
CHLORINE
HYDROGEN ION
SODIUM ION
CALCIUM ION
MAGENSIUM ION
CARBONATE ION
PETROLEUM ACID IN OIL
WATER
CALCIUM MONOHYDROXIDE ION
MAGNESIUM MONOHYROXIDE ION
CA (HC03) +
MG (HC03) -t-
PETRLEUM ACID ANION
HYDROXIDE ION
BICARBONATE ION
DISSOLVED CARBON MONOHYDROXIDE
AQUEOUS CALCIUM CARBONATE
AQUEOUS MAGNESIUM CARBONATE
PETROLEUM ACID IN OIL
CALCIUM CARBONATE(SOLID)
MAGNESIUM CARBONATE (SOLID)
CALCIUM HYDROXIDE (SOLID)
MAGNESIUM HYDROXIDE(SOLID) (
SORBED HYDROGEN ION
SORBED SODIUM ION
SORBED CALCIUM ION
SORBED MAGNESIUM ION (•
SURF. ASSOCIATED SODIUM ION
SURF. ASSOCIATED CALCIUM ION
SURF. ASSOCIATED MAGNESIUM ION
4
0.
1.
0.
0.
0.
1.
0.
0.
1.
0.
0.
0.
1.
0.
1.
0.
0.
0.
0.
0.
0.
0.
1.
0.
0.
0.
0.
0.
0.
0.
1.
0.
1.
1.
0.
0.
0.
0.
0.
0.
1.
1.
0.
0.
0.
0.
0.
0.
1.
0.
0.
1.
0.
0.
1.
0.
0.
0.
0.
0.
0.
0.
0.
1.
0.
1.
1.
0.
0.
0.
2.
0.
1.
0.
0.
0.
0.
0.
0.
1.
0.
0.
1.
0.
0.
0.
0.
0.
1.
0.
0.
2.
0.
0.
1.
0.
0.
0.
0.
0.
0. 1. 0. 0. 0. 0. 0.
0. 0. 0. 0.
1. 1. 0.
1. 1.
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
1.
1.
1. 1. 0. 1. 1. 2.
1- 0. 0. 0. 0. 0. 1. 0. 0. 0.
102
-------
Section 8 - EQBATCH Program Description
Table 8.22. Sample UTCHEM Input File Generated From EQBATCH Program (cont.)
i. o. o.
0. 0. 0.
0. 0. 0.
1.0 0.0 0.0 0.0
0.0 0.0
0.0 1.0 0.0 0.0
0.0 0.0
0.0 0.0 1.0 0.0
0.0 0.0
0.0 0.0 0.0 1.0
0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0 .0.0 0.0
0.0 0.0
-1.0 0.0 1.0 0.0
0.0 0.0
-1.0 0.0 0.0 1.0
0.0 0.0
1.0 0.0 1.0 0.0
0.0 0.0
1.0 0.0 0.0 1.0
0.0 0.0
-1.0 0.0 0.0 0.0
0.0 0.0
-1.0 0.0 0.0 0.0
0.0 0.0
1.0 0.0 0.0 0.0
0.0 0.0
2.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0 1.0 0.0
0.0 0.0
0.0 0.0 0.0 1.0
0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0 0.0 0.0
1.0 0.0
0.0 0.0 0.0 0.0
0.0 1.0
0.0 0.0 1.0 0.0
0.0 0.0 0.0 1.0
-2.0 0.0 1.0 0.0
-2.0 0.0 0.0 1.0
1.0 1.0 2.0 2.0
-1.0 -1.0 0.0 0.0
1.0 1.0 2.0 2.0
0.1000000000000E+01
0.1000000000000E+01
0.1000000000000E+01
0.1412500000000E+12
0.1009300000000E-13
0.1584900000000E+04
0.7930000000000E+01
0.0 2.0 -1.0 0.0
0.0 0.0
0.0 2.0 0.0 -1.0
0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 ,0.0
1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0
0.0 0.0 1.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
1.0 0.0 0.0 0.0
1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0
0.0 0.0 0.0 0.0
1.0 0.0 0.0 0.0
1.0 0.0 0.0 0.0
1.0 0.0 0.0 0.0
1.0 0.0 0.0 0.0
0.0 1.0 0.0 0.0
0.0 0.0 0.0 1.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
1.0 0.0 0.0
1.0 0.0 0.0
0.0 0.0 0.0
0.0 0.0 0.0
-2.0 0.0 0.0 1.0
0.0 0.0
0.1000000000000E+01
0.1000000000000E+01
0.1205000000000E-12
0.5834500000000E+12
0.2138000000000E+11
0.4786300000000E+04
0.5200000000000E+01
0.0 0.0 0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
1.0 0.0
0.0 1.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
0.0 0.0
1.0 0.0
0.0 1.0
0.0 0.0
0.0 0.0
1.0 1.0 1.0 -1.0
0.1000000000000E+01
0.1000000000000E+01
0.3887100000000E-11
0.6249160552928E-12
0.3981000000000E+17
0.6249160552928E-04
0.2700000000000E+07
-2.0 1.0 0.0 0.0
0.0 0.0 0.0 0.0-2.0 0.0 1.0 0.0
103
-------
Section 8 - EQBATCH Program Description
Table 8.22. Sample UTCHEM Input File Generated From EQBATCH Program (cont.)
-i.o i.o
0.0 0.0
-1.0 -1.0 0.0
0.2048601756924E+00
0.4748510000000E-09
0.5604500000000E+17
1.0 2.0 2.0
0.2500000000000E+01
0.0 2.0 -1.0 0.0
1.0 0.0
0.0 2.0 0.0 -1.0
0.0 1.0
0.1900192355929E-01
0.5900000000000E-01
0.9429741461514E-01
0.7173721717434E-01
0.2915115922083E-01
0.7849769316806E-08
0.5387616767727E-04
0.5548234868752E+02
0.1210698590025E+01
O.OOOOOOOOOOOOOE+00
0.4405801704524E-01
0.2011004415971E-02
0.9999979287986E+00
0.1000000000000E-07
0.0 0.0 0.0 0.0 0.0 1.0 -1.0 0.0 0.0 0.0
0.7000000000000E-04 0.4731500000000E+23
0.2940000000000E+01
0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0
0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0
0.1916937102421E-06
0.3189083681892E-03
0.6880963477427E-08
0.7120600401936E-05
0.1110198137736E+03
0.4142411376630E-05
0.7529549105585E-01
0.2087910843759E-03
O.OOOOOOOOOOOOOE-t-00
0.1565212322140E+00
0.9856338158504E-I-00
0.5000000000000E+03
0.2274287723632E-05
0.1899585758862E-01
O.OOOOOOOOOOOOOE+00
0.1294588006201E-03
104
-------
Section 9
A 3-D NAPL Flow and Biodegradation Model
Biodegradation capabilities have been added to a three-dimensional, multi-phase, multi-component porous
media flow model. The model simulates the transport and biodegradation of lighter-than-water nonaqueous
phase liquids (LNAPLs) and denser-man-water nonaqueous phase liquids (DNAPLs). The biodegradation
model describes biological transformation of the organic contaminants originating from NAPL sources, and
can accommodate multiple substrates, electron acceptors, and biological species. The biodegradation model
includes inhibition, sequential use of electron acceptors, and cometabolism. Example simulations illustrate
the model capabilities.
9.1 Introduction
The University of Texas is completing improvements to a multi-phase flow simulator called UTCHEM.
Advanced biodegradation capabilities have recently been incorporated into UTCHEM that allow both the flow
of nonaqueous phase liquids (NAPLs) and the fate of organic NAPL constituents to be described within the
same model. This paper describes the biodegradation model components, discusses the biodegradation
model equations and features, and provides two example UTCHEM simulations that demonstrate some of
the capabilities of the combined NAPL flow and biodegradation model.
9.2 Model Description and Features
UTCHEM is a multi-phase, multi-component, three-dimensional, numerical model that simulates the fate and
transport of both dissolved and nonaqueous phase organic contaminants in porous media. The model
describes flow of the NAPL resulting from capillary, gravity and pressure, forces. Dispersion of organic
constituents in each phase is also modeled. The model can be used to simulate spills of either lighter-than-
water NAPLs (LNAPLs) or denser-than-water NAPLs (DNAPLs). The transfer of organic contaminants
from the NAPL to the aqueous phase is described through either equilibrium partitioning or a linear driving
force nonequilibrium mass transfer model. Adsorption of organic constituents is modeled through
equilibrium partitioning. An arbitrary number of injection and pumping wells can be specified so that
bioremediation schemes can be modeled and optimized. The full development of the UTCHEM flow model
is described in detail by Delshad et al. [1996] and Datta Gupta et al. [1986].
UTCHEM simulates the biodegradation of chemical compounds that can serve as substrates (carbon and/or
energy sources) for microorganisms. The model simulates the destruction of substrates, the consumption of
electron acceptors (e.g., oxygen, nitrate, etc.), and the growth of biomass. Substrates can be biodegraded by
free-floating microorganisms in the aqueous phase or by attached biomass present as microcolonies in the
manner of Molz et al. (1986). Multiple substrates, electron acceptors and biological species are
accommodated by the model. Important assumptions for the biodegradation model are:
1. Biodegradation reactions occur only in the aqueous phase.
2. Microcolonies are fully penetrated; i.e., there is no internal resistance to mass transport within the
attached biomass.
105
-------
Section 9 - A 3-D NAPL Flow and Biodegradation Model
3. Biomass is initially uniformly distributed throughout the porous medium.
4. Biomass is prevented from decaying below a lower limit by metabolism of naturally occurring
organic matter unless cometabolic reactions act to reduce the active biomass concentrations below
natural levels.
5. The area available for transport of organic constituents into attached biomass is directly proportional to
the quantity of biomass present.
6. The number of cells per microcolony, biomass density, and microcolony volume are constant, so that
mass per microcolony is also constant.
The biodegradation model includes the following features:
• Monod, first-order, or instantaneous biodegradation kinetics.
• Formation of biodegradation by-products.
• External mass transfer resistances to microcolonies (mass transfer resistances can be ignored by the
user if desired).
• Inhibition of biodegradation by electron acceptors and/or toxic substrates.
• Nutrient limitations to biodegradation reactions.
• First-order abiotic decay reactions.
• Enzyme competition between multiple substrates.
• Modeling of cometabolism with transformation capacities and reducing power limitations using the
model of Chang and Alvarez-Cohen [1995].
• Biodegradation reactions in both the vadose and saturated zones.
9.3 Biodegradation Equations and Solution Procedure
The biodegradation model equations describe the transport of substrate and electron acceptor from the
aqueous phase into attached biomass, the loss of substrate and electron acceptor through biodegradation
reactions, and the resulting growth of the free-floating or attached biomass. The flow and biodegradation
system is solved through operator splitting, in which the solution to the flow equations is used as the initial
conditions for the biodegradation reactions. This approach is convenient because modifications can be made
to the system of biodegradation equations without having to reformulate the partial differential equations that
describe advection and dispersion.
The biodegradation equations comprise a system of ordinary differential equations that must be solved at each
gridblock and each time step after the advection and dispersion terms are calculated. Because the mass
transfer terms can make the system of equations stiff, the system is solved using a Gear's method routine
published by Kahaner etal. [1989]. The characteristics and numerical solution of this system of equations is
discussed by de Blanc etal. [1996b].
For a simple system of a single substrate, electron acceptor and biological species, the system of
biodegradation equations is:
dS
dt
o\ M-
m.
(s-s)-
max-'
-Y-
-k
abio1-
(9.1)
106
-------
Section 9 - A 3-D MAPI Flow and Biodegradation Model
do pK / -jj-\ UrnaxPx 1
dt VCV ' Y (]
dA PKX, -} |lmaxX]
dt mc ^ ' ' Y
dA pK / ^ -j* M-maxPx1
dt Vc{* *> Y
dx = n:....xf s 'Y A
S Y A "| ^
Ks+SAKa+AJ
Bf S Y A }
(K,+S^K.+A.)
/ I_LL_I \ X ^^^ X
1 s } A 1
[Ks + slKa+Aj
hX ^
(9.2)
C9 3^
\y-J)
(9.4)
r9.5^
dX
(9.6)
S = aqueous phase substrate concentration (ML~3)
S = substrate concentration in attached biomass (ML'3)
A = aqueous phase electron acceptor concentration (ML~3)
A = electron acceptor concentration in attached biomass (ML'3)
X = aqueous phase concentration of unattached biomass (ML~3)
X = attached biomass concentration; mass of attached cells per volume of aqueous phase
(ML'3)
E = mass of electron acceptor consumed per mass of substrate biodegraded
(3 = surface area of a single microcolohy (L2)
k = mass transfer coefficient (LT'1)
l^max — maximum specific growth rate (T*1)
px = biomass density; mass of cells per volume of biomass (ML:3)
Vc = volume of a single microcolony (L3)
mc = mass of cells in a single microcolony; me = rxVc (M)
Y = yield coefficient; mass of cells produced per mass of substrate biodegraded
Ks = substrate half-saturation coefficient (ML~3)
Ka = electron acceptor half-saturation coefficient (ML"3)
b = endogenous decay coefficient (T'1)
kabio = first-order abiotic rate constant (T'1)
t = time(T)
These equations are similar to the system of equations solved by Molz et al. [1986] and Chen et al. [1992].
Equation 9.1 includes three mechanisms for loss of substrate from the aqueous phase: diffusion of substrate
across a stagnant liquid layer into attached biomass; biodegradation of substrate by unattached
107
-------
Section 9 - A 3-D NAPL Flow and Biodegradation Model
microorganisms in the aqueous phase; and abiotic loss of the substrate through first-order reactions. The
biodegradation reactions are limited by both the substrate and electron acceptor concentrations through the
Monod terms.
Equation 9.2 describes the loss of substrate within attached biomass and is written for a single microcolony
(Molz etal., 1986). This equation describes the diffusion of substrate into attached biomass, biodegradation
of the substrate within the biomass, and abiotic decay of the substrate.
Equations 9.3 and 9.4 describe the loss of the electron acceptor. These equations are of the same form as
Eqs. 9.1 and 9.2 in that they describe diffusion across a liquid film and loss in biodegradation reactions. The
biodegradation rate expressions are multiplied by the factor E, the mass of electron acceptor consumed per
mass of substrate biodegraded. Equations 9.5 and 9.6 describe the growth and decay of unattached and
attached biomass, respectively. The relationship between the attached biomass concentration X appearing in
Eqs. 9.1,9.3 and 9.6 to the biomass density, microcolony volume and microcolony mass is
v_ccPbmc
(9.7)
where Cc is the number of cells per mass of solid, pb is the bulk density, n is the number of cells per
microcolony (a constant), and is the porosity. Since the biomass density, number of cells per microcolony,
porosity, and mass per microcolony are assumed to be constant, changes in X actually correspond to changes
in Cc, or alternately, to Cc/n, the number of microcolonies (Molz et al,, 1986). The area available for
transport of species from the aqueous phase to the biomass is directly proportional to X because the surface
area per microcolony is constant.
If external mass transport is ignored, then the system of six equations is reduced to three equations consisting
of Eq. 9.6 and a single equation each for loss of the substrate and electron acceptor:
dt
dA = {ImaxXEr S Y A
dt Y ^Ks+sJ[Ka+A
abio^
(9.8)
(9.9)
where X is the concentration of attached biomass and all other concentrations are aqueous phase
concentrations.
When biodegradation reactions that involve more than one substrate are being modeled, equations of the same
form as Eqs. 9.1 and 9.2 (or 9.8) are solved for each additional substrate. Similarly, equations of the form of
Eqs. 9.3 and 9.4 (or 9.9) are solved for each additional electron acceptor. Substrates can be biodegraded by
microorganisms using more than one electron acceptor, and each electron acceptor can be used for
biodegradation of multiple substrates.
When substrate competition is considered, the half-saturation coefficient of each Monod term is modified in
the following manner (Bailey and Ollis, 1986):
K
+ S,
s,2.
108
-------
Section 9 - A 3-D NAPL Flow and Biodegradation Model
where:
Si, 82 = concentration of substrates 1 and 2, respectively (ML'3)
Ks,i, KS)2 = half-saturation coefficients of substrates 1 and 2, respectively (ML'3)
If sequential electron acceptor utilization occurs (e.g., oxygen consumption followed by consumption of
nitrate), then the biodegradation rate expressions in the equations for substrate loss, electron acceptor
consumption and biomass growth are multiplied by an inhibition factor of the form (Widdowson et al.,
1988):
where I is an experimentally determined inhibition constant. The inhibition factor approaches 0 as the
concentration of the inhibiting substance Qhb increases. For nitrate respiration, for example, this term keeps
denitrification rates very small until oxygen is nearly exhausted.
When cometabolic reactions are considered, the equations describing the loss of cometabolite and attached
biomass growth are, in the case of no mass transfer resistances (Chang and Alvarez-Cohen, 1995):
dt
dX
dt
(9.10)
(9.11)
where kc is the maximum specific cometabolite biodegradation rate (ML^T'1), C is the aqueous phase
cometabolite concentration, R is the reducing power (NAD(P)H) concentration within the cells, Kr is the
NAD(P)H half-saturation constant, KC is the cometabolite half-saturation coefficient, (imax,s is the maximum
specific growth rate on growth substrate, and Tc is the transformation capacity, defined as the maximum
possible mass of substrate biodegraded per mass of biomass. The second expression in Eq. 9.11 describes
the deactivation of biomass through cometabolism reactions, which can produce toxic by-products that
damage cells (Chang and Alvarez-Cohen, 1995). When reducing power limitations are considered, an
equation is also needed to describe the production of NAD(P)H by the growth substrate and the consumption
of NAD(P)H by the cometabolite:
dR
dt
-kcErcX|
(9.12)
where Erc is the mass of NAD(P)H consumed per mass of cometabolite biodegraded, and E,p is the mass of
NAD(P)H produced per mass of growth substrate biodegraded.
9.4 Example Simulations
The multi-phase flow and biodegradation capabilities of the model are demonstrated through the simulation of
hypothetical LNAPL and DNAPL spills. In these simulations, the modeling domain consists of a
homogeneous, initially uncontaminated, confined aquifer that is 125 m long by 54 m wide by 6 m thick (see
Fig. 9.1). The domain is simulated with 25 gridblocks in the x direction, 11 gridblocks in the y direction, and
5 gridblocks in the z direction. Groundwater is flowing in the positive x direction (left to right in all figures)
with an average velocity of 0.1 m/day. Other flow and physiochemical parameters are listed in Table 9.1.
The spills are modeled by injecting NAPL into the center of gridblock (x = 5, y = 6, z = 1), which is
109
-------
Section 9 - A 3-D NAPL Flow and Biodegradation Model
approximately 22 meters from the left boundary. All chemical species are assumed to be non-adsorbing.
There is no air phase in these simulations; the top boundary is a no-flow boundary.
For both of these examples, local equilibrium is assumed between the NAPL and the aqueous phase, so that
the concentration of organic constituents in the aqueous phase is calculated by the partitioning relationship:
Q,aq — Q,solxi,NAPL
(9.13)
where Q>aq is the aqueous phase concentration of component i, Q5SOi is the aqueous phase solubility of
component i, and X^NAPL is the volume fraction of component i in the NAPL.
9.4.1 LNAPL Simulation Example
Sequential use of electron acceptors and equilibrium partitioning of multiple components into the aqueous
phase are illustrated with an example LNAPL simulation. The LNAPL example simulates a leak of 3.8 m3 of
gasoline containing approximately 1% by volume of benzene and 6% by volume of toluene into a shallow,
confined aquifer. The leak is assumed to occur over a four-day period. The groundwater initially contains 8
mg/L oxygen and 10 mg/L nitrate. Parameters used for this simulation are listed in Table 9.2.
Figure 9.2 shows the NAPL saturation history in a vertical slice down the center of the aquifer in the x-z
plane. As seen in Fig. 9.2, the NAPL moves little once the NAPL lens is established. The NAPL lens
gradually decreases in size as the organic constituents dissolve into the flowing groundwater.
As the benzene and toluene partition out of the gasoline into the aqueous phase, they become available to
microorganisms as substrates. For simplicity, a single population of microorganisms capable of
biodegrading the benzene and toluene is assumed to exist in the aquifer. This biological species biodegrades
both benzene and toluene aerobically and biodegrades toluene anaerobically with nitrate as the electron
acceptor. Abiotic decay and biodegradation by free-floating microorganisms are assumed to be negligible
(kabio and X are 0). Biodegradation kinetic parameters used for the simulation were obtained from Chen et
al [1992].
Figure 9.3 compares the concentration of benzene in the aqueous phase at 500 days to the concentration of
benzene that would exist if no biodegradation reactions were occurring. This figure shows that significant
biodegradation of dissolved benzene has occurred. The toluene plume is also shown in Fig. 9.3. Although
the toluene solubility is three times less than the benzene solubility, the maximum toluene concentration in the
aqueous phase is higher than the maximum benzene concentration because its concentration in the gasoline is
six times the benzene concentration of the gasoline. Toluene concentrations are nearly as low as benzene
concentrations at the fringes of the plume because toluene is biodegraded both aerobically and anaerobically,
where oxygen is exhausted, but the benzene is not.
The concentrations of benzene, toluene, oxygen and nitrate at 500 days are compared in Fig. 9.4. Oxygen
immediately downgradient of the spill is practically exhausted. Nitrate is also nearly exhausted from the area
immediately downgradient of the spill because sufficient time has elapsed since oxygen depletion to allow
denitrification to occur. However, at the forward edge of the plume, relatively high nitrate concentrations still
exist in areas where oxygen has been depleted, but not exhausted.
9.4.2 DNAPL Simulation Example
Different model capabilities are illustrated with a DNAPL simulation in which trichloroethylene (TCE) is
biodegraded through cometabolism. In this simulation, 0.028 m3 of TCE are spilled in a single day. The
cometabolic process is illustrated by injecting water containing methane through five injection wells located
approximately 24 meters downgradient of the spill. The injected water contains 20 mg/L methane and 8 mg/L
oxygen. The water injection rate is 1.4 m3 per day per well. The groundwater is assumed to contain 8 mg/L
oxygen. Parameters used for the DNAPL simulation example are listed in Table 9.3.
110
-------
Section 9 - A 3-D NAPL Flow and Biodegradation ModeJ
A population of methanotrophic microorganisms, capable of biodegrading TCE aerobically through
cometabolism, is assumed to exist in the aquifer. The methanotrophs use methane as the primary substrate
and oxygen as the electron acceptor. TCE biodegradation is assumed to reduce the active biomass and
consume reducing power of the methanotrophs, so that TCE biodegradation both reduces the active biomass
concentration and reduces the active biomass's biodegradation effectiveness. Once biomass has become
deactivated, it does not become active again. Biodegradation rate parameters were obtained from Chang and
Alvarez-Cohen [1995]. External mass transport of chemical species from the aqueous phase to the biomass
was ignored for this example.
The effect of the methane injection wells is illustrated in Fig. 9.5, where concentrations of TCE, a hypothetical
TCE tracer, oxygen and methane are shown at 170 days. The TCE tracer is simply TCE that is not allowed to
biodegrade in the model so that the effects of biodegradation can be seen. Concentration contours of the
different constituents are shown in the top 1.2-m layer of the aquifer. Oxygen is depleted downgradient of the
plume, but only a small fraction of the oxygen is consumed upgradient of the methane injection wells. Most
of the oxygen upgradient of the wells remains because the high TCE concentrations deactivate the biomass
and consume reducing power, preventing the TCE from biodegrading. Even with a small TCE spill, TCE
concentrations in the aquifer are so high that most biomass immediately downgradient of the spill is rapidly
deactivated. Significant TCE biodegradation occurs only where appreciable methane is present to regenerate
the microorganism's reducing power and where TCE concentrations are low. These effects can be seen in
Fig. 9.5. The high concentration contours of the TCE and TCE tracer are nearly the same, but biodegradation
of the TCE causes a slight retardation in the progress of the TCE plume at low concentrations.
Ill
-------
Section 9 - A 3-D NAPL Flow and Biodegradation Model
spill
location
54 m, ny = 11
_125m, nx = 25
direction of groundwater flow
X
Figure 9.1. Modeling domain size and discretization.
.0-
I "
4 da1
300 days
0 distance in direction of 38
groundwater flow (m)
0.15
Oil saturation
distance in direction of 38
groundwater flow (m)
0.3
Figure 9.2. NAPL saturation history in the vicinity of a hypothetical
gasoline spill. The figure shows a vertical section along the x axis in the
center of the aquifer. This gasoline spill is simulated by injecting 3.8 m3 of
gasoline at a depth 0.6 m below the top of the confined aquifer.
112
-------
Section 9 - A 3-D NAPL Row and Biodegradation Model
Benzene concentration - no biodegradation
91.5
Benzene concentration - with biodegradation
S j
T3
6
0
30.5
I
61
91.5
0 30.5 61 91.5
Toluene concentration - with biodegradation
30.5 61 91.5
distance in direction of groundwater flow (m)
122
122
Toluene concentration - no biodegradation
122
122
Concentration (mg/L)
Figure 9.3. Comparison of benzene and toluene concentrations in the
aqueous phase 500 days after a gasoline spill. The figure shows a
vertical section along the x axis in the center of the aquifer. Gasoline was
injected at the location of the white circle. Concentrations of benzene and
toluene are compared for the assumptions of no biodegradation and
biodegradation of the two compounds.
113
-------
Section 9 - A 3-D NAPL Flow and Biodegradation Model
oxygen
nitrate
toluene
benzene
20 40 60 80 100 120
distance in direction of groundwater flow (m)
Figure 9.4. Concentrations of benzene without
biodegradation, benzene with biodegradation,
toluene, oxygen, and nitrate in upper 1.2 m of
aquifer along aquifer center line at 500 days.
TCE tracer
Methane
30.5 61 915 122 ° 30-5 61 91.5 122
TCE
I ' I ' I ' I ' I ' I ' I
30.5 61 915
distance in direction of groundwater tow (m)
122
30.5 61 91.5
distance indirection of groundwater flow (m)
122
• TCE Source
Methane injection well
Figure 9.5. Plan view of TCE, a hypothetical TCE tracer, methane and oxygen
concentrations in the upper 1.2 m of a confined aquifer 170 days after a TCE
spill. All concentrations are mg/L. Groundwater is flowing from left to right at
0.1 m/d. Shading is present for visualization purposes only and does not
correspond to specific chemical concentrations. Assumptions are: TCE
solubility =1,100 mg/L; initial oxygen concentration = 8 mg/L; methane
concentration in injected water = 20 mg/L. Biodegradation rate parameters are
from Chang and Alvarez-Cohen [1995].
114
-------
Section 9 - A 3-D NAPL Flow and Biodegradation Model
Table 9.1. Flow Parameters for All Simulations
average velocity, v (m/d)
porosity, §
bulk soil density, pb (g/cm3)
longitudinal dispersivity, (XL (m)
transverse dispersivity, (XT (m)
initial oxygen concentration, A0 (mg/L)
initial nitrate concentration, An (mg/L)
0.1
0.38
1.64
5
0.625
8.0
10.0
Table 9.2. Parameters for LNAPL Simulation Example
Simulation parameters
Spill volume (m3)
Spill duration (d)
Physiochemical parameters
Density of gasoline (g/cm3)
Density of benzene (g/cm3)
Density of toluene (g/cm3)
Solubility of benzene (mg/L)
Solubility of toluene (mg/L)
Initial benzene concentration in NAPL (volume %)
Initial toluene concentration in NAPL (volume %)
Mass transfer coefficient for benzene, Kb (m2/d)
Mass transfer coefficient for toluene, Kt (m2/d)
Mass transfer coefficient for oxygen, KO (m2/d)
Mass transfer coefficient for nitrate, Kn (m2/d)
Microbial parameters (from Chen et al, 1992)
Initial cell concentration, Cc (cells/g soil)
Colony population density, n (cells/microcolony)
Biomass density, px (g/cm3)
Microcolony surface area, P (m2/microcolony)
Microcolony volume, Vc (m3/microcolony)
Initial attached biomass concentration, X (mg/L)
Maximum specific growth rate on benzene, u,max b (
-------
Section 9 - A 3-D NAPL Flow and Biodegradation Model
Table 9.2. Parameters for LNAPL Simulation Example
Half-saturation coef. of toluene for nitrate respiration, K^1 (mg/L)
Half-saturation coef. of oxygen for benzene biodeg., K^0 (mg/L)
Half-saturation coef. of oxygen for toluene biodeg., K^0 (mg/L)
Half-saturation coef. of nitrate for toluene biodeg., K^11 (mg/L)
; Endogenous decay coefficient, b (d"l)
17.4
0.1
0.01
2.6
0.1
Table 9.3. Parameters for DNAPL Simulation Example
Simulation parameters
Spill volume (m3)
Spill duration (d)
Physiochemical parameters
Density of NAPL (g/cm3)
Density of TCE (g/cm3)
Solubility of TCE (mg/L)
Initial TCE concentration in NAPL (volume %)
Microbial parameters
Initial biomass concentration, X (mg/L)
Maximum biodegradation rate of TCE, kc (mg TCE/mg cells-d)
Maximum specific growth rate for methane, Hmax,m (d~*)
Yield coefficient for methane, Y (mg cells/mg methane)
TCE transformation capacity, Tc (mg TCE/mg cells)
Half-saturation coefficient for TCE, KC (mg/L)
Half-saturation coefficient for methane, Ks (mg/L)
Half-saturation coefficient for reducing power, Kr (mmol of e~/L)
Reducing power production coefficient, Ejp
(mmol e~ produced/mg methane biodegraded)
Reducing power consumption coefficient, ErC
(mmol e~ consumed/ mg TCE biodegraded)
Initial reducing power concentration in cells, (mmol e"/mg cells)
0.028
1
1.46
1 .46
1,100
50
4.31
4.2
0.31
0.33
0.1
7.0
1.1
0.54
0.5
0.15
0.0005
116
-------
Section 10
Well Models
10.1 Introduction
In this section, the well models in the UTCHEM simulator are described. The options available are:
• An arbitrary number of producers in any gridblock can be specified (Cartesian grid option only).
• Skin factor (S) and completion interval can be specified.
• Both the injection wells and the producers can be shut in or opened at anytime during the simulation.
The well type can also be changed during the simulation (e.g., an injector changed to a producer).
• Each injection well can inject multiple slugs with different component concentrations.
• Wells can be completed in any direction parallel to the axes (Cartesian and Curvilinear grid options
only).
10.2 Vertical Wells with Cartesian or Curvilinear Grid Options
Two basic well conditions of constant flow rate or constant flowing bottomhole pressure are implemented.
Application of Darcy's law to a wellblock (i,j,k) results in:
(10.1)
where P^ = PI + Pc^ and PI is the productivity index. For two-dimensional area! (x-y) and three-
dimensional simulation, the PI is given by:
PI, =
27CJkxkyAz
(10.2)
(0.15802) In-2- +S
I r,,,
and for one-dimensional and cross-sectional (x-z) simulation by:
PT -
~
AY
0.15802 —
2
(10.3)
117
-------
Section 10 - Well Models
where the constant in the above equations is the unit conversion factors where the permeability is in Darcy and
gridblock size in ft and Xrf = — in cp-1 to result PI in (psi)-1.
M-£
The equivalent radius, rQ, is calculated using Peaceman's model (Peaceman, 1983):
\l/2
J/2
-------
Section 10 - Welt Models
The total injection rate for the ijk block is given by:
nn
(10.10)
The above term is then added to the constant vector of the pressure equation at the ijk block. In Eq. 10.9, it is
assumed that the potential gradient between the wellbore and the gridblock pressure is the same for all the
layers in the reservoir model. Nolen and Deny [1972] have shown that including the potential differences in
Eq. 10.9 may result in stability problems. Equation 10.9 may give erroneous results in the case of large
vertical heterogeneity and especially when noncommunicating layers exist. However, in the absence of a
very low permeability zone or small crossflow, the above formulation does not produce a significant error.
10.2.1.2 Pressure Constraint
When bottomhole injection pressure for the first perforated layer, (Pwf)y j^, is specified, Eq. 10.1 is used.
nP
The term 2L PI^ (Pwf ~ PC!£ ) in Eq. 10. 1 is added to the constant vector of the pressure equation for block ijk
i=\ •
and term
to the (Pj)11"1"1 term (diagonal element in the pressure matrix).
After the pressure equation is solved, Eq. 10.1 is used to obtain the total injection rate at the end of the time
step, Q . The injected phase cuts for each layer are the same as the total injected cuts:
(10.11)
the phase injection rates, Qinj^, specified as input values, are treated as phase cuts.
10.2.2 Well Constraints for Production Wells
10.2.2.1 Rate Constraint
When the total production rate, input as a negative value (Qprod) is specified, the withdrawal rate for each layer
k is calculated using:
Q = Qprod
k=U=l
and the produced phase cuts are then calculated using:
(10.12)
(10.13)
119
-------
Section 10 - Well Models
10.2.2.2 Pressure Constraint
When bottomhole pressure for a producer is specified, Eq. 10.1 is used to calculate the total production rate
(Q) in the same manner as was described above for the injection well on pressure constraint. The produced
phase cuts are then obtained from:
_ Pit
(10.14)
10.3 Vertical Wells with Radial Grid Option
The boundary conditions for the radial option are
• no vertical flow at the upper and lower boundaries
• a rate constraint well at the center of the reservoir,
• a constant pressure outer boundary that is treated the same as a pressure constraint injector/producer
well.
The phase productivity index in the gridblock ijk for the injection or production well is calculated as
Ax
2
(10,15)
10.3.1 Rate Constraint Injector
Equations 10.9 and 10.10 are used to calculate the rate allocation to each layer.
10.3.2 Rate Constraint Producer
Equations 10.12 and 10.13 are used to calculate the rate withdrawal from each layer.
10.3.3 External Boundary
The amount of fluid that crosses each layer k from the last gridblock at the open boundary is calculated by
(10.16)
where the outer boundary aqueous phase pressure (Pi)e is maintained at the initial pressure for the duration of
the simulation as:
fork = 2,..,nbz (10.17a)
where j^ is calculated from Eqs. 10.6 and 10.7. The phase productivity index is calculated as:
(10.17b)
where the permeability and radius of the outermost gridblock (i = nr) are used. The calculation is implicit
similar to that for the pressure constrained wells discussed above. Once the pressure is known, total rate for
120
-------
Section 10 - Well Models
each layer is calculated from Eq. 10.16. The phase cuts for the fluids crossing the boundary are calculated
from Eq. 10.14.
10.4 Horizontal Well with Cartesian or Curvilinear Grid Options
Horizontal wells use the same well model equations as vertical wells. Only parameters related to the direction
of the wellbore were modified. When the wellbore is parallel to the z direction, the calculation of the
productivity index uses the gridblock height, Az, the permeability in the x direction, kx, and the permeability in
the y direction, ky:
(10.18)
where the constant 0.15802 is a unit conversion factor. kx and ky are in Darcy, Az, r0, and rw are in ft, and
~~l The equivalent wellblock radius, r0, is based on Peaceman [1983] and uses
IS 111 CO . J. Ll\s WVJIAJ. V CU.Wi.1.1. VV Viiiy±\_/WJ\- XCI.VJ-J.i4.Oj iO'
wellblock properties in the x and y directions such as the dimensions Ax and Ay and the permeability values
kx andky.
r0 = 0.28 ±
/2
Ax
1/2
vl/4
a/4
(10.19)
10.4.1 Productivity Index for Horizontal Wells
The productivity index calculations were generalized for horizontal wells parallel to either the x direction or the
y direction by taking into account the pertinent directional properties. When the wellbore is parallel to the x
direction, the productivity index calculation uses Ax as the wellblock dimension parallel to the wellbore. Since
the wellbore is perpendicular to the y and z directions, the productivity index calculation uses the permeability
in the y direction and the permeability in the z direction:
PI, =
0.15802
In L +S
(10.20)
When the wellbore is parallel to the y direction, the productivity index calculation uses Ay as the wellblock
dimension parallel to the wellbore. Since the wellbore is perpendicular to the x and z directions, the
productivity index calculation uses the permeability in the x direction and the permeability in the z direction:
(10.21)
121
-------
Section 10 - Well Models
10.4.1.1 Equivalent Wellblock Radius for Horizontal Wells (Peaceman, 1983)
The calculations of the equivalent wellblock radius were also generalized for horizontal wells by taking into
account reservoir properties perpendicular to the direction of the wellbore. In case the wellbore is parallel to
the x direction, the equivalent wellblock radius, based on Peaceman [1983], uses wellblock properties in the y
and z directions such as the dimensions Ay and Az and the permeability values ky and kz:
r0=0.28
k
0.5
(10.22)
In case the wellbore is parallel to the y direction, the equivalent wellblock radius uses wellblock properties in
the x and z directions such as the dimensions Ax and Az and the permeability values kx and kz:
r0 = 0.28
0.5
0.25
(10.23)
10.4.1.2 Equivalent Wellblock Radius (Babu etal., 1991)
In addition to Peaceman's formulation [1983], a formulation of the equivalent wellblock radius based on the
paper by Babu et di. [1991] was implemented in the simulator (Dakhlia et al, 1995). As published, the
gridblock sizes were assumed uniform and the equations depended on gridblock numbering. However,
numerical reservoir simulation is often carried out with non-uniform gridblock sizes. The equations were
therefore rearranged so that gridblock sizes were no longer required to be uniform and the equations no longer
h a
depended on the gridblock numbering. — was substituted for nz and — was substituted for nx. In case an
Az Ax
integer was needed, such as in the summation limits, the FORTRAN function NINT was used to calculate the
nearest integer to the argument. Therefore, NINT(—) was substituted for nz in the summation limit used in
Az
2x 2z
SXz- In addition, —— was substituted for v and —— was substituted for A, As a result, the applicability of
Ax Az
the formulation was extended to non-uniform grids. The assumption for these substitutions was that away
from the wellbore, the effect of a coarse and non-uniform grid was equivalent to the effect of a fine and
uniform grid on the pressure behavior near the wellbore.
The resulting formulation is given below for a wellbore parallel to the y direction. In case the wellbore was
parallel to either the x or z direction, the pertinent directional variables were modified accordingly.
+0.25 In
-In
. (nz
sin
w
^ h
-1.84-Bp-S
xz
(10.24)
122
-------
Section 10 - Well Models
where the boundary term, BE, is computed by
'271Z,
BE=ln(l-E1) + 0.51n
l-2cos|
and
= exp
27imin(xw,a-xw) fik
and the summation term, Sxz, is
Az
I
n=l
cos
2x
w
Ax
-2
Ax
sin
21
Az
2a
with oc, ccn, and xn defined as
Ax [E
_2_
^x
an = asm
xn=
Tin
Az
For symmetry purposes, the wellbore location (xw, zw) was temporarily adjusted so that
xw = min(xw, a- xw)
and
zw = min(zw, a- zw)
(10.25)
(10.26)
(27)
(10.28)
(10.29)
(10.30)
(10.31)
(10.32)
123
-------
Section 11
Effect of Alcohol on Phase Behavior
11.1 Introduction
This section is based on the Ph.D. dissertation by Saad [1989]. The phase behavior calculation for a mixture
of water, oil, and surfactant is discussed in Section 2. The effect of alcohol on the phase behavior is discussed
here. The presence of alcohol affects the effective salinities and causes a shift in the phase boundaries. The
effect of alcohol on the solubility is accounted for by shifting the maximum height of binodal curve. The
amount of alcohol that partitions in the excess phase(s) is modeled either by constant partitioning coefficients
as in Hirasaki's model (Hirasaki, 1982) or as a function of total composition with the concept of
pseudocomponent and pseudophase as in Provoust's model (Prouvost et al., 1984a,b, 1985). Following is a
discussion of the UTCHEM phase behavior model in the presence of alcohol (Pope and Nelson, 1978;
Prouvostejra/., 1984a,b, 1985; Camilleri et aL, 1987c; Saad, 1989).
The phase behavior is modeled as a tetrahedric diagram at a fixed salinity. Four pseudocomponents are
surfactant, alcohol, oil, and water represented in a tetrahedric diagram. Tielines and binodal curves are located
on the ternaries sliced through tetrahedrons. The pseudophases are (1) the aqueous consists of water and
alcohol(s), (2) oleic consists of oil and alcohol(s), and (3) microemulsion consists of surfactant and
alcohol(s). Similar to the no alcohol mixture, the phase behavior parameters such as binodal curve, plait point
and invariant point are calculated as a function of effective salinity using Hand's rule (Hand, 1939).
11.2 Alcohol Partitioning
The two options available in UTCHEM to calculate the alcohol partitioning are based on the models of
Hirasaki and Prouvost. Hirasaki's model assumes a constant partition coefficient whereas experimental
results show that alcohol partition coefficients vary with total composition. Prouvost extended the
pseudophase model to calculate variable alcohol partition coefficients and to be applicable to two alcohols.
The following intensive composition parameters are defined in the model:
(11.1)
(11.2)
(11.3)
where for K = 7, the value of subscript j = 1 and for K =8, j =2. Cj, C2, and C3 are the overall water, oil, and
surfactant volume fractions, respectively. Superscripts 1, 2, and 3 represent the association of alcohol with
124
-------
Section 11 - Effect of Alcohol on Phase Behavior
aqueous, oleic, and microemulsion pseudophases. Therefore, c] is the volume of alcohol 7 (component 7 in
UTCHEM) in the aqueous phase, and Cg is the volume of alcohol 8 (component 8) in the aqueous phase.
The partition coefficients used in Hirasaki's model can be defined using the above parameters:
KK=?- (11.4)
KK=^- (11.5)
where for K = 7, the value of subscript j = 1 and for K = 8 , j =2. In Prouvost's model, monomeric alcohol
reactions are considered. The following thermodynamic constants are used in the model:
kwi = partition coefficient of monomeric alcohol 7 between aqueous and oleic pseudophases
kmi = partition coefficient of monomeric alcohol 7 between interfacial and oleic pseudophases
• . k! = self-association constant of monomeric alcohol 7 in oleic pseudophase
a = ratio of molar volume of monomeric alcohol 7 to equivalent molar volume of surfactant
kW2> km2, k2, and b are similar constants for alcohol 8.
The above parameters are input to the simulator. A material balance gives the following relationships:
^ A.;Ci B;C3
CK = * + J forK = 7,j = 1 ;K = 8,j = 2 (11.6)
where
B =
Y2(l + k2)]
(11.7)
= {[1 + Y2
Yi
- km2)] - Yikml[l + Yl + y2(l + k2)]}
A2 = Y2kW2l + Y2
B2 = bY2km2[l + Y2
D2 = {[1 + YI + Y2(l
E2 = {[l + Yi + Y2(l
Y2
- kwl)] - Y2kw2[l
- kml)] - Y2km2[l
(11.8)
C7 and C8 are the overall volume fractions of alcohol 7 and alcohol 8 in the gridblock and are known values
from the solution of species conservation equations. Knowing C-j and Cg, Eqs. 1 1.7 and 1 1.8 are solved for
Yl and y2 using the Newton Raphson iteration method, and then the other four intensive parameters are
calculated:
125
-------
Section 11 - Effect of Alcohol on Phase Behavior
B
for j = 1,2
forj = l,
(11.9)
(11.10)
O ^
Once Aj, 7j, and Cj are determined, alcohol partition coefficients K£ , and KK are calculated using Eqs. 11.4
and 11.5. When only a single alcohol is used, Eq. 11.6 reduces to the following cubic equation:
A1 y3 + B1 y2 + C' Y + D' = 0
where
A' = (l-fk-km)(l+k-kw)
C2
C2
I* f^ I
C = kw — i~akm — (2 +2k — km — kw)— hi
D' = '
Then the partition coefficients are calculated using:
(11.11)
(11.12)
-kw (11.13)
(11.14)
(11.15)
=
7
-km)]
(11.16)
(11.17)
For two alcohols, the overall alcohol volumes are related to the overall volumes of water (Cj), oil (€3), and
surfactant (€3) pseudocomponents by:
CK = Aj GI + YJ C2 + Oj C3 for K = 7, j = 1 ; K = 8, j = 2
The above equations, can be written in terms of the alcohol partition coefficients as:
CK = XjCl +Xj K^ C2 + ?tjl4 C3 forK = 7J = 1 ;K=8,j = 2
From above equations the parameters Aj are defined as:
'K
for j = 1,2
(11.18)
(11.19)
(11.20)
Xj is then used in calculating the pseudocomponents that are the apexes of the pseudoternary diagram.
Cpi= (water volume) + (alcohol volumes associated with water) = Ci(l + A,i+?i2) (11-21)
126
-------
Section 11 - Effect of Alcohol on Phase Behavior
Cp2 = (oil volume) + (alcohol volumes associated with oil)
= €2(1 + 7!+Y2) = C2(l + TlK5+X2Ki)
Cp3 = (water volume) + (alcohol volumes associated with water)
(11.22)
Kg) (11.23)
The calculation of the pseudocomponent volumes is summarized below:
1. Using Newton Raphson iteration, calculate yj and y2 from Eqs. 11.3 and 11.4.
2. Calculate Xj and Oj using Eqs. 11.9 and 11.10.
3. a) Calculate K^ and K^ using Eqs. 11.4 and 11.5. If there is only one alcohol, use Eq. 11.11 to
calculate y. Then calculate the partition coefficients using Eqs. 11.16 and 11.17.
b) If constant partition coefficient option is used, KK and KK are input parameters.
c) Calculate A,j using Eq. 11.20.
4. Calculate the volume of the pseudocomponents, Cpj, Cp2, and Cp3, using Eqs. 11.21-11.23.
Above calculations are made in Subroutines ALCPTN and TWOALC.
11.3 Effective Salinity
Hirasaki [1982] introduced a model to account for the change in optimal salinity with respect to changes in the
concentration of alcohol and calcium. Camilleri et al. [1987c] extended Hirasaki's model to entire salinity
space to define an effective salinity for the case with one alcohol:
CSE =
-51
(11.24)
CSE is the effective salinity, and Pg and pK are the slope parameters for calcium and alcohol dilution effects.
o Q
fg is the fraction of calcium cations associated with surfactant micelles and is given in Section 2. f£is
defined as:
total volume of alcohol associated with, surfactant
-
total volume of surfactant pseudocomponent
1 + a
(11.25)
Pg and PK are determined by matching an experimental salinity requirement diagram such as those reported
by Nelson [1982] or equivalent diagrams (Satoh, 1984). For formulations containing only one alcohol, CSEL
and CSEU are constant for a fixed chemical formulation and are determined using Eq. 11.24. If there is no
calcium present, Eq. 11.24 represents a group of straight lines which pass through the fixed point (0, -1/PK).
If calcium is present, then it represents a group of planes which pass through the three fixed points (0, -1/PK,
0), (0, 0,1/PK), and (0, -l/pK, 1/P6). Due to the fact that Eq. 11.24 is nonlinear, these planes are not flat. The
calculated effective salinity becomes negative when f| > 1/P6 or PK is negative and f| > 1/IPKI-
Since different alcohols give different salinity limits, the following effective salinity is defined for the case
when there are two alcohols present:
127
-------
Section 11 - Effect of Alcohol on Phase Behavior
C51
CSE - —
where the effective salinity limits are not constant in this case and are calculated by:
r- IR fS\ , r> k fS
CSEL7 P7*7 +CSEL8 P8r
Cl I »
SEL
(11.26)
8*8
CSEU7|P7f7 | + CSEU8|P8f8
(11.27)
(11.28)
CSEL7» CSEL8> CSEU7' ^ CSEU8 are effective salinity limits for alcohol 7 and 8. CSEL7 and CSEU7 are
determined when alcohol 7 is the only alcohol present and are calculated using Eq. 11.24. Similar
o o
independent calculations are made for alcohol 8. For the two alcohol case, f7 and fg are defined as:
S _
total volume of alcohol k associated with surfactant
total volume of surfactant pseudocomponent
-4?-^- 5- forK=7,j = l;
(11.29)
KK and ^j are calculated as outlined in the previous section.
Once effective salinity is calculated, the phase environment (Fig. 11.1) for each gridblock is determined
according to:
CSE CSEU
Typell(-)
TYPe ^
Type n(+)
Effective salhiity is calculated in Subroutine CSECAL.
11.4 Flash Calculations
A binodal curve is an intercept of a binodal surface and a pseudoternary plane. The original simulator
introduced by Pope and Nelson [1978] could treat nonsymmetric binodal curves; however, the present
simulator can treat only a symmetric binodal curve. The effects of alcohol on the height of the binodal curve
was included which can increase as the total chemical increases. The following linear relationship between the
o
height of the binodal curve (C3max) and f£ is used for the case with one alcohol (Fig. 1 1.2):
3max,Km =
for m = 0, 1, 2; K = 7
(11.30)
where m = 0 means at zero salinity, 1 means at optimal salinity, and 2 means at two times the optimal
salinity, m,^ is the slope for maximum height of binodal curve vs. fraction of alcohol (alcohol 7 or alcohol
8 for the two alcohol case) associated with the surfactant pseudocomponent at salinity m. CKm is the intercept
of maximum height of the binodal curve at zero fraction of alcohol (alcohol 7 or alcohol 8 for the two alcohol
case) associated with the surfactant pseudocomponent at salinity m. Parameters mKm and CKm are obtained
128
-------
Section 11 - Effect of Alcohol on Phase Behavior
by matching the volume fraction diagrams corresponding to at least three different total chemical (alcohol +
surfactant) compositions. For the first iteration, the slope parameters are set to zero and the intercept
parameters are adjusted in order to obtain a reasonable match of the volume fraction diagrams; then the slope
parameters are obtained. Having obtained the slope parameters, the matching procedure is repeated for further
improvements. This matching is done using single alcohol experiments independently for alcohol 7 and
alcohol 8 using Eq. 1 1.30. The variables HBNC70, HBNC71, HBNC72 in Fig. 1 1.2 are the UTCHEM input
parameters for CKm at three values of m. The variables HBNS70, HBNS71, HBNS72 in Fig. 11.2 are the
UTCHEM input parameters for niKm at three values of m.
The following equations are used for calculating the height of the binodal curve for the two alcohol case:
C3max,Km=mKm(f7S+f8S) + CKm for K = 7 and 8 (11.31)
'7m
The following Hand equations are used for phase behavior calculations:
P3
-P2
C8m
ff+ff
(11.32)
(11.33)
(11.34)
Equation 11.33 defines the binodal curve for all types of phase behavior, and Eq. 11.34 defines the
distribution curve (tielines) when two phases exist (Type n(-) or Type !!(+)). CP1, CP2, and CP3 represent
pseudocomponents defined by Eqs. 11.21-11.23. CP2£, CP3£, CPU>, and CP3^ represent phase concentrations
of the pseudocomponents in the two pseudophases I and I'. Because pseudocomponent concentrations are in
volume fractions, they must add up to one; therefore the following constraints are used:
CP1+ CP2 + CP3 =
CPlf
(11.35)
(11.36)
(11.37)
The total composition, CP1, CP2, and CP3, is known. Therefore there are five equations and six unknowns
(Cpxtf , K = 1, 2, 3, ^ = 1, 2). Any phase concentration can be chosen and varied between 0 and 1 to sweep
the phase diagram. Since only symmetric binodal curves are modeled in the simulator, parameter B is equal
to -1 and parameter F is equal to 1. Parameter A in Eq. 11.33 is related to the height of the binodal curve by:
A =
_f 2C3max 1
1-C
3 max )
(11.38)
Linear interpolation is then used to determine the A parameter for arbitrary effective salinity values. The
reason for interpolating A instead of the maximum height of the binodal curve, C3max, is that, at high salinity,
129
-------
Section ;l 1 - Effect of Alcohol on Phase Behavior
C3max exceeds unity, which means the binodal curve is outside the ternary diagram. To avoid this problem,
the interpolation is done on A. The following linear interpolation equations are used:
-SE
CSEOP.
for'
SEOP
_Al)f i—^-l
I CSEOP J
for C > c
SE SEOp
(11.39)
(11.40)
where CSEOP is the optimum effective salinity (CSEOP = 1/2 (CSEL+CSEU)).
Parameter E is calculated from the location of the plait point. From the phase distribution equation
(Eq. 11.34) and the plait point P:
/
CP3P _ CP3P
(11.41)
and since the plait point is also on the binodal curve:
CP3P _ A| Cp3P 1
1 — £\\ ' ................ " " " I
CP2P VCP1P
Also:
+ Cp2p + CP3P = 1
(1L42)
(11.43)
For the case when B = -1 and F = 1 (symmetric binodal curve), all phase concentrations can be calculated
explicitly. FromEq. 11.36:
CPU = 1 -CP2i -CP31
Now substituting Eq. 1 1.44 in Eq. 1 1.33, CP31 can be calculated as a function of CP2i:
Cpal = |(-ACP21 +V(ACP2i)2+4ACP2i(l-Cp21))
and from Eq. 11.42:
CP2P
(11.44)
(11.45)
(11.46)
where Cp2p, the oil pseudocomponent concentration at the plait point, is an input parameter in the simulator,
and
P3P
+A/(ACP2P)2 + 4ACP2P(1-CP2P)")
j
Then from Eq. 11.36:
= 1 - CP2P - CP3p
(11.47)
(11.48)
130
-------
Section 11 - Effect of Alcohol on Phase Behavior
knowing CP1P, parameter E can be calculated from Eq. 11.46. Having calculated CP31 and CP11 from Eqs.
11.44 and 11.45, CP22 is calculated from the following:
CP22 =
where
h2+Ah + A
(11.49)
CP11
Then CP32 is calculated from
CP32 = h CP22
and
CP12 = 1 - CP22 - CP32
(11.50)
(11.51)
(11.52)
The above calculations are performed when there are only two phases present, for Type II(-) or Type II(+)
phase behavior. The only difference between the two cases is that for Type n(-) phase behavior CP2PR and
jt*
for Type II(+) phase behavior CP2PL, are used for CP2P in the above equations. The distribution of the three
pseudocomponents in the two phases for Type II(-) and Type n(+) phase behavior are summarized below:
11.4.1 For Type ll(-) Phase Behavior, CSE < CSEL
Known values for this case are C3max0, C3maxl, C3max2, CSE, CSEL, CSEU, CP2PR and overaU
concentration of the pseudocomponents, Cp^, Cp2, and, Cp3.
1. Calculate parameter A from Eq. 11.39.
2. Using CP2PR calculate CP3PR and CP1PR using Eqs. 11.47-11.48.
3. Calculate parameter E using Eq. 11.46 and CPiPR and CP2PR.
4. Vary the value of CP2i from 0 to CP2PR, calculate CP11 and CP31 using Eqs. 11.44-11.45.
5. Calculate h from Eq. 11.50.
6. Calculate CP22, CP32, and CP12 using Eqs. 11.49-11.52.
7. If (CP32 - CP3) (CP21 - CP2) - (CP31 - CP3) (CP22 - CP2) < e, where e is a sufficiently small number
(10" ), then stop; otherwise increment Cp2i using the half interval method and go to step 4.
11.4.2 For Type ll(+) Phase Behavior, CSE > CSEU
Known values for this case are C3max0, C3maxl, C3max2, CSEL, CSE, CSEU, CP2PL and overall
concentration of the pseudocomponents, CPj, CP2, and .CP3.
1. Calculate parameter A from Eq. 11.40.
131
-------
Section 11 - Effect of Alcohol on Phase Behavior
2. Using Cp2pL calculate Cp3PL and CP1PL from Eqs. 11.47-11.48.
j, jij
3. Calculate parameter E using Eq. 11.46 and CP1PL and CP2PL-
4-7. Steps 4-7 as in the Type H(-) described above.
For Type HI phase behavior, the tie lines for the left (Type !!(+)) and the right (Type (-)) lobes are calculated
separately. Because of the symmetric binodal curve assumption, the binodal curve is calculated in the same
manner as in the Type H(-) and Type n(+) cases. The invariant point M is calculated as follows:
CSE~CSEL
CSEU-CSEL
(11.53)
where
a"Cp2M = Cos 60°
CP3M
(11.54)
Therefore,
= 2(a -
Since the invariant point M is on the binodal curve, Eq. 11.33 can be used to calculate CP3M as a function of
using Eq. 11.45:
P3M =
(11.55)
Solving Eqs. 11.54-11.55 for CP2M>tne following is obtained:
'P2M ='
2a(4 - A) + A ± V(2a(4 - A) + A)2 - 16a2 (4 - A)
2(4-A)
(11.56)
The invariant point should disappear when C§E approaches CSEL (Cp2M = 0, a = 0) and when
approaches CSEU (Cp2M = 1, a = 1). These conditions hold only for the negative sign in Eq. 11.56.
Therefore, the composition at the invariant point is determined by Eq. 11.55, Eq. 11.56 with the negative sign,
and by
CP1M = ! - CP3M - CP2M
(11.57)
The plait point for the left lobe of the Type El phase environment must vary between zero and the plait point
for the Type n(+) value, Cp2pL- The plait point is calculated by salinity interpolation:
CP2PL =CP2PL+-
CP2PL
-SEU
-C
(11.58)
SEL
In order to apply the Hand equations to the left lobe, a coordinate transformation is made (Fig. 11.3). The
Hand distribution equation in the new coordinate system is :
CP32 _
i —
CP22 I
(11.59)
132
-------
Section 11 - Effect of Alcohol on Phase Behavior
where
•*•-« ' s\
P 2£ = P2-£ *^^^ ^
x— * *
^P 1€ = 1 " Cp 2^ - Cp 3^
(11.60)
(11.61)
(11.62)
Now let
(3 = Sec 0 =
+(CP3M)2
-P2M
P2M
(11.63)
(11.64)
Because of the symmetric binodal curve assumption (F=l), E can be calculated explicitly from:
t
C1 ^ft fv\(~* f^
PIP •*•"~~ \P"™" **/*-'P2P ~~ P3P
Jjr — , *" —•—
CP2P
(11.65)
where CP2p is equal to CP2pL calculated using Eq. 11.58, and CP3P and CP1P are calculated from Eqs. 11.47
and 11.48.
CP1 1 and CP3 1 are calculated by Eqs. 1 1 .44- 1 1 .45. Now Eq. 1 1 .59 can be solved as before:
C
P22
h'2+Ah'+A
where
. bECp31
(11.66)
P11
and
(11.67)
(11.68)
CP12 = 1 - CP22 - CP32 (1 1.69)
Therefore all phase concentrations for the two phases in the left lobe have been determined.
The calculations for the right lobe are very similar to the above calculations for the left lobe. The CP2P value
for the plait point in this case varies between 1 and the input value for the Type H(-) case, CP2PR, and is
calculated by:
/ -1 y~1
= CP2PR + "
(CSE~CSEL)
(11.70)
133
-------
Section 11 - Effect of Alcohol on Phase Behavior
Then Cp32 is calculated using Eq. 1 1.45 but as a function of CP12 instead of C
P32
and
Cp22 - 1
Now let
, ,
h' =
+ 4ACp12(l-CP12)
- CP32
ECP11
Then
CP11 =
h'2+Ah'+A
CP31 =h'CP11
Cp2i = 1 -CP11 -CP31
where
a _ CP3M
CP1M
-\/
CP3M +CP1M
PCPIP
and Cp2p are calculated using Eqs. 11.79-11.81 andEqs. 11.47-11.48.
(11.71)
(11.72)
(11.73)
(11.74)
(11.75)
(11.76)
(11.77)
(11.78)
(11.79)
(11.80)
(11.81)
(11.82)
When three phases exist, the water and oil pseudocomponents are assumed to contain no surfactant
pseudocomponent. This assumption is a consequence of the choice of phase behavior in the three phase
region which assumes that the two phase region below the three phase tie triangle is very small; therefore, any
composition in the three phase region will have three phases comprising of the surfactant-rich pseudophase
with the composition of the invariant point, water-rich pseudophase with the composition of the water
134
-------
Section 11 - Effect of Alcohol on Phase Behavior
pseudocomponent apex, and oil-rich pseudophase with the composition of the oil pseudocomponent apex.
Therefore:
CP11 =CP22=: 1
CP21 = CP31 = CP12 = CP32 =
(11.83)
(11.84)
The composition of the third phase, CP13, CP23, and CP33, is calculated using Eqs. 11.55-11.57. Phase
concentrations in the single phase region are the same as the overall composition, CP13 = CP1, CP23 = CP2,
CP33 = CP3. The other phase concentrations are zero.
The distribution of the three pseudocomponents in the two or three pseudophases for Type III phase behavior
are summarized below:
11.4.3 For Type III Phase Behavior, CSEL
-------
Section 11 - Effect of Alcohol on Phase Behavior
6. If the total composition is in Type IIM lobe of Type HI:
• Calculate CKPR from Eq. 11.70.
• Calculate a and P from Eqs. 11.77-11.78.
• Calculate CP3PR and CP1PR from Eqs. 11.47-11.48 using CP2PR.
• Calculate parameter E from Eq. 11.82.
** Using a value of CP12 from 0 to CP1PR, calculate CP32 and CP22 using Eqs. 11.71-11.72.
• Calculate CP31 and CP11 from Eqs. 11.79-11.80.
• Calculate h1 from Eq. 11.73.
• Calculate CP11, CP3 j, and CP2 L using Eqs. 11.74-11.76.
• If (CP32 - CP3) (CP23 - CP2) - (CP33 - CP3) (CP22 - CP2) < e , where e is a sufficiently small
number (10~4), then stop; otherwise increment CP12 using the half interval method and go back to
step **.
After the phase composition in the pseudoternary diagram and saturations are determined, the phase
concentrations are converted back to the pseudoquaternary diagram using Eqs. 11.21-11.23. Phase
compositions are calculated in Subroutine PHCOMP.
136
-------
Section 11 - Effect of Alcohol on Phase Behavior
water
Surfactant
oil
Surfactant
water
a) Type E(-)
b)TypeII(+)
Surfactant
invariant point
water
oil
two-phase
c) Type m
Figure 11.1. Schematic representations of a) Type ll(-), b) Type ll(+), and c) Type III.
137
-------
Section 11 - Effect of Alcohol on Phase Behavior
o
CD
Slope = HBNS70
Slope = HBNS71
O
CO
I
c
Slope = HBNS72
Figure 11.2. Effect of alcohol on the maximum height of binodal curve.
'1
Figure 11.3. Coordinate transformation for Type III.
138
-------
Section 12
Organic Dissolution Model in UTCHEM
12.1 Introduction
Both equilibrium and rate limited nonequilibrium solubility of organic component in the aqueous phase are
modeled in UTCHEM. The rate limited mass transfer equations are used for the enhance solubility of oil in
the presence of surfactant. The current implementation in UTCHEM is for under optimum Type II(-)
surfactant formulation. However, it can be applied to the Type El phase environment. This section discusses
the formulation and the method of solution for the case of single component oil phase. The formulation of the
multiple organic oleic phase is given in Section 7.
12.2 Saturated Zone (Gas Phase Is Not Present)
The overall component concentrations for water (K = 1), oil (K = 2), and surfactant (K = 3) in two-phase flow
of water/oil or microemulsion/oil from the conservation equations are
GI =C11S1+C12S2
where phase 2 refers to the oil phase and phase 1 in this section refers to either water or surfactant rich
microemulsion phase.
The overall concentrations for oil, water, and surfactant are obtained solving the conservation equations as
below
forK= 1,2,3
(12.2)
where the flux term is the sum of the convective and dispersive fluxes as
f or K = 1 or 2
(12.3)
The definitions of the dispersion tensor and the flux are given in Section 2. The nonequilibrium concentration
of oil in the aqueous phase is computed from the mass balance on oil species in the aqueous phase and using
the first order mass transfer rate equation for oil dissolution as
139
-------
Section 12 - Organic Dissolution Model in UTCHEM
£ _
-F21 =
(12.4)
where C2| is the known limit of solubility for oil in the aqueous phase. In the absence of the surfactant, the
C2^ is the limit of solubility for the specific organic contaminant and when surfactant is present the
equilibrium solubility is calculated from the Hand's equations (Section 2). M is the mass transfer coefficient
for the dissolution of organic species in the water phase and is assumed to be a constant. Equation 12.4 is
solved either explicitly or implicitly as described below.
12.2.1 Organic Solubility
12.2.1.1 Explicit Solution
The new time level, (n+1), concentration of oil solubilized in water is
(12.5)
+ (Q21 - V • F21 )At + MAtl C|] - C21) for
where the right-hand side of the equation is a known quantity. Therefore,
= (sic21;
4>
(12.6)
since the porosity is known either as a constant or is calculated based on the new time step pressure if rock
compressibility is not negligible.
12.2.1.2 Implicit Solution
= (4)S1C21)n +(Q21 -V-F21)At + MAt(cg -C^1) (12.7)
where we define RHS = ((j)S1C21)n + (Q21 - V • F21)At + MAtfc^ - Cgi
Substituting for Sf+1 from overall concentration for oil component (Eq. 12. Ib) and noting that €22 = 1 for
the flow conditions of oil/water and the Type H(-) with corner plait point and the sum of the saturations is
equal to one (Si + S2 = 1), we have
c-i
= RHS
(12.8)
The above equation can then be rearranged in terms of oil concentration in the aqueous phase (C2i) as
M At C21 + bterm C21 + cterm = 0 (12.9)
where
bterm = (j>C2 -
-------
Section 12 - Organic Dissolution Model in UTCHEM
2cterm
for bterm < 0
-4MAt(cterm)
2cterm
(12.12)
-bterm - -(bterm)2 - 4M At(cterm)
for bterm > 0
12.2.2 Phase Saturations
12.2.2.1 Oil/Water Phases (No Surfactant)
Substituting Cu = 0.0 and C22= 1-0, Eqs. 12. la and 12. Ib become
cl = cllsl
C2 = C21 Sl + S2
The equilibrium saturations and concentrations are computed first as
_ C2 -min(C2,Kow)
2 ~ l-min(C2,Kow)
(12.13)
(12.14)
(12.15)
i ^
where KQW is the limit of solubility of oil in water at equilibrium in the absence of surfactant or cosolvent and
is an input parameter. The minimum in Eq. 12.14 is taken to ensure that the input solubility is not greater
than the total oil available in a gridblock.
The nonequilibrium phase saturations and concentrations are computed as described below once the
equilibrium organic concentration is solved for from Eq. 12.4.
12.2.2.1.1 Explicit Method
Since the product of water saturation times the oil concentration is known using the explicit solution (Eq.
12.6), the new time step oil saturation from Eq. 12. Ib is
and Si= 1-S2
(12.16)
The overall oil concentration (C2) is computed from the oil material balance equation. The phase
compositions are then as follows
r — 1
Ml ~ 7T
C21 -
C22 = 1.
\n+l
(12.17)
If the calculated nonequilibrium concentration is greater than the equilibrium value (C2i >C2^), the
saturations are then set to the equilibrium values calculated from Eqs. 12.14 and 12.15.
141
-------
Section 12 - Organic Dissolution Model in UTCHEM
12.2.2.1.2 Implicit Method
From the implicit solution of the mass balance equation for oil component in the aqueous phase, we could
obtain the nonequilibrium organic dissolution in the aqueous phase (Eq. 12.12). The phase saturations and
phase compositions are then calculated as
(12.18)
Si =
i /-.noneq
$2=1-8!
and
C12=0.0
C22=1.0
12.2.2.2 Oil/Aqueous Phases (Surfactant Below CMC)
The phase concentrations and saturations are calculated as above and surfactant concentration is
(12.19)
C3l =
(12.20)
12.2.2.3 Oil /Microemulsion Phases ( Type II (-) With Corner Plait Point)
For the case of corner plait point we have
C22 = 1.0,
and C32 = 0.0
and the equilibrium concentrations of surfactant, oil, and water in microemulsion phase [C^ , C^ , C^ j are
calculated from Hand's equations described in Section 2. Substituting these in the overall component
concentrations, we have
G! = CnSi
^t ^™t o
C3 -C31S!
The equilibrium saturations are then computed as
(12.21)
(12.22)
The nonequilibrium concentration of oil (€21 for the implicit solution or SiC2i for the explicit solution) is
computed from Eq. 12.4 using an explicit or implicit method. The following section gives the phase
saturations and phase compositions for both the implicit and explicit solutions of the organic mass balance
equation.
142
-------
Section 12 - Organic Dissolution Model in UTCHEM
12.2.2.3.1 Explicit Solution
The phase saturations are computed using the overall oil concentration and the product of microemulsion
saturation times organic concentration in the microemulsion phase from Eq. 12.12.
n 4-1
S/~1 //"i C1 \*lTl
9 = L^o — 1^91^1 ;
^F ^1 \ Zx 1 JL /
Si = 1.-S2
The phase compositions are then computed as
(12.23)
cn=7T
, \n+O
>l)
~C21
(12.24)
C31 =1--
C22=1.0
C12 = 0.0
C32=0.0
If the calculated nonequilibrium concentration is greater than the equilibrium value (C2i> C|^ ), the saturations
are then set to the equilibrium values.
12.2.2.3.2 Implicit Method
From the implicit solution of mass balance equation for oil component in the microemulsion phase, we could
obtain the nonequilibrium organic dissolution (Eq. 12.12). The phase saturations and phase compositions are
calculated as
(12.25)
Si=l-S2
and
r _
L.I i =
Si
C31 =1-C11-C21
C12 = 0.0, C22 = 1.0, C32 = 0.0
(12.26)
12.3 Vadose Zone
The solubility of organic species in three-phase flow of water/oil/gas in the vadose zone in the absence of
surfactant is modeled in UTCHEM. Similar to the previous section, the overall concentrations for oil, water,
and gas are obtained solving the conservation equations.
143
-------
Section 12 - Organic Dissolution Model in UTCHEM
forK=l,2,8
(12.27)
The nonequilibrium concentration of oil in the aqueous phase is calculated from the mass balance on oil
species in the aqueous phase and using the first order mass transfer equation for oil solubility as
_
-F21 =
where the flux term is defined as
-VC
21
(12.28)
(12.29)
Equation 12.29 is solved explicitly to obtain the rate-limited solubility of contaminant in the aqueous phase in
the vadose zone. The new time level, (n+1), concentration of oil solubilized in water is
(12.30)
= (C^), the saturations
and phase concentrations are set back to those at the equilibrium.
12.4 Nomenclature
Q,K = Total concentration of species K in gridblock i, L3/L3 PV
144
-------
Section 12 - Organic Dissolution Model in UTCHEM
CK =
Ceq
K =
K =
Overall concentration of species K in the mobile phases, L3/L3
Equilibrium concentration of species K, L3/L3
Concentration of species K in phase I, L3/L3
Dispersion coefficient, L2H
Tr
J^'Kf - Dispersion tensor for species K in phase £, L2
M = Mass transfer coefficient, t'1
QK = Source/sink for species K, L3/T
S^ = Saturation of phase £, L3/L3 PV
t = Time, t
Atn, Atn+1 = Time-step size at nth and ri+lth time level, t
u^ = Darcy flux, Lf1
Greek Symbols
-------
Appendix A
UTCHEM 6.1 User's Guide
A.1 INTRODUCTION
UTCHEM is a three-dimensional chemical flooding simulator. The solution scheme is
analogous to IMPES, where pressure is solved for implicitly, but concentrations rather than
saturations are then solved for explicitly. Phase saturations and concentrations are then solved in a
flash routine. An energy balance equation is solved explicitly for reservoir temperature. The energy
balance equation includes heat flow between the reservoir and the over- and underburden rocks. The
major physical phenomena modeled in the simulator are:
dispersion
diffusion
dilution effects
adsorption for oil, surfactant and polymer
interfacial tension
relative permeability
capillary pressure
hysteresis in relative permeability and
capillary pressure
capillary trapping
cation exchange
phase density
compositional phase viscosity
phase behavior (pseudoquaternary)
aqueous reactions
partitioning of chemical species between
oil and water
dissolution/precipitation
cation exchange reactions involving more
than two cations
in-situ generation of surfactant from acidic
crude oil
pH dependent surfactant adsorption
organic biodegradation capability
multiple organic species
equilibrium and nonequilibrium organic
dissolution in aqueous phase
dual porosity option for simple phase
tracer flow
polymer properties: shear thinning
viscosity, inaccessible pore volume,
permeability reduction, adsorption
gel properties: viscosity, permeability
reduction, adsorption
tracer properties: partitioning, adsorption,
radioactive decay, reaction (ester
hydrolization), dead-end pore
(capacitance)
temperature dependent properties:
viscosity, tracer reaction, gel reactions,
Surfactant phase behavior
gas mobility reduction due to foam
See Section 2 of this report for the general formulation of the simulator.
146
-------
Appendix A - UTCHEM 6.1 User's Guide
A.2 OPERATION OF THE SIMULATOR
The UTCHEM simulator is ran on a CRAY J90 at the Texas Advanced Computing Center
affiliated with The University of Texas at Austin (UNICOS operating system), a number of DEC
Alpha systems (DEC 4000/610, 3000/500 & 3000/300X) at the Department of Petroleum and
Geosystems Engineering (OSF/1 operating system), and a DEC Alpha system (DEC 3000/500) at
the Department of Petroleum and Geosystems Engineering (OpenVMS operating system), a number
of IBM RS6000 workstations, and a WINDOWS-based PC workstation. The same code is executed
on all systems, except for the use of double precision (64-bit words) on the DEC, RS6000 and PC
machines—we differentiate between "Cray" and "double precision" versions of the code by adding a
"V" prior to the version number for the "Cray" version and a "D" prior to the version number for the
"double-precision". Several intrinsic Cray functions need to be implemented when not running on the
Cray; these routines are "commented" out in the "Cray" version. Please check the source code for
additional information about necessary changes when running on different computers.
2.1 Input and Output Files
UTCHEM requires one input file for non-restart runs. The program expects this file to be
named INPUT. For restart runs, a restart file (named INPUT2) is required in addition to the original
input data file used for the previous ran. A detailed input data description is given in Section A.3 of
this appendix and the data in the restart data file is documented in Section 4.3 of this appendix. A
number of UTCHEM input example files demonstrating a variety of petroleum oil-field and
groundwater applications are available to UTCHEM users. The oil-field applications include water,
single-well tracer, interwell tracer, polymer, profile control using gel, surfactant/polymer, and high pH
alkaline/surfactant/polymer flooding. The groundwater applications include contaminant infiltration,
water flushing, partitioning interwell tracer, surfactant enhanced aquifer remediation, and
bioremediation.
We provide all users with two sample input files for testing purposes (see distribution disks
for copies of the files). The first sample input file (exOl) is for a 3D surfactant/polymer flood. In that
file, the surfactant properties are for petroleum sulfonate and the polymer properties are based on the
typical data for xanthan gum. CPU usage for the EX01 example run is about 10 minutes on a DEC
Alpha 4000/610 and about 153 seconds on a CRAY J90. The second sample input file (EX21) is for
a 2-D contamination event in the saturated zone of an aquifer. CPU usage for the EX21 example ran
is about 264 seconds on a DEC Alpha 4000/610 and about 52 seconds on a CRAY J90. If you
would like to receive additional sample input files, please contact Joanna L. Castillo
(joanna@mail.utexas.edu or 512-471-3229) for details.
The number of output files generated by UTCHEM varies depending upon several control
flags set by the user in the input file. The number of history plot files depends on the value of the
MXW parameter in the PARAM. INC source file. The FORTRAN unit number for the history plot
file is incremented by one for each well. For example, if MXW is equal to three, then three history
plot files would be generated corresponding to FORTRAN unit numbers 19, 20, and 21 even if the
ran only has two wells. The input and output files are summarized in the following table.
Unit Number
1
2
3
4
5
6
7
File Name
TEMPL
ECHO
MESH
PROFIL
INPUT
TTABLE
RESTAR
Contents
Analytical temp, profile, created if IENG=1 and IANAL=1
Echo print of the input file information
Number of gridblocks and distances to center of gridblocks in each
direction.
Formatted profile data; described in Section A.4 of this appendix
Input data; described in detail in Section A.3 of this appendix
Table of time steps and Courant numbers
Stored restart ran data; described in Section A.4 of this appendix
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8
9
10
11
12
13
14
15
16
17
18
19
20
• • •
i
£+1
1+2
• » •
n
CONCP
OVERAL
GFILEP
PRESP
SATP
TRACP
CAPP
ALKP
INPUT2
WARN
TEMPP
HIST01
HIST02
HIST£
TRAC01
TRAC02
TRACn
Component concentration profile plotting data, created if IPCTOT>0
History of overall properties; described in Section A.4 of this
appendix
Gel property profile plotting data, created if IREACT=1
Phase pressure profile plotting data, created if IPPRES>0
Phase saturation profile plotting data, created if IPSAT>0
Phase tracer concentration profile plotting data, created if IPTRAOO
Capacitance property profile or dual porosity plotting data, created if
IPCAP>1
Alkaline option related profile plotting data, created if IREACIM
Restart run data (input file created by an earlier run)
Warning messages
Temperature profile, created if IENG=1 and IPTEMP=1
Well history plotting data for well #1; described in Section A.4 of this
appendix
Well history plotting data for well #2
Well history plotting data for last well
Aqueous (or gas) phase tracer concentration for the 1st tracer at
observation points, created if IPOBS>0; described in Section A.4 of
this appendix
Aqueous (or gas) phase tracer concentration for 2nd tracer at
observation points
Aqueous (or gas) phase tracer concentration for the last tracer at
observation points
2.2 Source Code Array Dimensions
The parameters in the table below are used by the simulator to define array sizes. All
parameter values must be equal to or greater than the size of the grid dimensions specified in the input
file, unless otherwise noted. All parameters used in UTCHEM are defined in the PARAM. INC source
file. This file should be edited before compilation and linking of the source code to define the
maximum global discretization size. Example PARAM. INC source file:
PARAMETER (NNX=96,NNY=9 6,NNZ=2,MXC=11,MXP=3)
PARAMETER (MXW=2,MXWB=2,MXNT=3,MXMO=1)
PARAMETER (MXELE=1,MXFLD=1,MXSLD=1,MXSORB=1,MXACAT=1,MXEX=1)
PARAMETER (MHM=1,MVM=1)
PARAMETER (MAXBIO=9,MAXBS=9 ,MAXMET=4)
The following table contains definitions of the parameter variables used in the PARAM. INC
file.
Parameter Definition
NNX
Number of gridblocks in X-direction (must be set equal or larger to NX in the input
file)
NNY
Number of gridblocks in Y-direction (must be set equal or larger to NY in the input
file)
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NNZ
MXC
MXP
MXW
MXWB
MXNT
MXELE
MXFLD
MXSLD
MXSORB
MXACAT
MXEX
MVH
MHM
MAXBIO
MAXMET
MAXBS
MXMO
Number of gridblocks in Z-direction (must be set equal or larger to NZ in the input
file)
Maximum number of components (cannot be less than 8)
Number of phases (must be set equal to 3 when there is no gas phase and must be set
equal to 4 if gas is present)
Maximum number of wells
Maximum number of well blocks
Maximum number of tracers (check if NT>0)
Maximum number of elements (check for IREACT>1)
Maximum number of reactive fluid species (check for IREACIM)
Maximum number of solids (check for IREACT>1)
Maximum number of adsorbed species (check for IREACT>1)
Maximum number of cations associated with surfactant (check for IREACT>1)
Maximum number of insoluble exchangers (check for IREACT>1)
Maximum number of subgrids in vertical direction (check for ICAP=2)
Maximum number of subgrids in lateral direction (check for ICAP=2)
Maximum number of chemical and biological species participating in biodegradation
reactions
Maximum number of metabolic combinations of substrate, electron acceptor, and
biological species
Maximum number of biological species (check for H3IO=1)
Maximum number of organic components (check for NO>1)
2.3 Compilation and Execution on Workstations
The UTCHEM distribution package for workstations contains the following files:
Makefile-alpha, PARAM. INC, UTCHEMD6P1. for, ddriv2 . f, DPUTIL. for, exOl .data,
and ex21. data. Make sure you place all seven files in the same directory on your workstation.
Then, follow these steps:
1. Split the UTCHEMD6P1. f or and DPUTIL. for files using the UNIX "f split"
command.
2. To build an executable file called utchem. exe, issue the command:
make -f Makefile-alpha
Note that the example makefile included on the distribution disks assumes the use of
the f 77 FORTRAN compiler. You will need to modify the Makefile-alpha file
if you wish to use another compiler (xlf on IBM RS6000 workstations, for example).
3. Run UTCHEM in the background using a command file (in the example below, the
file is called work. j ob). Note that the work. j ob file needs to be executable. Use
any text editor to create your job file and then issue the command:
chmod +x work.job
at the UNIX prompt to make sure the work. j ob file is executable. Then, submit the
job file by issuing the following command:
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2.4
work.j ob &
at the UNIX prompt. Example work. j ob file:
rm -r exOl.dir
mkdir exOl.dir
cd EXOl.dir
In -s ../exOl.data INPUT
time ../utchem.exe
mv TTABLE exOl.ttable
mv ECHO exOl.echo
mv MESH exOl.mesh
mv PROFIL exOl.prof
mv CONCP exOl.con
mv PRESP exOl.presp
#mv ALKP exOl.alkp
mv SATP exOl.satp
mv GFILEP exOl.gel
mv TEMPP exOl.temp
mv HIST01 exOl.histOl
mv HIST02 ex01.hist02
mv HIST03 ex01.hist03
mv HIST04 ex01.hist04
#mv HIST05 ex01.hist05
#mv HIST06 exOl.histOS
#mv HIST07 ex01.hist07
mv OVERAL exOl.overal
mv RESTAR exOl.rest
mv WARN exOl.warn
The work. j ob file needs to be modified to reflect the directory structure you create
for running UTCHEM jobs as well as the names you wish to use for input and output
files. See Section A.9 of this appendix for a description of the contents of the
work. j ob file.
Compilation and Execution on the CRAY J90
The UTCHEM distribution package for the Cray contains the following files: Makef ile-
cray, PARAM. INC, UTCHEMV6P1. for, SDRIV2 . f, exOl .data, and ex21 .data. Make sure
you place all six files in the same directory on your Cray account. Then, follow these steps:
1. Split the UTCHEMV6P1. for file using the UNIX "f split" command.
2. To build an executable file called utchem. exe, issue the command:
make -f Makefile-Cray
3. Submit your job request to the Cray. A sample job file follows:
workdir="/insert_path/utchem/"
workdirl="/insert_path/'utchem/exO1"
set -xS
cd $TMPDIR
ja jacct$$
rep $workdir/exOl.data INPUT
#rcp $workdirl/exOl.rest INPUT2
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rep $workdir/utchem.exe a.out
a. out
rep TTABLE
rep ECHO
rep MESH
rep PROFIL
rep SATP
rep TEMPP
rep PRESP
rep CONCP
#rcp ALKP
rep GFILEP
rep HIST01
rep HIST02
rep HIST03
rep HIST04
rep OVERAL
rep RESTAR
rep WARN
$workdirl/ex01.ttable
$workdirl/ex01.echo
$workdirl/ex01.mesh
$workdirl/ex01.prof
$workdirl/ex01.satp
$workdirl/ex01.temp
$workdirl/ex01.presp
$workdirl/ex01.concp
$workdirl/ex01.alkp
$workdirl/ex01.gel
$workdirl/ex01.hisl
$workdirl/ex01.his2
$workdirl/ex01.his3
$workdirl/exO1.hi s 4
$workdirl/ex01.overal
$workdir1/exO1.res t
$workdirl/ex01.warn
This job file assumes the code and input file reside in a directory called "utchem" and
that the output files will be placed in the "exO 1" directory which is one level below the
"utchem" directory. Replace insert_path with the actual path to the "utchem"
directory.
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A.3 INPUT DATA DESCRIPTION
The UTCHEM input file consists of comment lines and data lines. All comment lines are
ignored by the UTCHEM simulator. It is important to note, however, that the number of comment
lines between data lines is fixed. The first twenty-two lines of the input file are reserved for comment
lines used to briefly describe the input file. Each data line is preceded by three comment lines (except
for the input described in Section 3.5 of this appendix). The input file is basically divided into seven
sections and each of those input sections (except Section 3.5) is preceded by an additional seven
comment lines. The user should update the comment lines as the input file is modified in order to
make using the simulator easier.
All data is free-formatted. This means that for each read statement, it is only necessary to
leave a blank space between data elements. Note that the first data element for a given read statement
must be on a new line in the input file. Subsequent data elements for that read statement can span as
many lines as necessary. Implicit type matching is used; that is, all REAL variables begin with the
letters A-H or O-Z and all integer variables begin with the letters I-N.
The following is a list of variables as they are read by UTCHEM. The variable names appear
in all-caps on a single line in the order they are read by the program (variables that are new to the latest
version of UTCHEM are printed in italicized boldface as well). Every list of variables is followed by
a description of each variable and corresponding units or possible values if applicable. All of the
variables listed in the input description will be read by the program unless otherwise noted: therefore, a
dummy value will be read by the program for variables not pertinent to the problem being run.
3.1. Title and Reservoir Description Data
The first input section consists of the title and reservoir description data. Please remember that
there are 22 comment lines at the beginning of this section and that each data line is preceded by three
comment lines.
3.1.1 RUNNO
RUNNO - Run number.
Note: The run number can consist of any combination of alphanumeric characters on a single
line (not to exceed 80 characters). This information will be printed as the first line of
every output file.
3.1.2 TITLE
TITLE - Title and run description.
Note: The title can consist of any combination of alphanumeric characters spanning three
lines in the input file (not to exceed 80 characters per line). The tide must span three
lines and any of those lines can be blank.
3.1.3 IMODE, IMES, IDISPC, ICWM, ICAP, IREACT, IBIO, ICOORD, ITREAC, ITC, IGAS, IENG
IMODE - Flag indicating if the problem to be run is a first run or a restart simulation.
Possible Values:
1 - First simulation run
2 - Restart simulation
Note: See Section A.4 of this appendix for more details on how to run restart simulations.
IMES - Flag indicating if a constant or automatic time-step is to be used.
Possible Values:
1 - Constant time-step size is used
2 - Automatic time-step size selector based on method of relative changes for the first
three components is used
3 - Automatic time-step size selector based on method of relative changes for all the
components is used
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4 - Automatic time-step size selector based on changes in dimensionless concentration
for all the components is used
Note: The automatic time-step selector is recommended. See input lines 3.7.9 through 3.7.13
and Section A.8 of this appendix for more details on the above options.
IDISPC - Flag indicating which type of numerical dispersion control is used.
Possible Values:
0 - Single point upstream method is used
2 - Two point upstream method is used
3 - Improved total variation diminishing third order method is used
Note: These methods are applied to both concentration and relative permeability.
ICWM - Flag indicating if the concentration well model is used or not.
Possible Values:
0 - Concentration well model is not used
1 - Concentration well model is used
Note: The concentration well model (ICWM=1) can only be used with vertical wells
!(IDIR(M)=3).
ICAP - Flag indicating if the capacitance model is used or not.
Possible Values:
0 - Capacitance model or dual porosity option is not used
1 - Capacitance model is used
2 - Dual porosity option is used for single phase tracer flow
Note: The dual porosity option (ICAP=2) is available only if IMODE=1, IUNIT=0, and
ICOORD=1.
IREACT - Flag indicating if gel reactions or alkaline options are used or not.
Possible Values:
0 - Gel reactions are not used
1 - Gel reactions are used
2 - Geochemistry option with no acidic crude is used
3 - Geochemistry option with acidic crude is used
4 - IREACT=2 and gel reactions are used
IBIO - Flag indicating whether or not biodegradation reactions occur
Possible Values:
0 - No biodegradation reactions
1 - Biodegradation reactions occur
ICOORD - Flag indicating which coordinate system is used.
Possible Values:
1 - Cartesian coordinate system is used
2 - Radial coordinate system is used
3 - Cartesian coordinate system with variable-width gridblock is used (2-D cross
section only)
4 - Curvilinear grid definition of the X-Z cross section is used (2-D or 3-D)
Note: For ICOORD=4, the 3-D grid consists of the 2-D cross sectional grid repeated at
specified intervals (uniform or non-uniform) in the Y direction, according to the definition of
DY1. The curvilinear grid option is not available with the temperature equation option.
ITREAC - Flag indicating if a tracer reaction is used or not.
Possible Values:
0 - Tracer reactions are not used
1 - Tracer reactions are used
ITC - Flag indicating if second-order time approximation is used or not.
Possible Values:
0 - Second-order time approximation is not used
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1 - Second-order time approximation is used
Note: We recommend that second-order time approximation (ITC=1) only be used with
higher-order dispersion methods (IDISPCM),
IGAS - Flag indicating if gas phase is considered or not.
Possible Values:
0 - Gas is not present
1 - Gas is present
2 - Gas is present and foam option is used
IENG - Flag indicating if temperature variation is considered or not.
Possible Values:
0 - Isothermal simulation
1 - Temperature equation is solved
3,1.4 NX, NY, NZ, IDXYZ, IUNIT
NX - Number of gridblocks along X-axis (ICOORD=1, 3, or 4) or number of gridblocks in radial
direction (ICOORD=2).
Note; This value should be equal to or smaller than the NNX parameter in UTCHEM.
NY - Number of gridblocks along Y-axis.
Note: This value should be equal to or smaller than the NNY parameter in UTCHEM. It
should be set equal to 1 if the user is running a 1-D problem or a 2-D cross sectional problem.
If ICOORD=2, this value is automatically set equal to 1.
NZ - Number of gridblocks along Z-axis.
Note: This value should be equal to or smaller than the NNZ parameter in UTCHEM. It
should be set equal to 1 if the user is running a 1-D problem or a 2-D area! problem.
IDXYZ - Flag indicating constant or variable grid size.
Possible Values:
0 - Constant grid size
1 - Variable grid size on a regional basis
2 - Variable grid size
Note: IDXYZ must be set equal to 2 if ICOORD-3.
IUNIT - Flag indicating English or Metric units.
Possible Values:
0 - English unit
1 - Metric unit
Note: UTCHEM must be compiled and run with the NX, NY, and NZ input values being equal to
or smaller than the NNX, NNY, and NNZ parameters in the code. All parameters used in
UTCHEM are defined in the PARAM. INC source file."
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Appendix A - UTCHEM 6.1 User's Guide
Simulation Gridbiock Sizes (Lines 3.1.5-3.1.23)
Refer to the following flowchart to help determine which input lines should be used to specify the gridblock
size input values for different options:
ICOORD
1 IDXYZ
2 IDXYZ
3 IDXYZ
31 e
fv
\S
1
IV
f
2 ,.
0
IV
I?
1
2
r».
L?
2 D
l?
0 ,s
IDXYZ H
1 IV
l>
2
3.1.6
3.1.9,3.1.10,3.1
.11
3.1.16,3.1.17,3.
1.19
3.1.7
3.1.12,3.1.13,3.
1.14
3.1.20,3.1.21,3.
1.22
3.1.9,3.1.10,3.1
.11
3.1.16,3.1.18,3.
1.19
3.1.8
3.1. 15
3.1. 17
3.1.5 XCORD(I), ZCORD(I), for 1=1, (NX+l)x(NZ+l) (This line is read only if ICOORD=4)
XCORD - Gridblock coordinate of Ith corner point in X-direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
ZCOORD - Gridblock coordinate of Ith corner point in Z-direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
Note: The coordinates of the corners (or vertices) of the 2-D X-Z cross section gridblocks are input
in pairs as follows:
XCORD(l), ZCORD(l)
XCORD(nodes), ZCORD(nodes)
where nodes = (NX+1) x (NZ+1) and is the total number of corner points defining the X-Z
cross section and Z is positive downward. The following figure illustrates the input order for
an example X-Z cross section grid:
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Appendix A - UTCHEM 6.1 User's Guide
Top (surface) of reservoir
XCORD(l), ZCORD(l) XCORD(2), ZCORD(2)
1 2
3.1.6
3.1.7
3.1.8
3.1.9
XCORD(9), ZCORD(9)
The number of gridblocks is equal to NX x NZ and the number of coordinate pairs (or nodes)
is equal to (NX+1) x (NZ+1).
Cautionary warning: The X-Z cross section grid should be constructed by the user such that
the curvilinear coordinate system is at least quasi-orthogonal. Departure from
orthogonality will lead to numerical errors in the solution.
DX1, DY1, DZ1 (This line is read only if IDXYZ=0 and ICOORD=1 or 3)
DX1 - Gridblock size in X direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
DY1 - Gridblock size in Y direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
DZ1 - Gridblock size in Z direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
R(l), DX1, DZ1 (This line is read only if IDXYZ=0 and ICOORD=2)
R(l) - Wellbore radius.
Units: feet (IUNIT=0) or m (IUNIT=1)
DX1 - Distance between nodes in radial direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
DZ1 - Gridblock size in Z direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
DY1 (This line is read only if IDXYZ=0 and ICOORD=4)
DY1 - Gridblock size in Y direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
III, H2, DX1 (This line is read only if IDXYZ=1 and ICOORD=1 or 3)
III - First index for gridblocks with same size in X direction.
112 - Last index for gridblocks with same size in X direction.
DX1 - Gridblock size in X direction
Units: feet (IUNIT=0) or m (IUNIT=1)
Note: This line is repeated until sizes for each of the NX gridblocks in the X direction have been
specified. The first line in the set must have 111=1 and the last line must have II2=NX.
Example: If NX=11 and the first three gridblocks in the X direction are 3 feet in size, the fourth
through ninth gridblocks in the X direction are 2 feet in size, and the last two gridblocks in the
X direction are 2.5 feet in size, this line would need to be repeated three times to fully describe
the X direction gridblocks as follows:
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Appendix A - UTCHEM 6.1 User's Guide
1
4
10
3
9
11
3.0
2.0
2.5
3.1.10 JJ1, JJ2, DY1 (This line is read only if IDXYZ=1 and ICOORD=1 or 3)
JJ1 - First index for gridblocks with same size in Y direction.
JJ2 - Last index for gridblocks with same size in Y direction.
DY1 - Gridblock size in Y direction.
Units: feet (IUNIT=0) or m(IUNIT=l)
Note: This line is repeated until sizes for each of the NY gridblocks in the Y direction have been
specified. The first line in the set must have JJ1=1 and the last line must have JJ2=NY. See
the example for input line 3.1.9.
3.1.11 KK1, KK2,DZ1 (This line is readonly if IDXYZ=1 andICOORD=1 or 3)
KK1 - First index for gridblocks with same size in Z direction.
KK2 -;Last index for gridblocks with same size in Z direction.
DZ1 - Gridblock size in Z direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
Note: This line is repeated until sizes for each of the NZ gridblocks in the Z direction have been
specified. The first line in the set must have KK1=1 and the last line must have KK2=NZ.
See the example for input line 3.1.9.
3.1.12 R(l) (This line is read only if ZDXYZ=1 and ICOORD=2)
R(l)-Wellbore radius.
Units: feet (IUNIT=0) or m (IUNIT=1)
3.1.13 HI, 112, DX1 (This line is read only if IDXYZ=1 and ICOORD=2)
III - First index for radial node distances of the same size.
112 - Last index for radial node distances of the same size.
DX1 - Distance between nodes in radial direction.
Units: feet (IUNIT=0) or m(IUNIT=l)
Note: This line is repeated until the NX-1 distances between the NX nodes in the radial direction
have been specified. The first line in the set must have 111=1 and the last line must have
II2=NX-1.
Example: If NX=35 and the first ten gridblocks in the X direction are 1 foot in size and the rest are 2
feet in size, this line would need to be repeated twice to fully describe the radial direction
nodes as follows:
1 10 1.0
11 34 2.0
3. l: 14 KK1, KK2, DZ1 (This line is read only if IDXYZ=1 and ICOORD=2)
KK1 - First index for gridblocks with same size in Z direction.
KK2 - Last index for gridblocks with same size in Z direction.
DZ1 - Gridblock size in Z direction.
Units: feet (IUNIT=0) orm(IUNIT=l)
Note: This line is repeated until sizes for each of the NZ gridblocks in the Z direction have been
specified. The first line in the set must have KK1=1 and the last line must have KK2=NZ.
See the example for input line 3.1.9.
3.1.15 JJ1, JJ2, DY1 (This line is read only if IDXYZ=1 and ICOORD=4)
JJ1 - First index for gridblocks with same size in Y direction.
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JJ2 - Last index for gridblocks with same size in Y direction.
DY1 - Gridblock size in Y direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
Note: This line is repeated until sizes for each of the NY gridblocks in the Y direction have been
specified. The first line in the set must have JJ1=1 and the last line must have JJ2=NY. See
the example for input line 3.1.9.
3.1.16 DX(I), for 1=1, NX (This line is read only if IDXYZ=2 and ICOORD=1 or 3)
DX(I) - Grid size of Ith block in X direction.
Units: feet (IUNTT=0) or m(IUNIT=l)
3.1.17 DY(J), for J=l, NY (This line is read only if IDXYZ=2 and ICOORD=1 or 4)
DY(J) - Grid size of Jth block in Y direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
3.1.18 DY(I), for 1=1, NX (This line is read only if IDXYZ=2 and ICOORD=3)
DY(I) - Thickness of Ith block.
Units: feet (IUNIT=0) or m (IUNIT=1)
3.1.19 DZ(K), for K= 1, NZ (This line is read only if IDXYZ=2 and ICOORD= 1 or 3)
DZ(K) - Grid size of Kth block in Z direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
3.1.20 R(l) (This line is read only ifTDXYZ=2 and ICOORD=2)
R(l) - Wellbore radius.
Units: feet (IUNIT=0) or m(IUNIT=l)
3.1.21 DX(I), for 1=1, NX-1 (This line is read only if IDXYZ=2 and ICOORD=2)
DX(I) - Distance between the Ith node and the 1+1* node in the radial direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
3.1.22 DZ(K), for K=l, NZ (This line is read only if IDXYZ=2 and ICOORD=2)
DZ(K) - Grid size of Kth block in Z direction.
Units: feet (IUNIT=0) or m(IUNIT=l)
3.1.23 N, NO, NTW, NTA, NGC, NG, NOTH
N - Total number of components in the run (including tracers and reactive components).
Value must be set equal to: N=8+NO+NTW+NTA+NGC+NG+NOTH
NO - Total number of NAPL phase organic components in the run.
Note: If IBIO=1, set NO=0 if no NAPL phase is present and all biodegrading species are
present only in the aqueous phase; otherwise, set NO to the number of organic
species.
NTW - Number of water/oil tracers.
NTA - Number of oil/gas tracers.
NGC - Number of components for geochemistry option.
NG - Number of gel components.
NOTH - Total number of other chemical and biological species that are considered in biodegradation
reactions, including products generated by biodegradation reactions, nutrients required for
biological growth, electron acceptors, and biological species.
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Note: See Section A.7 of this appendix for the component numbering scheme used in UTCHEM
and Section 9 of this report for more details on the microbiological population model options.
3.1.24 SPNAMEQ.), for 1=1, N
SPNAME(I) - Name of Ith species.
Note: The name of each component may not exceed 8 characters and each name must be on
a separate line of the input file.
3.1.25 ITRU(I), for 1=1, NTW (This line is read only if NTW>0 and ITREAC=1)
ITRU(I) - Flag indicating the units of the Ith water tracer.
Possible Values:
1 - Ith tracer units are in volume %
2 - Ith tracer units are in weight %
3.1.26 ICF(KC), for KC=1, N
ICF(KC) - Flag indicating if KG1*1 component is included in the calculations or not.
Possible Values:
0 - The KC* component is not included in the calculations
1 - The KG1*1 component is included in the calculations
Example: If 11 components are considered but Alcohol 2 is not present, this line would appear as
follows:
11111110111
3.2 Output Option Data
The second input section consists of output options. Please remember that there are seven
comment lines at the beginning of this section and that each data line is preceded by three comment
lines.
3.2.1 ICUMTM, ISTOP
ICUMTM - Flag indicating if the output intervals indicated by the CUMPR1, CUMHI1, WRHPV,
WRPRF and RSTC variables on input line 3.7.8 are specified in pore volumes or days.
Possible Values:
0 - Data will be written in day intervals
1 - Data will be written in pore volume intervals
Note: The day interval output option (ICUMTM=0) is particularly useful if there is a shut in
period.
ISTOP - Flag indicating if the maximum and injection times (variables TMAX on input line 3.3.1 and
TINT on input line 3.7.8) are specified in pore volumes or days.
Possible Values:
0 - TMAX and TINT are specified in days
1 - TMAX and TINT are specified in pore volumes
Note: A 3rd variable (ICOPSM) which used to control printing to UNIT 3 is no longer available
with the latest version of UTCHEM.
3.2.2 IPRFLG(KC), for KC=1, N
IPRFLG(KC) - Flag indicating if profile of KCth component should be written to UNIT 8.
Possible Values:
0 - Profile of KCth component will not be written
1 - Profile of KCth component will be written
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Note: If IPCTOT=0, none of the component profiles will be written.
Example: If 11 components are present and only profiles for the oil, surfactant, and polymer
components are desired, this line would appear as follows:
01110000000
3.2.3 IPPRES, IPSAT, IPCTOT, EPTRAC, IPCAP, IPGEL, IPALK, IPTEMP, IPOBS, IBPR
IPPRES - Flag indicating if profile of phase pressures should be written to UNIT 11.
Possible Values:
0 - Profile of phase pressures will not be written
1 - Profile of phase pressures will be written
IPSAT - Flag indicating if profile of phase saturations should be written to UNIT 12.
Possible Values:
0 - Profile of phase saturations will not be written
1 - Profile of phase saturations will be written
IPCTOT - Flag indicating if profile of component concentrations should be written to UNIT 8.
Possible Values:
0 - Profile of component concentrations will not be written
1 - Profile of component concentrations will be written
IPTRAC - Flag indicating if profile of tracer phase concentrations should be written to UNIT 13.
Possible Values:
0 - Profile of tracer phase concentrations will not be written
1 - Profile of tracer phase concentrations will be written
IPCAP - Flag indicating if profile of capacitance properties should be written to UNIT 14.
Possible Values:
0 - Profile of capacitance properties will not be written
1 - Profile of capacitance properties will be written
IPGEL - Flag indicating if profile of gel properties should be written to UNIT 10.
Possible Values:
0 - Profile of gel properties will not be written
1 - Profile of gel properties will be written
IPALK - Flag indicating if profile of properties related to the alkaline option should be written to
UNIT 15.
Possible Values:
0 - Profile of properties related to the alkaline option will not be written
1 - Profile of properties related to the alkaline option will be written
IPTEMP - Flag indicating if profile of reservoir temperature should be written to UNIT 18.
Possible Values:
0 - Profile of temperature will not be written
1 - Profile of temperature will be written
IPOBS - Flag indicating if aqueous phase tracer concentration at observation points should be written
to the TRACxx output files.
Possible Values:
0 - Aqueous phase tracer concentrations at observation points will not be written
1 - Aqueous phase tracer concentrations at observation points will be written
IBPR - Flag indicating if chemical and biological species concentrations in the aqueous phase and
within attached biomass should be written to UNITS 4, 8, and HIST£
Possible Values:
0 - Aqueous and intra-biomass concentrations will not be written
1 - Aqueous and intra-biomass concentrations will be written
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3.2.4 IPHP, IADS, ICKL, IVEL, IVIS, IPER, ICNM, IRKF, IPHSE, ICSE
IPHP - Flag indicating if oleic and microemulsion phase pressure data should be printed.
Possible Values:
0 - Oleic and microemulsion phase pressure data will not be printed
1 - Oleic and microemulsion phase pressure data will be printed
IADS - Flag indicating if surfactant, polymer, calcium, gel, chromium, hydrogen, and sodium
adsorption data should be printed.
Possible Values:
0 - Adsorption data will not be printed
1 - Adsorption data will be printed
ICKL - Flag indicating if component concentration data in each phase should be printed.
Possible Values:
0 - Component concentration data in each phase will not be printed
1 - Component concentration data in each phase will be printed
IVEL - Flag indicating if X, Y, and Z direction phase fluxes should be printed.
Possible Values:
0 - X, Y, and Z direction phase fluxes will not be printed
1 - X, Y, and Z direction phase fluxes will be printed
IVIS - Flag indicating if phase viscosities should be printed.
Possible Values:
0 - Phase viscosities will not be printed
1 - Phase viscosities will be printed
IPER - Flag indicating if relative permeabilities should be printed.
Possible Values:
0 - Relative permeabilities will not be printed
1 - Relative permeabilities will be printed
ICNM - Flag indicating if phase capillary numbers and interfacial tensions should be printed.
Possible Values:
0 - Capillary numbers, residual saturations, and interfacial tensions will not be printed
1 - Capillary numbers, residual saturation, and interfacial tensions will be printed
IRKF - Flag indicating if permeability reduction factors should be printed.
Possible Values:
0 - Permeability reduction factors, polymer viscosities, and equivalent shear rate will
not be printed
1 - Permeability reduction factors, polymer viscosities, and equivalent shear rate will be
printed
IPHSE - Flag indicating if phase environment indexing should be printed.
Possible Values:
0 - Phase environment indexing will not be printed
1 - Phase environment indexing will be printed
Note: The indices for the phase environment are as follows:
1 - single phase
2 - two phase oil/water or oil/microemulsion or water/microemulsion
3 - three phase oil/microemulsion/water
4-loben(+)oftypem
5-loben(-)oftypem
ICSE - Flag indicating if effective salinity should be printed.
Possible Values:
0 - Effective salinity information will not be printed
1 - Effective salinity will be printed to PROFIL and history data files
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Note: These flags give the option of printing a very detailed description (all tags = 1) every
CUMPR1 pore volume interval or a very limited description (all flags =.0) to UNIT 4, See
Section A.4 of this appendix for a list of the values that are written to UNIT 4 automatically.
3.2.5 NOBS (This line is read only if IPOBS=1)
NOBS - Number of tracer concentration observation points.
3.2.6 IOBS(I), JOBS®, KOBS(I), for 1=1, NOBS (This line is read only if IPOBS=1 and NQBS>0)
IOBS(I) - Index of Ith observation point in X direction.
JOBS(I) - Index of Ith observation point in Y direction.
KOBS(I) - Index of Ith observation point in Z direction.
Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in
UTCHEM.
3.3. Reservoir Properties
The third input section consists of the reservoir properties. Please remember that there are
seven comment lines at the beginning of this section and that each data line is preceded by three
comment lines.
3.3.1 TMAX
TMAX - Total injection period (maximum simulation time).
Units: days or pore volumes (dependent on value of ISTOP flag in line 3,2.,1)
3.3.2 COMPR, PSTAND
COMPR - Rock compressibility.
Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)
PSTAND - Reference pressure at which pore volume and fluid compressibilities are specified.
Units: psi (IUNIT=0) or kPa(IUNIT=l)
Reservoir/Aquifer Properties (Lines 3.1.3-3.1.17')
3.3.3 IPOR1, IPERMX, IPERMY, IPERMZ, IMOD
IPOR1 - Flag indicating constant or variable porosity for reservoir.
Possible Values:
0 - Constant porosity for whole reservoir
1 - Constant porosity for each layer
2 - Variable porosity over reservoir
IPERMX - Flag indicating constant or variable X direction permeability (ICOORD=1 or 3) or radial
direction permeability (ICOORD=2) for reservoir.
Possible Values:
0 - Constant permeability for whole reservoir
1 - Constant permeability for each layer in the X direction (ICOORD=1 or 3) or radial
direction (ICOORD=2)
2 - Variable permeability over reservoir
IPERMY - Flag indicating constant or variable Y direction permeability for reservoir.
Possible Values:
0 - Constant permeability for whole reservoir
1 - Constant permeability for each layer in the Y direction
2 - Variable permeability over reservoir
3 - Y direction permeability is dependent on X direction permeability
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IPERMZ - Flag indicating constant or variable Z direction permeability for reservoir.
Possible Values:
0 - Constant permeability for whole reservoir
1 - Constant permeability for each layer in the Z direction
2 - Variable permeability over reservoir
3 - Z direction permeability is dependent on X direction permeability
IMOD - Flag indicating whether the reservoir properties are modified or not.
Possible Values:
0 - No property is modified
1 - Allow for property modification
Refer to the following flowchart to help determine which input lines should be used to specify the porosity
and permeability values for different options:
IPOR1
IPERMX
IPERMY
(only if
ICOORD 9t 2)
IPERMZ
u
1
2
0
1
2
0
1
2
3
0
1
2
3
— I*J T T A
P| o.o.o
P| o.o.u
P| o.o./
P| 3.3.8
P| o.o.y
P| 3.3.10
P| 3.3.11
P| o.o.l<£
Pj O.vJ.U
P| o.o.l 4
P| o.o.lo
P| o.o.lu
PJ O.O.I/
3.3.4 PORC1 (This line is read only if IPOR1=0)
PORC1 - Reservoir porosity.
Units: fraction
Note: All elements of the FOR array will be set equal to PORC1.
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3.3.5 POR(K), for K=1,NZ (This line is read only if IPOR1=1)
POR(K) - Porosity of K^1 layer.
Units: fraction
Note: NZ values are actually read into a workspace array (WKSP1) and then the first set of
NX x NY elements (corresponding to layer 1) of the POR array are set equal to WKSPl(l),
the second set of NX x NY elements (corresponding to layer 2) of the POR array are set equal
toWKSPl(2),ete.
3.3.6 POR(I), for 1=1, NBL (This line is read only if IPOR1=2)
POR(I)-Porosity of Ith gridblock
Units: fraction
Notes:
1) The three-dimensional grid system is being read into a one-dimensional array. The
first index (column) of the three-dimensional system varies fastest, the second index
(row) varies next fastest, and the third index (layer) varies slowest. The total number
of gridblocks, NBL, is NX x NY x NZ.
Example: If you had a 4 x 3 x 2 system (4 columns—NX=4, 3 rows—NY=3, and 2
layers—NZ=2), the values would be read in the following order:
1,1,1 2,1,1 3,1,1 4,1,1
1,2,1 2,2,1 3,2,1 4,2,1
1,3,1 2,3,1 3,3,1 4,3,1
1,1,2 2,1,2 3,1,2 4,1,2
1,2,2 2,2,2 3,2,2 4,2,2
1,3,2 2,3,2 3,3,2 4,3,2
2) The transmissibilities are set to zero for gridblocks with porosity values less than or
equal to 0.01 (ICOORD=1).
3) To specify certain gridblocks as inactive, the user needs to set the porosity for the
inactive cells to a very small number (e.g. 10'6)-
3.3.7 PERMXC (This line is read only if IPERMX=0)
PERMXC - Permeability of the reservoir in the X direction or in the radial direction (ICOORD=2).
Units: millidarcies = 10"3 |0,m2
Note: All elements of the PERMX array will be set equal to PERMXC.
3.3.8 PERMX(K), for K=l, NZ (This line is read only if IPERMX=1)
PERMX(K) - Permeability of the Kth layer in the X direction or in the radial direction (ICOORD=2).
Units: millidarcies = 10"3 um2
Note: See the note for input line 3.3.5.
3.3.9 PERMX(I), for 1=1, NBL (This line is read only if IPERMX=2)
PERMX(I) - Permeability of the Ith gridblock in the X direction or in the radial direction
(ICOORD=2).
Units: millidarcies = 10~3 (im2
Note: See the note and example for input line 3.3.6 for the order of the permeability values.
3.3.10 PERMYC (This line is read only if IPERMY=0 and ICOORD*2)
PERMYC - Permeability of the reservoir in the Y direction.
Units: millidarcies = 10~3 um2
Note: All elements of the PERMY array will be set equal to PERMYC.
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3.3.11 PERMY(K), for K=l, NZ (This line is read only if IPERMY=1 and ICOORD*2)
PERMY(K) - Permeability of the K* layer in the Y direction.
Units: millidarcies = 1O3 |0,m2
Note: See note for input line 3.3.5.
3.3.12 PERMY(I), for 1=1, NBL (This line is read only if IPERMY=2 and ICOORD*2)
PERMY(I) - Permeability of the Ith gridblock.
Units: millidarcies = 10'3 jam2
Note: See the note and example for input line 3.3.6 for the order of the permeability values.
3.3.13 FACTY (This line is read only if IPERMY=3 and ICOORD*2)
FACTY - Constant permeability multiplier for Y direction permeability.
Units: dimensionless
Note: The X direction permeabilities are multiplied by FACTY to obtain the Y direction
permeabilities.
3.3.14 PERMZC (This line is read only if IPERMZ=0)
PERMZC - Permeability of the reservoir in the Z direction.
Units: millidarcies = 10"3 |j,m2
Note: All elements of the PERMZ array will be set equal to PERMZC.
3.3.15 PERMZ(K), for K=l, NZ (This line is read only if IPERMZ=1)
PERMZ(K) - Permeability of the Kth layer in the Z direction.
Units: millidarcies = 10'3 (im2
Note: See note for input line 3.3.5.
3.3.16 PERMZ(I), for 1=1, NBL (This line is read only if IPERMZ=2)
PERMZ(I) - Permeability of the Ith gridblock.
Units: millidarcies (10~3 Jim2)
Note: See the note and example for input line 3.3.6 for the order of the permeability values.
3.3.17 FACTZ (This line is read only if IPERMZ=3)
FACTZ - Constant permeability multiplier for Z direction permeability.
Units: dimensionless
Note: The X direction permeabilities are multiplied by FACTZ to obtain the Z direction
permeabilities.
Initial Reservoir/Aquifer Data (Lines 3.3.18-3.3.36)
3.3.18 IDEPTH, IPRESS, ISWI
IDEPTH - Flag indicating type of depth measurement of the top layer.
Possible Values:
0 - Single value for depth of the top layer is specified
1 - Depth of top gridblock (1,1,1) and the reservoir dip angles are specified
2 - Depth of each gridblock in the top layer is specified
Note: If ICOORD=2, this value is automatically set equal to 0. The depth is specified at the
middle of a gridblock.
IPRESS - Flag indicating type of reservoir initial pressure measurement.
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Possible Values:
0 - Single value for reservoir initial pressure is used for all gridblocks
1 - Initial pressure for a point at a specified depth is specified by user
2 - Initial pressure for each gridblock is specified by user
ISWI - Flag indicating type of initial water saturation measurement.
Possible Values:
0 - Single value for initial water saturation is used for all gridblocks
1 - Constant value for water saturation for each layer is specified by user
2 - Initial water saturation for each gridblock is specified by user
Refer to the following flowchart to help determine which input lines should be used to specify the initial
properties such as depth, pressure, initial water saturations, initial gas saturations when IGAS>1, and initial
organic concentrations when NO>1:
IDEPTH
ISWI
IPRESS
ISGI
(only if
IGAS=1)
u
1 o
2
3.3.29
3.3.30
3.3.31
(only if
NO>1)
3.3.19 Dill (This line is read only if IDEPTH=0)
Dill- Depth of the top layer of the reservoir measured from the surface (reference plane), positive
downward.
Units: feet (IUNIT=0) or m (IUNIT=1)
Note: If IDEPTH=0 and ICOORD=4, Dl 11 is the reference depth of the first gridblock.
3.3.20 Dill, THETAX, THETAY (This line is read only if IDEPTH= 1)
Dill- Depth of the first gridblock (1,1,1).
Units: feet (IUNIT=0) or m (IUNIT=1)
THETAX - Reservoir dip angle in X direction, positive downward.
Units: radians
THETAY - Reservoir dip angle in Y direction, positive downward.
Units: radians
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Note: If ICOORD=4, set THETAY equal to 0 (dip angle in X-Z plane).
3.3.21 EL(I), for 1=1, NX x NY (This line is read only if IDEPTH=2)
EL(I) - Depth of Ith gridblock in the top layer (K=l).
Units: feet (IUNIT=0) or m (IUNIT=1)
Note: See the note and example for input line 3.3.6 for the order of the gridblock depths.
3.3.22 PRESS 1 (This line is read only if IPRESS=0)
PRESS 1 - Initial reservoir pressure.
Units: psi (IUNIT=0) or kPa (IUNIT=1)
3.3.23 PINIT, HINIT (This line is read only if IPRESS=1)
PINIT - Initial reservoir pressure at HINIT depth.
Units: psia (IUNIT=0) or kPa (IUNIT=1)
HINIT - Depth of the point where PINIT initial pressure is specified.
Units: feet (IUNIT=0) or m (IUNIT=1)
Note: Initial pressure is assumed to be the aqueous phase pressure.
3.3.24 P(I), for 1=1, NBL (This line is read only if IPRESS=2)
P(I) - Initial pressure of each gridblock in the reservoir.
Units: psia (IUNIT=0) or kPa(IUNIT=l)
Note: See the note and example for input line 3.3.6 for the order of the initial pressure
values. This is assumed to be the aqueous phase pressure.
3.3.25 SWI (This line is read only if ISWI=0)
SWI - Initial water saturation for all gridblocks of the reservoir.
Units: fraction of pore volume
3.3.26 S(K,1), for K=l, NZ (This line is read only if ISWI=1)
S(K,1) - Initial water saturation for Kth layer.
Units: fraction of pore volume
Note: See the note for input line 3.3.5.
3.3.27 S(I,1), for 1=1, NBL (This line is read only if ISWI=2)
S(I,1) - Initial water saturation for Ith block.
Units: fraction of pore volume
Note: See the note and example for input line 3.3.6 for the order of the initial water
saturation values.
3.3.28 ISGI (This line is read only if IGAS>1)
ISGI - Flag indicating type of initial gas saturation.
Possible Values:
0 - Constant initial gas saturation for whole reservoir
1 - Constant initial gas saturation for each layer
2 - Initial gas saturation for each gridblock is specified by user
3.3.29 SGI (This line is read only if IGAS>1 and ISGI=0)
SGI - Initial gas saturation for all gridblocks of the reservoir.
Units: fraction of pore volume
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3.3.30 S(K,4), for K=l, NZ (This line is read only if IGAS>1 and ISGI=1)
S(K,4) - Initial gas saturation for K* layer.
Units: fraction of pore volume
Note: See the note for input line 3.3.5.
3.3.31 S(I,4), for 1=1, NBL (This line is read only if IGAS>1 and ISGI=2)
S(I,4) - Initial gas saturation for Ith gridblock.
Units: fraction of pore volume
Note: See the note and example for input line 3.3.6 for the order of the initial gas saturation
values.
Initial Organic Concentrations (Lines 3.3.32-3.3.35) — This section is required only if the multiple
organic option is used (NO>1).
3.3.32 ICOI (This line is read only if NO>1)
ICOI - Flag indicating type of initial oil phase compositions.
Possible Values:
0 - Constant initial oil phase concentration for whole reservoir
1 - Constant initial oil phase concentration for each layer
2 - Initial oil phase concentration for each gridblock
3.3.33 COI(KO), for KO=1, NO (This line is read only if NO>1 and ICOI=0)
COI(KO) - Initial oil phase concentration for oil component KO for the reservoir.
Units: volume fraction
3.3.34 COI(K,KO), for K=l, NZ, for KO=1, NO (This line is read only if NO>1 and ICOI=1)
COI(K, KO) - Initial oil phase concentration for oil component KO at Kth layer.
Units: volume fraction
3.3.35 COI(I,KO), for 1=1, NBL, for KO= 1 ,NO (This line is read only if NO> 1 and ICOI=2)
COI(I,KO) - Initial oil phase concentration for oil component KO at Ith gridblock.
Units: volume fraction
Reservoir Property Modification Data (Lines 3.3.36-3.3.46) — This section is required only if
IMOD=1.
3.3.36 IMPOR, IMKX, IMKY, IMKZ, IMSW (This line is read only if IMOD=1)
IMPOR - Flag indicating whether the porosity is modified or not.
Possible Values:
0 - No modification is considered in porosity values
1 - Allow modification in porosity
IMKX- Flag indicating whether the permeability in the X direction is modified or not.
Possible Values:
0 - No modification is considered in X permeability
1 - Allow modification in X permeability
IMKY- Flag indicating whether the permeability in the Y direction is modified or not.
Possible Values:
0 - No modification is considered in Y permeability
1 - Allow modification in Y permeability
IMKZ- Flag indicating whether the permeability in the Z direction is modified or not.
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Possible Values:
0 - No modification is considered in Z permeability
1 - Allow modification in Z permeability
IMSW- Flag indicating whether the initial water saturation is modified or not.
Possible Values:
0 - No modification is considered in initial water saturation values
1 - Allow modification in initial water saturation
3.3.37 NMODO (This line is read only if IMOD=1 and IMPOR=1)
NMODO - Number of regions with modified porosity.
3.3.38
3.3.39
3.3.40
3.3.41
IMIN, IMAX, JMIN, JMAX, KMIN, KM AX, IFACT, FACTX (This line is read only if IMOD=1
andNMOD>0)
IMIN - The first index in X direction.
IMAX - The last index in X direction.
JMIN - The first index in Y direction.
JMAX - The last index in Y direction.
KMIN - The first index in Z direction.
KMAX - The last index in Z direction.
IFACT - Flag indicating how porosity is modified.
. Possible Values:
1 - Replace porosity with FACTX
2 - Multiply porosity by FACTX
3 - Add FACTX to porosity
FACTX - The constant used to modify the porosity value.
Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in
UTCHEM. This line is repeated NMODO times.
NMOD1 (This line is read only if IMOD=1 and IMKX=1)
NMOD1 - Number of regions with modified X permeability.
IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if IMOD=1
andNMODl>0)
IMIN - The first index in X direction.
IMAX - The last index in X direction.
JMIN - The first index in Y direction.
JMAX - The last index in Y direction.
KMIN - The first index in Z direction.
KMAX - The last index in Z direction.
IFACT - Flag indicating how X permeability is modified.
Possible Values:
1 - Replace X permeability with FACTX
2 - Multiply X permeability by FACTX
3 - Add FACTX to X permeability
FACTX - The constant used to modify the X permeability value.
Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in
UTCHEM. This line is repeated NMOD1 times.
NMOD2 (This line is read only if IMOD=1 and IMKY=1)
NMOD2 - Number of regions with modified Y permeability.
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3.3.42 IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if IMOD=1
and NMOD2>0)
IMIN - The first index in direction.
IMAX - The last index in X direction.
JMIN - The first index in Y direction.
JMAX - The last index in Y direction.
KMIN - The first index in Z direction.
KMAX - The last index in Z direction.
IFACT - Flag indicating how Y permeability is modified.
Possible Values:
1 - Replace Y permeability with FACTX
2 - Multiply Y permeability by FACTX
3 - Add FACTX to Y permeability
FACTX - The constant used to modify the Y permeability value.
Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in
UTCHEM. This line is repeated NMOD2 times.
3.3.43 NMOD3 (This line is read only if JMOD= 1 and IMKZ= 1)
NMOD3 - Number of regions with modified Z permeability.
3.3.44 IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if
IMOD=1 and NMOD3>0)
IMIN - The first index in X direction.
IMAX - The last index in X direction.
JMIN - The first index in Y direction.
JMAX - The last index in Y direction.
KMIN - The first index in Z direction.
KMAX - The last index in Z direction.
IFACT - Flag indicating how Z permeability is modified.
Possible Values:
1 - Replace Z permeability with FACTX
2 - Multiply Z permeability by FACTX
3 - Add FACTX to Z permeability
FACTX - The constant used to modify the Z permeability value.
Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in
UTCHEM. This line is repeated NMOD3 times.
3.3.45 NMOD4 (This line is read only if IMOD=1 and IMSW=1)
NMOD4 - number of regions with modified initial water saturation.
3.3.46 IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if IMOD=1
and NMOD4>0)
IMIN - The first index in X direction.
IMAX - The last index in X direction.
JMIN - The first index in Y direction.
JMAX - The last index in Y direction.
KMIN - The first index in Z direction.
KMAX - The last index in Z direction.
IFACT - Flag indicating how initial water saturation is modified.
Possible Values:
1 - Replace initial water saturation with FACTX
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Appendix A - UTCHEM 6.1 User's Guide
2 - Multiply initial water saturation ,by FACTX
3 - Add FACTX to initial water saturation
FACTX - The constant used to modify the initial water saturation value.
Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in
UTCHEM. This line is repeated NMOD4 times.
3.3.47 NMOD5 (This line is read only if IMOD=1, IMSW=1, and IGAS>1)
NMOD5 - number of regions with modified initial gas saturation.
3.3.48 IMIN, IMAX, JMIN, JMAX, KMIN, KMAX, IFACT, FACTX (This line is read only if IMOD=1
and NMOD5>0)
IMIN - The first index in X direction.
IMAX - The last index in X direction.
JMIN - The first index in Y direction.
JMAX - The last index in Y direction.
KMIN - The first index in Z direction.
KMAX - The last index in Z direction.
IFACT - Flag indicating how initial gas saturation is modified.
Possible Values:
1 - Replace initial gas saturation with FACTX
2 - Multiply initial gas saturation by FACTX
3 - Add FACTX to initial gas saturation
FACTX - The constant used to modify the initial gas saturation value.
Note: See the note for input line 3.3.6 for a description of how the gridblocks are ordered in
UTCHEM. This line is repeated NMOD5 times.
3.3.49 C50,C60
C50 - Initial brine salinity.
Units: meq/ml of brine
Note: This is assumed to be ail the anions (in equivalents).
C60 - Initial divalent cation concentration of brine.
Units: meq/ml of brine
Note: C5Q and C60 are replaced by the input values of C5I and C6I on input line 3.5.34 when
IREACT>1.
3.4 General Physical Property Data
The fourth input section consists of the general physical property data. Please remember that
there are seven comment lines at the beginning of this section and that each data line is preceded by
three comment lines. J
Surfactant/Cosolvent Phase Behavior Data (Lines 3.4.1-3.4.21^
3.4.1 C2PLC, C2PRC, EPSME, IHAND
C2PLC - Oil concentration at plait point in type H(+) region.
Units: volume fraction
C2PRC - Oil concentration at plait point in type H_(-) region.
Units: volume fraction
EPSME - Critical micelle concentration (CMC)—minimum surfactant concentration for the formation
or micelles.
Units: volume fraction
IHAND - Flag to specify whether modified Hand's rule is considered or not.
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Appendix A - UTCHEM 6.1 User's Guide
Possible Values:
0 - Original Hand's rule is considered for phase behavior (default)
1 - Modified Hand's rule is considered for Phase behavior
Note: The option of IHAND=1 is available only for oil/microemulsion, Type II(-) phase
behavior, and IMASS=1.
3.4.2 IFGHBN
IFGHBN - Flag indicating type of phase behavior parameters.
Possible Values:
0 - Input height of binodal curve (default)
1 - Input solubilization ratio (new option)
Note: The input height of binodal curve option (IFGHBN=1) is currently only available for the
multiple organic option (NO>1). The effect of temperature or alcohol on phase behavior is not
currently modeled for IFGHBN=1. See Sections 2 & 11 of this report for more details on the
input height of binodal curve option and Section 7 for more details on the input solubilization
ratio option.
Binoda! Curve Input Option (Lines 3.4.3-3.4.11) — This section is required only ifIFGHBN=0.
3.4.3 HBNS70, HBNC70, HBNS71, HBNC71, HBNS72, HBNC72 (This line is read only if
IFGHBN=0)
HBNS70 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1 associated with
surfactant at zero salinity.
Units: volume fraction
HBNC70 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 1 (associated
with surfactant at zero salinity.
Units: volume fraction
HBNS71 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1 associated with
surfactant at optimal salinity.
Units: volume fraction
HBNC71 - Intercept of maximum height of binodal curve at zero fraction of Alcohol associated with
surfactant at optimal salinity.
Units: volume fraction
HBNS72 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1 associated with
surfactant at twice optimal salinity.
Units: volume fraction
HBNC72 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 1 associated
with surfactant at twice optimal salinity.
Units: volume fraction
Note: If alcohol is not present, the maximum height of binodal curves at three different
salinities are the only parameters used in the phase behavior calculations.
3.4.4 HBNT70, HBNT71, HBNT72, CSET (This line is read if IFGHBN=0 and IENG=1)
HBNT70 - Slope of height of binodal curve versus temperature at zero salinity
Units: volume fraction/(°F) (IUNIT=0) or volume fraction/°C (IUNIT=1)
HBNT71 - Slope of height of binodal curve versus temperature at optimal salinity
Units: volume fraction /(°F) (IUNIT=0) or volume fractionfC (IUNIT=1)
HBNT72 - Slope of height of binodal curve versus temperature at twice optimal salinity
Units: volume fraction /(°F) (IUNIT=0) or volume fraction/°C (IUNIT=1)
CSET - The Slope parameter, PT, for temperature dependency of the three-phase window
Units: ('F)-1 (IUNTT=0) or ('C)-1 (IUNTT=1)
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3.4.5 HBNS80, HBNC80, HBNS81, HBNC81, HBNS82, HBNC82 (This line is read if IFGHBN=Q)
HBNS80 - Slope for maximum height of binodal curve vs. fraction of Alcohol 2 associated with
surfactant at zero salinity.
Units: volume fraction
HBNC80 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 2 associated
with surfactant at zero salinity.
Units: volume fraction
HBNS81 - Slope of maximum height of binodal curve vs. fraction of Alcohol 2 associated with
surfactant at optimal salinity.
Units: volume fraction
HBNC81 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 2 associated
with surfactant at optimal salinity.
Units: volume fraction
HBNS82 - Slope for maximum height of binodal curve vs. fraction of Alcohol 2 associated with
surfactant at twice optimal salinity.
Units: volume fraction
HBNC82 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 2 associated
with surfactant at twice optimal salinity.
Units: volume fraction
3.4.6 CSEL7, CSEU7, CSEL8, CSEU8 (This line is read if IFGHBN=0)
CSEL7 - Lower effective salinity limit for type IE phase region determined when Alcohol 1 and
calcium approach zero.
Units: meq/ml
CSEU7 - Upper effective salinity limit for type in phase region determined when Alcohol 1 and
calcium approach zero.
Units: meq/ml
CSEL8 - Lower effective salinity limit for type III phase region determined when Alcohol 2 and
calcium approach zero.
Units: meq/ml
CSEU8 - Upper effective salinity limit for type IE phase region determined when Alcohol 2 and
calcium approach zero.
Units; meq/ml
3.4.7 BETA6, BETA7, BETAS (This line is read if IFGHBN=0)
BETA6 - The effective salinity slope parameter for calcium.
Units: dimensionless
BETA7 - The effective salinity slope parameter for Alcohol 1.
Units: dimensionless
BETAS - The effective salinity slope parameter for Alcohol 2.
Units: dimensionless
3.4.8 IALC, OPSK7O, OPSK7S, OPSK8O, OPSK8S (This line is read if IFGHBN=0)
IALC - Flag indicating choice of alcohol partition model to use.
Possible Values:
0 - Hirasaki's model will be used
1 - Prouvost's model will be used
OPSK7O - Alcohol partition coefficient (oil/water) for Alcohol 1.
Units: dimensionless
OPSK7S - Alcohol partition coefficient (surfactant/water) for Alcohol 1.
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Units: dimensionless
OPSK8O - Alcohol partition coefficient (oil/water) for Alcohol 2.
Units: dimensionless
OPSK8S - Alcohol partition coefficient (surfactant/water) for Alcohol 2.
Units: dimensionless
Note: If IALC=0 then OPSK7O, OPSK7S, OPSK8O, and OPSK8S remain fixed. If OPSK7O,
OPSK7S, OPSK8O, and OPSK8S are equal to zero and IALC=0, then alcohol is lumped
with surfactant as a single component (total chemical). OPSK7O, OPSK7S, OPSK8O, and
OPSK8S are only used when Hirasaki's model is chosen. See Section 11 of this report for
more details on the alcohol partition models.
3.4.9 NALMAX, EPSALC (This line is read if IFGHBN=0)
NALMAX - Maximum number of iterations for alcohol partitioning for two alcohol system.
Note: The suggested value is 20 and a value of zero would result in no iterations.
EPSALC - Tolerance for convergence of iterations for two alcohol system.
Note: Suggested values are 10'3 and 10'4.
3.4.10 AKWC7, AKWS7, AKM7, AK7, PT7 (This line is read if IFGHBN=0)
AKWC7, AKWS7 - Parameters used to determine partition coefficient of monomeric Alcohol 1
between aqueous and oleic pseudophases.
Units: dimensionless
AKM7 - Partition coefficient of monomeric Alcohol 1 between surfactant and oleic pseudophases.
Units: dimensionless
AK7 - Self-association constant of Alcohol 1 in oleic pseudophase.
Units: dimensionless
PT7 - Ratio of molar volume of Alcohol 1 to equivalent molar volume of surfactant.
Units: dimensionless
3.4.11 AKWC8, AKWS8, AKM8, AK8, PT8 (This line is read if IFGHBN=0)
AKWC8, AKWS8 - Parameters used to determine partition coefficient of monomeric Alcohol 2
between aqueous and oleic pseudophases.
Units: dimensionless
AKM8 - Partition coefficient of monomeric Alcohol 2 between surfactant and oleic pseudophases.
Units: dimensionless
AK8 - Self-association constant of Alcohol 2 in oleic pseudophase.
Units: dimensionless
PT8 - Ratio of molar volume of Alcohol 2 to equivalent molar volume of surfactant.
Units: dimensionless
Solubilization Ratio Input Option (Lines 3.4.12-3.4.21) — These lines are required only if the phase
behavior calculation is based on the solubilization ratio (IFGHBN=1).
3.4.12 IOD (This line is read ifTFGHBN=l and NO>1)
IOD - Flag indicating whether phase behavior depends on organic composition
Possible Values:
0 - Phase behavior and properties depend on organic composition
1 - Phase behavior and properties are independent of organic composition (default)
3.4.13 NCOMP (This line is read only if IFGHBN=1 and IOD=0)
NCOMP - Number of organic components in the first solubility measurement.
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3.4.14 ONAME(I) for 1=1, NCOMP (This line is read only if IFGHBN=1 and IOD=0)
ONAME(I) - Name of organic species in the first solubility measurement. Currently the values in the
following table can be specified.
ONAME
Value
DECANE
OCTANE
HEXANE
PCE
PXYLEN
TOLUEN
CCL4
TCE
DCB
TCA
DCE
CHCL3
CH2CL2
C2CL4
Formula
CioH22
CgHig
C6H14
C2C14
CC14
C2HC13
1,2-C6H4C12
CH3CC13
1,2-C2H4C12
CHC13
CH2C12
1,1,2,2-C2H2C14
Name
Decane
Octane
Hexane
Tetrachloro-
ethylene
P-xylene
Toluene
Carbon
tetrachloride
Trichloro-
ethylene
1,2-dichloro-
benzene
1,1,1-trichloro-
ethene
Molecular
Weight
142
114
86
165.8
106
92
153.8
131.4
146.9
133.35
98.9
119.4
84.9
167.8
Equivalent
Alkane
Carbon No.
(EACN)
10
8
6
2.9
2
1
-0.06
-3.81
-4.89
-2.5
-12.1
-13.67
-13.79
-22.15
3.4.15 OCOMP(I), for 1=1, NCOMP (This line is read only if IFGHBN=1 and IOD=0)
OCOMP(I) - concentration of Ith organic component in the first solubility measurement.
Units: mole fraction
3.4.16 CSO, SCSO, CS1, SCSI, CS2, SCS2, DCS20 (This line is read only if IFGHBN=1)
CSO - Effective salinity which is between the lower and optimal effective salinity limits for type III
phase region; CSEL
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Appendix A - UTCHEM 6.1 User's Guide
Units: volume fraction
DCS20 - The difference of the upper and the lower effective salinity limits for type III phase region;
CSEU - CSEL-
3.4.17 NCOMP (This line is read only if IFGHBN=1 and IOD=0)
NCOMP - Number of organic components in the second solubility measurement.
3.4.18 ONAME(I), for 1=1, NCOMP (This line is read only if IFGHBN=1 and IOD=0)
ONAME(I) - Name of organic species in the second solubility measurement.
Note: See input line 3.4.14 for a list of available species names.
3.4.19 OCOMP(I), for 1=1, NCOMP (This line is read only if IFGHBN=1 and IOD=0)
OCOMP(I) - concentration of Ith organic component hi the second solubility measurement.
Units: mole fraction
3.4.20 CSO, SCSO, CS1, SCSI, CS2, SCS2, DCS20 (This line is read only if IFGHBN=1 and IOD=0)
CSO - Effective salinity which is between the lower and optimal effective salinity limits for type III
phase region; CSEL
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Units: Dimensionless
3.4.24 CHUH, AHUH (This line is read only if IFT=1)
CHUH - Constant in modified Hub's interfacial tension correlation.
Typical Values: 0.1 - 0.35
AHUH - Constant in modified Hub's interfacial tension correlation
Typical values: 5-20
3.4.25 XIFTW
XIFTW - logio awo where CTWO is the interfacial tension of the water-oil interface.
Units: dynes/cm = mN/m
Organic Mass Transfer Data (Lines 3.4.26-3.4.29)
3.4.26 IMASS
IMASS - Flag indicating the choice of oil solubility in water.
Possible Values
0 - No solubility of oil in water in the absence of surfactant
1 - Allow for solubility of oil in water in the absence of surfactant or allow for
nonequilibriurn transfer of oil in water
3.4.27 WSOL, CNEM2, ISOL (This line is read only if NO<1 and IMASS=1 and IGAS=0 with surfactant
being present)
WSOL - Equilibrium concentration of oil in water in the absence of surfactant.
Units: volume fraction
CNEM2 - Coefficient of nonequilibriurn mass transfer of oil in aqueous phase with or without
surfactant.
Units: vol. of water/(bulk vol.-day)
Note: The input value of zero for CNEM2 represents an equilibrium mass transfer. The
nonequilibriurn mass transfer (CNEM2>0) calculation is valid for type II(-) with the
plait point in the corner (C2PLC=0) and in the absence of gas phase (IGAS=0).
ISOL - Flag indicating the solution scheme for the nonequilibrium mass transfer calculations
Possible Values
0 - Implicit method is used
1 - Explicit method is used
Note: The explicit method (ISOL=1) is the only option available when gas is present
Note: See Section 12 of this report for more details on the rate limited organic dissolution model.
3.4.28 (WSOL(KO), for KO=1, NO), CNEM2, ISOL (This line read only if NO>1, IMASS=1, and
IGAS=0 with surfactant being present)
WSOL(KO) - Water/oil equilibrium partition coefficient for oil component KO in the absence of
surfactant
Units: volume fraction
CNEM2 - Coefficient of nonequilibrium mass transfer of oil components in aqueous phase when
surfactant is present.
Units: vol. of water / (bulk vol.-day)
ISOL - Flag indicating whether the mass transfer calculation is implicit or explicit when surfactant is
present.
Possible Values:
0 - Implicit method is used
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1 - Explicit method is used
3.4.29 CNEMK(KO), for KO=1, NO (This line read only if NO>1, IMASS=1, and WSOL(KO)>0)
CNEMK(KO) - Coefficient of nonequilibrium mass transfer of oil component KO in aqueous phase
when surfactant is not present.
Units: vol. of water / (bulk vol.-day)
Note: See Section 7 of this report for more details on the rate limited multiple organic dissolution
model.
3.4.30 rrRAP,Tll,T22,T33
ITRAP - Flag indicating whether residual saturations and relative permeabilities are dependent on
capillary number or not.
.Possible Values:
0 - Residual saturations are not dependent on capillary number; endpoint and exponent
of relative permeability curves are constant
1 - Residual saturations and relative permeabilities are dependent on capillary number
2 - Residual saturations and relative permeabilities are dependent on trapping number
Note: ITRAP=2 is currently not available with the curvilinear grid option (ICOORD=4) or
when gas is present (IGAS>1)
Til- Capillary desaturation curve parameter for aqueous phase.
T22 - Capillary desaturation curve parameter for oleic phase.
T33 - Capillary desaturation curve parameter for microemulsion phase.
Note: Options ITRAP=1 and ITRAP=2 are identical for 1-d displacement in the vertical direction
with zero capillary pressure. See Section 2 of this report for more information on the
capillary and trapping number options.
Relative Permeability Data (Lines 3.4.31-3.4.57^
3.4.31 IPERM, fflYST, IPARK
IPERM - Flag indicating which relative permeability and capillary pressure model is used.
Possible Values:
0 - Imbibition Corey
1 - First drainage Corey (only for two phase water/oil flow)
2- Parker and Lenhard's model
Note: See Section 2 of this report for more details on this option.
IHYST - Flag indicating whether the hysteresis is used with Parker and Lenhard's model
(IPERM=2)
Possible Values:
0 - Hysteretic model is not used
1 - Hysteretic model is used
Note: See Section 3 of this report for more details on this option.
IPARK - Flag indicating the model used to calculate the oil trapping for hysteretic model
Possible Values:
0 - Kalurachchi and Parker's model is used
1 - Parker and Lenhard's model is used
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Low Capillary Number Data (Lines 3.4.32-3.4.54)
Refer to the following flowchart to help determine which input lines should be used to specify the relative
permeability parameters for different options:
IPERM
0,1
2
ISRW
IPRW
IEW
ISRW
u
2
0
2
0
2
0
2
3.4.34
3.4.35-3.4.37
3.4.38-3.4.40
3.4.41
3.4.42-3.4.44
3.4.45-3.4.47
3.4.48
3.4.49-3.4.51
3.4.52-3.4.54
3.4.34
3.4.35-3.4.37
3.4.38-3.4.40
3.4.32 ISRW, IPRW, ffiW (This line is read only for IPERM< 2)
ISRW - Flag indicating type of residual saturation.
Possible Values:
0 - Constant residual saturation for entire reservoir
1 - Constant residual saturation for each layer
2 - Residual saturation for each gridblock
IPRW - Flag indicating type of endpoint relative permeability.
Possible Values:
0 - Constant endpoint relative permeability for entire reservoir
1 - Constant endpoint relative permeability for each layer
2 - Constant endpoint relative permeability for each gridblock
IEW - Flag indicating type of relative permeability exponent.
Possible Values:
0 - Constant relative permeability exponent for entire reservoir
1 - Constant relative permeability exponent for each layer
2 - Constant relative permeability exponent for each gridblock
3.4.33 ISRW (This line is read only if IPERM=2)
ISRW - Flag indicating type of residual saturation.
Possible Values:
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0 - Constant residual saturation for entire reservoir
1 - Constant residual saturation for each layer
2 - Residual saturation for each gridblock
3.4.34 S1RWC, S2RWC, S3RWC (This line is read only if ISRW=0)
S1RWC - Residual saturation of aqueous phase displaced by oil at low capillary number for entire
reservoir.
Units: fraction
S2RWC - Residual saturation of oleic phase displaced by water at low capillary number for entire
reservoir.
Units: fraction
S3RWC - Residual saturation of microemulsion phase displaced by water at low capillary number
for entire reservoir.
Units: fraction
3.4.35 SlRWC(K),forK=l,NZ (This line is read only if ISRW=1)
SIRWC(K) - Residual saturation of aqueous phase displaced by oil or gas at low capillary number
for Kth layer.
Units: fraction
Note: S 1RWC(K) must begin a separate line in the input file for each layer.
3.4.36 S2RWC(K), for K=l, NZ (This line is read only if ISRW=1)
S2RWC(K) - Residual saturation of oleic phase displaced by water at low capillary number for Kth
layer.
Units: fraction
Note: S2RWC(K) must begin a separate line in the input file for each layer.
3.4.37 S3RWC(K), for K=l, NZ (This line is read only if ISRW=1)
S3RWC(K) - Residual saturation of microemulsion phase displaced by water or oil at low capillary
number for Kth layer.
Units: fraction
Note: S3RWC(K) must begin a separate line in the input file for each layer.
3.4.38 S 1RW(I), for 1=1, NBL (This line is read only if ISRW=2)
S1RW(I) - Residual saturation of aqueous phase displaced by oil or gas at low capillary number for
Ith gridblock.
Units: fraction
3.4.39 S2RW(I), for 1=1, NBL (This line is read only if ISRW=2)
S2RWC(K) - Residual saturation of oleic phase displaced by water at low capillary number for Ith
gridblock.
Units: fraction
3.4.40 S3RW(I), for 1=1, NBL (This line is read only if ISRW=2)
S3RW(I) - Residual saturation of microemulsion phase displaced by water or oil at low capillary
number for Ith gridblock,
Units: fraction
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Relative Permeability Endpoint and Exponent Data (Lines 3.4.41-3.4.54) — These lines are required
only if Corey function (IPERM<2) is used.
3.4.41 P1RWC, P2RWC, P3RWC (This line is read only if IPERM<2 and IPRW=0)
P1RWC - End point relative permeability of water at low capillary number for entire reservoir.
Units: dimensionless
P2RWC - End point relative permeability of oil at low capillary number for entire reservoir.
Units: dimensionless
P3RWC - End point relative permeability of microemulsion at low capillary number for entire
reservoir.
Units: dimensionless
3.4.42 PIRWG(K), for K=l, NZ (This line is read only if IPERM<2 and IPRW=1)
PIRWC(K) - Constant endpoint relative permeability of water at low capillary number for Kth layer.
Units: dimensionless
3.4.43 P2RWC(K), for K=l, NZ (This line is read only if IPERM<2 and IPRW=1)
P2RWC(K) - Constant endpoint relative permeability of oil at low capillary number for K* layer.
- Units: dimensionless
3.4.44 P3RWC(K), for K=l, NZ (This line is read only if IPERM<2 and IPRW=1)
P3RWC(K) - Constant endpoint relative permeability of microemulsion at low capillary number for
Kth layer.
Units: dimensionless
3.4.45 P1RW(I), forI=l,NBL (This line is read only if IPERM<2 and IPRW=2)
P1RW(I) - Endpoint relative permeability of water at low capillary number for Ith gridblock.
Units: dimensionless
3.4.46 P2RW(I), for 1=1, NBL (This line is read only if IPERM<2 and IPRW=2)
P2RW(I) - Endpoint relative permeability of oil at low capillary number for Ith gridblock.
Units: dimensionless
3.4.47 P3RW(I), for 1=1, NBL (This line is read only if IPERM<2 and IPRW=2)
P3RW(I) - Endpoint relative permeability of microemulsion at low capillary number for Ith
gridblock.
Units: dimensionless
3.4.48 ElWC, E2WC, E3WC (This line is read only if IPERM<2 and IEW=0)
ElWC - Phase relative permeability exponent for aqueous phase at low capillary number for entire
reservoir.
Units: dimensionless
E2WC - Phase relative permeability exponent for oleic phase at low capillary number for entire
reservoir.
Units: dimensionless
E3WC - Phase relative permeability exponent for microemulsion phase at low capillary number
system for entire reservoir.
Units: dimensionless
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3.4.49 E1WC(K), for K=l, NZ (This line is read only if IPERM<2 and ffiW=l)
E1WC(K) - Relative permeability exponent of aqueous phase at low capillary number for Kth layer.
Units: dimensionless
3.4.50 E2WC(K), for K=l, NZ (This line is read only if IPERM<2 and IEW=1)
E2WC(K) - Relative permeability exponent of oleic phase at low capillary number for Kth layer.
Units: dimensionless
3.4.51 E3WC(K), for K=l, NZ (This line is read only if IPERM<2 and ffiW=l)
E3WC(K) - Relative permeability exponent of microemulsion phase at low capillary number for Kth
layer.
Units: dimensionless
3.4.52 ElW(I),forI=l,NBL (This line is read only ifTPERM<2 and IEW=2)
E1W(I) - Relative permeability exponent of aqueous phase at low capillary number for Ith gridblock.
Units: dunensionless
3.4.53 E2W(I), for 1=1, NBL (This line is read only if IPERM<2 and IEW=2)
E2W(I) - Relative permeability exponent of oleic phase at low capillary number for Ith gridblock.
Units: dimensionless
3.4.54 E3W(I), for 1=1, NBL (This line is read only if IPERM<2 and ffiW=2)
E3W(I) - Relative permeability exponent of microemulsion phase at low capillary number for Ith
gridblock.
Units: dunensionless
High Capillary Number Data (Lines 3.4.55-3.4.57)
ITRAP=2.
These lines are required only if ITRAP=1 or
3.4.55 S IRC, S2RC, S3RC (This line is read only if ITRAP=1 or 2)
S1RC - Residual saturation of aqueous phase at high capillary number.
Units: fraction
S2RC - Residual saturation of oleic phase at high capillary number.
Units: fraction
S3RC - Residual saturation of microemulsion phase at high capillary number.
Units: fraction
Note: The residual saturations at high capillary number can not be set equal to those at low capillary
number.
3.4.56 P1RC, P2RC, P3RC (This line is read only for ITRAP=1 or 2 and IPERMk 2)
P1RC - End point relative permeability of aqueous phase at high capillary number condition.
Units: dimensionless
P2RC - End point relative permeability of oleic phase at high capillary number condition.
Units: dimensionless
P3RC - End point relative permeability of microemulsion phase at high capillary number condition.
Units: dimensionless
3.4.57 E13C, E23C, E31C (This line is read only for ITRAP=1 or 2 and IPERM< 2)
E13C, E23C, E31C - Parameters used for calculating exponents for relative permeability calculations
at high capillary number.
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Units: dimensionless
Viscosity Data (Lines 3.4.58-3.4.63)
3.4.58 VIS1, VIS2,TSTAND
VIS 1 - Water viscosity at reference temperature.
Units: cp = rnPa.s
VIS2 - Oil viscosity at reference temperature.
Units: cp = rnPa.s
TSTAND - Reference temperature
Units: °F (IUNIT=0) or °C (IUNIT=1)
Note: For IENG=0, if TSTAND=0.0, the water component viscosity will be constant and
equal to the input value VIS1. If TSTAND>0.0, water component viscosity will be
calculated as a function of reservoir temperature, pressure, and local salinity for each
gridblock.
3.4.59 IOVIS (This line read only if NO>1)
IOVIS - Flag indicating whether the viscosity is a function of organic composition.
Possible Values:
0 - Viscosity does not depend on the organic species concentration.
1 - Viscosity depends on the organic species concentration.
Note: See Section 2 of this report for more information on the IOVIS=0 option and Section
7 for more information on the IOVIS=1 option.
3.4.60 OVIS(K), for K=l, NO (This line is read only if NO>1 and IOVIS=1)
OVIS(K) - Viscosity for organic component K at reference temperature.
Units: cp = mPa.s
3.4.61 VIS4, VSLOPG (This line is read only if IGAS>1)
VIS4 - Gas viscosity at reference temperature and reference pressure.
Units: cp = mPa.s
VSLOPG - Slope of gas viscosity.
Units: (psi)-1 (IUNIT=0) or (kPa)'1 (IUNIT=1)
3.4.62 BVI(1),BVI(2) (This line is read only if IENG=1)
BVI(l) - Parameter for calculating water viscosity as a function of reservoir temperature.
Units: ("K)-1
B VI(2) - Parameter for calculating oil viscosity as a function of reservoir temperature.
Units: ("K)-1
3.4.63 BVI(4) (This line is read only if IGAS>1 and ffiNG=l)
BVI(4) - Parameter for calculating gas viscosity as a function of reservoir temperature.
Units: ("K)-1
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Corey Option Gas Relative Permeability Data (Lines 3.4.64-3.4.75) — These lines are required only if
IGAS£landIPERM=0.
Refer to the following flowchart to help determine which input lines should be used to specify the gas relative
permeability parameters for different options:
mr"l"5R>i f\
IPERM-0
ir»Aq_i
IORVU
lonvv
IPRW
ir nvv
IPW
u
-1
1 rs
I?
0.
IS
r\
r^
IS
p
3.4.64 |
3 A RK. Q A RR
.4.OO-0. 4. DO
3.4.67-3.4.68
3.4.69
^ 4 7n
3.4.71
3.4.72
>0 A 7Q
G.*T. /O
3.4.74
3.4.64 S2RWC4, S4RWC (This line is read only if ISRW=0)
S2RWC4 - Constant residual oil saturation to displacing gas phase for entire reservoir.
Units: fraction
S4RWC - Constant residual gas saturation for entire reservoir.
Units: fraction
3.4.65 S2RWC4(K), for K= 1, NZ (This line is read only if ISRW= 1)
S2RWC4(K) - Constant residual oil saturation to displacing gas phase for Kth layer.
Units: fraction
3.4.66 S4RWC(K), for K=l, NZ (This line is read only if ISRW=1)
S4RWC(K) - Constant residual gas saturation for Kth layer.
Units: fraction
3.4.67 S2RW4(I), for 1= 1, NBL (This line is read only if ISRW=2)
S2RW4(I) - Constant residual oil saturation to displacing gas phase for Ith gridblock.
Units: fraction
3.4.68 S4RW(I), for 1= 1, NBL (This line is read only if ISRW=2)
S4RW(I) - Residual gas saturation for Ith gridblock.
Units: fraction
3.4.69 P4RWC (This line is read only if IPRW=0)
P4RWC - Constant gas endpoint relative permeability for entire reservoir.
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Units: dimensionless
3.4.70 P4RWC(K), for K=l, NZ (This line is read only if IPRW=1)
P4RWC(K) - Constant gas endpoint relative permeability for Kth layer.
Units: dimensionless
3.4.71 P4RW(I), for 1=1, NBL (This line is read only if IPRW=2)
P4RW(I) - Constant gas endpoint relative permeability for Ith gridblock.
Units: dimensionless
3.4.72 E4WC (This line is read only if IEW=0)
E4WC - Constant gas relative permeability exponent for entire reservoir.
Units: dimensionless
3.4.73 E4WC(K),forK=l,NZ (This line is readonly if ffiW=l)
E4WC(K) - Constant gas relative permeability exponent for Kth layer.
Units: dimensionless
3.4.74 E4WC(I), for 1=1, NBL (This line is read only if IEW=2)
E4WC(I) - Constant gas relative permeability exponent for Ith gridblock.
Units: dimensionless
3.4.75 S4RC, P4RC, E4C, T44 (This line is read only if ITRAP=1)
S4RC - Residual gas saturations at high capillary number.
Units: fraction
P4RC - Gas endpoint relative permeability at high capillary number.
Units: dimensionless
E4C - Gas relative permeability exponent at high capillary number.
Units:, dimensionless
T44 - Gas phase trapping parameter.
Units: dimensionless
3.4.76 XIFTG,XIFTGW (This line is read only if IGAS>1)
XIFTG - Log of interfacial tension between gas and oil.
Units: dyne/cm = mN/m
XIFTGW - Log of interfacial tension between gas and water.
Units: dyne/cm = mN/m
Microemulsion Viscosity Data (Line 3.4.77)
3.4.77 ALPHAV(I), for 1=1, 5
ALPHAV(I) - Compositional phase viscosity parameters.
Units: dimensionless
Note: All five viscosity parameters must be positive values.
Note: See Section 2 of this report for more information on the compositional viscosity model.
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Polymer Property Data (Lines 3.4.78-3.4.81) — See Section 2 of this report for information on the
polymer property models.
3.4.78 API, AP2, APS
API, AP2, APS - Parameters used for calculating polymer viscosity at zero shear rate as a function
of polymer and electrolyte concentrations.
Units: (wt. %)-*, (wt. %)-2, (wt. %)-3
3.4.79 BETAP, CSE1, SSLOPE
BETAP - Parameter for calculating the effective divalent salinity used to calculate polymer viscosity.
Units: dimensionless
CSE1 - Value below which the polymer viscosity is considered to be independent of salinity.
Units: meq/ml
SSLOPE - Slope of viscosity vs. effective salinity on a log-log plot—assumed to be constant.
Units: dimensionless
Note: This value is usually large and negative for hydrolyzed polyacrylamides and small and
positive for polysaccharides.
3.4.80 GAMMAC, GAMHF, POWN
GAMMAC - Coefficient in shear rate equation below.
2 a/2
(IUNIT=1)
ft — sec m — sec
GAMHF - Shear rate at which polymer viscosity is one half polymer viscosity at zero shear rate.
Units: sec~*
POWN - Exponent for calculating shear rate dependence of polymer viscosity.
Units: dimensionless
3.4.81 IPOLYM, EPHI3, EPHI4, BRK, CRK
IPOLYM - Flag indicating type of polymer partitioning.
Possible Values:
0 - All polymer exists in aqueous phase if aqueous phase exists; otherwise, it exists
completely in microemulsion phase
1 - Partitioning of polymer to water component is constant
EPHI3 - Effective porosity for surfactant—ratio of apparent porosity for surfactant to actual porosity.
Units: dimensionless
EPHI4 - Effective porosity for polymer—ratio of apparent porosity for polymer to actual porosity.
Units: dimensionless
BRK - Parameter for calculating permeability reduction factor.
n . . volume of polymer - rich phase
weight% polymer
CRK - Parameter for calculating permeability reduction factor.
Units: (darcy)1/2 (100 g/g)-1/3 = (^im2)1/2 (100 g/g)-1/3)
Note: EPHI3 and EPHI4 are used to account for inaccessible pore volume in the case of surfactant
and polymer.
surfactant = <|> X EPHI3
polymer = <|> X EHPI4
The effect of permeability reduction or residual resistance is to reduce the mobility of the
polymer rich phase. This is accounted for by multiplying the viscosity of the phase by BRK.
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Component Density Data (Lines 3.4.82-3.4.88)
3.4.82 DEN1, DEN2, DEN23, DENS, DENT, DENS, IDEN, IODEN
DEN1 - Specific weight or density of water (Component 1).
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
DEN2 - Specific weight or density of oil (Component 2).
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
DEN23 - Coefficient of oil in microemulsion phase density calculations.
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
DENS - Specific weight or density of surfactant (Component 3).
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
DEN7 - Specific weight or density of Alcohol 1 (Component 7).
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
DENS - Specific weight or density of Alcohol 2 (when IGAS=0) or gas (when IGAS>1)
(Component 7).
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
IDEN - Flag indicating if gravity effect should be considered.
Possible Values:
1 - Do not consider gravity effect
2 - Consider gravity effect
IODEN - Flag indicating if specific weight/density is a function of organic species concentration for
NO>1.
Possible Values:
0 - Does not depend on organic species concentration
1 - Depends on organic species concentration
Note: See Section 2 of this report for information on the IODEN=0 option or Section 7 for
information on the IODEN=1 option.
Note: Specific weight for pure water is 0.433 psi/ft (density of 1 g/cm3). IODEN must be set to 1
if any non-aqueous phase species (those with indices < (8+NO)) participate in biodegradation
equations.
Multiple Organic Density Data (Lines 3.4.83-3.4.84) — These lines are required only if IODEN=1 and
NO>1.
3.4.83 DNOILC(K), for K=l, NO (This line is read only if IODEN=1 and NO>1)
DNOILC(K) - Specific weight or density of organic component K for oleic phase.
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
3.4.84 DNOME(K), for K=l, NO (This line is read only if IODEN=1 and NO>1)
DNOME(K) - Specific weight or density of organic component K for microemulsion phase.
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
Multiple Organic Data (Lines 3.4.85-3.4.88) — These lines are required only if NO>1. Furthermore, if
(I£GHBN=1 and IQD=0) or IQVIS=1.
3.4.85 INAME (This line is read only if NO>1 and ((IFGHBN=1 and IOD=0) or IOVIS=1)))
INAME - Flag indicating whether name of the organic components will be provided by user.
Possible Values:
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0 - Name of the organic components will be provided; the molecular weight and
equivalent alkane carbon number will be obtained from the built-in database
1 - Molecular weight and equivalent alkane carbon number for each organic
components will be provided.
3.4.86 ONAME(K), for K=l, NO (This line is read only if NO>1 and ((IFGHBN=1 and IOD=0) or
IOVIS=1)) and INAME=0)
ONAME(K) - Name of organic component K. See input line 3.4.14 for a list of valid component
names.
3.4.87 OMWT(K), for K=l, NO (This line is read only if NO>1 and ((IFGHBN=1 and IOD=0) or
IOVIS=1)) and INAME=1)
OMWT(K) - Molecular weight for organic component K.
3.4.88 OEACN(K), for K=l, NO (This line is read only if NO>1 and ((IFGHBN=1 and IOD=0) or
IOVIS=1)) and INAME=1)
OEACN(K) - equivalent alkane carbon number for organic component K.
Note: See Section 7 of this report for information on the equivalent alkane carbon number.
3.4.89 ISTB
ISTB - Flag indicating the units to be used when printing injection and production rates.
Possible Values:
0 - Rates printed at bottomhole condition in ft3 or m3
1 - Rates printed at surface condition in bbls
3.4.90 FVF(L), for L=l, MXP (This line is read only if ISTB=1 and IUNIT=0)
FVF(L) - Formation volume factor for Lth phase.
Units: SCF/ft3
Note: MXP=3 when IGAS=0 and MXP=4 when IGAS>1.
Fluid Compressibility Data (Lines 3.4.91-3.4.93)
3.4.91 COMPC(l), COMPC(2), COMPC(3), COMPC(7), COMPC(8)
COMPC(l) - Compressibility of brine (Component 1).
Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)
COMPC(2) - Compressibility of oil (Component 2).
Units: 1/psi (IUNTT=0) or l/kPa(IUNIT=l)
COMPC(3) - Compressibility of surfactant (Component 3).
Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)
COMPC(7) - Compressibility of Alcohol 1 (Component 7).
Units: 1/psi (IUNIT=0) or l/kPa(IUNIT=l)
COMPC(8) - Compressibility of Alcohol 2 (when IGAS=0) or gas (when IGAS>1) (Component 8).
Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)
Note: For incompressible fluids, values of zero should be used for the COMPC values listed above.
3.4.92 ICOMPO (This line is read only if NO>1)
ICOMPO - Flag indicating whether each organic component has different compressibility.
Possible Values:
0 - All organic components have the same compressibility as COMPC(2)
1 - Each organic component has different compressibility
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3.4.93 COMPO(K), for K=l, NO (This line is read only if NO>1 and ICOMPO=1)
COMPO(K) - Compressibility of organic component K.
Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)
Capillary Pressure Data (Lines 3.4.94-3.4.117^ — See Section 2 of this report for capillary pressure
information.
3.4.94 ICPC, IEPC, IOW
ICPC - Flag indicating type of capillary pressure endpoint.
Possible Values:
0 - Constant capillary pressure endpoint for entire reservoir
1 - Constant capillary pressure endpoint for each layer
2 - Capillary pressure endpoint for each gridblock
IEPC - Flag indicating type of capillary pressure exponent.
Possible Values:
0 - Constant capillary pressure exponent for entire reservoir
1 - Constant capillary pressure exponent for each layer
2 - Capillary pressure exponent for each gridblock
IOW - Flag indicating the wettability for two-phase oil/water capillary pressure calculations using
imbibition Corey function (IPERM=0).
Possible Values:
0 - The capillary pressure curve is for strongly water-wet rock (default)
1 - The capillary pressure curve is for strongly oil-wet rock
2 - The capillary pressure curve is for mixed-wet rocks
Note: IOW=1 and 2 are available only for IPERM=0.
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Refer to the following flowchart to help determine which input lines should be used to specify the capillary
pressure data for different options:
IPERM
0
IOW=2
ICPC
0,1
0
IOW=0, 1
ICPC
3.4.95
3.4.96
3.4.97
IOW=0, 1
IEPC
3.4.101
3.4.102
3.4.103
0
ICPC
IOW=0
3.4.98
3.4.100
0
3.4.104
3.4.105
3.4.106
3.4.107
3.4.108-3.4.112
3.4.113-3.4.117
Capillary Pressure Data for Strongly Water- or Oil-Wet Rocks (Lines 3.4.95-3.4.106^ — These lines are
required only ifIOW<2.
3.4.95 CPCO (This line is read only if IOW<2 and ICPC=0 and IPERM<2)
CPCO - Capillary pressure endpoint for entire reservoir.
Units: psiVdarcies (IUNIT=0) or kPa-\/u,m2 (IUNIT=1)
3.4.96 CPC(K), for K=l, NZ (This line is read only if IOW<2 and ICPC=1 and IPERM<2)
CPC(K) - Capillary pressure endpoint for Kth layer.
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Units: psiVdarcies (IUNIT=0) or
(IUNIT=1)
3.4.97 CPC(I), for 1=1, NBL (This line is read only if IOW<2 and ICPC=2 and IPERM<2)
CPC(I) - Capillary pressure endpoint for Ith gridblock.
(IUNIT=1)
Units: psiVdarcies (IUNIT=0) or
3 .4.98 CPCO (This line is read only if IOW=0 and ICPC=0 and IPERM=2)
CPCO - van Genuchten capillary pressure parameter, a, for entire reservoir.
Units: (psiVdarcies)"1 (IUNIT=0) or ^m2 /kPa (IUNIT=1)
3.4.99 CPC(K), for K=l, NZ (This line is read only if IOW=0 and ICPC=1 and IPERM=2)
CPC(K) - van Genuchten capillary pressure parameter, a, for K* layer.
Units: (psiVdarcies)"1 (IUNIT=0) or ^/um2 / kPa (IUNIT=1)
3.4. 100 CPC(I), for 1=1, NBL (This line is read only if IOW=0 and ICPC=2 and IPERM=2)
CPC(I) - van Genuchten capillary pressure parameter, a, for Ith gridblock.
Units: (psiVdarcies)"1 (IUNIT=0) or ^m2 / kPa (IUNIT=1)
3 .4. 1 0 1 EPCO (This line is read only if IOW<2 and ffiPC=0 and IPERM<2)
EPCO - Capillary pressure exponent for entire reservoir.
Units: dimensionless
3.4. 102 EPC(K), for K=l, NZ (This line is read only if IOW<2 and IEPC=1 and IPERM<2)
EPC(K) - Capillary pressure exponent for K* layer.
Units: dimensionless
3.4. 103 EPC(I), for 1=1, NBL (This line is read only if IOW<2 and IEPC=2 and IPERM<2)
EPC(I) - Capillary pressure exponent for Ith gridblock.
Units: dimensionless
3.4.104 EPCO (This line is read only if IOW=0 and ffiPC=0 and IPERM=2)
EPCO - van Genuchten capillary pressure parameter, n, for entire reservoir.
Units: dimensionless
3.4.105 EPC(K), for K=l, NZ (This line is read only if IOW=0 and ffiPC=l and IPERM=2)
EPC(K) - van Genuchten capillary pressure parameter, n, for K* layer.
Units: dimensionless
3.4. 106 EPC(I), for 1=1, NBL (This line is read only if IOW=0 and IEPC=2 and IPERM=2)
EPC(I) - van Genuchten capillary pressure parameter, n, for Ith gridblock.
Units: dimensionless
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Capillary Pressure Data for Mixed-Wet Rocks (Lines 3.4.107-3.4.117) — These lines are required only
ifIPERM=0 and IOW=2.
3.4.107 CPCW, EPCW, CPCO, EPCO, SSTAR (This line is read only if IPERM=0 and IOW=2 and
ICPC=0)
CPCW - Capillary pressure endpoint for entire reservoir for positive branch.
Units: psWdarcies (IUNIT=0) or IcPa^^m2 (IUNIT=1)
EPCW - Capillary pressure exponent for entire reservoir for positive branch.
Units: dimensionless
CPCO - Capillary pressure endpoint for entire reservoir for negative branch.
Units: psWdarcies (IUNIT=0) or kPa^m2 (IUNIT=1)
EPCO - Capillary pressure exponent for entire reservoir for negative branch.
Units: dimensionless
SSTAR - Water saturation where the capillary pressure is zero.
Units: dimensionless
3.4.108 CPCW(K), for K=l, NZ (This line is read only if IPERM=0 and IOW=2 and ICPC=1)
CPCW - Capillary pressure endpoint for kth layer for positive branch.
Units: psi-Vdarcies (IUNIT=0) or kPa^um2 (IUNIT=1)
3.4. 109 EPCW(K), for K=l, NZ (This line is read only if IPERM=0 and IOW=2 and ICPC=1)
EPCW (K) - Capillary pressure exponent for entire reservoir.
Units: dimensionless
3.4. 1 10 CPCO(K), for K=l, NZ (This line is read only if IPERM=0 and IOW=2 and ICPC=1)
CPCO (K) - Capillary pressure endpoint for Kth layer for negative branch.
Units: psiVdarcies (IUNIT=0) or kPa^lim2 (IUNIT=1)
3.4.1 1 1 EPCO(K), for K=l, NZ (This line is read only if IPERM=0 and IOW=2 and ICPC=1)
EPCO (K) - Capillary pressure exponent for Kth layer for negative branch.
Units: dimensionless
3.4. 1 12 SSTAR(K), for K=l, NZ (This line is read only if IPERM=0 and IOW=2 and ICPC=1)
SSTAR (K) - Water saturation for K* layer where the capillary pressure is zero.
Units: dimensionless
3.4. 1 13 CPCW(I), for 1=1 , NBL (This line is read only if IPERM=0 and IOW=2 and ICPC=2)
CPCW (I) - Capillary pressure endpoint for Ith gridblock for positive branch.
Units: psiVdarcies (IUNIT=0) or kPaVfim2 (IUNIT=1)
3.4. 1 14 EPCW(I), for 1=1, NBL (This line is read only if IPERM=0 and IOW=2 and ICPC=2)
EPCW (I) - Capillary pressure exponent for Ith gridblock for positive branch.
Units: dimensionless
3.4. 1 15 CPCO(I), for 1=1, NBL (This line is read only if IPERM=0 a'nd IOW=2 and ICPC=2)
CPCO - Capillary pressure endpoint for Ith gridblock for negative branch.
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Units: psiVdarcies (IUNIT=0) or
(IUNIT=1)
3.4. 1 16 EPCO(I), for 1=1, NBL (This line is read only if IPERM=0 and IOW=2 and ICPC=2)
EPCO - Capillary pressure exponent for Ith gridblock for negative branch.
Units: dimensionless
3.4. 1 17 SSTAR(I), for 1= 1, NBL (This line is read only if IPERM=0 and IOW=2 and ICPC=2)
SSTAR (I) - Water saturation in Ith gridblock where the capillary pressure is zero.
Units: dimensionless
Diffusion and Dispersion Data (Lines 3.4.118-3.4.125)
3.4.118 D(KC,l),forKC=l,N
D(KC,1) - Molecular diffusion coefficient of KCth component in aqueous phase.
Units: ft2/day (IUNIT=0) orm2/day (IUNIT=1)
3.4.119 D(KC,2),forKC=l,N
D(KC,2) - Molecular diffusion coefficient of KCth component in oleic phase.
Units: ft2/day (IUNIT=0) or m2/day (IUNIT=1)
3.4.120 D(KC,3), forKC=l,N
D(KC,3) - Molecular diffusion coefficient of KCth component in microemulsion phase.
Units: ft2/day (IUNIT=0) orm2/day (IUNIT=1)
3.4. 121 D(KC,4), for KC=1, N (This line is read only if IGAS>1)
D(KC,4) - Molecular diffusion coefficient of KCth component in gas phase.
Units: ft2/day (IUNIT=0) or m2/day (IUNIT=1)
Note: The input diffusion coefficient should be divided by tortuosity (DAc) where the value
of tortuosity is greater than one.
3.4.122 ALPHAL(l), ALPHAT(l)
ALPHAL(l) - Longitudinal dispersivity of aqueous phase.
Units: feet (IUNIT=0) orm(IUNIT=l)
ALPHAT(l) -Transverse dispersivity of aqueous phase.
Units: feet (IUNn=0) or m (IUNIT=1)
3.4.123 ALPHAL(2), ALPHAT(2)
ALPHAL(2) - Longitudinal dispersivity of oleic phase.
Units: feet (IUNIT=0) or m (IUNIT=1)
ALPHAT(2) - Transverse dispersivity of oleic phase.
Units: feet (IUNIT=0) orm(IUNIT=l)
3.4.124 ALPHAL(3), ALPHAT(3)
ALPHAL(3) - Longitudinal dispersivity of microemulsion phase.
Units: feet (IUNIT=0) or m (IUNIT=1)
ALPHAT(3) - Transverse dispersivity of microemulsion phase.
Units: feet (IUNIT=0) or m (IUNIT=1)
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3.4.125 ALPHAL(4), ALPHAT(4) (This line is read only if IGAS>1)
ALPHAL(4) - Longitudinal dispersivity of gas phase.
Units: feet (IUNTT=0) or m (IUNIT=1)
ALPHAT(4) - Transverse dispersivity of gas phase.
Units: feet (IUNIT=0) or m (IUNIT=1)
Adsorption Data (Lines 3.4.126-3.4.1291
3.4.126 IADSO
IADSO - Flag to specify organic adsorption calculation.
Possible Values
0 - Organic adsorption calculation is not considered
1 - Organic adsorption calculation is considered
3.4.127 FOC, AKOC, DENS (This line is read only if IADSO=1 and NO<1)
FOC - fraction of organic carbon in soil.
Units: dimensionless
AKOC - Organic adsorption coefficient.
j, . . l-lg adsorbed/g organic carbon
jig/ml solution
DENS - grain density
Units: lb/ft3 (IUNTT=0), g/cc (IUNIT=1)
Note: See Section 2 of this report for information on the organic adsorption model.
3.4.128 FOC, (AKOCK(K), for K=l, NO), DENS (This line is read only if IADSO=1 and NO>1)
FOC - Fraction of organic carbon in soil.
Units: dimensionless
AKOCK(K) - Organic adsorption coefficient for oil component K.
jj . . M-g adsorbed/g organic carbon
|ig/ml solution
DENS - grain density.
Units: lb/ft3 (KJNIT=0), g/cc (IUNIT=1)
Note: See Section 7 of this report for information on the multiple organic adsorption model.
3.4.129 AD31, AD32, BSD, AD41, AD42, B4D, IADK, IADS1, FADS
ADS 1 - Surfactant adsorption parameter.
Units: dimensionless
AD32 - Surfactant adsorption parameter.
Units: ml/meq
BSD - Surfactant adsorption parameter.
TT . volume of water
Units: —
volume of surfactant
AD41 - Polymer adsorption parameter.
Units: dimensionless
AD42 - Polymer adsorption parameter.
Units: ml/meq
B4D - Polymer adsorption parameter.
TT . volume of water
Units:
weight% polymer
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IADK - Permeability dependent adsorption flag
Possible Values:
0 - Surfactant and polymer adsorption is independent of permeability
1 - Surfactant and polymer adsorption is dependent on permeability
IADS 1 - Flag to specify the competitive surfactant adsorption in the presence of polymer
Possible Values:
0 - Surfactant and polymer adsorption are independent
1 - Competitive surfactant and polymer adsorption is considered
FADS - Parameter to adjust the competitive adsorption calculation
Note: See Section 2 of this report for information on the surfactant and polymer adsorption model.
3.4.130 QV, XKC, XKS, EQW
QV - Cation exchange capacity of clays.
Units: meq/ml of pore volume
XKC - Cation exchange constant for clays.
Units: (meq/ml)-1
XKS - Cation exchange constant for surfactant.
Units: (meq/ml)-*•.
EQW - Equivalent weight of surfactant.
Note: See Section 2 of this report for information on the cation exchange model.
Tracer Data (Lines 3.4.131-3.4.143) — These lines are required only if NTW+NTA>0. See Section 4 of
this report for more details on tracer modeling in UTCHEM.
3.4.131 TK(I), for 1=1, NTW+NTA (This line is read only if NTW+NTA>0)
TK(I) - Tracer partitioning coefficient for Ith water/oil tracer at initial chloride concentration and
reference temperature. A value of 0.0 indicates a water or gas tracer and a value of -1.0
indicates an oil tracer.
Units: fraction
3.4.132 TKS(I), for 1=1, NTW (This line is read only if NTW>0)
TKS(I) - Parameter for calculating water/oil tracer partitioning coefficient for Ith tracer as a function
of salinity.
Units: (meq/ml)-1
3.4.133 TKT(I), for 1=1, NTW+NTA (This line is read only if NTW+NTA>0 and ffiNG=l)
TKT(I) - Parameter for calculating tracer partitioning coefficient for Ith tracer as a function of
reservoir temperature.
Units: ("F)-1 (IUNIT=0) or fC)-1 (IUN1T=1)
3.4.134 RDC(I), for 1=1, NTW+NTA (This line is read only if NTW+NTA>0)
RDC(I) - Radioactive decay coefficient for Ith tracer. A value of 0.0 indicates a non-radioactive
tracer.
Units: I/days
3.4.135 RET(I), for 1=1, NTW+NTA (This line is read only if NTW+NTA>0)
RET(I) - Tracer adsorption parameter (adsorbed concentration/flowing concentration). A value of
0.0 indicates no retardation.
Units: dimensionless
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Appendix A - UTCHEM 6.1 User's Guide
Dead-end Pore Model Data (Lines 3.4.136-3.4.139) — These lines are required only if NTW+NTA>0
and ICAP=1.
3.4.136 FFL(l), FFH(l), CM(I,1), for 1=1, NTW+NTA (This line is read only if NTW+NTA>0 and
ICAP=1)
FFL(l) - Water phase flowing fraction at fractional flow = 0.0.
Units: dimensionless
FFH(l) - Water phase flowing fraction at fractional flow = 1.0.
Units: dimensionless
CM(1,1) - Mass transfer coefficients for Ith tracer in water phase.
Units: I/sec
3.4.137 FFL(2), FFH(2), CM(I,2), for 1=1, NTW+NTA (This line is read only if NTW+NTA>0 and
ICAP=1)
FFL(2) - Oil phase flowing fraction at fractional flow = 0.0.
Units: dimensionless
FFH(2) - Oil phase flowing fraction at fractional flow = 1.0.
Units: dimensionless
CM(I,2) - Mass transfer coefficients for Ith tracer in oil phase.
Units: I/sec
3.4.138 FFL(3), FFH(3), CM(I,3), for 1=1, NTW+NTA (This line is read only if NTW+NTA>0 and
ICAP=1)
FFL(3) - Microemulsion phase flowing fraction at fractional flow = 0.0.
Units: dimensionless
FFH(3) - Microemulsion phase flowing fraction for at fractional flow = 1.0.
Units: dimensionless
CM(I,3) - Mass transfer coefficients for Ith tracer in microemulsion phase.
Units: I/sec
3.4.139 FFL(4), FFH(4), CM(I,4), for 1=1, NTW+NTA (This line is read only if NTW+NTA>0 and
ICAP=1 and IGAS>1)
FFL(4) - Value of flowing fraction for gas phase when fractional flow = 0.0.
Units: dimensionless
FFH(4) - Value of flowing fraction for gas phase when fractional flow = 1.0.
Units: dimensionless
CM(I,4) - Mass transfer coefficients for Ith tracer in gas phase.
Units: I/sec
Reacting Tracer Data (Lines 3.4.140-3.4.143) — The following lines are required only if NTW>0 and
ITREAC=1.
3.4.140 NRT,TAK(I),forI=l,NRT (This line is read only if NTW>0 and ITREAC=1)
NRT - Number of reacting tracers.
Possible Values: 1 or 2
TAK(I) - Rate constant for a first-order aqueous phase reaction at reference temperature for reacting
tracer I
Units: days'1
Note: First reacting tracer is tracer 2 hydrolyzes to form tracer 3. The second reacting tracer if
present is tracer 4 hydrolyzes to form tracer 5.
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Appendix A - UTCHEM 6.1 User's Guide
3.4.141 TMW(I), for 1=1, NTW (This line is read only if NTW>0 and ITREAC=1)
TMW(I) - Molecular weight of the Ith tracer.
Units: The user can specify the molecular weight in any unit as long as the units are the
same for all the tracers. It is assumed that the reaction of 1 mole of primary tracer
produces 1 mole of secondary tracer. If not, use "equivalent" molecular weights.
3.4.142 TDEN(I),forI=l,NTW (This line is readonly if NTW>0 and ITREAC=1)
TDEN(I) - Density of the Ith tracer.
Units: g/cm^
3.4.143 TAKT(I), for 1=1, NRT (This line is read only if NTW>0 and ITREAC=1 and ffiNG=l)
TAKT(I) - Parameter for calculating rate constant for a first-order aqueous phase reaction as a
function of reservoir temperature for reacting tracer I.
Units: (°K)-1
Dual Porosity Data (Lines 3.4.144-3.4.162) _ This section is required for dual porosity option
(ICAP=2) only. This option works only with English unit (IUNIT=0) and the Cartesian coordinate
(ICOORD=lj. See Section 5 of this report for more details on this option. The capability of dual porosity
option at this time is limited to single phase water and one tracer component. Restart capability (IMODE=2)
is not currently available for the dual porosity option.
3.4.144 NSUB, MSUB, ISUB (This line is read only if ICAP=2)
NSUB - Number of subgrids in lateral direction.
MSUB - Number of subgrids in vertical direction.
ISUB - Mode of subgridding
Possible Values:
0 - Uniform matrix block dimension
1 - Variable matrix block size dimension in each direction
2 - Variable matrix block dimension in whole reservoir
3.4.145 XL1,YL1,ZL1 (This line is read only if ICAP=2 and ISUB=0)
XL1, YL1 and ZL1 - Uniform matrix block sizes in x y, and z directions.
Units: feet
3.4.146 III, 112, XL1 (This line is read only if ICAP=2 and ISUB=1)
III, 112 - First and last index for gridblocks with same size in X direction.
XL1- Matrix block size in X direction.
Units: feet
3.4.147 JJ1,JJ2, YL1 (This line is read only if 1CAP=2 and ISUB=1)
JJ1, JJ2 - First and last index for gridblocks with same size in Y direction.
YL1 - Matrix block size in Y direction.
Units: feet
3.4.148 KK1,KK2,ZL1 (This line is readonly if 1C AP=2 and ISUB=1)
KK1, KK2 - First and last index for gridblocks with same size in Z direction
ZL1 - Matrix block size in Z direction.
Units: feet
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Appendix A - UTCHEM 6.1 User's Guide
3.4.149 XL(I), for 1=1, NBL (This line is read only if ICAP=2 and ISUB=2)
XL(I) - Matrix block size in X direction for Ith reservoir gridblock.
Units: feet
3.4.150 YL(I), for 1=1, NBL (This line is read only if ICAP=2 and ISUB=2)
YL(I) - Matrix block size in Y direction for I1*1 reservoir gridblock.
Units: feet
3.4.151 ZL(I),forI=l,NBL (This line is read only if ICAP=2 and ISUB=2)
ZL(I), - Matrix block size in Z direction for Ith reservoir gridblock.
Units: feet
3.4.152 VFRACM(J), for J=l, NSUB (This line is read only if ICAP=2)
VFRACM(J) — Volume fraction of Jth subgrid. These values are used to generate subgrids in the
lateral direction.
3.4.153 ZFRACM(J), for J=l, MSUB (This line is read only if ICAP=2)
ZFRACM - Thickness fraction of Ith vertical subgrid. These values are used to generate subgrids in
the vertical direction.
3.4.154 KPH, KKX, KKZ (This line is read only if ICAP=2)
KPH — Flag for matrix porosity distribution.
Possible Values:
0 - Uniform matrix porosity
1 - Variable matrix porosity
KKX - Flag for diffusion coefficient distribution in lateral direction in matrix.
Possible Values:
0 - Uniform matrix diffusion coefficient
1 - Uniform matrix diffusion coefficient in each reservoir layer
2 - Variable matrix diffusion coefficient at each reservoir node
KKZ - Flag for diffusion coefficient distribution in vertical direction in matrix.
Possible Values:
0 - Uniform matrix diffusion coefficient
1 - Uniform matrix diffusion coefficient in each reservoir layer
2 - Variable matrix diffusion coefficient at each reservoir node
3.4.155 PHIC (This line is read only if ICAP=2 and KPH=0)
PHIC - Matrix porosity.
3.4.156 PORCM(I,1,1), for 1=1, NBL (This line is read only if ICAP=2 and KPH=1)
PORCM(I,1,1) - Matrix porosity of the Ith reservoir node.
3.4.157 DMC (This line is read only if ICAP=2 and KKX=0)
DMC - Matrix diffusion coefficient in lateral direction.
Units: ft2/day
3.4.158 DMX(K), for K= 1, NZ (This line is read only if 1CAP=2 and KKX= 1)
DMX(K) - Matrix diffusion coefficient in Kth reservoir layer in lateral direction.
Units: ft2/day
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Appendix A - UTCHEM 6.1 User's Guide
3.4.159 DMX(I), for 1=1, NBL (This line is read only if ICAP=2 and KKX=2)
DMX(I) - Matrix diffusion coefficient at Ith reservoir node in lateral direction.
Units: ft2/day
3.4.160 DMC (This line is read only if ICAP=2 and KKZ=0)
DMC - Matrix diffusion coefficient in vertical direction.
Units: ft2/day
3.4.161 DMZ(K), for K=l, NZ (This line is read only if ICAP=2 and KKZ=1)
DMZ(K) - Matrix diffusion coefficient in K* reservoir layer in vertical direction.
Units: ft2/day
3.4.162 DMZ(I), for 1=1, NBL (This line is read only if ICAP=2 and KKZ=2)
DMZ(I) - Matrix diffusion coefficient at Ith reservoir node in vertical direction.
Units: ft2/day
Gel Reaction Data (Lines 3.4.163-3.4.167) _ These Unes ^ required only tf IREACT=1 or
IREACT=4 and NG>0. Refer to Section 6 of this report for more details on this option.
3.4.163 KGOPT, AK1, AK2, SCR, X4, X13, X14, X16, WM4 (This line is read only if IREACT=1 or 4
andNG>0)
KGOPT - Flag to specify the gelation type used.
Possible Values:
1 - Polymer/chromium chloride gel
2 - Polymer/chromium malonate gel
3 - Silicate gel
AK1 - Kinetic rate coefficient for NG1 and NG2 at reference temperature (KGOPT=1).
Units: ppnr1 days'1
AK2 - Kinetic rate coefficient for gel at reference temperature .
Units: (mole/liter) 1'X4-X14+X16 days'1 for KGOPT=1
(mole/liter)1-X4-xl3+X16 days'1 for KGOPT=2
(mole/liter) 1-X4+X14 days'1 for KGOPT=3
SCR - Stoichiometric ratio in mass between Cr3+ and polymer.
Units: dimensionless
X4 - Exponent to be used for polymer or silicate in gelation reaction.
Units: dimensionless
X13 - Exponent to be used for component (NG2) in gelation reaction for KGOPT=2.
Units: dimensionless
X14 - Exponent to be used for the third gel option component (NG3) in gelation reaction.
Units: dimensionless
X16 - Exponent to be used for hydrogen ion component (NG5) of gelation reaction.
Units: dimensionless
WM4 - Molecular weight of polymer (KGOPT= 1 or 2) or silicate (KGOPT=3).
Units: g/mole
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Appendix A - UTCHEM 6.1 User's Guide
Note: The following tables define different gelation options and corresponding gel components.
For IREACT=1:
Component No.
4
NG1
NG2
NG3
NG4
NG5
KGOPT=1
Polymer
Na2Cr2O7
CSN2H4
Cr(HI)
Gel
Hydrogen
KGOPT=2
Polymer
-
Malonate ion
Cr(lH)
Gel
Hydrogen
KGOPT=3
Silicate
-
-
OH-
Gel
-
For IREACT=4:
Component NO.
4
NGC1
NGC2
NGC3
NGC4
NGC5
NGC6
NG1
NG2
NG3
NG4
KGOPT=1
Polymer
Sodium
Hydrogen
Magnesium
Carbonate
Chromium*
Silica
Na2Cr2O7
CSN2H4
Cr(III)**
Gel
KGOPT=2
Polymer
Sodium
Hydrogen
Magnesium
Carbonate
Chromium*
Silica
-
Malonate ion
Cr(III)**
Gel
Where NG and NGC are the gel option and geochemistry option species.
3.4.164 AK1T, AK2T (This line is read only if IREACT=1 or 4 and NG>0 and IENG=1)
AK1T - Parameter for calculating Kinetic rate coefficient for Cr3+ as a function of reservoir
temperature.
Units: ("K)-1
AK2T - Parameter for calculating Kinetic rate coefficient for gel as a function of reservoir
temperature.
Units: (°K)-1
3.4.165 AG1, AG2, CRG, AGK, BGK (This line is read only if IREACT=1 or 4 and NG>0)
AG1 - Flory-Huggins parameter for gel viscosity.
Units: cp ppnr1 = m = Pa.s ppnr1
AG2 - Flory-Huggins parameter for gel viscosity.
Units: cp ppnr2 = mPa.s ppnr2
CRG - Constant hi the dimensionless pore radius reduction group. This constant depends on the gel
type.
Units: ^/darcy(wt%)1/'3 = ^\im2 (wt%)1/3
AGK, BGK - Permeability reduction parameters for Langmuir correlation with gel concentration.
Units: dimensionless
200
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Appendix A - UTCHEM 6.1 User's Guide
3.4.166 A15D, B15D, ICREX, A14D, B14D, CRNAK, HNAK, C160 (This line is read only if
IREACT=1 or 4 and NG>0)
A15D, B15D - Gel adsorption parameters.
Units: vol. of water / ppm gel
ICREX - Flag indicating if Cr3+ will be allowed to exchange with clays.
Possible Values:
0 - Cr3+ exchange with clays is not allowed
1 - Cr3+ exchange with clays is allowed
A14D, B14D - Chromium adsorption parameters.
Units: vol. of water / ppm chromium
CRNAK - Chromium-sodium exchange reaction equilibrium constant.
HNAK - Hydrogen-sodium exchange reaction equilibrium constant.
C160 - Initial hydrogen ion concentration.
Units: meq/ml
Note: The input values of CRNAK, HNAK, and C160 are ignored for IREACT=4
3.4.167 IP1, IP2 (This line is read only if IREACT=1 or 4 and NG>0 and NY=1 and NZ=1)
IP1, IP2 - Gridblock locations where calculated pressure values should be printed to UNIT 19.
Note: These values are intended to be used for comparison with pressure tab data of 1-D
experiments.
Temperature Data (Lines 3.4.168-3.4.171) — These lines are required only if temperature variation is
considered in the simulation for IENG=1.
3.4.168 TEMPI (This line is readonly if ffiNG=l)
TEMPI- Constant initial reservoir temperature.
Units: °F (IUNIT=0) or °C (IUNIT=1)
3.4.169 DENS, CRTC, CVSPR, (CVSPL(L), for L=l, MXP) (This line is read only if IENG=1)
DENS - Reservoir rock density.
Units: lb/ft3 (IUNIT=0) or g/cm3 (IUNIT=1)
CRTC - Reservoir thermal conductivity.
Units: Btu (day-ft-T)-1 (IUNIT=0) or kJ (day-m-'K)-1 (IUNIT=1)
CVSPR - Reservoir rock heat capacity.
Units: Btu (Ib-'F)-1 (IUNIT=0) or kJ (kg-°K)-! (IUNIT=1)
CVSPL(L) - Phase L heat capacity (MXP is equal to 3 (IGAS=0) or 4 (IGAS>1)).
Units: Btu (Ib-T)-1 (IUNIT=0) or kJ (kg-0K)-! (IUNIT=1)
3.4.170 IHLOS, IANAL (This line is read only if IENG=1)
IHLOS - Flag indicating if the heatloss calculation to overburden and underburden rock is
considered or not.
Possible Values:
0 - Heatloss is not considered
1 - Heatloss is considered
IANAL - Flag indicating if the temperature profile is calculated from analytical solution (only 1-D).
Possible Values:
0 - Analytical solution is not considered
1 - Analytical solution is considered
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3.4.171 TCONO, DENO, CVSPO, TCONU, DENU, CVSPU (This line is read only if IHLOS=1 and if
ffiNG=l)
TCONO - Thermal conductivity of overburden rock.
Units: Btu (day-fVF)-1 (IUNIT=0) or kJ (day-m-'K)-1 (IUNIT=1)
DENO - Density of overburden rock.
Units: lb/ft3 (IUNIT=0) or g/cm3 (IUNIT=1)
CVSPO - Heat capacity of overburden rock.
Units: Btu (Ib-T)'1 (IUNIT=0) or kJ (kg^K)-1 (IUNIT=1)
TCONU - Thermal conductivity of underbidden rock.
Units: Btu (day-ft-'F)-1 (IUNIT=0) or kJ (day-m-'K)-1 (IUNIT=1)
DENU - Density of underburden rock.
Units: lb/ft3 (rUNIT=0) or g/cm3 (IUNIT=1)
CVSPU - Heat capacity of underburden rock.
Units: Btu (Ib-'F)-1 (IUNIT=0) or kJ (kg-'K)-1 (IUNIT=1)
Foam Model Data (Lines 3.4.172 and 3.4.173) — These lines are required only if the foam option is
considered (IGAS=2).
3.4.172 RFMAX, SOSTAR, CSTAR, EPXLO, SHRTN, VELGR (This line is read only if IGAS=2)
RFMAX- Maximum foam "R" parameter.
Units: dimensionless
SOSTAR - Critical oil saturation above which foam is not generated.
Units: dimensionless
CSTAR - Critical surfactant concentration below which foam is not generated.
Units: volume fraction
EPXLO - Water saturation tolerance parameter in foam model.
Units: dimensionless
SHRTN - Gas shear thinning exponent.
Units: dimensionless
VELGR - Reference gas velocity.
Units: ft/day (IUNIT=0) or m/day (IUNIT=1)
3.4.173 SWSTAR(I), for 1=1, NBL (This line is read only if IGAS=2)
SWSTAR(I)- Water saturation at critical capillary pressure for Ith gridblock.
Units: dimensionless
Note: SWSTAR(I) is assumed to be corrected for the permeability used in the simulation.
3.5 Physical Property Data for Geochemical Options
The fifth input section consists of physical property data for geochemistry option and it is
required only if IREACT>1. The data for this section is generated by a preprocessor program
(EQBATCH) and does not have the same format as the rest of the input data for UTCHEM. This
input section is read by a separate routine called GEOREAD not preceded by the usual seven
comment lines and individual data lines are not preceded by three comment lines. Section A.5 of this
appendix gives an example for the list of elements, fluid species, solid species, and adsorbed species
for geochemicai options. See Section 8 of this report for information on the EQBATCH program.
3.5.1 IRSPS, IPHAD
IRSPS - Flag indicating if the reactive species concentrations should be printed.
Possible Values:
0 - Reactive species concentrations will not be printed
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Appendix A • UTCHEM 6.1 User's Guide
1 - Independent aqueous reactive species, solid species, and sorbed species
concentrations will be printed
2 - All aqueous species, solid species, and sorbed species concentrations will be printed
IPHAD - Flag indicating whether surfactant adsorption is pH dependent or not.
Possible Values:
0 - Surfactant adsorption is not pH dependent
1 - Surfactant adsorption is pH dependent
3.5.2 PHC, PHT, PHT1, HPHAD (This line is read only if IPHAD>0)
PHC - Critical pH above which surfactant adsorption is pH dependent.
PHT - Extrapolated pH value at zero surfactant adsorption.
PHT1 - pH value above which surfactant adsorption is constant.
HPHAD - Fraction of the low-pH adsorption plateau retained at a pH above PHT1.
3.5.3 CSELP, CSEUP (This line is read only if IREACT=3)
CSELP - Lower optimum salinity limit for generated surfactant.
Units: meq/ml
CSEUP - Upper optimum salinity limit for generated surfactant.
Units: meq/ml
3.5.4 NELET, NFLD, NSLD, NSORB, NACAT, ICHRGE
NELET - Total number of elements less non reacting element.
NFLD - Total number of fluid species.
NSLD - Total number of solid species.
NSORB - Total number of sorbed species.
NACAT - Total number of surfactant associated cations.
ICHRGE - Flag indicating whether an oxygen balance or a charge balance will be used.
Possible Values:
0 - Oxygen balance used
1 - Charge balance in solution used
Note: If solid SiO2 is considered, the oxygen balance must be used.
3.5.5 NIAQ, NEX, NSLEL, NSURF1
NIAQ - Total number of independent fluid species. •
NEX - Total number of insoluble exchangers.
NSLEL - Total number of elements comprising the solid species.
NSURF1 - Position number corresponding to the insitu generated surfactant anion in the fluid species
array FLDSPS.
Note: NSURF1 is automatically set to 0 by the program if IREACT=2.
3.5.6 NH, NNA, NCA, NMG, NCARB
NH - Position number corresponding to the hydrogen element in the element array ELEMNT.
NNA - Position number corresponding to the sodium element in the element array ELEMNT.
NCA - Position number corresponding to the calcium element in the element array ELEMNT.
NMG - Position number corresponding to the magnesium element in the element array ELEMNT.
NCARB - Position number corresponding to the carbonate pseudo-element in the element array
ELEMNT.
Note: A value of zero is required if the element is not considered.
3.5.7 NALU, NSILI, NOXY
NALU - Position number corresponding to the aluminum element in the element array ELEMNT.
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Appendix A - UTCHEM 6.1 User's Guide
NSILI - Position number corresponding to the silicon element in the element array ELEMNT.
NOXY - Position number corresponding to the oxygen element in the element array ELEMNT.
Note: A value of zero is required if the element is not considered.
3.5.8 NACD (This line is read only if IREACT=3)
NACD - Position number corresponding to the petroleum acid pseudo-element in the element array
ELEMNT.
3.5.9 NCR, NHFD, NCRFD (This line is read only if IREACT=4)
NCR - Position number corresponding to the chromium element in the element array ELEMNT.
NHFD - Position number corresponding to the hydrogen ion element in the fluid species array
FLDSPS.
NCRFD - Position number corresponding to the CR(ni) ion in the fluid species array FLDSPS.
3.5.10 ELEMNT(I), ELCRG(I) for 1=1, NELET
ELEMNT(I) - Name of the Ith element.
ELCRG(I) - Charge for Ith element
Note: The name of each element may not exceed 32 characters and each name and charge must be
on a separate line of the input file. The order in which these elements must be listed
corresponds to the order in which the injection concentrations need to be specified on input
line 3.7.7.a with the exceptions of calcium and chloride (if they exist) since Components 5
and 6 are reserved for these elements.
3.5.11 FLDSPS(I), for 1=1, NFLD
FLDSPS(I) - Name of the Ith fluid species.
Note: The name of each fluid species may not exceed 32 characters and each name must be
on a separate line of the input file. If IREACT=3, the last fluid species must be HAW
(petroleum acid in water).
3.5.12 SLDSPS(I), for 1=1, NSLD (This line is read only if NSLD>0)
SLDSPS(I) - Name of the Ith solid species.
Note: The name of each solid may not exceed 32 characters and each name must be on a
separate line of the input file.
3.5.13 SORBSP(I), for 1=1, NSORB (This line is read only if NSORB>0)
SORBSP(I) - Name of the I* adsorbed cation.
Note: The name of each adsorbed cation may not exceed 32 characters and each name must
be on a separate line of the input file.
3.5.14 ACATSP(I), for 1= 1, NACAT (This line is read only if NACAT>0)
ACATSP(I) - Name of the Ith surfactant adsorbed cation.
Note: The name of each surfactant adsorbed cation may not exceed 32 characters and each
name must be on a separate line of the input file.
3.5.15 NSORBX(I),forI=l,NEX (This line is read only if NSORB>0)
NSORBXCO - Number of cations for Ith exchanger.
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3.5.16 AR(I,J), for J= 1, NFLD, for 1= 1, NELET « or »
AR(I,J), for J=l, NFLD, for 1=1, NELET-1
AR(I,J) - Stoichiometric coefficient of Ith element in Ith fluid species.
Note: If ICHRGE=0, then NFLD x NELET values are required by the program. If ICHRGE=1,
then NFLD x (NELET-1) values are required by the program.
3.5.17 BR(LJ), for J=l, NSLD, for 1=1, NELET « or »
BR(I,J), for J=l, NSLD, for 1=1, NELET-1 (This line is read only if NSLD>0)
BR(I,J) - Stoichiometric coefficient of Ith element in Jth solid species.
Note: If ICHRGE=0, then NSLD x NELET values are required by the program. If ICHRGE=1,
then NSLD x (NELET-1) values are required by the program.
3.5.18 DR(LJ), for J=l, NSORB, for 1=1, NELET «or»
DR(IJ), for J=l, NSORB, for 1=1, NELET-1 (This line is read only if NSORB>0)
DR(I,J) - Stoichiometric coefficient of Ith element in Jth sorbed species.
Note: If ICHRGE=0, then NSORB x NELET values are required by the program. If ICHRGE= 1,
then NSORB x (NELET-1) values are required by the program.
3.5.19 ER(LJ), for J=l, NACAT, for 1=1, NELET «or»
ER(I,J), for J=l, NACAT, for 1=1, NELET-1 (This line is read only if NACAT>0)
ER(I,J) - Stoichiometric coefficient of Ith element in Jth surfactant associated cation.
Note: If ICHRGE=0, then NACAT x NELET values are required by the program. If ICHRGE= 1,
then NACAT x (NELET-1) values are required by the program.
3.5.20 BB(LJ), for J=l, NIAQ+NSORB+NACAT, for 1=1, NFLD+NSORB+NACAT
BB(I,J) - Exponent of the Jth independent fluid species concentration when the Ith fluid species is
expressed in terms of independent species concentrations.
3.5.21 EXSLD(IJ), for J=l, NIAQ, for 1=1, NSLD (This line is read only if NSLD>0)
EXSLD(IJ) - Exponent of the Jth independent fluid species concentration in the solubility product
definition of the Ith solid.
3.5.22 CHARGE(I), for 1=1, NFLD
CHARGE® - Charge of the Ith fluid species.
3.5.23 SCHARG(I,J), for 3=1, NSORBX(I), for 1=1, NEX (This line is read only if NSORB>0)
SCHARG(I,J) - Charge of the Jth sorbed species on the Ith exchanger.
3.5.24 EQK(I), for 1=1, NFLD
EQK(I) - Equilibrium constant for Ith fluid species when expressed in independent species
concentrations only.
3.5.25 EXK(I,J), for J=l, NSORBX(I)-!, for 1=1, NEX (This line is read only if NEX>0)
EXK(I,J) - Exchange equilibrium constant for Jth exchange equilibrium of the Ith insoluble
exchanger.
3.5.26 EXEX(I,J,K), for K=l, NIAQ+NSORB+NACAT, for J=l, NSORBX(I)-!, for 1=1, NEX (This
line is read only if NEX>0)
EXEX(I, J,K) - Exponent of Kth independent species in Ith equilibrium relation of the Ith exchanger
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3.5.27 REDUC(I,J), for J=l, NSORBX(I)-!, for 1=1, NEX (This line is read only if NEX>0)
REDUC(I,J) - Valence difference of the two cations involved in the exchange reaction J on exchanger
I.
Note: This value is positive if the higher valence cation bulk concentration has a positive exponent in
EXEX(I,J) definition and is negative otherwise.
3.5.28 EXCAI(I), for 1=1, NEX (This line is read only if NEX>0)
EXCAI(I) - Exchange capacity of Ith insoluble exchanger.
Units: meq/ml pore volume
3.5.29 SPK(I), for 1=1, NSLD (This line is read only if NSLD>1)
SPK(I) - Solubility product of Ith solid defined in terms of independent fluid species concentrations
only.
3.5.30 CHACATO), for 1=1, NACAT (This line is read only if NACAT>1)
CHACAT(I) - Charge of Ith surfactant associated cation.
3.5.31 ACATK(I), for 1=1, NACAT-1 (This line is read only if NACAT>1)
ACATK(I) - Equilibrium constant for Ith exchange equilibrium for cation exchanges on surfactant.
3.5.32 EXACAT(IJ) for J=l, NIAQ+NSORB+NACAT, for 1=1, NACAT-1 (This line is read only if
NACAT>1)
EXACAT(IJ) - Exponent of Ith independent species in Ith equilibrium for cation exchange on
surfactant.
3.5.33 CI(J), for J=l, NACAT (This line is read only if NACAT>1)
CI(J) - Initial concentration of Ith surfactant associated cation.
Units: moles/liter pore volume
3.5.34 C5I.C6I
C5I - Initial concentration of non-reacting anions.
Units: equivalents/liter
C6I - Initial concentration of calcium in aqueous phase.
Units: equivalents/liter
3.5.35 CELAQI(J), for J=l, NGC
CELAQI(J) - Initial concentrations of Jth geochemistry component.
Units: equivalents/liter
3.5.36 CAC2I (This line is read only if IREACT=3)
CAC2I - Initial concentration of acid in oil.
Units: moles/liter oil
3.5.37 CAQI(J), for J=l, NIAQ
CAQI(J) - Initial guesses for Jth independent species concentration.
Units: moles/liter water
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3.5.38 CSLDI(I),forI=l,NSLD (This line is read only NSLD>0)
CSLDI(I) - Initial concentration of Ith solid.
Units: moles/liter pore volume
3.5.39 CSORBI(I),forI=l,NSORB (This line is readonly if NSORB>0)
CSORBI(I) - Initial concentration of Ith adsorbed cation.
Units: moles/liter pore volume
3.5.40 C1I, C2I (This line is read only if IREACT=3)
CII - Initial concentration of water in aqueous phase.
Units: volume fraction
C2I - Initial concentration of oil in oleic phase.
Units: volume fraction
3.5.41 ACIDIS,EQWPS (This line is read only if IREACT=3)
ACIDIS - Dissociation constant of the petroleum acid.
EQWPS - Equivalent weight of petroleum acid.
3.6 Data for Biodegradation Option
The sixth input section consists of physical property data that is required only if IBIO=1.
This section includes the biodegradation and mass transfer parameters required to model the
biodegradation of chemical species. This section is read only if IBIO=1. The data is read by a
separate subroutine called BIOREAD, and is input in the standard UTCHEM format. Section 9 of
this report gives more details on this option.
3.6.1 DIAMP, DENBLK, CMIN, EPSBIO
DIAMP - Average particle size diameter (used to calculate mass transfer coefficient). A value of
DIAMP must be input whether or not mass transfer is considered. The value is ignored if
mass transfer is not considered.
Units: cm
DENBLK - Bulk density of the porous medium (mass of porous medium per unit total volume).
Units: g/cm3
CMIN - Minimum concentration of substrate and electron acceptor that is of interest. This parameter
is used for two purposes. First, if concentrations of all substrates and electron acceptors in a
gridblock are below CMIN, then biodegradation reactions are assumed negligible at the
gridblock and are not modeled. Second, when the concentration of all substrates and electron
acceptors fall below CMIN during solution of the biodegradation reaction expressions, further
biodegradation reactions are assumed to be negligible and program execution returns to the
main program.
Units: mg/L
EPSBIO - Convergence tolerance for solution of the biodegradation equations.
Note: Values of 10'4 to 10~6 are recommended, although larger values can also result in
accurate simulations. Small values ensure accurate solutions of the biodegradation
equations but increase run times, while larger values decrease run times at the expense
of some accuracy.
3.6.2 NBC, NMET, IBKTN
NBC - Total number of chemical and biological species that are considered in biodegradation
reactions, including oil components, surfactants, products generated by abiotic and
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biodegradation reactions, nutrients required for biological growth, electron acceptors, and
biological species.
NMET - Number of substrate-electron acceptor-biological species metabolic combinations. Include
combinations of biodegrading products-electron acceptor-biological species for each product
that also biodegrades.
IBKIN - Flag specifying the type of biodegradation kinetics.
Possible Values:
0 - No reaction (useful for restart runs)
1 - Monod kinetics and external mass transfer resistances
2 - Monod kinetics with no mass transfer
3 - Instantaneous kinetics (stoichiometric reactions)
Note: First order kinetics can be also be modeled by adjusting the values of the Monod parameters.
See input line 3.6.6 below.
3.6.3 KC(I), ITYPE(I), CINIT(I), RABIO(I), NPABIO(I), for 1=1, NBC
Note: One line is required for each chemical and biological species that participates in biodegradation
reactions.
KC(I) - Index of the Ith chemical or biological species.
ITYPEOO - Flag indicating whether the I'* component is a chemical or biological species.
Possible values:
1 - The Ith component is a chemical species
2 - The Ith component is a biological species
CINrr(I) - Initial concentration of chemical or free-floating (unattached) biological species I in the
aqueous phase.
Units: mg/t
Note: Although a value of CINIT must be entered for organic species that participate in
biodegradation reactions, these values are ignored by the program. Initial
concentrations of these components are input on input lines 3.3.32 through 3.3.35.
RABIO(I) - First-order abiotic reaction rate constant.
Units: I/days
Note: Although a value of RABIO can be specified for biological as well as chemical species,
biomass decay should not be controlled with RABIO. Instead, use the parameters
ENDOG and ENDOGB to control endogenous decay of unattached and attached
biomass, respectively. RABIO should normally be set to 0.0 for biological species.
NPABIO(I) - Number of products generated by a first-order abiotic reaction of chemical species I.
Note: A value must be entered for biological species as well, although the value is ignored by
the program because generation of products from decay of biomass is not allowed.
3.6.4 KC(I), DENBIO(I), RCOL(I), TCOL(I), COLNUM(I), ENDOG(I), ENDOGB(I), CBI(I),
CBIOMN(I) for 1=1, NBS
Note: One line is required for each biological species.
KC(I) - Index of the biological species.
DENBIO(I) - density of attached biological species I (biofilm density).
Units: g cells / cm3 biomass
RCOL(I) - radius of an attached microcolony of biological species I.
Units: cm
Note: The parameter RCOL is used to calculate the surface area of a single attached
microcolony. Although microcolonies are assumed to be disk-shaped by the model,
the user may specify any desired surface area per microcolony using RCOL. TCOL
can then be adjusted to obtain the desired volume of the microcolony since the
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thickness of the microcolony does not affect external mass transfer into the attached
biomass.
TCOL(I) - Thickness of a single attached microcolony of biological species I.
Units: cm
COLNUM(I) - Number of bacterial cells per microcolony of biological species I.
Units: cells/colony
ENDOG(I) - endogenous decay coefficient of unattached cells of biological species I.
Units: I/days
ENDOGB(I) - endogenous decay coefficient of attached cells of biological species I.
Units: I/days
CBI(I) - Number of attached bacterial cells of biological species I per gram of dry soil.
Units: cells/gram of solid.
CBIOMN(I) - Lower limit of number of attached bacterial cells of biological species I.
Units: cells/gram of solid.
Note: A population of attached microorganisms, sustained by naturally occurring organic
matter, is assumed to exist in the porous media regardless of the concentration of other
chemical species. This concentration is CBIOMN, and the concentration of biomass is
not allowed to fall below this value.
3.6.5 ISUB(I), IEA(I), IBS(I), BRMAX(I), BRMAXB(I), YXS(I), AKS(I), AKA(I), FEA(I), for 1=1,
NMET
Note: One line is read for each metabolic combination.
ISUB(I) - Substrate index for metabolic combination I.
IEA(I) - Electron acceptor index for metabolic combination I.
IBS(I) - Biological species index for metabolic combination I.
BRMAX(I) - maximum specific growth rate of unattached microorganisms for metabolic
combination I.
Units: I/days
BRMAXB(I) - Maximum specific growth rate of attached microorganisms for metabolic
combination I.
Units: I/days
YXS(I) - Yield coefficient for metabolic combination I.
Units: mg/£
AKS(I) - Substrate half-saturation coefficient for metabolic combination I.
Units: mg/£
AKA(I) - Electron acceptor half-saturation coefficient for metabolic combination I.
Units: mg/^
FEA(I) - Electron acceptor utilization coefficient (mass of electron acceptor consumed per mass of
substrate biodegraded).
3.6.6 ISUB(I), IEA(I), IBS(I), NCOMPS(I), NfflB(I), NPROD(I), NNUT(I), ICOMET(I), for 1=1,
NMET
Note: One line is read for each metabolic combination.
ISUB(I) - Substrate index for metabolic combination I.
IEA(I) - Electron acceptor index for metabolic combination I.
IBS(I) - Biological species index for metabolic combination I.
NCOMPS(I) - Number of other substrates competing with substrate ISUB in metabolic combination
NIHB(I) - Number of other chemical species that inhibit metabolic combination I.
NPROD(I) - Number of products generated from metabolic combination I.
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NNUT(I) - Number of nutrients that limit the biodegradation rate through Monod terms for metabolic
combination I.
ICOMET(I) - Flag indicating whether or not the substrate in metabolic combination I is biodegraded
through aerobic cometabolism.
Possible Values:
0 - Substrate ISUB(I) serves as a primary substrate
1 - Substrate ISUB(I) is biodegraded through aerobic cometabolism
Note: Users may specify multiple competing substrates, nutrients, and inhibiting constituents for
each metabolic combination. Substrate competition, inhibition and cometabolism cannot be
modeled if instantaneous kinetics are selected. However, values for the biodegradation rate
parameters must be specified even if instantaneous kinetics are specified.
First-order biodegradation kinetics can be modeled by using a very large value of KS, and
adjusting the ratio of /Xmax/#S to be equal to the desired first-order biodegradation rate
coefficient.
3.6.7 ISUB(p, EBA(I), ffiS(I), (ICSUB(IJ), for J=l, Number of competing substrates), for 1=1, NMET
(This line is read only if there are competing substrates)
Note: One line is read for each metabolic combination for which there is substrate competition
between two or more substrates.
ISUB(I) - Substrate index for metabolic combination I.
IEA(I) - Electron acceptor index for metabolic combination I.
IBS(I) - Biological species index for metabolic combination I.
ICSUB(J) - Indices of other substrates that compete with substrate ISUB(I) in metabolic combination
I.
Note: The number of input lines required must equal the number of species that are competing, since
complementary lines are required to fully describe the competition. For example, if substrate
12 in metabolic combination 12-15-16 must compete with substrates 13 and 14 that are also
biodegraded by biological species 16 using electron acceptor 15, then the required input lines
are:
12 15 16 13 14
13 15 16 12 14
14 15 16 12 13
3.6.8 ISUB(I), ffiA(I), ffiS(I), fflB(I), BSIHB(I), for 1=1, Number of metabolic combination and
inhibiting compound associations (This line is only read if there are metabolic combination and
inhibiting compound associations)
Note: One input line is read for each association of metabolic combination and inhibiting compound.
ISUB(I) - Substrate index for metabolic combination I.
IEA(I) - Electron acceptor index for metabolic combination I.
IBS(I) - Biological species index for metabolic combination I.
IHB(I) - Index of chemical species that inhibits metabolic combination I.
BSIHB(I) - Inhibition constant for metabolic combination I.
Units: mg/£
Note: The total number of lines are
NMET
1=2 NIHB(J).
J=l
For example, suppose there are two substrate-electron acceptor-biological species metabolic
combinations: 9-10-12 and 9-11-12. Metabolic combination 9-10-12 is inhibited by the
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substrate itself (9) and electron acceptor 11, while metabolic combination 9-11-12 is inhibited
by only the substrate. Then the input lines for this scenario would be:
9 10 12 9 0.001
9 10 12 11 0.001
9 11 12 9 0.001
3.6.9 ISUB(I), ffiA(I), IBS(I), IPR(I), FPR(I), for 1=1, Number of biodegradation product formation and
metabolic combination associations (This line is read only if there are biodegradation product
formation described with Monod kinetics and metabolic combination associations)
Note: One line is read for each association of product formation and metabolic combination.
ISUB(I) - Substrate index for metabolic combination I.
IEA(I) - Electron acceptor index for metabolic combination I.
IBS(I) - Biological species index for metabolic combination I.
IPR(I) - Index of product generated by metabolic combination I.
FPR(I) - Product generation coefficient (stoichiometric ratio - mass of product generated per mass of
substrate biodegraded).
Note: Number of lines are
NMET
1= Y NPRODT(J).
3.6.10
3.6.11
For example, if metabolic combination 9-14-15 generates products 10 and 11, and metabolic
combination 12-14-15 generates product 13, then the input lines would be:
9 14 15 10 2.0
9 14 15 11 1.0
12 14 15 13 1.5
Parameters for generation of products through first-order reactions are described on input line
3.6.10.
ISUB(I), IPR(I), FPR(I), for 1=1, Number of products generated by first-order reactions of the
biodegradation species. (This line is read only if there are products of first-order reactions of
biological species)
ISUB(I) - Index of chemical species that reacts abiotically to generate a product.
IPR(I) - Index of product generated by abiotic reaction of ISUB(I).
FPR(I) - Product generation coefficient (stoichiometric ratio - mass of product generated per mass of
reactant reacted).
Note: Number of lines are
NBC
1= 2 NPABIO(J).
J=l '
For example, if the abiotic products 11,12 and 13 were generated from the first-order reaction
of biodegradation species 9 and 10, then the input lines would be:
9 11 1.0
9 12 1.0
10 13 2.0
ISUB(I), ffiA(I), IBS(I), INUT(I), AKN(I), FN(I), for 1=1, Number of metabolic combination and
limiting nutrient associations (This line is read only if there are metabolic combination and limiting
nutrient associations)
Note: One line is read for each association of metabolic combination and limiting nutrient.
ISUB(I) - Substrate index for metabolic combination I.
IEA(I) - Electron acceptor index for metabolic combination I.
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D3S(I) - Biological species index for metabolic combination I.
INUT(I) - Index of nutrient limiting the rate of biodegradation through a Monod term in metabolic
combination I.
AKN(I) - Nutrient half-saturation coefficient for metabolic combination I.
Units:
FN(I) - Nutrient utilization coefficient (mass of nutrient consumed per mass of substrates
biodegraded) for metabolic combination I.
NMET
Note: Number of lines are I = ]£ NNUTT(J).
J=l
3.6.12 ISUB(I), IEA(I), D3S(I), TC(I), IRLIM(I), for 1=1, Number of cometabolic combinations for which
aerobic cometabolism exists (This line is read only if there are cometabolic combinations for which
aerobic cometabolism exists for at least one metabolic combination specified in line 3.6.6)
Note: One input line is required for each cometabolic combination for which aerobic cometabolism
exists.
ISUB(I) - Substrate index for metabolic combination I.
EEA(I) - Electron acceptor index for metabolic combination I.
D3S(I) - Biological species index for metabolic combination I.
TC(I) - Transformation capacity for cometabolism of substrate ISUB(I) (mass of substrate utilized
per mass of biomass destroyed).
IRLIM(I) - Flag indicating whether reducing power limitations are considered for cometabolic
combination I.
Possible Values:
0 - No reducing power limitations are considered
1 - Cometabolic reaction consumes reducing power
Note: Reducing power limits the biodegradation rate through Monod terms in the manner of
Chang and Alvarez-Cohen [1995]. The loss of a biological species' reducing power
reduces its activity toward all substrates, not just the cometabolite.
NMET
Note: The total number of lines are I = COMET(J).
J=l
3.6.13 ISUB(I), IEA(I), IBS(I), IGROW(I), REDI(I), AKR(I), FRP(I), FRC(I),-for 1=1, Number of
cometabolic biodegradation reactions in which reducing power limitations are considered (This line
is read only if there are cometabolic biodegradation reactions in which reducing power limitations are
considered and IRLIM(I)>0 for at least one metabolic combination specified in line 3.6. 1 1)
Note: One line is required for each cometabolic biodegradation reaction in which reducing power
limitations are considered.
ISUB(I) - Substrate index for metabolic combination I.
IEA(I) - Electron acceptor index for metabolic combination I.
IBS(I) - Biological species index for metabolic combination I.
IGROW(I) - Index of growth substrate for cometabolism of substrate ISUB(I).
REDI(I) - Initial intracellular reducing power (NADH) concentration.
Units: mmol/mg of biomass
AKR(I) - Reducing power half-saturation coefficient.
Units: mmol/mg of biomass
FRP(I) - Reducing power generation coefficient for metabolic combination (IGROW(I), IEA(I),
IBS(I) (mmol reducing power generated per mg of growth substrate consumed).
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FRC(I) - Reducing power consumption coefficient for cometabolic combination (ISUB(I), IEA(I),
IBS (I)) (mmol reducing power consumed per mg of substrate consumed by cometabolism).
Note: The total number of lines are
K
where
I = ^IRLIM(J)
J=l
NMET
K= £ COMET(J).
J=l
3.7 Recurrent Injection/Production Data Set
The sixth input section consists of the recurrent injection/production well data. Please
remember that there are seven comment lines at the beginning of this section and that each line is
preceded by three comment lines.
3.7.1
3.7.2
3.7.3
3.7.4
IBOUND
IBOUND - The flag to specify if constant potential boundaries at the left and right sides of the
simulation model are specified.
Possible Values:
0 - No boundary is specified
1 - Boundary is specified
Note: This option of IBOUND=1 is not currently available for the vadose zone or when gas
is present (IGAS>1)
IBL, 1BR (This line is read only if ffiOUND=l)
IBL - The flag to specify if the left hand side constant potential boundary is specified.
Possible Values:
0 - No boundary is specified
1 - Boundary is specified
IBR - The flag to specify if the right hand side constant potential boundary is specified.
Possible Values:
0 - No boundary is specified
1 - Boundary is specified
PEL, C1BL, C5BL, C6BL (This line is read only if IBOUND=1 and IBL=1)
PEL- Pressure at the center of the top layer at the left boundary.
Units: psia (IUNTT=0) or kPa (IUNIT=1)
C1BL- Concentration of water in aqueous phase at the left boundary.
Units: volume fraction
C5BL - Concentration of chloride in aqueous phase at the left boundary.
Units: meq/ml
C6BL - Concentration of calcium in aqueous phase at the left boundary.
Units: meq/ml
PER, C1BR, C5BR, C6BR (This line is read only if IBOUND=1 and IBR=1)
PER - Pressure at the center of the top layer at the right boundary.
Units: psia (IUNIT=q) or kPa (IUNIT=1)
C1BR - Concentration of wafer in aqueous phase at the right boundary.
Units: volume fraction
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C5BR - Concentration of chloride in aqueous phase at the right boundary.
Units: meq/ml
C6BR - Concentration of calcium in aqueous phase at the right boundary.
Units: meq/ml
Note: For the biodegradation option (IBIO=1), the concentrations of all species considered at the
boundary are set to the initial concentrations.
3.7.5 NWELL, IRQ, ITIME, NWREL
NWELL - Number of wells used for the simulation including the pseudowells to mimic an open
boundary.
Note: If ICOORD=2, NWELL must be equal to 1 and the MXW parameter in the source
code must be set equal to 2.
IRQ - Flag indicating the equivalent well radius model to be used.
Possible Values:
1 - Babu and Odeh model is used
2 - Peaceman model is used
Note: The Babu and Odeh model (IRO=1) does not work for ICOORD=4.
ITIME - Flag indicating the units to be used when specifying the minimum and maximum time step.
Possible Values:
0 - Minimum and maximum time steps are input in days
1 - Minimum and maximum time steps are input as Courant numbers
Note: This option is only used if IMES>1 and is not a shut-in period. If IMES=1, this flag
is ignored. For a shut-in period you need to use ITIME=0
NWREL - Number of actual wells used for the simulation excluding the pseudowells.
Note: The history data are written only for NWREL wells.
Note: See Section A.8 of this appendix for more details on the Courant number and time step
selection options.
The following values for minimum and maximum Courant numbers are recommended for
different simulations as follows:
Process
Waterflood/tracer
Polymer-flood
Surfactant/polymerflood
Geochemical process
Min. Courant #
0.04
0.02
0.01
0.01
Max. Courant #
0.4
0.2
0.1
0.1
See Section 10 of this report for well model information.
3.7.6 The data on input lines 3.7.6.a through 3.7.6.d are repeated for M=l to NWELL times.
Important note: Input the actual wells first (NWREL) and then the pseudowells.
3.7.6.a IDW(M), IW(M), JW(M), IFLAG(M), RW(M), SWELL(M), IDIR(M), IFIRST(M), ILAST(M),
IPRF(M)
IDW(M) - Well I.D. number for the Mth well.
Possible Values: Must be between 1 and MXW (the source code parameter indicating the
maximum number of wells)
Note: This number is used by UTCHEM to keep track of which well is being described in
the recurrent injection/production well section. The history profile data for the well
indicated by IDW(M) will be written to FORTRAN UNIT number 18 + IDW(M).
IW(M) - First index of the reservoir gridblock containing the Mth well.
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Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
Note: If the Mth well is completed parallel to the X-axis, IW(M) is the Y direction
index—if the well is completed parallel to the Y- or Z-axis, IW(M) is the X direction
index. See example below.
If ICOORD=2, IW(1)=JW(1)=1.
JW(M) - Second index of the reservoir gridblock containing the Mth well.
Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
Note: If the Mth well is completed parallel to the X- or Y-axis, JW(M) is the Z direction
index—if the well is completed parallel to the Z-axis, JW(M) is the Y direction
index. See example below.
If ICOORD=2, IW(1)=JW(1)=1.
IFLAG(M) - Flag indicating type of well constraint specification for Mth well.
Possible Values:
1 - Rate constrained injection well
2 - Pressure constrained production well (This option is available only if
ICOORD=1 or 3)
3 - Pressure constrained injection well (This option is available only if ICOORD=1
or 3)
4 - Rate constrained production well
RW(M) - Radius of M*h well.
Units: feet (IUNIT=0) or m (IUNIT=1)
SWELL(M) - Skin factor for M* well.
Units: dimensionless
IDIR(M) - Flag indicating the direction in which the Mth well is completed.
Possible Values:
1 - Well completed parallel to the X-axis
2 - Well completed parallel to the Y-axis
3 - Well completed parallel to the Z-axis
Note: If ICOORD=2, IDIR( 1) must be equal to 3.
IFIRST(M) - Index of the first block in which the Mth well is completed.
Possible Values: Between 1 and the number of gridblocks. in the pertinent direction,
inclusive
ILAST(M) - Index of the last block in which the Mth well is completed.
Possible Values: Between IFIRST(M) and the number of gridblocks in the pertinent
direction, inclusive
IPRF(M) - Flag indicating if partial completion of the well is considered.
Possible Values:
0 - The well is fully completed
1 - The well is partially completed
Example: For a vertical well (completed through all the layers) as illustrated in the 4 x 4 x 3
example below, note the values of IDIR(M), IW(M), JW(M), IFIRST(M), and ILAST(M):
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X
IDIR(M) = 3
IW(M) = 1
JW(M) = 1
IFIRST(M) = 1
ILAST(M) = 3
For a horizontal well (completed from the first to last gridblock in the X direction and
parallel to the X-axis) as illustrated in the 4 x 4 x 3 example below, note the values of
IDIR(M), IW(M), JW(M), IFIRST(M), and ILAST(M):
/\/ / /
' S *• S S /
/ y/\/
/
/
/
/
.-••
/
r * ~
///
//
VW
IDIR(M) = 1
IW(M) = 2
JW(M) = 1
DFIRST(M) = 1
ILAST(M) = 4
Note: Horizontal wells can be used for 2-D X-Y or 3-D simulations.
3.7.6.b KPRF(M,IWB), for IWB=1, NWBC (This line is read only if IPRF=1)
KPRF(M,IWB) - Flag indicating if the IWE* well block of the Mth well is perforated or not.
Possible Values:
0 - The well block is not perforated
1 - The well block is perforated
3.7.6.C WELNAM(M)
WELNAM(M) - Name of the Mth well.
Note: The name can consist of any combination of up to 18 alphanumeric characters. This
information will be printed—along with the well I.D. number, IDW(M)—at the
beginning of the history output files.
3.7.6.d ICHEK(M), PWFMIN(M), PWFMAX(M), QTMIN(M), QTMAX(M)
ICHEK(M) - The flag to specify whether to check the rate or pressure caps for the Mth well.
Possible Values:
0 - There will be no check on the rate or pressure limits and no automatic shut in for
the pressure constraint injector
1 - There will be no automatic shut in for the pressure constraint injector but the
pressure or rate limits are checked
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2 - There will be both the automatic shut in and the check on the pressure or rate
limits
PWFMIN(M) - Minimum flowing bottom hole pressure (specified at the top layer) for the Mth
well.
Units: psi (IUNIT=0) orkPa(IUNIT=l)
PWFMAX(M) - Maximum flowing bottom hole pressure (specified at the top layer) for the Mth
well.
Units: psi (IUNIT=0) or kPa (IUNIT=1)
QTMIN(M) - Minimum total flow rate (specified at the top layer) for the Mth well.
Units: ft3/day (IUNIT=0) or irP/day (IUNIT=1)
QTMAX(M) - Maximum total flow rate (specified at the top layer) for the Mth well.
Units: ft3/day (IUNIT=0) orm3/day (IUNIT=1)
Note: - PWFMIN(M) and PWFMAX(M) are the pressure caps for a rate constraint injector or
producer well. QTMIN(M) and QTMAX(M) are the total rate caps for a pressure constraint
injector or producer well. If the M^1 pressure constraint injector or producer produces at total
rate less than QTMIN(M), the Mth well will be switched to a rate constraint well with total
rate of QTMIN(M) for the rest of the injector or production period. On the other hand, if the
total rate is greater than the QTMAX(M), the Mth well then will be switched to a rate
constraint well with the total rate of QTMAX(M). The similar concept is applied to a rate
constraint injector or producer.
- The user can skip the well control calculation by specifying very small values for
QTMIN(M) and PWFMIN(M) and very large values for QTMAX(M) and PWFMAX(M).
- The code still has the automatic option for shut in of a pressure constraint injector injecting
at a rate of less than QTMIN(M).
3.7.7 The data on input lines 3.7.7.a, 3.7.7.b, 3.7.7.C, and 3.7.7.d are repeated for M=l to NWELL times.
Notes: - For injection wells that are on rate constraint only injection rates and concentrations for
each phase are listed. For injection wells that are on pressure constraint the injection pressure
is also specified. In this case the injection rates are treated as phase cuts in the injected fluid.
For producer pressure constraint only the bottom hole pressure is specified. For producer
rate constraint only the total production rate is specified.
- The user can shut in a pressure constraint well by specifying a negative bottom hole
pressure or a rate constraint well by specifying a value of zero for rate (QI).
3.7.7.a ID(M), (QI(M,L), (C(M,KC,L), for KOI, N), for L=l, MXP) (This set of data is read only if
IFLAG(M)=1 or 3)
ID(M) - Well I.D. number for the M* well.
Possible Values: Must be between 1 and MXW (the source code parameter indicating the
maximum number of wells)
Note: See note for IDW(M) on input line 3.7.6.a.
QI(M,L) - Injection rate of Lth phase in Mth well (see note below).
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
C(M,KC,L) - Concentration of KCth component in L* phase in M* well.
Units: vary according to component (see note below)
Notes: - See Section A.7 of this appendix for component and phase numbering scheme and the
I concentration units for each species.
|- The KG index changes the fastest, the L index changes the next fastest, and the M index
I changes the slowest. A separate data line should be in the input file for each phase—that is,
iM x L lines will be read by the program. MXP is equal to 3 (IGAS=0) or 4 (IGAS>1).
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3.7.7.b ID(M), PWF(M) (This line is read only if IFLAG(M)=2 or 3)
BD(M) - Well ID. number for the M* well.
Possible Values: Must be between 1 and MXW (the source code parameter indicating the
maximum number of wells)
Note: See note for IDW(M) on input line 3.7.6.a. For IFLAG(M)=3, the rates (QI(M,L))
are used an injected volume fraction for each phase.
PWF(M) - Flowing bottom hole pressure for the Mth well.
Units: psia (IUNIT=0) orkPa(IUNIT=l)
3.7.7.C ID(M), TEMINJ(M) (This line is read only if IENG=1 and IFLAG(M)=1 or 3)
ID(M) - Well I.D. number for the M* well.
Possible Values: Must be between 1 and MXW (the source code parameter indicating the
maximum number of wells)
Note: See note for IDW(M) on input line 3.7.6.a.
TEMINJ(M) - Injection temperature for Mth well.
Units: °F (IUNIT=0) or °C (IUNIT=1)
3.7.7.d ID(M), QI(M, 1) (This line is read only if IFLAG(M)=4)
ID(M) - Well ID. number for the Mth well.
Possible Values: Must be between 1 and MXW (the source code parameter indicating the
maximum number of wells)
Note: See note for IDW(M) on input line 3.7.6.a.
QI(L) - Total production rate for Mth well.
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
Note: This value needs to be input as a negative number.
3.7.8 TINJ, CUMPR1, CUMHIl, WRHPV, WRPRF, RSTC
TINJ - Cumulative injection time.
Units: days or pore volumes (dependent on value ofTSTOP flag on input line 3.2.1)
CUMPR1 - Indicates interval at which profiles should be written to UNIT 4.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)
CUMHI1 - Indicates interval at which production data should be written to UNIT 4.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)
WRHPV - Indicates interval at which production histories should be written to output file(s) for
history plotting.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)
Note: If WRHPV > total pore volume injected or maximum simulation time, the data will
not be printed. The unit number of the file to be written to starts at 19 and continues
upward. For example, for a run with three producers, UNITS 19, 20 and 21 would be
used. The history of reservoir properties and overall rates from all the producing wells
is written to UNIT 9.
WRPRF - Indicates interval at which concentration, pressure, saturation, tracer phase concentration,
capacitance property, gel property, alkaline property, and temperature profiles should be
written to UNITS 8, 11, 12, 13, 14, 10, 15, and 18 respectively.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)
Note: If WRPRF > total pore volume injected or maximum simulation time, the data will not
be written.
RSTC - Indicates the interval at which restart data should be written to UNIT 7.
Units: pore volumes or days (dependent on value ofTCUMTM flag on input line 3.2.1)
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Note: A 7th variable (CUMH12) which used to control production data printing to UNIT 3 is no
longer available with the latest version of UTCHEM.
Time Step Selection Data (Lines 3.7.9-3.7.131
See Section A.8 of this appendix for more details on the time step selection options.
3.7.9 DT (This line is read only if IMES=1 and ITIME=0)
DT - Time step size for constant time step option.
Units: days
3.7.10 DT, DCLIM, DTMAX, DTMIN (This line is read only if IMES=2 and ITIME=0)
DT - Initial time step size.
Units: days
DCLIM - Tolerance for concentration change for the first three components.
Units: volume fraction
DTMAX - Maximum time step size.
Units: days
DTMIN - Minimum time step size.
Units: days
3.7.11 DT, DCLIM, CNMAX, CNMIN (This line is read only if MES=2, ITIME=1, and at least one well
is not shut-in.)
DT - Initial time step size.
Units: days
DCLIM - Tolerance for concentration changes for the first three components.
Units: volume fraction
CNMAX - Maximum Courant number.
Units: dimensionless
CNMIN - Minimum Courant number.
Units: dimensionless
3.7.12 DT, (DELC(KC), for KC=1, N), DTMAX, DTMIN (This line is read only if IMES=3 or 4 and
ITIME=0)
DT - Initial time-step size.
Units: days
DELC(KC) - Tolerance for concentration change of KCth component (IMES=3) or relative tolerance
for concentration change of KCth component (IMES=4).
Units: IMES=3: volume fraction, weight percent, meq/ml, or ppm (depending on which
component the tolerance is for—see note for input line 3.7.7.a)
IMES=4: dimensionless
Note: DELC(KC) is the dimensionless relative change in concentration. For example:
DELC(3)=0.1 indicates a 10% change in concentration of component 3.
DTMAX - Maximum time step size.
Units: days
DTMIN - Minimum time step size.
Units: days
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3.7.13 DT, (DELC(KC), for KC=1, N), CNMAX, CNMIN (This line is read only if IMES=3 or 4,
ITIME=1, and all the wells are not shut-in)
DT - Initial time step size.
Units: days
DELC(KC) - Tolerance for concentration change of KG* component (IMES=3) or relative tolerance
for concentration change of KG* component (IMES=4).
Units: IMES=3: volume fraction, weight percent, meq/ml, or ppm (depending on which
component the tolerance is for—see note for input line 3.7.7.a)
IMES=4: dimensionless
CNMAX - Maximum Courant number.
Units: dimensionless
CNMIN - Minimum Courant number.
Units: dimensionless
IMPORTANT NOTE: The data on lines 3.7.14 through 3.7.23 describe the changes in boundary
conditions and are repeated until the injected time (TINJ on input line 3.7.8) is greater than or equal to the
maximum simulation time (TMAX on input line 3.3.1).
3.7.14 IRQ, ITIME, (EFLAG(M), for M=l, NWELL)
IRQ - Flag indicating the equivalent well radius model to be used.
Possible Values:
1 - Babu and Odeh model is used
2 - Peaceman model is used
ITIME - Flag indicating the units to be used when specifying the minimum and maximum time step.
Possible Values:
0 - Minimum and maximum time steps are input in days
1 - Minimum and maximum time steps are input as Courant numbers
Note: This option is only used if IMES>1 and it is not a shut-in period. If IMES=1, this
flag is ignored.
IFLAG(M) - Flag indicating type of well constraint specification for Mth well.
Possible Values:
1 - Rate constrained injection well
2 - Pressure constrained production well (This option is available only if ICOORD=1
or 3)
3 - Pressure constrained injection well (This option is available only if ICOORD=1 or
3)
4 - Rate constrained production well
3.7.15 NWEL1
NWEL1 - Number of wells with changes in location (IW(M), JW(M)), skin, direction, perforation,
name, or minimum and maximum bottomhole pressure or minimum or maximum rate.
3.7.16 The data on input lines 3.7.16.a through 3.7.16.d are repeated for M=l to NWEL1 times.
3.7.16.a ID, IW(ID), JW(ID), RW(ID), SWELL(ID), IDIR(ID), IFIRST(ID), ILAST(ID), IPRF(ID)
ID - Well ID number with changes from the previous slug injection period.
IW(ID) - First index of the reservoir gridblock containing the IDth well.
Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
Note: See note for input line 3.7.6.a.
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JW(ID) - Second index of the reservoir gridblock containing the IDth well.
Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
Note: See note for input line 3.7.6.a.
RW(ID) - Radius of IDth well.
Units: feet (IUNIT=0) or m (IUNIT=1)
SWELL(ID) - Skin factor for ID* well.
Units: dimensionless
IDIR(ID) - Flag indicating the direction in which the IDth well is completed.
Possible Values:
1 - Well completed parallel to the X-axis
2 - Well completed parallel to the Y-axis
3 - Well completed parallel to the Z-axis
Note: IfICOORD=2,IDIR(l)mustbeequalto3.
IFIRST(ID) - Index of the first block in which the IDth well is completed.
Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
ILAST(ID) - Index of the last block in which the IDth well is completed.
Possible Values: Between IFIRST(ID) and the number of gridblocks in the pertinent
direction, inclusive
Note: At this time, UTCHEM assumes the well is completed continuously between
IFIRST(ID) and ILAST(ID).
IPRF(ID) - Flag Indicating if partial completion of the well is considered.
Possible Values:
0 - The well is fully completed
1 - The well is partially completed
3.7.16.b KPRF(ID,IWB), for IWB=1, NWBC (This line is readonly if IPRF=1)
KPRF(ID,IWB) - Flag indicating if the IWB* well block of the ID* weu is perforated or not.
Possible Values:
0 - The well block is not perforated
1 - The well block is perforated
3.7.16.C WELNAM(ID)
WELNAM(ID) - Name of the ID* well.
Note: The name can consist of any combination of up to 18 alphanumeric characters. This
information will be printed—along with the well I.D. number, IDW(ID)—at the
beginning of the history output files.
3.7.16.d ICHEK(ID), PWFMIN(ID), PWFMAX(ID), QTMIN(ID), QTMAX(ID)
ICHEK(ID) - The flag to specify whether to check the rate or pressure caps for the ID* well.
Possible Values:
0 - There will be no check on the rate or pressure limits and no automatic shut in for
the pressure constraint injector
1 - There will be no automatic shut in for the pressure constraint injector but the user
specified pressure or rate limits are checked
2 - There will be both the automatic shut in and the check on the user specified
pressure or rate limits
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PWFMIN(ID) - Minimum flowing bottom hole pressure (specified at the top layer) for the IDth
well.
Units: psi (IUNIT=0) or kPa (IUNIT=1)
PWFMAX(ID) - Maximum flowing bottom hole pressure (specified at the top layer) for the IDth
well.
Units: psi (IUNIT=0) or kPa (IUNIT=1)
QTMINQD) - Minimum total flow rate (specified at the top layer) for the IDth well.
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
QTMAX(ID) - Maximum total flow rate (specified at the top layer) for the IDth well.
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
Note: See the note for input line 3.7.6.d.
3.7.17 NWEL2, (IDWW(J), for J=l, NWEL2)
NWEL2 - Number of wells with changes in rate, concentration or bottomhole pressure.
IDWW(J) - ID number for Jth well with changes.
3.7.18 The data on input lines 3.7.18.a through 3.7.18.d are repeated for M=l to NWEL2 times.
3.7.18.a ID, QI(ID,L), (C(ID,KC,L), for KC=1,N), for L=l, MXP (This set of data is read only if
IFLAG(ID)=1 or 3)
ID - Well ID number with changes from the previous slug injection period.
QI(ID,L) - Injection rate of Lth phase in 10th well (see note for input line 3.7.7.a).
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
C(ED,KC,L) - Concentration of KCth component in L* phase for IDth well.
Units: vary according to component (see note for line 3.7.7.a)
Note: IfIGAS=0, thenMXP=3. If IGAS>1, thenMXP=4.
3.7.18.b ID, PWF(ID) (This line is read only if IFLAG(ID)=2 or 3)
ID - Well ID number with changes from the previous slug injection period.
PWF(ID) - Flowing bottom hole pressure for the ID* well.
Units: psia (IUNIT=0) or kPa (IUN1T=1)
3.7.18.C ID, TEMINJ(ID) (This line is read only if ffiNG=l and IFLAG(ID)=1 or 3)
ID - Well ID number with changes from the previous slug injection period.
TEMINJ(ID) - Injection temperature for the IDth well.
Units: °F (IUNIT=0) or °C (IUNIT=1)
3.7.18.d ID, QI(ID,1) (This line is read only if IFLAG(ID)=4)
ID - Well ID number with changes from the previous slug injection period.
QI(ID,1) - Total production rate for IDth well.
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
Note: This value needs to be input as a negative number.
3.7.19 TINJ, CUMPR1, CUMHI1, WRHPV, WRPRF, RSTC
TINT - Cumulative injection time.
Units: days or pore volumes (dependent on value of ISTOP flag on input line 3.2.1)
CUMPR1 - Indicates interval at which profiles should be written to UNIT 4.
Units: pore volumes or days (dependent on value ofTCUMTM flag on input line 3.2.1)
CUMHI1 - Indicates interval at which production data should be written to UNIT 4.
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Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)
WRHPV - Indicates interval at which production histories should be written to output file(s) for
history plotting.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)
Note: If WRHPV > total pore volume injected or maximum simulation time, the data will
not be printed. The unit number of the file to be written to starts at 19 and continues
upward. For example, for a run with three producers, UNITS 19, 20, and 21 would
be used. The history of reservoir properties and the total rate from all the producing
wells is written to UNIT 9.
WRPRF - Indicates interval at which concentration, pressure, saturation, tracer phase concentration,
capacitance property, pressure difference, gel property, alkaline property, and temperature
profiles should be written to UNITS 8, 11, 12, 13, 14, 10, 15 and 18 respectively.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)
Note: If WRPRF > total pore volume injected or maximum simulation time, the data will
not be written.
RSTC - Indicates the interval at which restart data should be written to UNIT 7.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 3.2.1)
Note: A 7th variable (CUMH12) which used to control production data printing to UNIT 3 is no
longer available with the latest version of UTCHEM.
3.7.20 DT (This line is read only if IMES=land ITIME=0)
DT - Time step size for constant time step option.
Units: days
3.7.21 DT, DCLIM, DTMAX, DTMIN (This line is read only if IMES=2 and ITIME=0)
DT - Initial time step size.
Units: days
DCLIM - Tolerance for concentration change for the first three components.
Units: volume fraction
DTMAX - Maximum time step size.
Units: days
DTMIN - Minimum time step size.
Units: days
3.7.22 DT, DCLIM, CNMAX, CNMDSf (This line is read only if IMES=2, ITIME=1, and at least one well
is not shut-in)
DT - Initial time step size.
Units: days
DCLIM - Tolerance for concentration changes for the first three components.
Units: volume fraction
CNMAX - Maximum Courant number.
Units: dimensionless
CNMIN - Minimum Courant number.
Units: dimensionless
3.7.23 DT, (DELC(KC), for KC=1, N), DTMAX, DTMIN (This line is read only if IMES=3 or 4 and
ITIME=0)
DT - Initial time-step size.
Units: days
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DELC(KC) - Tolerance for concentration change, ACiim,K, of KCth component (IMES=3) or relative
tolerance for concentration change of KC* component (IMES=4).
Units: IMES=3: volume fraction, weight percent, meq/ml, or ppm (depending on which
component the tolerance is for—see note for input line 3.7.7.a)
IMES=4: dimensionless
DTMAX - Maximum time step size.
Units: days
DTMIN - Minimum time step size.
Units: days
3.7.24 DT, (DELC(KC), for KC=1, N), CNMAX, CNMIN (This line is read only if IMES=3 or 4,
ITIME=1, and reservoir is not shut-in)
DT - Initial time step size.
Units: days
DELC(KC) - Tolerance for concentration change of KCth component (IMES=3) or relative tolerance
for concentration change of KCth component (IMES=4).
Units: IMES=3: volume fraction, weight percent, meq/ml, or ppm (depending on which
component the tolerance is for—see note for input line 3.7.7.a)
IMES=4: dimensionless
CNMAX - Maximum Courant number.
Units: dimensionless
CNMIN - Minimum Courant number.
Units: dimensionless
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A.4 OUTPUT FILES
The following sections describe: (4.1) data that is automatically written to the profile data file,
(4.2) restart run procedure, (4.3) data written to stored restart data file, (4.4) data written to history files
for each well, (4.5) data written to history of reservoir properties and overall injection and production
rates from all the wells, and (4.6) data written to aqueous phase tracer concentration data files.
4.1 Default Data Written to Profile Data File
The information in the following lists is always written to the profile data file (PROFIL) and is
not controlled by the various print control flags in the input files.
Printed at each CUMHI1 interval:
Time, number of time steps
Time step size
Courant number
Cumulative pore volume injected
Original in place for each component
Cumulative injection for each component
Cumulative production for each component
Amount retained for each component
Relative error for each component
Fraction of oil recovered
IfIREACT>2:
Average number of iterations, computation time
For each well:
Position of the well, first and last well block completed
Cumulative injection/production
Bottomhole pressure for each well block
All well related information (such as pressure for each phase, phase concentration,
phase cut, etc.)
Producer wellbore temperature and phase cut and concentration
Printed at each CUMPR1 interval:
Reservoir temperature if IENG=1
Phase saturation profile for each phase
Aqueous phase pressure profile
Concentration of each component in the fluid
IfIBIO=l andmPR=l:
Concentration of aqueous phase biodegradation species
IfIBKIN=l:
Concentration of biodegradation species within attached biomass
If tracers are present and ICAP=£0:
Flowing concentration
Dendiritic concentration
Flowing saturation
Dendiritic saturation
4.2 Restart Run Procedure
The restart procedure is available with UTCHEM. This enables a user to continue a run past
the initial time period or to break a large run up into smaller segments. Each time you run UTCHEM,
a file .called RESTAR is created. This file (described in Section 6.3) contains all the information
necessary to continue the run at a later time. In order to do so, the user needs to:
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1.- Rename the output file RESTAR from the previous run to INPUT2
2.- Set the variable EVIODE equal to 2 on line 3.1.3 of input file INPUT
3.- Change the value of TMAX on input line 3.3.1 of file INPUT to the new injection period being
simulated in the restart run
4.- Change the value of TINT on input line 3.7.8 of file INPUT if appropriate
5.- Add additional information for input lines 3.7.14 through 3.7.24 of file INPUT if the well
conditions are different for the new injection period
Note: Make sure the source code you run the restart problem (IMODE=2) has the same values for
the array sizes in the parameter statement as the one used in original run (IMODE=1).
4.3 Data Written to Stored Restart Run Data File
The information hi the following list is always written to the stored restart data file (RESTAR).
If the user is running a RESTART run, this data file needs to be renamed to correspond to the
INPUT2 input file. The values in parentheses are the FORTRAN variable names as they appear in the
code.
Printed at the end of each run:
Time (T), injection time (TDSTJ), time step size (DT), number of time steps (ICNT)
New slug injection or restart flag (IINJ), number of time step reduction (INEC), cumulative
pore volume injection (CUMPV), number of blocks in X-direction minus 1 (NXM1)
Cumulative injection (CUMI), cumulative production (CUMP), original in place (OIP) for
each component
Cumulative injection/production (CUMQI and CUMQP) for each well
Phase concentration (C), phase saturation (S), effective salinity (CSE), overall concentration
(CTOT), number of phases (NPHASE)
If ICOORD=2:
Boundary concentration (CE), boundary pressure (PE)
Viscosity (VIS), relative permeability (RPERM), injection rate (QI), total rate for each well
(QT), phase rate (Q), bottomhole pressure (PWF)
Pressure (P)
If IADSO=1:
Organic adsorption (C2ADSS)
IfLMO=l:
Multiple organic adsorption (CS1DSK)
Surfactant adsorption (C3ADSS), surfactant adsorption parameter (A3DS), polymer
adsorption (C4ADSS)
Permeability reduction factor (RKF), calcium concentration (C6JO), calcium adsorbed by clay
(C6ADSS), calcium adsorbed by surfactant (C6HATS)
Alcohol 7 partitioning coefficient (X7OLD), alcohol 8 partitioning coefficient (X8OLD)
Oil breakthrough (BTO), tracer breakthrough (TBT), tracer injection concentration (CINJT),
tracer retardation factor (TRD)
Lower effective salinity (CSEL), upper effective salinity (CSEU)
Density (DEN), capillary pressure (PRC)
Total surfactant (TSURF)
If IPERM=2 and IHYST=1:
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Minimum water saturation (SWMIN)
IfICAP=l:
Dendiritic concentration (CD), dendiritic saturation (SD), flowing saturation (SF), total
flowing concentration (CTF)
IfNG*0:
Chromium adsorption (C14ADS), gel adsorption (C15ADS), cation exchange capacity
of clay (QW)
IfIENG=l:
Cum. heat inj. (CUMHI), cum. heat prod. (CUMHP), temperature (TEM), total
volumetric heat capacity (TVHC)
IfIENG=l andIHLOS=l:
Cum. heat loss (TQLOS), integral for overburden and underburden heatloss
calculations (RING, RINU), time of change of overburden temp, from the reservoir
block (TTCHG), overburden temperature (TEMPOB), underburden temperature
(TEMPUB)
If ffiNG =1 and ICOORD =2:
Boundary enthalpy (ENTHE)
IfIREACT>l:
Solid concentration (CSLDT), adsorbed concentration (CSORBT), species
concentration (CAQSP), surf, associated cation concentration (CACATT), cation
concentration (CACAT)
Cumulative no. of iteration for geochem option (UCUM)
IfIBIO=l:
Concentrations of attached biomass and intra-biomass concentrations of chemical
species (CB)
Concentrations of reducing power in aqueous phase biomass (RED) and attached
biomass (REDB)
4.4 Data Written to Well History Plotting Data File(s)
The information in' the following list is always written to the well history plotting data files
(HISTOl-HISTO for each production well.
Printed at each WRHPV interval:
Cumulative pore volume, time [days], cumulative production [ft3, m3, or STB], water oil ratio,
cumulative oil recovery, total production rate [ft3/day, m3/day, or STB/day]
If IGAS =1: Water cut, oil cut, microemulsion cut, gas cut
Wellbore pressure for each well block [psi or kPa]
If IENG =1: Wellbore temperature [°F or °C]
For 1=1, N:
If ICF(I) =1: phase concentration for component N (C(I,L), L=1,MXP), total
concentration of component N (CTOT(I))
If IREACT>1 or ICF(3)=1: Lower effective salinity, upper effective salinity, effective salinity
IfIBIO=landIBPR=l:
Concentrations of attached biomass and intra-biomass concentrations of chemical
species (CMGL) [mg/l]
If IBIO=1, IBPR=1, and there are cometabolic biodegradation reactions in which reducing
power limitations are considered:
Concentrations of reducing power (NADH) in aqueous phase and attached biomass
IfIREACT>l:
Independent species concentration (CAQSP(KK), KK=1, NIAQ) [mole/liter of water]
227
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Appendix A - UTCHEM 6.1 User's Guide
If IRSPS >0: Dependent species concentration (CAQSP(KK), KK=NIAQ+1,NFLD)
[mole/liter of water]
If IRE ACT =3 or 5: Phase concentration of injected + generated surfactant
(PSURF(I,L), L=l,3), total concentration of injected + generated surfactant
(TSURF)
If NSLD >0: Concentration of solid components (CSLDT(KK), KK=1, NSLD)
[mole/liter of pore volume]
If ICNM >0: Logio of interfacial tension between water/microemulsion and
oil/microemulsion (XIFT1, XIFT2) [dyne/cm]
The information in the following list is always written to the well history plotting data files for each
injection well.
Printed at each WRHPV interval:
Cumulative pore volume, time in days, cumulative injection [ft3, m3, or STB],
injection rate [ft3/day, m3/day, or STB/day]
Wellbore pressure for each well block [psi or kPa]
Pressure drop between the wells (for the specific case of one injector and one producer
only) or pressure drop between the pressure tabs (when NG>0, NY=1, NZ=1,
see line 3.4.167) [psi or kPa]
4.5 Data Written to Overall History Plotting Data File
The information in the following list is always written to the overall history plotting data file
(OVERAL).
Printed at each WRHPV interval:
Cumulative pore volume, time in days, volumetric averaged reservoir pressure (psi or kPa),
cumulative oil produced (%OOIP), cumulative oil produced (bbls or m3), volumetric
averaged reservoir temperature (°F or °C) (only if IENG=1)
Total injection rate (B/D or m3/day), total production rate (B/D or m3/day), total fluid injected
(1000 bbls or m3), total fluid produced (1000 bbls or m3) [Note: The fluid injected
and produced values are calculated for the last time step before the print interval.]
Overall production rate for each phase (QBAR(L) for L=l, MXP where MXP=3 if IGAS=0
and MXP=4 if IGAS =1) (B/D or m3/day)
Average cut for each phase (FBAR(L) for L=l, MXP where MXP=3 ifTGAS=0 and MXP=4
if IGAS =1)
Average saturation for each phase (SBAR(L) for L=l, MXP where MXP=3 if IGAS=0 and
MXP=4ifIGAS=l)
If ICF(3)=1: Cumulative surfactant injected (bbls or m3), Cumulative surfactant produced
(bbls or m3), adsorbed surfactant (bbls or m3), retained surfactant (bbls or m3),
adsorbed surfactant (ml/ml PV)
If ICF(4)=1: Cumulative polymer injected (wt%), Cumulative polymer produced (wt%),
adsorbed polymer (wt%), retained polymer (wt%), adsorbed polymer (wt. % / PV)
4.6 Data Written to Tracer Concentration Observation Point Data File(s)
The information in the following list is written to the tracer observation history plotting data
files (TRACOl-TRACn) for each tracer (if IPOBS=0). ,
Printed at each WRHPV interval:
228
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Appendix A • UTCHEM 6.1 User's Guide
Time in days, cumulative pore volume
IfIGAS=0:
Aqueous phase tracer concentration at NOBS observation locations
IfIGAS>l:
Gas phase tracer concentration at NOBS observation locations
A.5 GEOCHEMISTRY OPTION (IREACT>1)
This section gives an example list of elements and reactive species for the geochemistry
options of IREACT=2 or IREACT=4.
Elements or pseudo-element:
Indeendent aueous or oleic secies:
Hydrogen (reactive), Sodium, Calcium, Magnesium,
Carbonate, Aluminum, Silicon, Oxygen, Chlorine, S
(Injected surfactant)
"-, Na+,Ca2+, Mg2+, A13+, CO2" , Cl", S", H4SiO4, H2O
Dependent aqueous or oleic species: Ca(OH)+, Mg(OH)+, A1(OH)2-,A1(OH)2-, Ca(HCO3)+,
Mg(HC03)+, OH-, HCOg , H3Si04-, H2SiO42-, HSi2O63-,
Si2052-, A1(OH)4-, H2C03,
Solid species:
CaCO3 (Calcite), Al2Si2O5(OH)4 (Kaolinite), MgCO3
(Magnesite), NaAlSi2O6.H2O (Analcite), SiO2 (Silica),
Mg(OH)2 (Magnesium Hydroxide)
Adsorbed cations on rock surface:
Adsorbed cations on micelles:
, Ca 2+, Mg
2+
Aqueous reactions
H20 ^f H+ + OH~
H+ + CO2" ^ HCOJ
Keq
Ca2+ + H2O ^ Ca(OH)+ + H+
Keq
Mg2+ + H2O ^ Mg(OH)+ + H+
Keq
A13+ + H2O ^f A1(OH)2+ + H+
A13+ + 2H2O ^6 A1(OH)2+ + 2H+
Equilibrium constant
K" r Tj+i r /^TJ-T
\ — l ti J L Url J
_eq [HC03_
K2 - + - 2_-
eq [ca(OH)+
k3 " Lca2+
^eq [M§(OH)+_
k4 " [Mg24
[H+]
[H+]
^eq [A1(OH)2+][H+]
k5 ~ [A13+]
weq [A1(OH)2+][H+]2
kb ~ [A13+]
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Appendix A - UTCHEM 6.1 User's Guide
Aqueous reactions (cont.)
Keq
A13+ + 4H2O ^»7 A1(OH)4- + 4H+
Keq
H4SiO4 ^f H+ + H3Si04~
K9q + 2
H4SiO4 ^£ 2H+ + H2Si04
Ca2+ + H+ + CO2' ^4° Ca(HCO3)+
Mg2+ + H+ + Co|" £• Mg(HCO3)+
O TUT*" i r^C\^~ 4 2 TT /~»/"\
2H +CU3 ^4 H2C03
2H4SiO4 ^43 2H20 + 3H++HSi2O63"
2H4SiO4 ^44 2H+ + 3H20 + Si2052'
Equilibrium constant (cont.)
^eq [Al(OH)4-][H+]4
"7 ~ [AP+]
,eq [H+][H3Si041
kg ~ [H4Si04]
eq [H+]2[H2Si042-]
ky ~ [H4Si04]
eq
Ca(HCO3)+
[Ca2+] [CO|][H+]
TC
Mg(HC03)+
[Mg2+J[c023-][H+]
req [H2C°3]
"12 CO2' [H+]2
^eq [H+]3|_HSi2063-_
M3 ~ [H4Si04]2
• eq [H+]2Si2052'
KC4 "r. , J
14 ~ 9
[H4Si04]2
Solid snecies
CaCO3
MgCO3
SiO2
Al2Si205(OH)4
NaAlSi2O6.H2O
Mg(OH)2
Solubility product
Ksf =[Ca2+] CC
Kf =[Mg2+] 0
>!-
4
KS3P =[H4SiO4]
KS4P =[H+] -6[A13+] 2[H4Si04] 2
KS5P = [H+] -4[Na+] [ A13+] [H4Si04]
2
KS6P =[Mg2+] [H+]-2
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Appendix A • UTCHEM 6.1 User's Guide
Exchange reactions (on matrix)
+ Kex
2Na +Ca2+ ^ 2Na+ + Ca2+
+ Kex 2
2Na + Mg + ^ 2Na + Mg
_ + . Kex _.+
H +Na+ + OH ^ Na + H2O
Exchange eauilibrium constant
.C"a2+.
[Na+]
[Ca2+]
ex
.Mg2+_
K2 _
[Mg2+]
ex
3
_Na+_
_Na _
_Na
_Na+
_Na
H
I
2
2
2
k]
Exchange reactions ( on micelle)
Exchane euilibrium constant
o i JS. •• + = 0+
Ca2+ r*1 2Na + Ca +
K
exm
~|fa+J2[Ca2+]
where
2Na + Mg
2+
2Na +Mg
K
2 =
I" n
[Na+J
+2 [Mg2+]
T^ ^
where K 2 = P 2
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Appendix A - UTCHEM 6.1 User's Guide
A.6 MAIN PROGRAM FLOW OUTLINE
The following outline represents the basic flow through the main program of UTCHEM (that
is, the order in which major subroutines are called).
I. INOUT
A. FBLEl
B. PRINTS
C. PRINTI
D. INNAME (called only if NO>1 and IOD is not equal to 1)
E. MOPPST (called only if NO>1)
1. SLV2EQ
F. PRINTO (called only if NO>1)
G. WMEACN (called only if NO>1 and IOD is not equal to 1)
H. GEOREAD (called only if IREACIM)
I. BIOREAD (called only if ffiIO=l)
J. METRIC (called only if IUNIT=1)
K. WELLIX
1. RADIUS
L. FILES
M. FILE2
N. GRDFAC
II. RSTART (called only if IMODE=2)
A. NSLUG
B. WELLIX
1. RADIUS
HI. TIMEO
A. OMOFR (called only if NO>1)
B. DENSTY
IV. TRAN1
V. ASIGN1
VI. TRANS (Transmissibilities)
VH. SOLMAT (Pressure Eq.)
A. WELL
B. BUNDRY (called only if IBOUND=1)
C. JCG
VIII. QRATE
IX. CONEQ (Conservation Eq.)
A. GEL
X. ADSORB
XI. REACTR (called only if IREACT>1)
A. RENAM1
B. TOTALS
C. MANIPL
D. JACUP
1. GAUSS
2. SOLVE
E. RENAM2
XII. CSECAL
A. ALCPTN (called only if IALC=1)
1. TWOALC
2. CUBIC
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B.
C.
D.
4,
5.
6.
7.
8.
B.
C.
CSEOD (called only if NO>1 and IOD is not equal to 1)
IONCNG
PHASC (called only if surfactant is not present and IREACT<1)
1. NONEQ
2. GDIS WO (called only if NO>1)
a. NONEQK
PHCOMP (called only if surfactant is present or IREACIM)
1. NONEQ
2. ODISWO
3. TffiLIN
a. TRY
REVISE
VGAMMA
SINGLE
ODISTM (called only if IHAND=0)
ODISTM1 (called only if IHAND=1)
XIII. BIOSOLVE (called only if IBIO=1)
A. INST (called only if IBKIN =3)
SDRIV2 (called only if IBKIN = 1 or 2 and running Cray version of code)
2. G
DDRIV2 (called only if IBKIN = 1 or 2 and running double precision version of
code)
1. F
2. G
XIV. OMOFR (called only if NO>1)
XV. TCAP (called only if ICAP=1)
XVI. TDIFFU (called only if ICAP=2)
XVII. DENSTY
XVIII. ASIGN2
XIX. ENGB AL (called only if IENG= 1)
XX. LAUWER (called only if IENG=1 and IANAL=1)
XXI. CAPNUM (called only if ITRAP=1)
XXII. TRAPNO (called only if ITRAP=2 and IGAS=0)
XXIII. TRAP (called only if IGAS=0)
XXIV. TRAPG (called only if IGAS>1)
XXV. HYST1 (called only if IPERM=2)
XXVI. UTFOAM (called only if IGAS=2)
XXVII. VISCOS
XXVIH. WELLCK
XXIX. OUTDT1
XXX. OUTDT2
A. PRINTI
B. PRINTS
XXXI. NSLUG
A. WELLIX
1. RADIUS
XXXII. RSTART
XXXIII. Go to step V (ASIGN1) if not done
XXXIV. SUMTAB
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A.7 PHASES AND SPECIES IN UTCHEM
This section gives the component numbering scheme in UTCHEM and the unit for each
component.
The following values for L correspond to the indicated phase:
L Phase
1 Aqueous phase
2 Oleic phase
3 Microemulsion phase
4 Gas phase
The following indices correspond to the indicated components [corresponding concentration units are
listed in square brackets]:
For all values of IREACT:
Index Component Fconc. units]
1 Water [volume fraction]
2 Oil [volume fraction]
3 Surfactant [volume fraction]
4 Polymer or silicate (KGOPT=3) [weight percent]
5 Total nonsorbing anions concentration, assumed to all be
chloride anions [meq/ml]
6 Divalent cations, assumed to all be calcium for IREACT<2
[meq/ml]
7 Alcohol 1 [volume fraction]
8 Alcohol 2 or Gas [volume fraction]
Organic species (IBIO=0 and NO>1):
Index Component [cone, units]
9 First organic species [volume fraction]
8+NO Last organic species [volume fraction]
Tracers (NT>0):
Index
9+NO
8+NO+NTW+NTA
Component [cone, units!
First tracer [dependent on user input]
Last tracer [dependent on user input]
Geochemistry option species (IREACT=2 or IRECAT=3):
Index
9+NO+NTW+NTA
8+NO+NTW+NTA+NGC
Component Tconc. units]
First geochemistry component
[meq/ml]
Last geochemistry component
[meq/ml]
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Appendix A • UTCHEM 6.1 User's Guide
Gel model species (IREACT=1 and NG>0):
Index
NG1*
NG2
NG3
NG4
NG5
KGOPT=1
Component
Fconc. units]
Na2Cr2O7 [ppm]
CSN2H4 [ppm]
Cr3+ [ppm]
Gel [ppm]
Hydrogen [meq/ml]
KGOPT=2
Component
[cone, units]
—
Malonate ion [ppm]
Cr3+ [ppm]
Gel [ppm]
Hydrogen [meq/ml]
KGOPT=3
Component
Fconc. units]
—
—
OH- [ppm]
Gel [ppm]
—
*where NG1 = 9+NO+NTW+NTA
Geochemistry/Gel option species (IREACT=4 and NG>0):
Index
9+NO+NTW+NTA
8+NO+NTW+NTA+NGC
Component [cone, units]
First geochemistry component
[meq/ml]
Last geochemistry component
[meq/ml]
KGOPT=1
Index Component fconc. units]
NG1* Na2Cr207 [ppm]
NG2 CSN2H4 [ppm]
NG3 Cr3+ [ppm]
NG4 Gel [ppm]
KGOPT=2
Component Fconc. units]
Malonate ion [ppm]
Cr3+ [ppm]
Gel [ppm]
*where NG1 = 9+NO+NTW+NTA+NGC
Biological model species (3BIO=1):
Index
9+NO+NTW+NTA+NGC+NG
Component
Fconc. units!
First biological species
[mgtf]
8+NO+NTW+NTA+NGC+NG+NOTH Last biological species
[mgtf]
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Appendix A - UTCHEM 6.1 User's Guide
A.8
TIME-STEP SELECTION
This section discusses the automatic time-step selection options available in UTCHEM: (E. 1)
selector based on method of relative changes for the first three components, (E.2) selector based on
method of relative changes for all the components, and (E.3) selector based on changes in
dimensionless concentration for all the components.
The Courant number, C, is defined as:
Q At
Ax Ay Az (j)
where Q is maximum injection/production per wellblock.
8.1 Method of Relative Changes for First Three Components (IMES=2)
Minimum and maximum time step in days (option ITIME=0):
The time step selection is based on the method of relative changes for the first three
components (water, oil, and surfactant) as:
8.2
Atn+1=Atnmin
im
NBL, I
max AC; v\
' 1)K|
K=l,2, 3
(E.I)
where Atn+1 is limited to: Atmin^Atn+1
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Appendix A - UTCHEM 6.1 User's Guide
8.3
Atn+i = Atn
NBL
max
K= 1,..., nc
V 1=1 /
where Atn+1 is limited to: Atmin3 = 0.1 x C$ where €3 is the total concentration of component 3. If
ACiim)K of the KCth component is entered as zero, that component is not considered in the time-step
size selection.
Method of Relative Changes Using Dimensionless Concentration for All Components
(IMES=4)
For IMES=4, the method of relative changes is applied to all the components in the simulation
run:
Atn+1 = Atn min
Rlim,K
NBL
max
ACijK
K=
where Atn+1 is limited to:1 Atmin
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Appendix A - UTCHEM 6.1 User's Guide
A.9 DESCRIPTION OF work.job FILE
This section contains a detailed description of the contents of the example work. j ob file
found in Section 2.3 of this appendix.
Command line
rm -r EXOl.dir
mkdir EX01 . dir
cd EXOl.dir
In -s ../exOl.data INPUT
time . . /utchem.exe
mv TTABLE exOl.ttable
mv ECHO exOl.echo
mv MESH exOl.mesh
mv PROFIL exOl.prof
mv CONCP exOl.con
mv PRESP exOl.presp
#mv ALKP exOl.alkp
mv SATP exOl.satp
mv GFILEP exOl.gel
mv TEMPP exOl.temp
mv HIST01 exOl.histOl
mv HIST02 ex01.hist02
mv HIST03 exOl.histOS
mv HIST04 ex01.hist04
tmv HIST05 ex01-.hist05
#mv HIST06 ex01.hist06
tmv HIST07 exOl.histOV
mv OVERAL exOl.overal
mv RESTAR exOl.rest
mv WARN exOl.warn
gzip *
Description
Removes the EXOl.dir directory if it
already exists. Make sure you've copied
files from previous runs (if you want to
save them) to another location before
executing the work . j ob file because all
files in the EX01 .dir directory will be
deleted when the directory is deleted.
Create a subdirectory in which to place
the new simulation results.
Make EXOl.dir the current working
directory.
Create a symbolic link to the
exOl.data input data file (which is
located up one level in the directory
structure). When the program looks for
the file INPUT, it will automatically be
pointed to the exOl . data file.
Run the program (which is located up
one level in the directory structure).
Change the default UTCHEM output file
names to something more meaningful.
The main reason for doing this optional
step is to simplify identification of files
at a later date. Files that do not appear as
part of the current run are commented
out using the pound sign (#) in the first
column of the work . j ob file.
Add this line to the work . j ob file to
compress all files in order to save space
(if necessary).
238
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Appendix B
UTCHEM Local Grid Refinement User's Guide
B.I INTRODUCTION
UTCHEM is a three-dimensional chemical flooding simulator. The solution scheme is
analogous to IMPES, where pressure is solved for implicitly, but concentrations rather than
saturations are then solved for explicitly. Phase saturations and concentrations are then solved in a
flash routine. An energy balance equation is solved explicitly for reservoir temperature. The energy
balance equation includes heat flow between the reservoir and the over- and underburden rocks. The
major physical phenomena modeled in the simulator are:
dispersion
dilution effects
adsorption
interfacial tension
relative permeability
capillary trapping
cation exchange
phase density
compositional phase viscosity
phase behavior (pseudoquaternary)
aqueous reactions
partitioning of chemical species between oil and water
dissolution/precipitation
cation exchange reactions involving more than two cations
in-situ generation of surfactant from acidic crude oil
pH dependent adsorption
polymer properties: shear thinning viscosity, inaccessible pore volume, permeability reduction,
adsorption
gel properties: viscosity, permeability reduction, adsorption
tracer properties: partitioning, adsorption, radioactive decay, reaction (ester hydrolization)
temperature dependent properties: viscosity, tracer reaction, gel reactions
The following options are available with UTCHEM: isothermal or non-isothermal conditions,
a constant or variable time-step, constant pressure or constant rate well conditions, horizontal and
vertical wells, and a radial or cartesian geometry. Please refer to the dissertation "Field Scale
Simulation of Chemical Flooding" by Naji Saad [1989] for a more detailed discussion of the
UTCHEM simulator and its formulation.
239
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Appendix B - UTCHEM Local Grid Refinement User's Guide
B.2 LOCAL GRID REFINEMENT SPECIFICATIONS
This section describes the special requirements unique to the Local Grid Refinement (LGR)
version of UTCHEM.
Input Notes;
This code is applicable to water flooding, Surfactant flooding and Tracer flooding.
Can use components: (1,2, 3, 5, 6,7, 8, 9,10, 11)
Methods
Single Point upstream, 2 point upstream, higher order
Models
Water flooding
Salinity
Adsorption
Tracer
Surfactant / alcohol
phase behavior
Capillary number
Interfacial Tension
Full tensor physical diffusion
Capillary pressure
Solubilization (oil in water)
hysteresis
Wells - Peaceman Model
Global flow gradient
Gravity
Variable Permeability
The reservoir is initially defined by a coarse grid (called a base grid) with NXCxNYCxNZC standard
cells (gridblocks).
Subject to memory limitations any combination of the base grid cells can be refined by one local level
NXFxNYFxNZF which is of fixed resolution for all refined cells.
The locally refined cells are called ZONES.
Memory and ARRAYS.
Arrays must be set in PARAMS.INC and UTCHEMLGR.FOR
Edit PARAMS.INC to see 3 sections:
1) UTwork space, 2) Coarse, 3) Fine
Coarse and Fine correspond to the base grid and Zone requirements respectively. Note NREFI defines
maximum number of zones and total memory is proportional to
NXXCxNYYCxNZZC + NREFI * NXXFxNYYFxNZZF
+
max(NXXCxNYYCxNZZC , NXXFxNYYFxNZZF)
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Appendix B - UTCHEM Local Grid Refinement User's Guide
UTwork space arrays = max(Coarse, Fine)
e.g. NNX = max (NNXC, NNXF)
UTB ASE.F only contains work space arrays; e.g., NNX only (not NNXC or NNXF)
LOCAL REFINEMENT = ADD ZONES
New Input Parameters
The input data set consists of the usual UTCHEM data set for the base grid, and a UTCHEM data set
for each ZONE (i.e., each refined base cell) again with appropriate minor modifications described
below. The input format is identical to the standard UTCHEM manual in each case.
Coordinate Definition
LGR is used with ICOORD = 1
For BASE grid data set
READ (5,*) NXC,NYC,NZC,IDXYZ,IUNIT
READ (5,*) DXC,DYC,DZC
For ZONE data set
READ (5,*) NXF,NYF,NZF,IDXYZ,IUNIT
READ (5,*) DXF,DYF,DZF
(Must have NXF > 1, NYF > 1, NZF > 1 in 3-D)
Note: for uniform grids
DXF = DXC / NXF
DYF = DYC / NYF
DZF = DZC / NZF
otherwise for non-uniform grids
DXC = ]T.DXFj, DYC = 2-DYFj? DZC = £.DZFj
Note: neighboring non-uniform grids must have the same spacing in the direction tangential to the
common interface.
Gravity
Dl 11 is the depth of the center of the first BASE cell in the top layer.
If a coarse cell is refined the corresponding depths of the local ZONE cells are appropriately defined
by the code.
Set Dl 11 = 0 in all ZONE domain data sets following the BASE data set.
Permeability
A pre-processing program LGRPERM is supplied which will extract portions of a. fine grid global
permeability map that correspond to zones chosen by the user.
241
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Appendix B - UTCHEM Local Grid Refinement User's Guide
The approach is as follows;
Define a base grid.
Refine the base grid to a specified level.
Create a fine grid permeability map for the entire fine domain then use LGRPERM to
define the permeability maps for the local zones. An LGR simulation can then be
performed with the specified zones that correspond locally to the fine domain. In effect
some base cells are unrefined and appropriate upscaling should be employed for rock
properties of these cells. At present LGRPERM assigns an average value to these cells.
Alternatively the user is free to define the local variation over each zone.
Caution: The larger the grid interface ratio (number of fine cells adjacent to a coarse cell) the larger the
potential for error in the solution. A large variation in permeability over the interface may give rise to
spurious pressure distributions, and in extreme cases may even cause convergence problems for the
pressure equation solver.
WELL DATA
Inflow - Outflow
A fine zone can be adjacent to an inflow or out flow boundary. In this case the local zone data set is of
identical format to the standard spec and
IBOUND =1.
If the zone is adjacent to an inflow boundary
EBL=l,ffiR = 0.
If the zone is adjacent to an outflow boundary
IBL = 0,IBR=1.
WELLS
Wells can either be completed through adjoining base cells which are NOT refined, OR through
adjoining ZONES. Wells are NOT allowed to be completed across any coarse-fine interface between
a ZONE and a non-refined base cell.
Spatial (i,j,k) Indexing
Base grid: as per standard.
Zones: as per standard with respect to the local domain. The well spatial (i,j,k) indexing works with
respect to the local domain.
Each well has a globally unique ID number; i.e., upon entering a new domain the "counting" of the
wells begins from current ID number + 1. -If a well is completed through neighboring zones then it
has the same ID in both zones, otherwise the same ID cannot be assigned to different wells in separate
domains.
Caution: By definition, the method will give relatively poor results if wells are placed in fine cells at
coarse/fine interfaces of the grid.
242
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Appendix B - UTCHEM Local Grid Refinement User's Guide
SLUGS
Slug data for the base grid and all zones is tagged on the very end of the entire input file. First input the
base grid well data modifications followed by each of the ZONE well data modifications as per
standard spec. If the base grid or a ZONE is not modified or has no wells then this is flagged by
8 standard lines
CC
cc
then input
IROJTIME, (IFLAG(IDW(M)), M= 1 , NWELL)
enter all zeros if no wells,
or .
repeat previous data if wells unchanged.
CC
CC
-1
Similarly repeat for each unchanged well in a domain.
NOTE: TINJ should have the same time value for each domain section until the very last specification
of TINJ, which should have TINJ > TMAX.
Restart Data
Currently a single line is added to the top of the restart data set to handle well data for the zones.
Enter
1
for each existing zone (of the first simulation) not containing a well and for each new zone that has
been added.
Enter
-1
for each existing zone (of the first simulation) containing a well so that the restart well data is read,
this data can only be modified via a slug.
The order of entry is strictly according to the occurrence of each zone with respect to the global index
HG(L) = I + (J - 1) * NXC + (K - 1) * NXC*NYC.
e.g., if in the first simulation there are 3 zones with a well in the first zone and 5 restart zones are
flagged, then (assuming the new zone global indices are greater than the first zone global index) upon
restarting the calculation enter
-11111
243
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Appendix B - UTCHEM Local Grid Refinement User's Guide
OUTPUT
The output is written per domain in standard UTCHEM format. The base cell and refinement number
are printed at the top of each domain data set, "layers" now refers to layers in the local domain.
The velocity field is written for each cell face of each zone. Therefore neighboring interior zones will
have the same face velocity field at the common interface locations.
B.3 OPERATION OF THE SIMULATOR
The UTCHEM simulator is run on a CRAY Y/MP at the University of Texas High
Performance Computing Facility (UNICOS operating system), a number of DEC Alpha systems
(DEC 4000/610, 3000/500 & 3000/300X) at the Department of Petroleum and Geosystems
Engineering (OSF/1 operating system), and a DEC Alpha system (DEC 3000/500) at the Department
of Petroleum and Geosystems Engineering (OpenVMS operating system). The same code is
executed on all three systems, except for the use of double precision (64-bit words) on the DEC
machines—we differentiate between "Cray" and "DEC" versions of the code by adding a "V" prior to
the version number for the "Cray" version and a "D" prior to the version number for the "DEC" (or
double-precision) version. Several intrinsic Cray functions need to be implemented when not running
on the Cray; these routines are "commented" out in the "Cray" version. Please check the source code
for additional information about necessary changes when running on different computers.
B.3.1 Input and Output Files
UTCHEM requires one input file for non-restart runs. For restart runs, a restart file is required
in addition to the original input data file used for the previous run. A detailed input data description is
given in section B.3 of this appendix and the data in the restart data file is documented in section B.6.
The number of output files generated by UTCHEM varies depending upon several control flags set by
the user in the input file. The number of history plot files depends on the value of the MXW
parameter in the source code. The FORTRAN unit number for the history plot file is incremented by
one for each well. For example, if MXW is equal to three, then three history plot files would be
generated corresponding to FORTRAN unit numbers 19, 20, and 21 even if the run only has two
wells. The input and output files are summarized in the following table.
Unit Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
File Name Contents
TEMPL Analytical temp, profile, created if IENG= 1 and IANAL= 1
ECHO Echo print of the input file information
SUMARY Summary data
PROFIL Formatted profile data; described in section 6.1 of this appendix
INPUT Input data; described in detail in section B.3 of this appendix
TTABLE Table of time steps and Courant numbers
RESTAR Stored restart run data; described in section 6.3 of this appendix
CONCP Component concentration profile plotting data, created if IPCTOT>0
OVERAL History of overall properties; described in section 6.5 of this appendix
GFILEP Gel property profile plotting data, created if IRE ACT= 1
PRESP Phase pressure profile plotting data, created if IPPRES>0
S ATP Phase saturation profile plotting data, created if IPSAT>0
TRACP Phase tracer concentration profile plotting data, created if IPTRAC>0
CAPP Capacitance property profile plotting data, created if IPCAP>1
ALKP Alkaline option related profile plotting data, created if IREACT> 1
INPUT2 Restart run data (input file created by an earlier run)
WARN Warning messages
TEMPP Temperature profile, created if IENG = 1 and IPTEMP= 1
244
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Appendix B - UTGHEM Local Grid Refinement User's Guide
B.4
19
20
£
£+1
£+2
n
HIST01
HIST02
HIST7
TRAC01
TRAC02
Well history plotting data for well #1; described in section 6.4 of this
appendix
Well history plotting data for well #2
Well history plotting data for last well
Aqueous phase tracer concentration at 1st observation point, created if
IPOBS>0; described in section 6.6 of this appendix
Aqueous phase tracer concentration at 2nd observation point
TRACn Aqueous phase tracer concentration at last observation point
B.3.2
Source Code Array Dimensions
The parameters in the following table are used by the simulator to define array sizes All the
parameter values must be equal to or greater than the size of the grid dimensions specified in the input
file, unless otherwise noted. Additionally, all instances of each parameter must be the same
throughout the code, so if you want to change the value of one of the parameters, please make sure
you make a global substitution. Please see the note in Section 2 on memory and arrays for LGR code.
Parameter Definition
NNX Number of gridblocks in X-direction (must be set equal or larger to NX in the input
file) r
NNY £^ber of Sridblocks ^ Y-direction (must be set equal or larger to NY in the input
NNZ
MXC
MXP
MXW
MXWB
MXNT
MXELE
MXFLD
MXSLD
MXSORB
MXACAT
MXEX
Number of gridblocks in Z-direction (must be set equal or larger to NZ in the input
file) ^
Maximum number of components (cannot be less than 8)
Number of phases (must be set equal to 3 when there is no gas phase and must be set
equal to 4 if gas is present)
Maximum number of wells
Maximum number of well blocks
Maximum number of tracers
Maximum number of elements
Maximum number of reactive fluid species
Maximum number of solids
Maximum number of adsorbed species
Maximum number of cations associated with surfactant
Maximum number of insoluble exchangers
INPUT DATA DESCRIPTION
T?r™PU- ^ ^?- °f comment lines ** data &**- All comment lines are
TCHEM simulator. It is important to note, however, that the number of comment
« fS 1SuflXeud- The &St twentv-two l^ of *e input file are reserved for comment
used to briefly describe the input file. Each data line is preceded by three comment lines (^ep
sectitsTnd Sh" oflm SeCti°n,4'5 °f thif aPPendix)' ^ inpUt ffl* is basic*Uy divided iSoS
sections and each of those input sections (except section 4.5 of this appendix) is preceded by an
additional seven comment lines. The user should update the comment lines as me input fil fc
modified in order to make using the simulator easier.
All data is free-formatted. This means that for each read statement, it is only necessary to
kave a blank space between data elements. Note that the first data element for a given read st
must be on a new line in the input file. Subsequent data elements for that read statement can
245
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Appendix B - UTCHEM Local Grid Refinement User's Guide
many lines as necessary. Implicit type matching is used; that is, all REAL variables begin with the
letters A-H or O-Z and all integer variables begin with the letters I-N.
The following is a list of variables as they are read by UTCHEM. The variable names appear
in all-caps on a single line in the order they are read by the program. Every list of variables is
followed by a description of each variable and corresponding units or possible values if applicable.
All of the variables listed in the input description will be read by the program unless otherwise noted:
therefore, a dummy value will be read by the program for variables not pertinent to the problem being
run.
B .4.1 Title and Reservoir Description Data
The first input section consists of the title and reservoir description data. Please remember that
there are 22 comment lines at the beginning of this section and that each data line is preceded by three
comment lines.
4.1.1 RUNNO
RUNNO - Run number.
Note: The run number can consist of any combination of alphanumeric characters on a single
line (not to exceed 80 characters). This information will be printed as the first line of
every output file.
4.1.2 TITLE
TITLE - Title and run description.
Note: The title can consist of any combination of alphanumeric characters spanning three lines
in the input file (not to exceed 80 characters per line). Please note that the title must
span three lines and that any of those lines can be blank.
4.1.3 NRINIT, IRESTZONE
NRINIT - Number of refined zones.
IRESTZONE - Number of refined zones for restart run.
4.1.4 IXG(J), IYG(J), IZG(J), for J= 1, NRINIT
IXG(J), IYG(J), IZG(J) - Base grid integer coordinates of the refined cells.
4.1.5 IXRG(J), lYRG(J), IZRG(J), for J=l, NRINIT (This line is read only if IRESTZONE > 0)
IXRG(J), IYRG(J), IZRG(J) - Base grid integer coordinates of the cells to be refined at restart.
Repeat for IRESTZONE refined base cells.
4.1.6 MODE, IMES, IDISPC, ICWM, ICAP, IREACT, ICOORD, ITREAC, ITC, IGAS, IENG
IMODE - Flag indicating if the problem to be ran is a first ran or a restart problem.
Possible Values:
1 - First ran problem
2 - Restart problem
IMES - Flag indicating if a constant or automatic time-step is to be used.
Possible Values:
1 - Constant time-step size is used
2 - Automatic time-step size selector based on method of relative changes for the first
three components is used
3 - Automatic time-step size selector based on method of relative changes for all the
components is used
4 - Automatic time-step size selector based on changes in dimensionless concentration
for all the components is used
246
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Note: The automatic time-step selector is recommended. See input lines 4.5.9 through 4.5.12
for more details on the above options. In addition, IMES=1 is the only option fully tested
with the LGR code.
IDISPC - Flag indicating which type of numerical dispersion control is used.
Possible Values:
0 - Single point upstream method is used
1 - Chaudhari's method is used (this method is not available if ICOORD = 2)
2 - Two point upstream method is used
3 - Improved total variation diminishing third order method is used
Note: These methods are applied to both concentration and relative permeability.
ICWM - Flag indicating if the concentration well model is used or not.
Possible Values:
0 - Concentration well model is not used
1 - Concentration well model is used
Note: The concentration well model (ICWM = 1) can only be used with vertical wells
(IDIR(M) = 3).
ICAP - Flag indicating if the capacitance model is used or not.
Possible Values:
0 - Capacitance model is not used
1 - Capacitance model is used
IREACT - Flag indicating if gel reactions or alkaline options are used or not.
Possible Values:
0 - Gel reactions are not used
1 - Gel reactions are used
2 - Alkaline option 1 (no silicon, aluminum, or acid)
3 - Alkaline option 2 (no silicon or aluminum; with acidic crude)
4 - Alkaline option 3 (with silicon and aluminum; no acid)
5 - Alkaline option 4 (with silicon, aluminum, and acidic crude)
6 - Alkaline option 3 and gel reactions are used
Note: IREACT=0 is the only option available with the LGR code.
ICOORD - Flag indicating which coordinate system is used.
Possible Values:
1 - Cartesian coordinate system is used
2 - Radial coordinate system is used
3 - Cartesian coordinate system with variable-width gridblocfc is used (2-D cross
section only)
4 - Curvilinear grid definition of the X-Z cross section is used (2-D or 3-D)
Note: For ICOORD=4, the 3-D grid consists of the 2-D cross sectional grid repeated at
specified intervals (uniform or non-uniform) in the Y direction, according to the
definition of DY1. The curvilinear grid option is not available for the temperature
equation option (IENG must be set to 0 on this input line). In addition, ICOORD=1 is
the only option available with the LGR code.
ITREAC - Flag indicating if a tracer reaction is used or not.
Possible Values:
0 - Tracer reaction is not used
1 - Tracer reaction is used
ITC - Flag indicating if second-order time approximation is used or not.
Possible Values:
0 - Second-order time approximation is not used
1 - Second-order time approximation is used
247
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Note: We recommend that second-order time approximation (ITC =1) only be used with
higher-order dispersion methods (IDISPC > 1).
IGAS - Flag indicating if gas phase is considered or not.
Possible Values:
0 - Gas is not present
1 - Gas is present
EENG - Flag indicating if temperature variation is considered or not.
Possible Values:
0 - Isothermal simulation
1 - Temperature equation is solved
Note: IENG must be set equal to 0 if the curvilinear grid option (ICOORD=4 on this input
line) option is used. In addition, IENG=0 is the only option available with the LGR
code.
4.1.7 NX, NY, NZ, IDXYZ, IUNIT
NX - Number of gridblocks along X-axis (ICOORD = 1 or 3) or number of gridblocks in radial
direction (ICOORD = 2).
Note: This value should be equal to or smaller than the NNX parameter in UTCHEM.
NY - Number of gridblocks along Y-axis.
Note: This value should be equal to or smaller than the NNY parameter in UTCHEM. It
should be set equal to 1 if the user is running a 1-D problem or a 2-D cross sectional
problem. If ICOORD = 2, this value is automatically set equal to 1.
NZ - Number of gridblocks along Z-axis.
Note: This value should be equal to or smaller than the NNZ parameter in UTCHEM. It
should be set equal to 1 if the user is running a 1-D problem or a 2-D areal problem.
IDXYZ - Flag indicating constant or variable grid size.
Possible Values:
0 - Constant grid size
1 - Variable grid size on a regional basis
2 - Variable grid size
Note: IDXYZ must be set equal to 2 if ICOORD = 3.
IUNIT - Flag indicating English or Metric units.
Possible values:
0 - English unit
1 - Metric unit
Note: UTCHEM must be compiled and run with the NX, NY, and NZ input values being equal to or
smaller than the NNX, NNY, and NNZ parameters in the code. All 38 occurrences of the
NNX, NNY, and NNZ parameters in the code must be set to the same values which must be
equal to or larger than the NX, NY, and NZ input values. Additionally, since parameter
statements are used for dimensioning arrays in UTCHEM, any time any parameter statement
is changed in the FORTRAN source code, all occurrences of that parameter statement must be
changed (and set to the same value throughout the code) or the code will not function properly.
4.1.8 XCORD (I), ZCORD(I), for I = 1, (NX+1) x (NZ+1) (This line is read only if ICOORD = 4)
XCORD - Gridblock coordinate of Ith corner point in X-direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
ZCOORD - Gridblock coordinate of Ith corner point in Z-direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
Note: The coordinates of the corners (or vertices) of the 2-D X-Z cross section gridblocks are input in
pairs as follows:
248
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Appendix B - UTCHEM Local Grid Refinement User's Guide
XCORD(l),
ZCORD(l)
XCORD(nodes), ZCORD(nodes)
where nodes = (NX+1) x (NZ+1) and is the total number of corner points defining the X-Z
cross section and Z is positive downward. The following figure illustrates the input order for
an example X-Z cross section grid:
Top (surface) of reservoir
XCORD(l), ZCORD(l)
1
XCORD(2), ZCORD(2)
2
XCORD(9), ZCORD(9)
The number of gridblocks is equal to NX x NZ and the number of coordinate pairs (or nodes)
is equal to (NX+1) x (NZ+1).
Cautionary warning: The X-Z cross section grid should be constructed by the user such that
the curvilinear coordinate system is at least quasi-orthogonal. Departure from
orthogonality will lead to numerical errors in the solution.
4.1.9 DX1, DY1, DZ1 (This line is read only if IDXYZ = 0 and ICOORD = 1)
DX1 - Gridblock size in X direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
DY1 - Gridblock size in Y direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
DZ1 - Gridblock size in Z direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
4.1.10 R(l), DX1,DZ1 (This line is read only if IDXYZ = 0 and ICOORD = 2)
R(l)-Wellbore radius.
Units: feet (IUNIT=0) or m (IUNIT=1)
DX1 - Distance between nodes in radial direction.
Units: feet (IUNIT=0) or m (IUNTT=1)
DZ1 - Gridblock size in Z direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
4.1.11 DY1 (This line is read only if IDXYZ = 0 and ICOORD = 4)
DY1 - Gridblock size in Y direction.
Units: feet (IUNIT=0) or m (IUN]T=1)
249
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Appendix B - UTCHEM Local Grid Refinement User's Guide
4.1.12 III, 112, DX1 (This line is read only if IDXYZ = 1 and ICOORD = 1 or 3)
El - First index for gridblocks with same size in X direction.
112 - Last index for gridblocks with same size in X direction.
DX1 - Gridblock size in X direction
Units: feet (IUNIT=0) or m(IUNIT=l)
Note: This line is repeated until sizes for each of the NX gridblocks in the X direction have been
specified. The first line in the set must have III = 1 and the last line must have 112 = NX.
Example: If NX =11 and the first three gridblocks in the X direction are 3 feet in size, the fourth
through ninth gridblocks in the X direction are 2 feet in size, and the last two gridblocks in the
X direction are 2.5 feet in size, this line would need to be repeated three times to fully describe
the X direction gridblocks as follows:
1 3 3.0
4 9 2.0
10 11 2.5
4.1.13 JJ1, JJ2, DY1 (This line is read only if IDXYZ = 1 and ICOORD = 1 or 3)
JJ1 - First index for gridblocks with same size in Y direction.
JJ2 - Last index for gridblocks with same size in Y direction.
DY1 - Gridblock size in Y direction.
Units: feet (IUNIT=0) or m(IUNIT=l)
Note: This line is repeated until sizes for each of the NY gridblocks in the Y direction have been
specified. The first line in the set must have JJ1 = 1 and the last line must have JJ2 = NY.
See the example for input line 4.1.9.
4.1.14 KK1, KK2, DZ1 (This line is read only if IDXYZ = 1 and ICOORD = 1 or 3)
KK1 - First index for gridblocks with same size in Z direction.
KK2 - Last index for gridblocks with same size in Z direction.
DZ1 - Gridblock size in Z direction.
Units: feet (IUNIT=0) or m(IUNIT=l)
Note: This line is repeated until sizes for each of the NZ gridblocks in the Z direction have been
specified. The first line in the set must have KK1 = 1 and the last line must have KK2 = NZ.
See the example for input line 4.1.9.
4.1.15 R( 1) (This line is read only if IDXYZ = 1 and ICOORD = 2)
R(l)-Wellbore radius.
Units: feet (IUNIT=0) or m(IUNIT=l)
4.1.16 III, 112, DX1 (This line is read only if IDXYZ = 1 and ICOORD = 2)
III - First index for radial node distances of the same size.
112 - Last index for radial node distances of the same size.
DX1 - Distance between nodes in radial direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
Note: This line is repeated until the NX-1 distances between the NX nodes in the radial direction
have been specified. The first line in the set must have III = 1 and the last line must have 112
= NX-1.
4.1.17 KK1, KK2, DZ1 (This line is read only if-IDXYZ = 1 and ICOORD = 2)
KK1 - First index for gridblocks with same size in Z direction.
KK2 - Last index for gridblocks with same size in Z direction.
DZ1 - Gridblock size in Z direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
250
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Note: This line is repeated until sizes for each of the NZ gridblocks in the Z direction have been
specified. The first line in the set must have KK1 = 1 and the last line must have KK2 = NZ.
See the example for input line 4.1.9.
4.1.18 JJ1, JJ2, DY1 (This line is read only if IDXYZ=1 and ICOORD=4)
JJ1 - First index for gridblocks with same size in Y direction.
JJ2 - Last index for gridblocks with same size in Y direction.
DY1 - Gridblock size in Y direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
Note: This line is repeated until sizes for each of the NY gridblocks in the Y direction have been
specified. The first line in the set must have JJ1 = 1 and the last line must have JJ2 = NY.
See the example for input line 4.1.9.
4.1.19 DX(I), for I = 1, NX (This line is read only if IDXYZ = 2 and ICOORD = 1 or 3)
DX(I) - Grid size of Ith block in X direction.
Units: feet (IUNIT=0) or m (IUNTT=1)
4.1.20 D Y(J), for J = 1, N Y (This line is read only if IDXYZ = 2 and ICOORD = 1 or 4)
DY(J) - Grid size of Jtb block in Y direction.
Units: feet (IUNIT=0) or m(IUNIT=l)
4.1.21 DY(I), for I = 1, NX (This line is read only if IDXYZ = 2 and ICOORD = 3)
DY(I) - Thickness of I* block.
Units: feet (IUNIT=0) or m(IUNIT=l)
4.1.22 DZ(K), for K = 1, NZ (This line is read only if IDXYZ = 2 and ICOORD = 1 or 3)
DZ(K) - Grid size of Kth block in Z direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
4.1.23 R(l) (This line is read only if IDXYZ = 2 and ICOORD = 2)
R(l)-Wellbore radius.
Units: feet (IUNIT=0) or m(IUNIT=l)
4.1.24 DX(I), for 1=1, NX-1 (This line is read only if IDXYZ = 2 and ICOORD = 2)
DX(I) - Distance between the Ith node and the I+lth node in the radial direction.
Units: feet (IUNIT=0) or m(IUNIT=l)
4.1.25 DZ(K), for K = 1, NZ (This line is read only if IDXYZ = 2 and ICOORD = 2)
DZ(K) - Grid size of K* block in Z direction.
Units: feet (IUNIT=0) or m (IUNIT=1)
4.1.26 N,NTW, NTA, NG
N - Total number of components in the run (including tracers and reactive components)
Possible Values: 1-21
NTW - Number of water/oil tracers.
Possible Values: see note
NTA - Number of oil/gas tracers.
Possible Values: see note
NG - Number of gel components.
Possible Values: 4 or 5 when IREACT = 1
251
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Note:
4 when IREACT = 6
The combined total number of water/oil and oil/gas tracers (NTW+NTA) must be:
1) less than or equal to MXNT (see section 3.2) and
2) between 0 and 3 (inclusive) if IREACT>1 or between 0 and 13 (inclusive) if
IREACT=1.
The components will be listed in the following order for the corresponding values of
IREACT:
Inde
X
1
2
3
! ' 4
5
6
7
8
9
10
11
! 12
£rl3'
iiv,ir
ifc'iS'
: ar:
Pi! ' !=
Ill; i^tliilllliljjj
: --T7
!;:ii:
,«, ;, M!,,,™
""»,.!"„, liilllill
!::,'19
i' 20
«'21
Component
(IREACT =
0)
Water
Oil
Surfactant
Polymer
Chloride
Calcium
Alcohol 1
Alcohol 2
or Gas
Tracer 1
Tracer 2
Tracer 3
Tracer 4
Tracer 5
Tracer 6
Tracer" 7
!/' '.Tracer's'"''
Tracer 9
Tracer 10
Tracer 1 1
Tracer 12
Tracer 13
Component
(IREACT =
„ „ 1)
Water
Oil
Surfactant
Polymer
Chloride
Calcium,
Alcohol 1
Alcohol 2
or Gas
Tracer 1
Tracer 2
" Tracer 3
Na2Cr2Q7
CSN2H4
Cr3+
Gel
Hydrogen
* — •
- —
—
—
Component
(IREACT =
,- 2)
Water
Oil
Surfactant
Polymer
Chloride
Calcium
Alcohol 1
Alcohol 2 ,
" "or Gas
Tracer 1
Tracer 2
Tracer 3 '
Sodium
Hydrogen
'Magnesium
Carbonate
>—
. , —
, ^-~
—
„_
—
Component
(IREACT = ,
3X
Water
Oil
Surfactant
Polymer
Chloride
Calcium
Alcohol 1
Alcohol 2
or Gas
Tracer 1
Tracer 2
Tracer 3 <"
S6dium
Hydrogen
Magnesium
Carbonate'.
'Acid Comp.
of Crude-
Oil '
' , , *•
at - "S
,
Component
,(IRBACT =
,*>'
' Water
' Oil
Surfactant
Polymer
1 Chloride
Calcium
Alcohol 1
Alcohol 2
or Gas
Tracer 1
Tracer 2
Tracer 3
Sodium
Hydrogen
Magnesium
Carbonate
Aluminum
" Silica
—
—
—
Component
(IREACT =
5)
Water
Oil
Surfactant
Polymer
Chloride
Calcium
Alcohol 1
_ Alcohol 2
or Gas
Tracer 1
Tracer 2
' Tracer 3
Sodium
Hydrogen
Magnesium
Carbonate
Aluminum
Silica
Acid Comp.
1 ; of Crude
Oil
—
—
—
Component
(IREACT =
- 6) '
' Water
Oil
Surfactant
Polymer
Chloride
Calcium
Alcohol 1
Alcohol 2
or Gas
Tracer 1
Tracer 2
Tracer 3
Sodium
Hydrogen
Magnesium
Carbonate
Aluminum
Silica
]Sfa2Cr207
CSN2H4
Cr3+
Gel
If IREACT > 0, N must be set to the maximum number of components shown for each case
in the above table, whether all the components are present or not. For example, if IREACT =
3, N must be set to 16. The shaded cells indicate options not available to the LGR code.
4.1.27 TRNAME(IT), for IT = 1, NTW+NTA (This line is read only if NTW+NTA > 0)
TRNAME(IT) - Name ofTT™ tracer.
Note: The name of each tracer may not exceed 16 characters and each name must be on a
separate line of the input file.
4.1.28 ITRU(I), for I = 1, NTW (This line is read only if NTW > 0 and ITREAC = 1)
ITRU(I) - Flag indicating the units of the Ith tracer.
Possible Values:
1 - Im tracer units are in volume %
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Appendix B - UTCHEM Local Grid Refinement User's Guide
2 - Ith tracer units are in weight %
4.1.29 ICF(KC), for KG = 1, N
ICF(KC) - Flag indicating if KCth component is included in the concentration calculations or not.
Possible Values:
0 - The KCth component is not included in the calculations
1 - The KCth component is included in the calculations
Example: If 11 components are considered but Alcohol 2 is not present, this line would appear as
follows:
11111110111
B.4.2 Output Option Data
The second input section consists of output options. Please remember that there are seven
comment lines at the beginning of this section and that each data line is preceded by three comment
lines.
4.2.1 ICOPSM, ICUMTM, ISTOP
ICOPSM - Flag indicating if data will be written to UNIT 3.
Possible Values:
0 - Data will be written to UNIT 3 as directed by CUMHI2 flag
1 - Data will not be written to UNIT 3
ICUMTM - Flag indicating if the output intervals indicated by the CUMPR1, CUMHI1, CUMHI2,
WRHPV, WRPRF and RSTC variables on input line 4.5.8 are specified in pore volumes or
days.
Possible Values:
0 - Data will be written in pore volume intervals
1 - Data will be written in day intervals
Note: The day interval output option (ICUMTM = 1) is particularly useful if there is a shut in
period.
ISTOP - Flag indicating if the maximum and injection times (variables TMAX on input line 4.3.1 and
TINJ on input line 4.6.8) are specified in pore volumes or days.
Possible Values:
0 - TMAX and TINT are specified in days
1 - TMAX and TINJ are specified in pore volumes
4.2.2 IPRFLG(KC), for KG = 1, N
IPRFLG(KC) - Flag indicating if profile of KCth component should be written to UNIT 8.
Possible Values:
0 - Profile of KG* component will not be written
1 - Profile of KG* component will be written
Note: If IPCTOT=0, none of the component profiles will be written.
Example: If 11 components are present and only profiles for the oil, surfactant, and polymer
components are desired, this line would appear as follows:
01110000000
4.2.3 IPPRES, IPSAT, IPCTOT, IPTRAC, IPCAP, IPGEL, IPALK, IPTEMP
IPPRES - Flag indicating if profile of phase pressures should be written to UNIT 11.
Possible Values:
0 - Profile of phase pressures will not be written
1 - Profile of phase pressures will be written
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IPS AT - Flag indicating if profile of phase saturations should be written to UNIT 12.
Possible Values:
0 - Profile of phase saturations will not be written
1 - Profile of phase saturations will be written
IPCTOT - Flag indicating if profile of component concentrations should be written to UNIT 8.
Possible Values:
0 - Profile of component concentrations will not be written
1 - Profile of component concentrations will be written
IPTRAC - Flag indicating if profile of tracer.phase concentrations should be written to UNIT 13.
Possible Values:
0 - Profile of tracer phase concentrations will not be written
1 - Profile of tracer phase concentrations will be written
IPCAP - Flag indicating if profile of capacitance properties should be written to UNIT 14.
Possible Values:
0 - Profile of capacitance properties will not be written
1 - Profile of capacitance properties will be written
IPGEL - Flag indicating if profile of gel properties should be written to UNIT 10.
Possible Values:
0 - Profile of gel properties will not be written
1 - Profile of gel properties will be written
IPALK - Flag indicating if profile of properties related to the alkaline option should be written to
UNIT 15.
Possible Values:
0 - Profile of properties related to the alkaline option will not be written
1 - Profile of properties related to the alkaline option will be written
IPTEMP - Flag indicating if profile of reservoir temperature should be written to UNIT 18.
Possible Values:
0 - Profile of temperature will not be written
1 - Profile of temperature will be written
4.2.4 IPHP, IADS, ICKL, IVEL, IVIS, IPER, ICNM, IRKF, IPHSE, ICSE
IPHP - Flag indicating if oleic and microemulsion phase pressure data should be printed.
Possible Values:
0 - Oleic and microemulsion phase pressure data will not be printed
1 - Oleic and microemulsion phase pressure data will be printed
IADS - Flag indicating if surfactant, polymer, calcium, gel, chromium, hydrogen, and sodium
adsorption data should be printed.
Possible Values:
0 - Adsorption data will not be printed
1 - Adsorption data will be printed
ICKL - Flag indicating if component concentration data in each phase should be printed.
Possible Values:
0 - Component concentration data in each phase will not be printed
1 - Component concentration data in each phase will be printed
IVEL - Flag indicating if X, Y, and Z direction phase fluxes should be printed.
Possible Values:
0 - X, Y, and Z direction phase fluxes will not be printed
1 - X, Y, and Z direction phase fluxes will be printed
IVIS - Flag indicating if phase viscosities should be printed.
Possible Values:
0 - Phase viscosities will not be printed
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1 - Phase viscosities will be printed
IPER - Flag indicating if relative permeabilities should be printed.
Possible Values:
0 - Relative permeabilities will not be printed
1 - Relative permeabilities will be printed
ICNM - Flag indicating if phase capillary numbers and interfacial tensions should be printed.
Possible Values:
0 - Capillary numbers and interfacial tensions will not be printed
1 - Capillary numbers and interfacial tensions will be printed
IRKF - Flag indicating if permeability reduction factors should be printed.
Possible Values:
0 - Permeability reduction factors, polymer viscosities, and equivalent shear rate will
not be printed
1 - Permeability reduction factors, polymer viscosities, and equivalent shear rate will be
printed
IPHSE - Flag indicating if phase environment indexing should be printed.
Possible Values:
0 - Phase environment indexing will not be printed
1 - Phase environment indexing will be printed
Note: The indices for the phase environment are as follows:
1 - single phase
2 - two phase oil/water or oil/microemulsion or water/microemulsion
3 - three phase oil/microemulsion/water
4 - lobe H(+) of type HI
5-lobe II(-) of type III
ICSE - Flag indicating if effective salinity should be printed.
Possible Values:
0 - Effective salinity information will not be printed
1 - Effective salinity will be printed to PROFIL and history data files
These flags give the option of printing a very detailed description (all flags = 1) every
CUMPR1 pore volume interval or a very limited description (all flags = 0) to UNIT 4. See
section B.6 for a list of the values that are written to UNIT 4 automatically.
Note:
4.3 Reservoir Properties
The third input section consists of the reservoir properties. Please remember that there are
seven comment lines at the beginning of this section and that each data line is preceded by three
comment lines.
4.3.1 TMAX
TMAX - Total injection period (maximum simulated time).
Units: days or pore volumes (dependent on value of ISTOP flag in line 4.2.1)
4.3.2 COMPR, PSTAND
COMPR - Rock compressibility.
Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)
PSTAND - Reference pressure at which pore volume and fluid compressibilities are specified
Units: psi (IUNIT=0) or kPa (IUNIT=1)
4.3.3 IPOR1, IPERMX, IPERMY, IPERMZ
IPOR1 - Flag indicating constant or variable porosity for reservoir.
Possible Values:
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0 - Constant porosity for whole reservoir
1 - Constant porosity for each layer
2 - Variable porosity over reservoir
IPERMX - Flag indicating constant or variable X direction permeability (ICOORD = 1 or 3) or radial
direction permeability (ICOORD = 2) for reservoir.
Possible Values:
0 - Constant permeability for whole reservoir
1 - Constant permeability for each layer in the X direction (ICOORD = 1 or 3) or radial
direction (ICOORD = 2)
2 - Variable permeability over reservoir
IPERMY - Flag indicating constant or variable Y direction permeability for reservoir.
Possible Values:
0 - Constant permeability for whole reservoir
1 - Constant permeability for each layer in the Y direction
2 - Variable permeability over reservoir
3 - Y direction permeability is dependent on X direction permeability
IPERMZ - Flag indicating constant or variable Z direction permeability for reservoir.
Possible Values:
0 - Constant permeability for whole reservoir
1 - Constant permeability for each layer in the Z direction
2 - Variable permeability over reservoir
3 - Z direction permeability is dependent on X direction permeability
4.3.4
4.3.5
PORC1 (This line is read only if IPOR1 = 0)
PORC1 - Reservoir porosity.
Units: fraction
Note: All elements of the POR array will be set equal to PORC1.
POR(K), for K = 1, NZ (This line is read only if IPOR1 = 1)
POR(K) - Porosity of Kth layer.
Units: fraction
Note: NZ values are actually read into a workspace array (WKSP1) and then the first set of
NX x NY elements (corresponding to layer 1) of the POR array are set equal to
WKSPl(l), the second set of NX x NY elements (corresponding to layer 2) of the
POR array are set equal to WKSP1(2), etc.
4.3.6
POR(I), for I = 1, NX x NY x NZ (This line is read only if IPOR1 = 2)
POR(I)- Porosity of Ith gridblock
Units: fraction
Note: The three-dimensional grid system is being read into a one-dimensional array. The
first index (column) of the three-dimensional system variej
fastest, the second index (row) varies next fastest, and the third index (layer) varies slowest.
Example: If you had a 4 x 3 x 2 system (4 columns—NX=4, 3
rows—NY=3, and 2 layers—NZ=2), the values would be read in the following order:
1,1,1 2,1,1 3,1,1 4,1,1
4,2,1
4,3,1
4,1,2
4,2,2
4,3,2
1,2,1
1,3,1
1,1,2
1,2,2
1,3,2
2,2,1
2,3,1
2,1,2
2,2,2
2,3,2
3,2,1
3,3,1
3,1,2
3,2,2
3,3,2
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4.3.7 PERMXC (This line is read only if IPERMX = 0)
PERMXC - Permeability of the reservoir in the X direction (ICOORD = 1 or 3) or in the radial
direction (ICOORD = 2).
Units: millidarcies = 10~3 |im2
Note: All elements of the PERMX array will be set equal to PERMXC.
4.3.8 PERMX(K), for K = 1, NZ (This line is read only if IPERMX = 1)
PERMX(K) - Permeability of the Kth layer in the X direction (ICOORD = 1 or 3) or in the radial
direction (ICOORD = 2).
Units: millidarcies = 10"3 |im2
Note: See the note for input line 4.3.5.
4.3.9 PERMX(I), for I = 1, NX x NY x NZ (This line is read only if IPERMX = 2)
PERMX(I) - Permeability of the Ith gridblock in the X direction (ICOORD = 1 or 3) or in the radial
direction (ICOORD = 2).
Units: millidarcies = 10~3 Jim2
Note: See the note and example for input line 4.3.6 for the order of the permeability values.
4.3.10 PERMYC (This line is read only if IPERMY = 0 and ICOORD = 1 or 3)
PERMYC - Permeability of the reservoir in the Y direction.
Units: millidarcies = 10~3 urn2
Note: All elements of the PERMY array will be set equal to PERMYC.
4.3.11 PERMY(K), for K = 1, NZ (This line is read only if IPERMY = 1 and ICOORD = 1 or 3)
PERMY(K) - Permeability of the Kth layer in the Y direction.
Units: millidarcies = 10"3 (im2
Note: See note for input line 4.3.5.
4.3.12 PERMY(I), for I = 1, NX x NY X NZ (This line is read only if IPERMY = 2 and ICOORD = 1 or
3)
PERMY(I) - Permeability of the Ith gridblock.
Units: millidarcies = 10~3 (im2
Note: See the note and example for input line 4.3.6 for the order of the permeability values.
4.3.13 FACTY (This line is read only if IPERMY = 3 and ICOORD = 1 or 3)
FACTY - Constant permeability multiplier for Y direction permeability.
Units: dimensionless
Note: The X direction permeabilities are multiplied by FACTY to obtain the Y direction
permeabilities.
4.3.14 PERMZC (This line is read only if IPERMZ = 0)
PERMZC - Permeability of the reservoir in the Z direction.
Units: millidarcies = 10~3 |im2
Note: All elements of the PERMZ array will be set equal to PERMZC.
4.3.15 PERMZ(K), for K = 1, NZ (This line is read only if IPERMZ =1)
PERMZ(K) - Permeability of the Kth layer in the Z direction.
Units: millidarcies•= 10'3 um2
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Note: See note for input line 4.3.5.
4.3.16 PERMZ(I), for I = 1, NX x NY x NZ (This line is read only if IPERMZ = 2)
PERMZ(I) - Permeability of the Ith gridblock.
Units: millidarcies (10'3 (im2)
Note: See the note and example for input line 4.3.6 for the order of the permeability values.
4.3.17 FACTZ (This line is read only if IPERMZ = 3 and ICOORD = 1 or 3)
FACTZ - Constant permeability multiplier for Z direction permeability.
Units: dimensionless
Note: The X direction permeabilities are multiplied by FACTZ to obtain the Z direction
permeabilities.
4.3.18 IDEPTH, IPRESS, ISWI
IDEPTH - Flag indicating type of depth measurement of the top layer.
Possible Values:
0 - Single value for depth of the top layer is specified
1 - Depth of top gridblock (1,1,1) and the reservoir dip angles are specified
2 - Depth of each gridblock in the top layer is specified
Note: If ICOORD = 2, this value is automatically set equal to 0.
The depth is specified at the middle of a gridblock.
IPRESS - Flag indicating type of reservoir initial pressure measurement.
Possible Values:
0 - Single value for reservoir initial pressure is used for all gridblocks
1 - Initial pressure for a point at a specified depth is specified by user
2 - Initial pressure for each gridblock is specified by user
ISWI - Flag indicating type of initial water saturation measurement.
Possible Values:
0 - Single value for initial water saturation is used for all gridblocks
1 - Constant value for water saturation for each layer is specified by user
' 2 - Initial water saturation for each gridblock is specified by user
4.3.19 Dill (This line is read only if IDEPTH = 0)
Dill - Depth of the top layer of the reservoir measured from the surface (reference plane), positive
downward.
Units: feet (IUNTT=0) or m(IUNIT=l)
Note: If IDEPTH=0 and ICOORD=4, Dl 11 is the reference depth of the first gridblock.
4.3.20 Dill, THETAX, THETAY (This line is read only if IDEPTH = 1)
Dill- Depth of the first gridblock (1,1,1).
Units: feet (IUNIT=0) or m (IUNIT=1)
THETAX - Reservoir dip angle in X direction, positive downward.
Units: radians
THETAY - Reservoir dip angle in Y direction, positive downward.
Units: radians
Note: If ICOORD=4, set THETAY equal to 0 (dip angle in X-Z plane).
4.3.21 EL(I), for I = 1, NX x NY (This line is read only if IDEPTH = 2)
EL(I) - Depth of Ith gridblock in the top layer (K=l).
Units: feet (IUNIT=0) orm(IUNIT=l)
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Note: See the note and example for input line 4.3.6 for the order of the gridblock depths.
4.3.22 PRESS 1 (This line is read only if IPRESS = 0)
PRESS 1 - Initial reservoir pressure.
Units: psi (IUNIT=0) or kPa (IUNIT=1)
4.3.23 PINIT, HINIT (This line is read only if IPRESS = 1)
PINIT - Initial reservoir pressure at HINIT depth.
Units: psia (IUNIT=0) or kPa (IUNIT=1)
HINIT - Depth of the point where PINIT initial pressure is specified.
Units: feet (IUNIT=0) orm(IUNIT=l)
Note: Initial pressure is assumed to be the aqueous phase pressure.
4.3.24 P(I), for I = 1, NX x NY x NZ (This line is read only if IPRESS = 2)
P(I) - Initial pressure of each gridblock in the reservoir.
Units: psia (IUNIT=0) or kPa (IUNIT=1)
Note: See the note and example for input line 4.3.6 for the order of the initial pressure
values. Thiis is assumed to be the aqueous phase pressure.
4.3.25 SWI (This line is read only if ISWI = 0)
SWI - Initial water saturation for all gridblocks of the reservoir.
Units: fraction of pore volume
4.3.26 S(K, 1), for K = 1, NZ (This line is read only if ISWI =1)
. S(K,1) - Initial water saturation for K* layer.
Units: fraction of pore volume
Note: See the note for input line 4.3.5.
4.3.27 S(I,l),I=l,NXxNYxNZ (This line is read only if ISWI = 2) •
S(I,1) - Initial water saturation for Ith block.
Units: fraction of pore volume
Note: See the note and example for input line 4.3.6 for the order of the initial water
saturation values.
4.3.28 ISGI (This line is read only if IGAS = 1)
ISGI - Flag indicating type of initial gas saturation.
Possible Values:
0 - Constant initial gas saturation for whole reservoir
1 - Constant initial gas saturation for each layer
2 - Initial gas saturation for each gridblock is specified by user
4.3.29 SGI (This line is read only if IGAS = 1 and ISGI = 0)
SGI - Initial gas saturation for all gridblocks of the reservoir.
Units: fraction of pore volume
4.3.30 S(K,4), for K = 1, NZ (This line is read only if IGAS = 1 and ISGI = 1)
S(K,4) - Initial gas saturation for K* layer.
Units: fraction of pore volume
Note: See the note for input line 4.3.5.
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4.3.31 S(I,4), I = 1, NX x NY x NZ (This line is read only if IGAS = 1 and ISGI = 2)
S(I,4) - Initial gas saturation for Ith block.
Units: fraction of pore volume
Note: See the note and example for input line 4.3.6 for the order of the initial gas saturation
values.
4.3.32 C50,C60
C50 - Initial brine salinity.
Units: meq/ml of brine
Note: This is assumed to be all the anions (in equivalents).
C60 - Initial divalent cation concentration of brine.
Units: meq/ml of brine
Note : C50 and C60 are replaced by the input values of C5I and C6I in line 4.5.33 when
IREACIM.
B.4.4 Physical Property Data
The fourth input section consists of the physical property data. Please remember that there are
seven comment lines at the beginning of this section and that each data line is preceded by three
comment lines.
4.4.1 C2PLC, C2PRC, EPSME
C2PLC - Oil concentration at plait point in type H(+) region.
Units: volume fraction
C2PRC - Oil concentration at plait point in type H(-j region.
Units: volume fraction
EPSME - Critical micelle concentration (CMC)—minimum surfactant concentration for the formation
of micelles.
Units: volume fraction
4.4.2 HBNS70, HBNC70, HBNS71, HBNC71, HBNS72, HBNC72
HBNS70 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1—Component
7—associated with surfactant at zero salinity.
Units: volume fraction
HBNC70 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 1—Component
7—associated with surfactant at zero salinity.
Units: volume fraction
HBNS71 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1—Component
7—associated with surfactant at optimal salinity.
Units: volume fraction
HBNC71 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 1—Component
7—associated with surfactant at optimal salinity.
Units: volume fraction
HBNS72 - Slope for maximum height of binodal curve vs. fraction of Alcohol 1—Component
7—associated with surfactant at twice optimal salinity.
Units: volume fraction
HBNC72 - Intercept of maximum height of binodal curve at zero fraction of Alcohol 1—Component
7—associated with surfactant at twice optimal salinity.
Units: volume fraction
Note: These parameters are obtained by matching the volume fraction diagrams corresponding to at
least three different total chemical (alcohol + surfactant) compositions. For the first iteration,
the slope parameters are set to zero and the intercept parameters are adjusted in order to obtain
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Appendix B - UTCHEM Local Grid Refinement User's Guide
a reasonable match of the volume fraction diagrams. Then the slope parameters are obtained
as follows:
o
CQ
I
h-
O
CQ
Slope = HBNS70
Slope = HBNS71
CM
I"-
O
CO
c
Slope = HBNS72
Having obtained the slope parameters, the matching procedure is repeated for further
improvements. See Satoh's thesis for example.
4.4.3 HBNS80, HBNC80, HBNS81, HBNC81, HBNS82, HBNC82
HBNS80 - Slope for maximum height of binodal curve vs. fraction of Alcohol
8—associated with surfactant at zero salinity.
Units: volume fraction
HBNC80 - Intercept of maximum height of binodal curve at zero fraction of Alcohol
8—associated with surfactant at zero salinity.
Units: volume fraction
HBNS81 - Slope of maximum height of binodal curve vs. fraction of Alcohol
8—associated with surfactant at optimal salinity.
Units: volume fraction
HBNC81 - Intercept of maximum height of binodal curve at zero fraction of Alcohol
8—associated with surfactant at optimal salinity.
Units: volume fraction
HBNS82 - Slope for maximum height of binodal curve vs. fraction of Alcohol
8—associated with surfactant at twice optimal salinity.
Units: volume fraction
HBNC82 - Intercept of maximum height of binodal curve at zero fraction of Alcohol
8—associated with surfactant at twice optimal salinity.
Units: volume fraction
Note: See the note for input line 4.4.2 to see how values should be determined.
2—Component
2—Component
2—Component
2—Component
2—Component
2—Component
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4.4.4 CSEL7, CSEU7, CSEL8, CSEU8
CSEL7 - Lower effective salinity limit for type HI phase region determined when Alcohol
1 — Component 7 — and calcium approach zero.
Units: meq/ml
CSEU7 - Upper effective salinity limit for type IE phase region determined when Alcohol
1 — Component 7 — and calcium approach zero.
Units: meq/ml
CSEL8 - Lower effective salinity limit for type HI phase region determined when Alcohol
2 — Component 8 — and calcium approach zero.
Units: meq/ml
CSEU8 - Upper effective salinity limit for type IE phase region determined when Alcohol
2 — Component 8 — and calcium approach zero.
Units: meq/ml
Note: The values are calculated as follows:
CSEU7 = lim (CSEU)
f?-»0
CSEL7= lim (CSEL)
f?->0
CSEU8 = lim (CSEU)
ff-»o
CSEL8 = lim (CSEL)
and
f|-»0
-SE =
-51
- P6f|)(l + P7fS7
4.4.5 BETA6, BETA7, BETAS
BETA6 - The CSE slope parameter, Pg, for calcium.
Units: dimensionless
BETA7 - The CSE slope parameter, P7, for Alcohol 1—Component 1,
Units: dimensionless
BETAS - The CSE slope parameter, Pg, for Alcohol 2—Component 8.
Units: dimensionless
Note: See notes for input line 4.4.4.
BETA6 is limited to less than —
f6
4.4.6 IALC, OPSK7O, OPSK7S, OPSK8O, OPSK8S
IALC - Flag indicating choice of alcohol partition model to use.
Possible Values:
0 - Hirasaki's model will be used
1 - Prouvost's model will be used
OPSK7O - Alcohol partition coefficient (oil/water) for Alcohol 1—Component 7.
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Units: dimensionless
OPSK7S - Alcohol partition coefficient (surfactant/water) for Alcohol 1—Component 7.
Units: dimensionless
OPSK8O - Alcohol partition coefficient (oil/water) for Alcohol 2—Component 8.
Units: dimensionless
OPSK8S - Alcohol partition coefficient (surfactant/water) for Alcohol 2—Component 8.
Units: dimensionless
Note: If IALC = 0 then OPSK7O, OPSK7S, OPSK8O, and OPSK8S remain fixed. If OPSK7O,
OPSK7S, OPSK8O, and OPSK8S are equal to zero and IALC = 0, then alcohol is lumped
with surfactant as a single component (total chemical). OPSK7O, OPSK7S, OPSK8O, and
OPSK8S are only used when Hirasaki's model is chosen.
. 4.4.7 NALMAX, EPSALC
NALMAX - Maximum number of iterations for alcohol partitioning for two alcohol system.
Note: The suggested value is 20 and a value of zero would result in no iterations.
EPSALC - Tolerance for convergence of iterations for two alcohol system.
Note: Suggested values are 10"3 and 1CH.
4.4.8 AKWC7, AKWS7, AKM7, AK7, PT7
AKWC7, AKWS7 - Parameters used to determine partition coefficient of monomeric Alcohol
1—Component 7—between aqueous and oleic pseudophases.
Units: dimensionless
AKM7 - Partition coefficient of monomeric Alcohol 1—Component 7—between surfactant and oleic
pseudophases.
Units: dimensionless
AK7 - Self-association constant of Alcohol 1—Component 7—in oleic pseudophase.
Units: dimensionless
PT7 - Ratio of molar volume of Alcohol 1—Component 7—to equivalent molar volume of surfactant.
Units: dimensionless
Note: These values can be calculated using PROPACK and are only required when using Prouvost's
model (IALC = 1).
4.4.9 AKWC8, AKWS8, AKM8, AK8, PT8
AKWC8, AKWS8 - Parameters used to determine partition coefficient of. monomeric Alcohol
2—Component 8—between aqueous and oleic pseudophases.
Units: dimensionless
AKM8 - Partition coefficient of monomeric Alcohol 2—Component 8—between surfactant and oleic
pseudophases.
Units: dimensionless
AK8 - Self-association constant of Alcohol 2—Component 8—in oleic pseudophase.
Units: dimensionless
PT8 - Ratio of molar volume of Alcohol 2—Component 8—to equivalent molar volume of surfactant.
Units: dimensionless
Note: These values can be calculated using PROPACK and are only required when using Prouvost's
model (IALC = 1).
4.4.10 G11,G12,G13,G21,G22,G23 (This line is read only if IFT = 0)
Gl 1, G12, G13 - Interfacial tension parameters for water-microemulsion interface.
G21, G22, G23 - Interfacial tension parameters for oil-microemulsion interface.
Units : Dimensionless
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Note: The equations used to calculate the interfacial tension parameters are discussed in Camilleri,
et. al [1987b].
4.4.11 XIFTW
XBFTW - logio crwo where awo is the interfacial tension of the water-oil interface.
Units: dynes/cm = mN/m
4.4.12 IMASS
IMASS - Flag indicating the choice of oil solubility in water.
Possible Values
0 - No solubility of oil in water in the absence of surfactant (component number 3)
1 - Allow for solubility of oil in water in the absence of surfactant or allow for
nonequilibrium transfer of oil in water
4.4.13 WSOL, CNEM2 (This line is read only if IMASS=1 and IGAS=0 in the presence of surfactant
(component no.3))
WSOL - Equilibrium concentration of oil in water in the absence of surfactant.
Units: volume fraction
CNEM2 - Coefficient of nonequilibrium mass transfer of oil in aqueous phase with or without
surfactant, M
Units: vol. ofwater/(bulkvol.-day)
Note: The input value of zero for CNEM2 represents an equilibrium mass transfer. The non-
equilibrium mass transfer (CNEM2>0) calculation is valid for type II(-) and lobe II(-) of type
in with the plait point in the corner (C2PLC = 0) and in the absence of gas phase (IGAS=0).
- C2£) ,
for I =1 or 3
is the computed composition from the hand equations when the surfactant is present and
is the input value of WSOL in the absence of surfactant or when
the surfactant concentration is below CMC.
4.4. 14 ITRAP, Til, T22, T33
ITRAP - Flag indicating whether residual saturations and relative permeabilities are dependent on
capillary number or not.
Possible Values:
0 - Residual saturations are not dependent on capillary number; endpoint and exponent
of relative permeability curves are constant
1 - Residual saturations and relative permeabilities are dependent on capillary number
Til- Capillary desaturation curve parameter, Tl5 for aqueous phase.
T22 - Capillary desaturation curve parameter, T2, for oleic phase.
T33 - Capillary desaturation curve parameter, T3, for microemulsion phase.
Note: The expressions for capillary desaturation are:
1 + T
, £=1,2,3
where
(2.23xlO~5) '
-,£=1,2,3
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For 1 = 1, GU< = awm. For i = 2, a«- = amo. For i = 3, GU< = awm if the aqueous
phase is mobile, amo otherwise.
Til, T22, and T33 are determined by matching experimental capillary desaturation curves.
4.4.15 IPERM
IPERM - Flag indicating the saturation history direction for relative permeability and capillary
pressure calculations
Possible Values:
. 0 - Imbibition Corey
1 - First drainage Corey (only for IOW=0 and two phase water/oil flow)
4.4.16 ISRW, IPRW, DEW
ISRW - Flag indicating type of residual saturation.
Possible Values:
0 - Constant residual saturation for entire reservoir
1 - Constant residual saturation for each layer
2 - Residual saturation for each gridblock
IPRW - Flag indicating type of endpoint relative permeability.
Possible Values:
0 - Constant endpoint relative permeability for entire reservoir
1 - Constant endpoint relative permeability for each layer
2 - Constant endpoint relative permeability for each gridblock
EEW - Flag indicating type of relative permeability exponent.
Possible Values:
0 - Constant relative permeability exponent for entire reservoir
1 - Constant relative permeability exponent for each layer
2 - Constant relative permeability exponent for each gridblock
4.4.17 S1RWC, S2RWC, S3RWC (This line is read only if ISRW = 0)
S1RWC - Residual saturation of aqueous phase displaced by oil at low capillary number for entire
reservoir.
Units: fraction
S2RWC - Residual saturation of oleic phase displaced by water at low capillary number for entire
reservoir.
Units: fraction
S3RWC - Residual saturation of microemulsion phase displaced by water at low capillary number
for entire reservoir.
Units: fraction
4.4.18 S 1RWC(K), for K = 1, NZ (This line is read only if ISRW = 1)
S 1RWC(K) - Residual saturation of aqueous phase displaced by oil or gas at low capillary number
for K* layer.
Units: fraction
4.4.19 S2RWC(K), for K = 1, NZ (This line is read only if ISRW = 1)
S2RWC(K) - Residual saturation of oleic phase displaced by water at low capillary number for Kth
layer.
Units: fraction
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4.4.20 S3RWC(K), for K = 1, NZ (This line is read only if ISRW = 1)
S3RWC(K) - Residual saturation of microemulsion phase displaced by water or oil at low capillary
number for K* layer.
Units: fraction
Note: See the note for input line 4.4.42. Additionally, S3RWC(K) must begin a separate line in the
input file for each layer.
4.4.21 S1RW(I), for I = 1, NX x NY x NZ (This line is read only ifTSRW = 2)
S1RW(I) - Residual saturation of aqueous phase displaced by oil or gas at low capillary number for
Ith gridblock.
Units: fraction
4.4.22 S2RW(I), for I = 1, NX x NY x NZ (This line is read only if ISRW = 2)
S2RWC(K) - Residual saturation of oleic phase displaced by water at low capillary number for Ith
gridblock.
Units: fraction
4.4.23 S3RW(I), for I = 1, NX x NY x NZ (This line is read only if ISRW = 2)
S3RW(I) - Residual saturation of microemulsion phase displaced by water or oil at low capillary
number for Ith gridblock.
Units: fraction
4.4.24 P1RWC, P2RWC, P3RWC (This line is read only if IPRW = 0)
P1RWC - End point relative permeability of water at low capillary number for entire reservoir.
Units: dimensionless
P2RWC - End point relative permeability of oil at low capillary number for entire reservoir.
Units: dimensionless
P3RWC - End point relative permeability of microemulsion at low capillary number for entire
reservoir.
Units: dimensionless
4.4.25 PIRWC(K), for K = 1, NZ (This line is read only if IPRW = 1)
PIRWC(K) - Constant endpoint relative permeability of water at low capillary number for Kth layer.
Units: dimensionless
4.4.26 P2RWC(K), for K = 1, NZ (This line is read only if IPRW =1)
P2RWC(K) - Constant endpoint relative permeability of oil at low capillary number for K* layer.
Units: dimensionless
4.4.27 P3RWC(K), for K = 1, NZ (This line is read only if IPRW = 1)
P3RWC(K) - Constant endpoint relative permeability of microemulsion at low capillary number for
K* layer.
Units: dimensionless
Note: See the note for input line 4.4.42. Additionally, PIRWC(K) must begin a separate line in the
input file for each layer.
4.4.28 P1RW(I), for I = 1, NX x NY x NZ (This line is read only if IPRW = 2)
P1RW(I) - Endpoint relative permeability of water at low capillary number for Ith gridblock.
Units: dimensionless
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4.4.29 P2RWQ), for I = 1, NX x NY x NZ (This line is read only if IPRW = 2)
P2RWC(K) - Endpoint relative permeability of oil at low capillary number for Ith gridblock.
Units: dimensionless
4.4.30 P3RW(I), for I = 1, NX x NY x NZ (This line is read only if IPRW = 2)
P3RW(I) - Endpoint relative permeability of microemulsion at low capillary number for Ith
gridblock.
Units: dimensionless
4.4.31 ElWC, E2WC, E3WC (This line is read only if IEW = 0)
ElWC - Phase relative permeability exponent for aqueous phase at low capillary number for entire
reservoir.
Units: dimensionless
E2WC - Phase relative permeability exponent for oleic phase at low capillary number for entire
reservoir.
Units: dimensionless
E3WC - Phase relative permeability exponent for microemulsion phase at low capillary number
system for entire reservoir.
Units: dimensionless
4.4.32 E1WC(K), for K = 1, NZ (This line is read only if IEW = 1)
E1WC(K) - Relative permeability exponent of aqueous phase at low capillary number for K* layer.
Units: dimensionless
4.4.33 E2WC(K), for K = 1, NZ (This line is read only if IEW = 1)
E2WC(K) - Relative permeability exponent of oleic phase at low capillary number for Kth layer.
Units: dimensionless
4.4.34 E3WC(K), for K = 1, NZ (This line is read only if IEW = 1)
E3WC(K) - Relative permeability exponent of microemulsion phase at low capillary number for Kth
layer.
Units: dimensionless
Note: See the note for input line 4.4.42. Additionally, E1WC(K) must begin a separate line in the
input file for each layer.
4.4.35 E1 W(I), for I = 1, NX x NY x NZ (This line is read only if IEW = 2)
E1W(I) - Relative permeability exponent of aqueous phase at low capillary number for Ith gridblock.
Units: dimensionless
4.4.36 E2W(I), for I = 1, NX x NY x NZ (This line is read only if IEW = 2)
E2WC(K) - Relative permeability exponent of oleic phase at low capillary number for Ith gridblock.
Units: dimensionless
4.4.37 E3W(I), for I = 1, NX x NY x NZ (This line is read only if ffiW = 2) '
E3W(I) - Relative permeability exponent of microemulsion phase at low capillary number for Ith
gridblock,
Units: dimensionless
4.4.38 S1RC, S2RC, S3RC
S1RC - Residual saturation of aqueous phase at high capillary number.
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Units: fraction
S2RC - Residual saturation of oleic phase at high capillary number.
Units: fraction
S3RC - Residual saturation of microemulsion phase at high capillary number.
Units: fraction
4.4.39 P1RC, P2RC, P3RC
P1RC - End point relative permeability of aqueous phase at high capillary number condition.
Units: dimensionless
P2RC - End point relative permeability of oleic phase at high capillary number condition.
Units: dimensionless
P3RC - End point relative permeability of microemulsion phase at high capillary number condition.
Units: dimensionless
4.4.40 E13C, E23C, E31C
E13C, E23C, E31C - Parameters used for calculating exponents for relative permeability calculations
at high capillary number.
Units: dimensionless
Note: For IGAS = 0, imbibition Corey relative permeabilities are calculated from:
where
for ITRAP=0
forITRAP=l
~ Slr
1-Slr~S2r ~S3r
and
S. -S,
t rw t r
s, -s,
t nv I re
/rw I'r
o ' o ,,-
t rw I re
for ITRAP=0
for ITRAP=1
The phase indices are assigned values according to the type of flow:
for water/oil: t = 1, f = 2, e^c = E13C, e^w = E1W
for water/microemulsion: £= 1, £' = 3, e^c = E23C, e£W = E2W
for oil/microemulsion: t = 2, £' = 3, e£C = E31C, e^w = E3W
For two phase oil/water drainage (IPERM =1), S2r is set to 0.0.
4.4.41 VIS1,VIS2,TSTAND
VIS1 - Water viscosity at reference temperature, Jli^ef-
Units: cp = mPa.s
VIS2 - Oil viscosity at reference temperature, |l2,ref •
Units: cp = mPa.s
TSTAND - Reference temperature, Tref.
Units: *F (IUNIT=0) or °C (IUNIT=1)
Note: For IENG=0, If TSAND = 0.0, the water component viscosity will be constant and
equal to the input value VIS1. If TSATND > 0.0, water component viscosity will be
calculated as a function of reservoir temperature, pressure, and local salinity for each
gridblock.
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4.4.42 VIS4, VSLOPG (This line is read only if IGAS = 1)
VIS4 - Gas viscosity at reference temperature and reference pressure, |J4,ref-
Units: cp = mPa.s
VSLOPG - Slope of gas viscosity, U4;S.
Units: (psi)-1 (IUNIT=0) or (IcPa)'1 (IUNIT=1)
Note: Gas viscosity is computed from:
M-4 =Kr
4.4.43 BVI( 1), BVI(2) (This line is read only if IENG =1)
BVI(l) - Parameter for calculating water viscosity as a function of reservoir temperature, bi.
Units: ("K)-1
B VI(2) - Parameter for calculating oil viscosity as a function of reservoir temperature, ba.
Units: ("K)-1
Note: The phase viscosities as a function of temperature are calculated from:
for 1=12
where T and Tref are in absolute °K.
4.4.44 B VI(4) (This line is read only if IGAS =1 and ffiNG = 1)
BVI(4) - Parameter for calculating gas viscosity as a function of reservoir temperature, b^.
Units: fK)-1
Note: Gas viscosity as a function of temperature is computed from:
exp 1 + bJ
IT M T T
L VT TrefJJ
where T and Tref are in absolute °K.
4.4.45 S2RWC4, S4RWC (This line is read only if IGAS = 1 and ISRW = 0)
S2RWC4 - Constant residual oil saturation to displacing gas phase for entire reservoir.
Units: fraction
S4RWC - Constant residual gas saturation for entire reservoir.
Units: fraction
4.4.46 S2RWC4(K), for K = 1, NZ (This line is read only if IGAS = 1 and ISRW = 1)
S2RWC4(K) - Constant residual oil saturation to displacing gas phase for Kth layer.
Units: fraction
4.4.47 S4RWC(K), for K = 1, NZ (This line is read only if IGAS = 1 and ISRW = 1)
S4RWC(K) - Constant residual gas saturation for K* layer.
Units: fraction
4.4.48 S2RW4(I), for I = 1, NX x NY x NZ (This line is read only if IGAS = 1 and ISRW = 2)
S2RW4(I) - Constant residual oil saturation to displacing gas phase for Ith gridblock.
Units: fraction
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4.4.49 S4RW(I), for I = 1, NX x NY x NZ (This line is read only if IGAS = 1 and ISRW = 2)
S4RW(I) - Residual gas saturation for Ith gridblock.
Units: fraction
4.4.50 P4RWC (This line is read only if IGAS = 1 and IPRW = 0)
P4RWC - Constant gas endpoint relative permeability for entire reservoir.
Units: dimensionless
4.4.51 P4RWC(K), for K = 1, NZ (This line is read only if IGAS = 1 and IPRW = 1)
P4RWC(K) - Constant gas endpoint relative permeability for Kth layer.
Units: dimensionless
4.4.52 P4RW(I), for I = 1, NX x NY x NZ (This line is read only if IGAS = 1 and IPRW = 2)
P4RW(I) - Constant gas endpoint relative permeability for Ith gridblock.
Units: dimensionless
4.4.53 E4WC (This line is read only if IGAS = 1 and IEW = 0)
E4WC - Constant gas relative permeability exponent for entire reservoir.
Units: dimensionless
4.4.54 E4WC(K), for K = 1, NZ (This line is read only if IGAS = 1 and IEW = 1)
E4WC(K) - Constant gas relative permeability exponent for Kth layer.
Units: dimensionless
4.4.55 E4WC(I), for I = 1, NX x NY x NZ (This line is read only if IGAS = 1 and IEW = 2)
E4WC(I) - Constant gas relative permeability exponent for Ith gridblock.
Units: dimensionless
4.4.56 S4RC, P4RC, E4C, T44, XEFTG (This line is read only if IGAS = 1)
S4RC - Residual gas saturations at high capillary number.
Units: fraction
P4RC - Gas endpoint relative permeability at high capillary number.
Units: dimensionless
E4C - Gas relative permeability exponent at high capillary number.
Units: dimensionless
T44 - Gas phase trapping parameter.
Units: dimensionless
XEFTG - Log of interfacial tension between gas and either water or oil.
Units: dyne/cm = mN/m
4.4.57 ALPHA1, ALPHA2, ALPHA3, ALPHA4, ALPHAS
ALPHA1 - Compositional phase viscosity parameter oci.
ALPHA2 - Compositional phase viscosity parameter 0x2.
ALPHAS - Compositional phase viscosity parameter 0.3.
ALPHA4 - Compositional phase viscosity parameter 0:4.
ALPHAS - Compositional phase viscosity parameter as.
Note: Compositional phase viscosity is calculated as:
V-e = Cn Up exp[cci (C2£ +
o exp[cc2
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Appendix B - UTCHEM Local Grid Refinement User's Guide
as exp[a4 Cu + «5
Polymer viscosity u.p is replaced by water viscosity when no polymer is present.
4.4.58 AP1,AP2, AP3
API, AP2, AP3 - Parameters used for calculating polymer viscosity at zero shear rate as a function
of polymer and electrolyte concentrations.
Units: (wt. %)-*, (wt. %)-2, (wt. %)-3
Note: Polymer viscosity at zero shear rate, (I0, is given by:
Api, Ap2, and Ap3 are empirical constants for a given polymer and are measured
experimentally.
4.4.59 BETAP, CSE1, SSLOPE
BETAP - Parameter, PP, for calculating the effective divalent salinity, CSEP, used to calculate
polymer viscosity (see the note for input line 4.4.60).
Units: dimensionless
Note: CSEP is given by:
_C9+ppC6
CSE1 - Value below which the polymer viscosity is considered to be independent of salinity
(minimum value of CSEP — see the note for input line 4.4.60).
Units: meq/ml
SSLOPE - Slope, Sp, of |I0 vs. CSEP on a log-log plot — assumed to be constant (see the note for
input line 4.4.60).
Units: dimensionless
Note: This value is usually large and negative for hydrolyzed polyacrylamides and small and
' positive for polysaccharides.
4.4.60 GAMMAC, GAMHF, POWN
GAMMAC - Coefficient, y c , in shear rate equation below.
day(darcy)'/2
(IUNrr=0)
ft — sec m — sec
GAMHF - Shear rate, jy2 , at which polymer viscosity is one half polymer viscosity at zero shear
rate.
Units: sec'1
POWN - Exponent, Pa, for calculating shear rate dependence of polymer viscosity.
Units: dimensionless
Note: The shear rate dependence of polymer viscosity is modeled by Meter's equation:
M-D=,
1 +
Teq
Pa-l
where the equivalent shear rate yeq is calculated as:
Yeq~l 4n
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where u is in ft/day, k is in Darcies, and yeq is in I/sec. Using n = 0.8 and with the unit
conversion we have yc = 3.94 C. The value of shear rate coefficient C can be calculated as:
1
• a
C = 4.8 Nv j
where Nv is in cm/sec. Nv is a dimensional group called viscosity number computed as:
_ ykkrw({)sw
Units:
Please refer to Wreath [1989] and Wreath, et al. [1990] for more detail.
4.4.61 IPOLYM, EPHI3, EPHI4, BRK, CRK
IPOLYM - Flag indicating type of polymer partitioning.
Possible values:
0 - All polymer exists in aqueous phase if aqueous phase exists; otherwise, it exists
completely in microemulsion phase
1 - Partitioning of polymer to water component is constant
EPHI3 - Effective porosity for surfactant—ratio of apparent porosity for surfactant to actual porosity.
Units: dimensionless
EPHI4 - Effective porosity for polymer—ratio of apparent porosity for polymer to actual porosity.
Units: dimensionless
BRK - Parameter for calculating permeability reduction factor Rfc.
volume of polymer - rich phase
weight % polymer
CRK - Parameter for calculating permeability reduction factor Rfc.
Units: (darcy)1/2 (100 g/g)'1/3 = (urn2)1/2 (100 g/g)'1/3)
Note: EPHI3 and EPHI4 are used to account for inaccessible pore volume in the case of surfactant
and polymer.
^surfactant = <|> X EPHI3
^polymer = § X EHPI4
The effect of permeability reduction or residual resistance is to reduce the mobility of the
polymer rich phase. This is accounted for by multiplying the viscosity of the phase by Rk>
4.4.62 DEN1, DEN2, DENS, DEN7, DENS, IDEN
DEN1 - Specific weight, yi, or density of water—Component 1.
Units: psi/ft (IUNIT=0) or g/cm3 (IUNTT=1)
DEN2 - Specific weight, 72, or density of oil—Component 2.
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
DENS - Specific weight, 73, or density of surfactant—Component 3.
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
DEN7 - Specific weight, 77, or density of Alcohol 1—Component 7.
Units: psi/ft (IUNTT=0) or g/cm3 (IUNTT=1)
DENS - Specific weight, yg, or density of Alcohol 2 (when IGAS = 0) or gas (when IGAS = 1)
—Component 8.
Units: psi/ft (IUNIT=0) or g/cm3 (IUNIT=1)
IDEN - Flag indicating if gravity effect should be considered.
Possible values:
1 - Do not consider gravity effect
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2 - Consider gravity effect
Note: Specific weight for pure water is 0.433 psi/ft (density of 1 g/cm3)
4.4.63 ISTB
ISTB - Flag indicating the units to be used when printing injection and production rates.
Possible Values:
0 - Rates printed at bottomhole condition in ft3 or m3
1 - Rates printed at surface condition in BBLS
4.4.64 FVF(L), for L = 1, MXP (This line is read only if ISTB = 1 and IUNIT=0)
FVF(L) - Formation volume factor for Lth phase.
Units: SCF/ft3
Note: MXP = 3 when IGAS = 0 and MXP = 4 when IGAS = 1.
4.4.65 COMPC(l), COMPC(2), COMPC(3), COMPC(7), COMPC(8)
COMPC(l) - Compressibility of brine—Component 1.
Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)
COMPC(2) - Compressibility of oil—Component 2.
Units: 1/psi (IUNIT=0) or l/kPa(IUNIT=l)
COMPC(3) - Compressibility of surfactant—Component 3.
Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)
COMPC(7) - Compressibility of Alcohol 1—Component 7.
Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)
COMPC(8) - Compressibility of Alcohol 2 (when IGAS = 0) or gas (when IGAS = 1)
—Component 8.
Units: 1/psi (IUNIT=0) or 1/kPa (IUNIT=1)
Note: For incompressible fluids, values of zero should be used for the COMPC values listed above.
4.4.66 ICPC, ffiPC, IOW
ICPC - Flag indicating type of capillary pressure endpoint, cpc.
Possible Values:
0 - Constant capillary pressure endpoint for entire reservoir
1 - Constant capillary pressure endpoint for each layer
2 - Capillary pressure endpoint for each gridblock
IEPC - Flag indicating type of capillary pressure exponent, npc.
Possible Values:
0 - Constant capillary pressure exponent for entire reservoir
1 - Constant capillary pressure exponent for each layer
2 - Capillary pressure exponent for each gridblock
IOW - Flag indicating the wettability for capillary pressure calculations.
Possible Values:
0 - The capillary pressure curve is for water-wet rock
1 - The capillary pressure curve is for oil-wet rock (zero at residual water saturations)
4.4.67 CPCO (This line is read only if ICPC = 0)
CPCO - Capillary pressure endpoint for entire reservoir, cpc.
Units: psiVdarcies (IUNIT=0) or kPa-^iim2 (IUNIT=1)
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4.4.68 CPC(K), for K = 1, NZ (This line is read only if ICPC = 1)
CPC(K) - Capillary pressure endpoint for K* layer, cpc.
" (IUNIT=1)
Units: psiVdarcies (IUNIT=0) or
4.4.69 CPC(I), for I = 1, NX x NY x NZ (This line is read only if ICPC = 2)
CPC(I) - Capillary pressure endpoint for Ith gridblock, cpc.
Units: psiVdarcies (IUNIT=0) or kPa^m2 (IUNIT=1)
4.4.70 EPCO (This line is read only if ffiPC = 0)
EPCO - Capillary pressure exponent for entire reservoir, npc.
Units: dimensionless
4.4.7 1 EPC(K), for K = 1 , NZ (This line is read only if ffiPC = 1)
EPC(K) - Capillary pressure exponent for Kth layer, npc.
Units: dimensionless
4.4.72 EPC(I), for I = 1 , NX x NY x NZ (This line is read only if ffiPC = 2)
EPC(I) - Capillary pressure exponent for Ith gridblock, npc.
Units: dimensionless
Note: The CPC and EPC values are determined by curve fitting a plot of water-oil capillary pressure
vs. normalized water saturation (see the note for input line 4.4.42). For imbibition two
phases:
>-a °wo
For three phases:
o _p _ ~
PC13 = PCwm ~ cpc T-
g
and
PC32 -
wm
-
wo
'mo
Sn2
'pc
For two phase oil/water drainage (IPERM =1):
— c
PC
-s
°
pc
The value for npc must be non-zero.
4.4.73 D(KC,1), for KG = 1, N
D(KC,1) - Molecular diffusion coefficient of KCth component in aqueous phase.
Units: ft2/day (IUNIT=0) orm2/day (IUNIT=1)
4.4.74 D(KC,2), for KG = 1, N
D(KC,2) - Molecular diffusion coefficient of KCth component in oleic phase.
Units: ft2/day (IUNIT=0) orm2/day (IUNIT=1)
4.4.75 D(KC,3), for KG = 1, N
D(KC,3) - Molecular diffusion coefficient of KC* component in microemulsion phase.
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Appendix B • UTCHEM Local Grid Refinement User's Guide
Units: ft2/day (IUNTT=0) or m2/day (IUNIT=1)
4.4.76 D(KC,4), for KG = 1, N (This line is read only if IGAS = 1)
D(KC,4) - Molecular diffusion coefficient of KCth component in gas phase.
Units: ft2/day (IUNIT=0) orm2/day (IUNIT=1)
4.4.77 ALPHAL(l), ALPHAT(l)
ALPHAL(l) - Longitudinal dispersivity of aqueous phase.
Units: feet (IUNIT=0) or m (IUNIT=1)
ALPHAT(l) - Transverse dispersivity of aqueous phase.
Units: feet (IUNIT=0) or m (IUNIT=1)
4.4.78 ALPHAL(2), ALPHAT(2)
ALPHAL(2) - Longitudinal dispersivity of oleic phase.
Units: feet (IUNIT=0) or m (IUNIT=1)
ALPHAT(2) - Transverse dispersivity of oleic phase.
Units: feet (IUNIT=0) or m (IUNIT=1)
4.4.79 ALPHAL(3), ALPHAT(3)
ALPHAL(3) - Longitudinal dispersivity of microemulsion phase.
Units: feet (IUNIT=0) orm(IUNIT=l)
ALPHAT(3) - Transverse dispersivity of microemulsion phase.
Units: feet (IUNIT=0) orm(IUNIT=l).
4.4.80 ALPHAL(4), ALPHAT(4) (This line is read only if IGAS = 1)
ALPHAL(4) - Longitudinal dispersivity of gas phase.
Units: feet (IUNIT=0) orm(IUNIT=l)
ALPHAT(4) - Transverse dispersivity of gas phase.
Units: feet (IUNIT=0) or m (IUNIT=1)
4.4.81 AD31, AD32, B3D, AD41, AD42, B4D
AD31 - Surfactant adsorption parameter,
TT . volume of phased
Units:
pore volume
AD32 - Surfactant adsorption parameter,
Units: ml/meq
BSD - Surfactant adsorption parameter, 03.
Units: 1
volume of surfactant in phase i
AD41 - Polymer adsorption parameter, 341.
Units: dimensionless
AD42 - Polymer adsorption parameter, 042-
Units: ml/meq
B4D - Polymer adsorption parameter, b4.
TT . volume of water
Units:
weight % polymer
Note: Langmuir-type isotherms are used to model surfactant and polymer adsorption. Surfactant
adsorption is irreversible with respect to surfactant concentration:
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- • *£&_
6 1 + b3Cci
Units:
volume of adsorbed surfactant
pore volume
as = asi + as2 CSE
When as2 = 0, there will be no salinity dependence.
A Langmuir-type isotherm is used to describe the adsorption level of polymer, component 4,
as a function of the concentration of polymer in the water as:
*
^ _ a4C4
4 ~ 1 a. K r*
i + D4l_4
T . weight % adsorbed polymer
Units: —
volume of water
where C4 = — — and a4 = &4\ + a42 CSEP
cl
4.4.82 QV, XKC, XKS, EQW
QV - Cation exchange capacity of clays.
Units: meq/ml of pore volume
XKC - Cation exchange constant, pc, for clays.
Units: (meq/ml)-1
XKS - Cation exchange constant, Ps, for surfactant.
Units: (meq/ml)-1
EQW - Equivalent weight of surfactant.
Note: The cation exchange model is:
for clay
_ »c
Qr -> f~,o
C6
EQW must be non-zero.
for micelles
4.4.83 TK(I), for I = 1, NTW+NTA (This line is read only if NTW+NTA > 0)
TK(I) - Tracer partitioning coefficient, KK;ref, for Ith water/oil tracer at initial chloride
concentration and reference temperature (TSTAND). A value of 0.0 indicates a water or gas
tracer and a value of -1.0 indicates an oil tracer.
Units: fraction
Note:
— K°
for oil/water tracer
KK,ref - '
for oil/gas tracer
4.4.84 TKS(I), for I = 1, NTW (This line is read only if NTW > 0)
TKS(I) - Parameter for calculating water/oil tracer partitioning coefficient, KK, for Ith tracer as a
function of salinity, TKSk-
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Units: (meq/ml)'1
Note: KK = KK)ref(l + TKSK(C51-C50))
4.4.85 TKT(I), for I = 1, NTW+NTA (This line is read only if NTW+NTA > 0 and ffiNG = 1)
TKT(I) - Parameter for calculating tracer partitioning coefficient, KK, for Ith tracer as a function of
reservoir temperature, TKTfc.
Units: ("F)-1 (IUNIT=0) or CQ-1 (IUNIT=1)
Note: KK = KK,ref (l + TKTK(T - Tref))
4.4.86 RDC(I), for I = 1, NTW+NTA (This line is read only if NTW+NTA > 0)
RDC(I) - Radioactive decay coefficient, X,K, for Ith tracer. A value of 0.0 indicates a non-radioactive
tracer.
Units: I/days
Note: C = C0e~^(t~to)
where
ln(0.5)
^k = ~ —<.
ul/2,k
t
1/2 k = half life of radioactive tracer, day
4.4.87 RET(I), for I = 1 , NTW+NTA (This line is read only if NTW+NTA > 0)
RET(I) - Tracer retardation factor DS — adsorbed concentration/flowing concentration. A value of 0.0
indicates no retardation. :
Units: dimensionless
Note: The retardation factor is defined as:
where i = 1 for oil/water tracer and i = 4 for gas/water tracer.
This factor causes a reduction in tracer velocity:
. L I + DS
4.4.88 FFL(l), FFH(l), CM(I,1), for I = 1, NTW (This line is read only if NTW > 0 and ICAP = 1)
FFL(l) - Value of flowing fraction for phase 1 when fractional flow = 0.0.
Units: dimensionless
FFH(l) - Value of flowing fraction for phase 1 when fractional flow =1.0.
Units: dimensionless
CM(I,1) - Mass transfer coefficients for Ith tracer in phase 1.
Units: I/sec
4.4.89 FFL(2), FFH(2), CM(I,2), for I = 1, NTW (This line is read only if NTW > 0 and ICAP = 1)
FFL(2) - Value of flowing fraction for phase 2 when fractional flow = 0.0.
Units: dimensionless
FFH(2) - Value of flowing fraction for phase 2 when fractional flow = 1.0.
Units: dimensionless
CM(I,2) - Mass transfer coefficients for Ith tracer in phase 2.
Units: I/sec
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Appendix B - UTCHEM Local Grid Refinement User's Guide
4.4.90 FFL(3), FFH(3), CM(I,3), for I = 1, NTW (This line is read only if NTW > 0 and ICAP = 1)
FFL(3) - Value of flowing fraction for phase 3 when fractional flow = 0.0.
Units: dimensionless
FFH(3) - Value of flowing fraction for phase 3 when fractional flow = 1.0.
Units: dimensionless
CM(I,3) - Mass transfer coefficients for Ith tracer in phase 3.
Units: I/sec
4.4.91 TAK1 (This line is read only if NTW > 0 and ITREAC = 1)
TAK1 - Rate constant for a first-order aqueous phase reaction at reference temperature (Tref) in which
Tracer 2 (component 10) hydrolyzes to form Tracer 3 (component 11) according to Cn,i =
TAK1 GIO.I.
Units: days'1
4.4.92 TMW(I), for I = 1, NTW (This line is read only if NTW > 0 and ITREAC = 1)
TMW(I) - Molecular weight of the Ith tracer.
Units: The user can specify the molecular weight in any unit as long as the units are the same
for all the tracers. It is assumed that the reaction of 1 mole of primary tracer produces
1 mole of secondary tracer. If not, use "equivalent" molecular weights.
4.4.93 TDEN(I), for I = 1, NTW (This line is read only if NTW > 0 and ITREAC = 1)
TDEN(I) - Density of the Ith tracer.
Units: g/cm3
4.4.94 TAKT (This line is read only if NTW > 0 and ITREAC = 1 and IENG = 1)
TAKT - Parameter for calculating rate constant for a first-order aqueous phase reaction as a function
of reservoir temperature.
Units: fK)'1
Note: TAK = TAK1 exp TAKrl — - — I
I I HP T1 I I
I, VT TrefJJ
4.4.95 AK1, AK2, SCR, X4, X14, X16, WM4 (This line is read only if NG>0)
AK1 - Kinetic rate coefficient for Cr3+ at reference temperature (Tref), AKlref.
Units: pprrr1 days'1
AK2 - Kinetic rate coefficient for gel at reference temperature (Tref), AK2ref.
Units: (molefliter)l-X4-xl4+xl6 days'1
Note: In order to achieve the same results achieved in versions previous to UTCHEM- V-
5.0, please use the following conversion:
AK2new =
new
SCRXM
ymerXl0
AK2
(1 + SCR)
SCR - Stoichiometric ratio in mass between Cr3+ and polymer.
Units: dimensionless
Note: SCR =
-3+
ivi polymer
X4 - Exponent to be used for polymer component of gelation reaction.
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Units: dimensionless
X14 - Exponent to be used for chromium component of gelation reaction.
Units: dimensionless
XI 6 - Exponent to be used for hydrogen ion component of gelation reaction.
Units: dimensionless
WM4 - Molecular weight of polymer.
Units: g/mole
4.4.96 AK1T, AK2T (This line is read only if NG>0 and IENG = 1)
AK1T - Parameter for calculating Kinetic rate coefficient for Cr3+ as a function of reservoir
temperature.
Units: ("K)-1
AK2T - Parameter for calculating Kinetic rate coefficient for gel as a function of reservoir
temperature.
Units: CK)-1
Note: The kinetic rate coefficients as a function of temperature are computed from:
AKl = AKlrefexp AK1TI- -- —
ICl r _ _
V VT TrefJJ
AK2 = AK2ref exp AK2T
rer r\
lr
4.4.97 AG1, AG2, CRG, AGK, BGK (This line is read only if NG>0)
AG1 - Flory-Huggins parameter for gel viscosity, Agi.
Units: cp ppnr1 = mPa.s ppnr1
AG2 - Flory-Huggins parameter for gel viscosity, Ag2-
Units: cp ppnr2 = mPa.s ppnr2
CRG - Constant, Cg, in the dimensionless pore radius reduction group. This constant depends on the
gel type.
Units: •N/darcy(wt%)1/3 = -^jim2 (wt%)1/3
AGK, BGK - Permeability reduction parameters, AIS and BIS, for Langmuir correlation with gel
concentration.
Units: dimensionless
Note: Dimensionless pore radius reduction group:
N8=C8
1/2
From this the permeability reduction factor for idealized case is expressed as:
RRF = kw » before gel treatment _ / _ \-4
max kw, after gel treatment ^ *'
The "Langmuir-type" isotherm for permeability reduction as a function of gel concentration
s:
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Appendix B - UTCHEM Local Grid Refinement User's Guide
RRF =
1 + B15 C15)1
Note: Gel viscosity is calculated from
Hgel = M-w l + Aglc15, 1 + Ag2C5)
if there is flowing polymer concentration, add (J,gei to the [Lp calculation. See note for input
line 4.4.62.
4.4.98 A15D, B 15D, ICREX, A14D, B 14D, CRNAK, HNAK, C160 (This line is read only if NG>0)
A15D, B15D - Gel adsorption parameters.
Units: vol. of water / ppm gel
ICREX - Flag indicating if Cr3+ will be allowed to exchange with clays.
Possible Values:
0 - Cr3+ exchange with clays is not allowed
1 - Cr3+ exchange with clays is allowed
AMD, B14D - Chromium adsorption parameters.
Units: vol. of water / ppm chromium
CRNAK - Chromium-sodium exchange reaction equilibrium constant.
HNAK - Hydrogen-sodium exchange reaction equilibrium constant.
C160 - Initial hydrogen ion concentration.
Units: meq/ml
Note: The "Langmuir-type" isotherm for chromium and gel adsorption is expressed as:
f!4 for chromium
7=T aK CK,1
W — ~ : -—
K
15for gel
4.4.99
The input values of CRNAK, HNAK, and C160 are ignored for IREACT=6
IP1 , IP2 (This line is read only if NG>0, NY = 1 and NZ = 1)
IP1, IP2 - Gridblock locations where calculated pressure values should be printed to UNIT 19.
Note: These values are intended to be used for comparison with pressure tab data of 1-D
experiments.
4.4. 100 TEMPI (This line is read only if IENG = 1)
TEMPI- Constant initial reservoir temperature.
Units: °F (IUNIT=0) or °C (IUNIT=1)
4.4. 1 0 1 DENS, CRTC, CVSPR, CVSPL(L), L= 1 ,MXP (This line is read only if IENG = 1 )
DENS - Reservoir rock density.
Units: lb/ft3 (IUNTT=0) or g/cm3 (IUNIT=1)
CRTC - Reservoir thermal conductivity.
Units: Btu (day-ft-T)-1 (IUNIT=0) or kJ (day-m-'K)-1 (IUNIT=1)
CVSPR - Reservoir rock heat capacity.
Units: Btu (Ib-T)-1 (IUNIT=0) or kJ (kg-'K)-1 (IUNIT=1)
CVSPL(L) - Phase L heat capacity (MXP is equal to 3 (IGAS=0) or 4 (IGAS=1)).
Units: Btu (Ib-'F)-1 (IUNIT=0) or kJ (kg-'K)-1 (IUNIT=1)
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Appendix B - UTCHEM Local Grid Refinement User's Guide
4.4.102 IHLOS, IANAL (This line is read only if ffiNG = 1)
IHLOS - Flag indicating if the heatloss calculation to overburden and underburden rock is
considered or not. Heat flux into the reservoir from the overburden/underburden is
calculated from the model of Vinsome and Westerveld [1980].
Possible Values:
0 - Heatloss is not considered
1 - Heatloss is considered
IANAL - Flag indicating if the temperature profile is calculated from analytical solution (only 1-D).
Possible Values:
0 - Analytical solution is not considered
1 - Analytical solution is considered
4.4.103 TCONO, DENO, CVSPO, TCONU, DENU, CVSPU (This line is read only if ffiNG = 1 and
IHLOS = 1)
TCONO - Thermal conductivity of overburden rock.
Units: Btu (day-ft-'F)-1 (IUNIT=0) or kJ (day-m-'K)-1 (IUNIT=1)
DENO - Density of overburden rock.
Units: lb/ft3 (IUNIT=0) or g/cm3 (IUNIT=1)
CVSPO - Heat capacity of overburden rock.
Units: Btu(lb-°F)-l(IUNIT=0)orkJ(kg-°K)-l(IUNIT=l)
TCONU - Thermal conductivity of underburden rock.
Units: Btu (day-ft-T)-1 (IUNIT=0) or kJ (day-m-°K)-l (IUNIT=1)
DENU - Density of underburden rock.
Units: lb/ft3 (IUNIT=0) or g/cm3 (IUNIT=1)
CVSPU - Heat capacity of underburden rock.
Units: Btu (Ib-T)-1 (IUNIT=0) or kJ (kg-'K)-1 (IUNIT=1)
B.4.5 Physical Property Data for Geochemical Options
The fifth input section consists of physical property data that is read only if IREACT > 1. The
data for this section is generated by a preprocessor program (EQB ATCH) and does not have the same
format as the rest of the input data for UTCHEM. This input section is not preceded by the usual
seven comment lines and individual data lines are not preceded by three comment lines. Sections 6.6
through 6.0 of this appendix give a list of elements, fluid' species, solid species, and adsorbed species
for geochemical options.
4.5.1
4.5.2
IRSPS, IPHAD (This line is read only if IREACT > 1)
IRSPS - Flag indicating if the reactive species concentrations should be printed.
Possible Values:
0 - Reactive species concentrations will not be printed
1 - Independent aqueous reactive species, solid species, and sorbed species
concentrations will be printed
2 - All aqueous species, solid species, and sorbed species concentrations will be printed
IPHAD - Flag indicating whether surfactant adsorption is pH dependent or not.
Possible Values:
0 - Surfactant adsorption is not pH dependent
1 - Surfactant adsorption is pH dependent
PHC, PHT, PHT1, HPHAD (This line is read only if IREACT > 1 and IPHAD > 0)
PHC - Critical pH above which surfactant adsorption is pH dependent.
PHT - Extrapolated pH value at zero surfactant adsorption.
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Appendix B - UTCHEM Local Grid Refinement User's Guide
PHT1 - pH value above which surfactant adsorption is constant.
HPHAD - Fraction of the low-pH adsorption plateau retained at a pH above PHT1.
4.5.3 CSELP, CSEUP (This line is read only if IREACT = 3 or 5)
CSELP - Lower optimum salinity limit for generated surfactant.
Units: meq/ml
CSEUP - Upper optimum salinity limit for generated surfactant.
Units: meq/ml
4.5.4 NELET, NFLD, NSLD, NSORB, NACAT, ICHRGE (This line is read only if IREACT > 1)
NELET - Total number of elements less non reacting element.
Maximum Value: 9
NFLD - Total number of fluid species.
NSLD - Total number of solid species.
NSORB - Total number of sorbed species.
NACAT - Total number of surfactant associated cations.
ICHRGE - Flag indicating whether an oxygen balance or a charge balance will be used.
Possible Values:
0 - Oxygen balance used
1 - Charge balance in solution used
Note: If solid SiO2 is considered, the oxygen balance must be used.
4.5.5 NIAQ, NEX, NSLEL, NSURF1 (This line is read only if IREACT > 1)
NIAQ - Total number of independent fluid species.
NEX - Total number of insoluble exchangers.
NSLEL - Total number of elements comprising the solid species.
NSURF1 - Position number corresponding to the in situ generated surfactant anion in the fluid species
array FLDSPS.
Note: NSURF1 is automatically set to 0 by the program if IREACT = 2 or 4.
4.5.6 NH, NNA, NCA, NMG, NCARB (This line is read only if IREACT > 1)
NH - Position number corresponding to the hydrogen element in the element array ELEMNT.
NNA - Position number corresponding to the sodium element in the element array ELEMNT.
NCA - Position number corresponding to the calcium element in the element array ELEMNT.
NMG - Position number corresponding to the magnesium element in the element array ELEMNT.
Note: If magnesium is not considered, NMG must be set equal to 0.
NCARB - Position number corresponding to the carbonate pseudo-element in the element array
ELEMNT.
4.5.7 NALU, NSILI, NOXY (This line is read only if IREACT > 3)
NALU - Position number corresponding to the aluminum element in the element array ELEMNT.
NSILI - Position number corresponding to the silicon element in the element array ELEMNT.
NOXY - Position number corresponding to the oxygen element in the element array ELEMNT.
4.5.8 NACD (This line is read only if IREACT = 3 or 5)
NACD - Position number corresponding to the petroleum acid pseudo-element in the element array
ELEMNT.
4.5.9 ELEMNT(I), for I = 1, NELET (This line is read only if IREACT > 1)
ELEMNT(I) - Name of the Ith element.
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Note: The name of each element may not exceed 32 characters and each name must be on a
separate line of the input file.
4.5.10 FLDSPS(I), for 1=1, NFLD (This line is read only if IREACT > 1)
FLDSPS(I) - Name of the Ith fluid species.
Note: The name of each fluid species may not exceed 32 characters and each name must be
on a separate line of the input file. If IREACT = 3 or 5, the last fluid species must be
HAW (petroleum acid in water).
4.5.11 SLDSPS(I), for I = 1, NSLD (This line is read only if IREACT > 1 and NSLD > 0)
SLDSPS(I) - Name of the Ith solid species.
Note: The name of each solid may not exceed 32 characters and each name must be on a
separate line of the input file.
4.5.12 SORBSP(I), for I = 1, NSORB (This line is read only if IREACT > 1 and NSORB > 0)
SORBSP(I) - Name of the Ith adsorbed cation.
Note: The name of each adsorbed cation may not exceed 32 characters and each name must
be on a separate line of the input file.
4.5.13 ACATSP(I), for I = 1, NACAT (This line is read only if IREACT > 1 and NACAT > 0)
ACATSP(I) - Name of the Ith surfactant adsorbed cation.
Note: The name of each surfactant adsorbed cation may not exceed 32 characters and each
name must be on a separate line of the input file.
4.5.14 NSORBX(I), for 1=1, NEX (This line is read only if IREACT > 1 and NSORB > 0)
NSORBX(I) - Number of cations for Ith exchanger.
4.5.15 AR(I,J), for J = 1, NFLD, for I = 1, NELET « or »
AR(I,J), for J = 1, NFLD, for I = 1, NELET-1 (This line is read only if IREACT > 1)
AR(I, J) - Stoichiometric coefficient of Ith element in Ith fluid species.
Note: If ICHRGE = 0, then NFLD x NELET values are required by the program. If ICHRGE = 1,
then NFLD x (NELET-1) values are required by the program.
4.5.16 BR(LJ), for J= 1, NSLD, forl= 1, NELET «or»
BR(LJ), for J = 1, NSLD, for 1=1, NELET-1 (This line is read only if IREACT > 1 and NSLD >
°)
BR(I,J) - Stoichiometric coefficient of Ith element in Jth solid species.
Note: If ICHRGE = 0, then NSLD x NELET values are required by the program. If ICHRGE = 1,
then NSLD x (NELET-1) values are required by the program.
4.5.17 DR(I,J), for J = 1, NSORB, for I = 1, NELET « or »
DR(I,J), for J = 1, NSORB, for 1=1, NELET-1 (This line is read only if IREACT > 1 and NSORB
> 1}
DR(I,J) - Stoichiometric coefficient of Ith element in Jth sorbed species.
Note: If ICHRGE = 0, then NSORB x NELET values are required by the program. If
ICHRGE = 1, then NSORB x (NELET-1) values are required by the program.
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4.5.18 ER(I,J), for J = 1, NACAT, for I = 1, NELET « or »
ER(I,J), for J = 1, NACAT, for I = 1, NELET-1 (This line is read only if IREACT > 1 and
NACAT > 1)
ER(I,J) - Stoichiometric coefficient of Ith element in Jth surfactant associated cation.
Note: If ICHRGE = 0, then NACAT x NELET values are required by the program. If
ICHRGE = 1, then NACAT x (NELET-1) values are required by the program.
4.5.19 BB(I,J), for J = 1, NIAQ+NSORB+NACAT, for I = 1, NFLD+NSORB+NACAT (This line is
read only if IREACT > 1)
BB(I,J) - Exponent of the Jth independent fluid species concentration when the Ith fluid species is
expressed in terms of independent species concentrations.
4.5.20 EXSLD(U), for J = 1, NIAQ, for I = 1, NSLD (This line is read only if IREACT > 1 and NSLD >
1)
EXSLD(IJ) - Exponent of the Jth independent fluid species concentration in the solubility product
definition of the Ith solid.
4.5.21 CHARGE®, for 1=1, NFLD (This line is read only if IREACT > 1)
CHARGE(I) - Charge of the Ith fluid species.
4.5.22 SCHARG(IJ), for J = 1, NSORBX(I), for I = 1, NEX (This line is read only if IREACT > 1 and
NSORB > 1)
SCHARG(I,J) - Charge of the Jth sorbed species on the Ith exchanger.
4.5.23 EQK(I), for 1=1, NFLD (This line is read only if IREACT > 1)
EQK(I) - Equilibrium constant for Ith fluid species when expressed in independent species
concentrations only.
4.5.24 EXK(I,J), for J = 1, NSORBX(I)-!, for I = 1, NEX (This line is read only if IREACT > 1 and
NEX > 0)
EXK(I.J) - Exchange equilibrium constant for Jth exchange equilibrium of the Ith insoluble
exchanger.
4.5.25 EXEX(I,J,K), for K = 1, NIAQ+NSORB+NACAT, for J = 1, NSORBX(I)-!, for I = 1, NEX
(This line is read only if IREACT > 1 and NEX > 0)
EXEX(I,J,K) - Exponent of Kth independent species in Jth equilibrium relation of the Ith exchanger.
4.5.26 REDUC(I,J), for J = 1, NSORBX(I)-!, for I = 1, NEX (This line is read only if IREACT > 1 and
NEX > 0)
REDUC(I,J) - Valence difference of the two cations involved in the exchange reaction J on exchanger
I.
Note: This value is 'positive if the higher valence cation bulk concentration has a positive
exponent in EXEX(I,J) definition and is negative otherwise.
4.5.27 EXCAI(I), for I = 1, NEX (This line is read only if IREACT > 1 and NEX >0)
EXCAI(I) - Exchange capacity of Ith insoluble exchanger.
Units: meq/ml pore volume
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4.5.28 SPK(I), for I = 1, NSLD (This line is read only if IREACT > 1 and NSLD > 1)
SPK(I) - Solubility product of Ith solid defined in terms of independent fluid species concentrations
only.
4.5.29 CHACAT(I), for I = 1, NACAT (This line is read only if IREACT > 1 and NACAT > 1)
CHACAT(I) - Charge of Ith surfactant associated cation.
4.5.30 ACATK(I), for I = 1, NACAT-1 (This line is read only if IREACT > 1 and NACAT > 1)
ACATK(I) - Equilibrium constant for Ith exchange equilibrium for cation exchanges on surfactant.
4.5.31 EXACAT(I,J) for J = 1, NIAQ+NSORB+NACAT, for I = 1, NACAT-1 (This line is read only if
IREACT > 1 and NACAT > 1)
EXACAT(I,J) - Exponent of Jth independent species in Ith equilibrium for cation exchange on
surfactant.
4.5.32 CI(J), for J = 1, NACAT (This line is read only if IREACT > 1 and NACAT > 1)
CI(J) - Initial concentration of Jth surfactant associated cation.
Units: moles/liter pore volume
4.5.33 C5I, C6I (This line is read only if IREACT > 1)
C5I - Initial concentration of non reacting anions.
Units: equivalents/liter
C6I - Initial concentration of calcium in aqueous phase.
Units: equivalents/liter
4.5.34 CELAQI(J), for J = 1, N-NO6 (This line is read only if IREACT > 1)
CELAQI(J) - Initial concentrations of (J+l l)th component.
Units: equivalents/liter
Note : NO6 = 11 for 1< IREACT<6
NO6 = 15 for IREACT = 6
4.5.35 CAC2I (This line is read only if IREACT = 3 or 5)
CAC2I - Initial concentration of acid in oil.
Units: moles/liter oil
4.5.36 CAQI(J), for J = 1, NIAQ (This line is read only if IREACT > 1)
CAQI(J) - Initial guesses for Jth independent species concentration.
Units: moles/liter water
4.5.37 CSLDI(I), for I = 1, NSLD (This line is read only if IREACT > 1 and NSLD > 1)
CSLDI(I) - Initial concentration of Ith solid.
Units: moles/liter pore volume
4.5.38 CSORBI(I), for 1=1, NSORB (This line is read only if IREACT > 1 and NSORB > 1)
CSORBI(I) - Initial concentration of Ith adsorbed cation.
Units: moles/liter pore volume
4.5.39 C1I, C2I (This line is read only if IREACT = 3 or 5)
C1I - Initial concentration of water in aqueous phase.
Units: volume fraction
C2I - Initial concentration of oil in oleic phase.
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Units: volume fraction
4.5.40 ACIDIS, EQWPS (This line is read only if IREACT = 3 or 5)
ACIDIS - Dissociation constant of the petroleum acid, Ka.
EQWPS - Equivalent weight of petroleum acid.
B .4.6 Recurrent Injection/Production Data Set
The sixth input section consists of the recurrent injection/production well data. Please
remember that there are seven comment lines at the beginning of this section and that each line is
preceded by three comment lines.
4.6.1 IBOUND
IBOUND - The flag to specify if constant potential boundaries at the left and right sides of the
simulation model are specified.
Possible Values:
0 : No boundary is specified
1 : Boundary is specified
4.6.2 IBL, mR (This line is read only if IBOUND = 1)
IBL - The flag to specify if the left-hand side constant potential boundary is specified.
Possible Values:
0 : No boundary is specified
1 : Boundary is specified
IBR - The flag to specify if the right-hand side constant potential boundary is specified.
Possible Values:
0 : No boundary is specified
1 : Boundary is specified
4.6.3 PBL, C1BL, C5BL, C6BL (This line is read only if IBOUND = 1 and IBL = 1)
PEL- Pressure at the center of the top layer at the left boundary.
Units : psia (IUNTT=0) or kPa (IUNIT=1)
C IBL- Concentration of water hi aqueous phase at the left boundary.
Units : volume fraction
C5BL - Concentration of chloride in aqueous phase at the left boundary.
Units : meq/ml
C6BL - Concentration of calcium in aqueous phase at the left boundary.
Units : meq/ml
4.6.4 PER, C1BR, C5BR, C6BR (This line is read only if IBOUND = 1 and IBR = 1)
PER - Pressure at the center of the top layer at the right boundary.
Units : psia (IUNIT=0) or kPa (IUNIT=1)
C1BR - Concentration of water in aqueous phase at the right boundary.
Units : volume fraction
C5BR - Concentration of chloride in aqueous phase at the right boundary.
Units : meq/ml
C6BR - Concentration of calcium in aqueous phase at the right boundary.
Units : meq/ml
4.6.5 NWELL, IRQ, ITIME
NWELL - Maximum number of wells used for the simulation.
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Note: If ICOORD = 2, NWELL must be equal to 1 and the MXW parameter in the source
code must be set equal to 2.
IRO - Flag indicating the equivalent well radius model to be used.
Possible Values:
1 - Babu and Odeh model is used
Note: This model (IRO=1) does not work for ICOORD = 4.
2 - Peaceman model is used (this was the default in versions previous to UTCHEM-
V-5.0)
Note: For information see Babu and Odeh [1989].
ITIME - Flag indicating the units to be used when specifying the minimum and maximum time step.
Possible Values:
0 - Minimum and maximum time steps are input in days
1 - Minimum and maximum time steps are input as Courant numbers
Note: This option is only used if IMES > 1 and is not a shut-in period. If IMES = 1, this
flag is ignored. For a shut-in period you need to use ITIME = 0
Note: The Courant number is defined as:
EMBED "Equation" "Word Object 1" \* mergeformat
The following values for minimum and maximum Courant numbers are recommended for
different simulations as follows:
Process
Waterflood/tracer
Polymerflood
Surfactant/polymerflood
Geochemical process
Min. Courant #
0.04
0.02
0.01
0.01
Max. Courant #
0.4
0.2
0.1
0.1
4.6.6 The data on input lines 4.6.6.a through 4.6.6.d are repeated for M = 1 to NWELL times.
4.6.6.a IDW(M), IW(M), JW(M), IFLAG(M), RW(M), SWELL(M), IDIR(M), IFIRST(M), ILAST(M),
IPRF(M)
IDW(M) - Well I.D. number for the Mth well.
Possible Values: Must be between 1 and MXW (the source code parameter indicating the
maximum number of wells)
Note: This number is used by UTCHEM to keep track of which well is being described in
the recurrent injection/production well section. The history profile data for the well
indicated by IDW(M) will be written to FORTRAN UNIT number 18 + IDW(M).
IW(M) - First index of the reservoir gridblock containing the M* well.
Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
Note: If the Mth well is completed parallel to the X-axis, IW(M) is the Y direction
index—if the well is completed parallel to the Y- or Z-axis, IW(M) is the X direction
index. See example below.
If ICOORD = 2, IW(1) = JW(1) = 1.
JW(M) - Second index of the reservoir gridblock containing the Mth well.
Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
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Note- If the M* well is completed parallel to the X- or Y-axis, JW(M) is the Z direction
index—if the well is completed parallel to the Z-axis, JW(M) is the Y direction
index. See example below.
If ICOORD = 2, IW(1) = JW(1) = 1.
IFLAG(M) - Flag indicating type of well constraint specification for Mth well.
Possible Values:
1 - Rate constrained injection well
2 - Pressure constrained production well (this option is available only if ICOORD =
1 or 3)
3 - Pressure constrained injection well (this option is available only if ICOORD = 1
or 3)
4 - Rate constrained production well
RW(M) - Radius of M* well.
Units: feet (IUNIT=0) or m (IUNIT=1)
SWELL(M) - Skin factor for Mth well.
Units: dimensionless
IDIR(M) - Flag indicating the direction in which the Mth well is completed.
Possible Values:
1: Well completed parallel to the X-axis
2 : Well completed parallel to the Y-axis
3 : Well completed parallel to the Z-axis
Note: If ICOORD = 2, IDIR( 1) must be equal to 3.
MRST(M) - Index of the first block in which the M* well is completed.
Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
ILAST(M) - Index of the last block in which the Mth well is completed.
Possible Values: Between EFIRST(M) and the number of gridblocks in the pertinent
direction, inclusive
IPRF(M) - Flag indicating if partial completion of the well is considered.
Possible Values:
0 - The well is fully completed
1 - The well is partially completed
Example: For a vertical well (completed through all the layers) as illustrated in the 4 x 4 x 3
example below, note the values of IDIR(M), IW(M), JW(M), IFIRST(M), and ILAST(M):
s
/
f'
jf
/
f."'
IDIR(M) = 3
IW(M) = 1
JW(M) = 1
IFIRST(M) = 1
ILAST(M) = 3
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For a horizontal well (completed from the first to last gridblock in the X direction and
parallel to the X-axis) as illustrated in the 4 x 4 x 3 example below, note the values of
IDIR(M), IW(M), JW(M), IFIRST(M), and ILAST(M):
///v///
/ ft S S J Sl\ f
/ S « r /' f -7 tl> y
7/
IDIR(M) = 1
IW(M) = 2
JW(M) = 1
IFIRST(M) = 1
ILAST(M) = 4
Note: Horizontal wells can be used for 2-D X-Y or 3-D simulations.
4.6.6.b KPRF(M,IWB), for IWB = 1, NWBC (This line is read only if IPRF = 1)
.KPRF(M,IWB) - Flag indicating if the IWB* well block of the Mth well is perforated or not.
Possible Values:
0 - The well block is not perforated
1 - The well block is perforated
4.6.6.C WELNAM(M)
' WELNAM(M)- Name of the Mth well.
Note: The name can consist of any combination of up to 18 alphanumeric characters. This
information will be printed—along with the well I.D. number, IDW(M)—at the
. beginning of the history output files.
4.6.6.d ICHEK(M), PWFMIN(M), PWFMAX(M), QTMIN(M), QTMAX(M)
ICHEK(M) - The flag to specify whether to check the rate or pressure caps for the Mth well.
Possible Values:
0 - There will be no check on the rate or pressure limits and no automatic shut in for
the pressure constraint injector
1 - There will be no automatic shut in for the pressure constraint injector but the
pressure or rate limits are checked
2 - There will be both the automatic shut in and the check on the pressure or rate
limits
PWFMIN(M) - Minimum flowing bottom hole pressure (specified at the top layer) for the Mth
well.
Units: psi (IUNIT=0) or kPa (IUNIT=1)
PWFMAX(M) - Maximum flowing bottom hole pressure (specified at the top layer) for the Mth
well.
Units: psi (IUNIT=0) or kPa (IUNrT=l)
QTMIN(M) - Minimum total flow rate (specified at the top layer) for the Mth well.
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
QTMAX(M) - Maximum total flow rate (specified at the top layer) for the Mth well.
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
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Note: - PWFMIN(M) and PWFMAX(M) are the pressure caps for a rate constraint injector or
producer well. QTMIN(M) and QTMAX(M) are the total rate caps for a pressure
constraint injector or producer well. If the Mth pressure constraint injector or producer
produces at total rate less than QTMIN(M), the Mth well will be switched to a rate
constraint well with total rate of QTMIN(M) for the rest of the injector or production period.
On the other hand, if the total rate is greater than the QTMAX(M), the Mth well then wiU be
switched to a rate constraint well with the total rate of QTMAX(M). The similar concept is
applied to a rate constraint injector or producer.
- The user can skip the well control calculation by specifying very small values for
QTMIN(M) and PWFMIN(M) and very large values for QTMAX(M) and
PWFMAX(M).
- The code still has the automatic option for shut in of a pressure constraint injector injecting
at a rate of less than QTMIN(M).
4.6.7 The data on input lines 4.6.7.a, 4.6.7.b, 4.6.7.C, and 4.6.7.d are repeated for M = 1 to NWELL times.
Note 1: For injection wells that are on rate constraint only injection rates and concentrations for each
phase are listed. For injection wells that are on pressure constraint the injection pressure is also
specified. In this case the injection rates are treated as phase cuts in the injected fluid. For
producer pressure constraint only the bottom hole pressure is specified. For producer rate
constraint only the total production rate is specified.
Note 2: The user can shut in a pressure constraint well by specifying a negative bottom hole pressure
or a rate constraint well by specifying a value of zero for rate (QI).
4.6.7.a ID(M), QI(M,L), (C(M,KC,L), for KC = 1, N), for L = 1, MXP (This set of data is read only if
IFLAG(M) = 1 or 3)
ED(M) - Well I.D. number for the Mth well.
Possible Values: Must be between 1 and MXW (the source code parameter indicating the
maximum number of wells)
Note: See note for IDW(M) on input line 4.6.6.a.
QI(M,L) - Injection rate of Lth phase in M* well (see note).
Units: ft3/day (IUNTT=0) or m3/day (IUNIT=1)
C(M,KC,L) - Concentration of KCth component in L* phase in Mth well.
Units: vary according to component (see note)
Note: The KC index changes the fastest, the L index changes the next fastest, and the M index
changes the slowest. A separate data line should be in the input file for each phase - - that is,
M x L lines will be read in. MXP is equal to 3 (IGAS = 0) or 4 (IGAS = 1).
— The following values for L correspond to the indicated phase:
1 - Aqueous phase
2 - Oleic phase
3 - Microemulsion phase
4 - Gas phase
- The following values for KC correspond to the indicated component (corresponding
concentration units are in parentheses):
For all values of IREACT:
1 - Water (volume fraction)
2 - Oil (volume fraction)
3 - Surfactant (volume fraction)
4 - Polymer (weight percent)
5 - Total nonsorbing anions concentration, assumed to all be chloride anions
(meq/ml)
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6 - Divalent cations, assumed to all be calcium for IREACT<2 (meq/ml)
7 - Alcohol 1 (volume fraction)
8 - Alcohol 2 (volume fraction) or Gas (volume fraction)
9 - Tracer 1
10-Tracer 2
11 - Tracer 3
For IREACT = 0:
12-Tracer 4
13 - Tracer 5
20-Tracer 12
21-Tracer 13
For IRE ACT = 1:
12 - Na2Cr2O7 (ppm)
13 - CSN2H4 (ppm)
14 - Cr3+ (ppm)
15 - Gel (ppm)
16 - Hydrogen (meq/ml)
For IREACT = 2, 3,4, 5, or 6:
12 - Sodium (meq/ml)
13 - Hydrogen (meq/ml)
14 - Magnesium (meq/ml)
15 - Carbonate (meq/ml)
For IREACT = 3:
16 - Acid component of crude oil (meq/ml)
For IREACT = 4 , 5, or 6:
16 - Aluminum (meq/ml)
17 - Silica (meq/ml)
For IREACT = 5:
18 - Acid component of crude oil (meq/ml)
For IREACT = 6
18 - Na2Cr2O7 (ppm)
19 - CSN2H4 (ppm)
20 - Cr3+(ppm)
21 - Gel (ppm)
4.6.7.b ID(M), PWF(M) (This line is read only if IFLAG(M) = 2 or 3)
ID(M) - Well I.D. number for the M* well.
Possible Values: Must be between 1 and MXW (the source code parameter indicating the
maximum number of wells)
Note: See note for IDW(M) on input line 4.6.6.a.
PWF(M) - Flowing bottom hole pressure for the M* well.
Units: psia (IUNIT=0) or kPa (IUNIT=1)
4.6.7.C ID(M), TEMINJ(M) (This line is read only if IENG=1 and IFLAG(M) = 1 or 3)
ID(M) - Well I.D. number for the M* well.
Possible Values: Must be between 1 and MXW (the source code parameter indicating the
maximum number of wells)
Note: See note for IDW(M) on input line 4.6.6.a.
TEMINJ(M) - Injection temperature for M* well.
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Units: °F (IUNIT=0) or °C (IUNIT=1)
4.6.7.d ID(M), QI(M, 1) (This line is read only if IFLAG(M) = 4)
ID(M) - Well I.D. number for the M* well.
Possible Values: Must be between 1 and MXW (the source code parameter indicating the
maximum number of wells)
Note: See note for IDW(M) on input line 4.6.6.a.
QI(L) - Total production rate for M* well.
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
Note: This value needs to be input as a negative number
4.6.8 TINT, CUMPR1, CUMHIl, CUMHI2, WRHPV, WRPRF, RSTC
TESFJ - Cumulative injection time.
Units: days or pore volumes (dependent on value of ISTOP flag on input line 4.2.1)
CUMPR1 - Indicates interval at which profiles should be written to UNIT 4.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
CUMHI1 - Indicates interval at which production data should be written to UNIT 4.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
CUMHI2 - Indicates interval at which production data should be written to UNIT 3.
Units: pore volumes or days (dependent on value ofTCUMTM flag on input line 4.2.1)
WRHPV - Indicates interval at which production histories should be written to output file(s) for
history plotting.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
Note: If WRHPV > total pore volume injected or maximum simulation time, the data will not
be printed. The unit number of the file to be written to starts at 19 and continues
upward. For example, for a run with three producers, UNITS 19, 20 and 21 would be
used. The history of reservoir properties and overall rates from all the producing wells
is written to UNIT 9.
WRPRF - Indicates interval at which concentration, pressure, saturation, tracer phase concentration,
capacitance property, gel property, alkaline property , and temperature profiles should be
written to UNITS 8,11, 12, 13, 14,10,15, and 18 respectively.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
Note: If WRPRF > total pore volume injected or maximum simulation time, the data will not
be written.
RSTC - Indicates the interval at which restart data should be written to UNIT 7.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
4.6.9 DT (This line is read only if IMES = 1 and ITIME = 0)
DT - Time step size for constant time step option.
Units: days
4.6.10 DT, DCLIM, DTMAX, DTMIN (This line is read only if IMES = 2 and ITIME = 0)
DT - Initial time step size, At[.
Units: days
DCLIM - Tolerance for concentration change for the first three components, ACiim.
Units: volume fraction
DTMAX - Maximum time step size, Atmax.
Units: days
DTMIN - Minimum time step size, Atmin.
Units: days
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Note: The time step selection is based on the method of relative changes for the first three
components (water, oil, and surfactant) as:
Atn+l = Atn min
NBL
max
• 1
1=1
i
AC; v
l»M
:=1,2,3
Atn+1 is limited to: At,™ < Atn+1 < At,
••max
4.6.11 DT, DCLIM, CNMAX, CNMIN (This line is read only if IMES = 2, ITIME = 1, and at least one
well is not shut-in.)
DT - Initial time step size, Atj.
Units: days
DCLIM - Tolerance for concentration changes for the first three components.
Units: volume fraction
CNMAX - Maximum Courant number.
Units: dimensionless
CNMIN - Minimum Courant number.
Units: dimensionless
Note: The minimum and maximum time steps in days are computed based on the minimum and
maximum Courant number as:
CNMIN
Atmin =
nwell/'nwbc
min max
M=l i=l
Qi
and
j <)){
At
CNMAX
max
nwell/nwbc
min max
Qi
=l^ i=l Ax, Ayj AZJ K, of KCth component (IMES = 3) or
relative tolerance for concentration change, Riim,K, of KG* component (IMES = 4).
Units: IMES = 3: volume fraction, weight percent, meq/ml, or ppm (depending on which
component the tolerance is for—see note for input line 4.6.7.a)
IMES = 4: dimensionless
DTMAX - Maximum time step size, Atmax.
Units: days
DTMIN - Minimum time step size, Atmin.
Units: days
Note: For IMES = 3, the method of relative changes is applied to all the components in the
simulation run:
Atn+1 = Atn min
AC
lim
NBL
max
ACiK
1>M
K=
.., nc
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Atn+1 is limited to: Atmin < Atn+1 < Atmax
ACiim>K is a fraction of the initial or injected concentration (whichever is larger) of the
KCth component. For example: ACiim,3 = 0.1 x €3 where Cs is the total
concentration of component 3. If ACiim)K of the KCth component is entered as zero,
that component is not considered in the time-step size selection.
For IMES = 4, the new time-step size is calculated according to:
Atn+1 = Atn min
R
lim,K
NBL
max
K= 1, ..., nc
Atn+1 is limited to: Atmjn < Atn+1 < Atmax
Rlim.K is the dimensionless relative change in concentration. For example: Riim,3 =
0.1 indicates a 10% change in concentration of component 3.
4.6.13 DT, (DCLIM(KC), for KG = 1, N), CNMAX, CNMIN (This line is read only if IMES = 3 or 4,
ITIME = 1, and reservoir is not shut-in.)
DT - Initial time step size, Atj.
Units: days
DCLIM(KC) - Tolerance for concentration change, ACiim,K, of KCth component (IMES = 3) or
relative tolerance for concentration change, Riim,K, of KCth component (IMES = 4).
Units: IMES = 3: volume fraction, weight percent, meq/ml, or ppm (depending on which
component the tolerance is for—see note for input line 4.6.7.a)
IMES = 4: dimensionless
CNMAX - Maximum Courant number.
Units: dimensionless
CNMIN - Minimum Courant number.
Units: dimensionless
Note: See note for input lines 4.6.11 and 4.6.12 for time step calculation information.
IMPORTANT NOTE: The data on lines 4.6.14 through 4.6.23 describe the changes in boundary conditions
and are repeated until the injected time (TINJ on input line 4.6.8) is greater than or equal to the maximum
simulation time (TMAX on input line 4.3.1).
4.6.14 IRQ, ITIME, IFLAG(M), M = 1, NWELL
IRO - Flag indicating the equivalent well radius model to be used.
Possible Values:
1 - Babu and Odeh model is used
2 - Peaceman model is used (this was the default in versions previous to UTCHEM-
V-5.0)
Note: For information see Babu and Odeh [ 1989].
ITIME - Flag indicating the units to be used when specifying the minimum and maximum time step.
Possible Values:
0 - Minimum and maximum time steps are input in days
1 - Minimum and maximum time steps are input as Courant numbers
Note: This option is only used if IMES > 1 and it is not a shut-in period. If IMES = 1, this
flag is ignored.
IFLAG(M) - Flag indicating type of well constraint specification for Mth well.
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Possible Values:
1 - Rate constrained injection well
2 - Pressure constrained production well (this option is available only if ICOORD = 1
or 3)
3 - Pressure constrained injection well (this option is available only if ICOORD = 1 or
3)
4 - Rate constrained production well
4.6.15 NWEL1
NWEL1 - Number of wells with changes in location (IW(M), JW(M)), skin, direction, perforation,
name, or minimum and maximum bottomhole pressure or minimum or maximum rate.
4.6.16 The data on input lines 4.6.16.a through 4.6.16.d are repeated for M = 1 to NWEL1 times.
4.6.16.aID, IW(ID), JW(ID), RW(ID), SWELL(ID), IDIR(ID), IFIRST(ID), ILAST(ID), IPRF(ID)
ID - Well ID number with changes from the previous slug injection period.
IW(ID) - First index of the reservoir gridblock containing the 10th well.
Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
Note: See note for input line 4.6.6.a.
JW(ID) - Second index of the reservoir gridblock containing the IDth well.
Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
Note: See note for input line 4.6.6.a,
RW(ID) - Radius of ID* well.
Units: feet (IUNIT=0) or m (IUNIT=1)
SWELL(ID) - Skin factor for ID* well.
Units: dimensionless
IDIR(ID) - Flag indicating the direction in which the IDth well is completed.
Possible Values:
1: Well completed parallel to the X-axis
2 : Well completed parallel to the Y-axis
3 : Well completed parallel to the Z-axis
Note: If ICOORD = 2, IDIR(l) must be equal to 3.
IFIRST(ID) - Index of the first block in which the ID* well is completed.
Possible Values: Between 1 and the number of gridblocks in the pertinent direction,
inclusive
ILAST(ID) - Index of the last block in which the IDth well is completed.
Possible Values: Between IFIRST(ID) and the number of gridblocks in the pertinent
direction, inclusive
Note: At this time, UTCHEM assumes the well is completed continuously between
IFIRST(ID) and ILAST(ID).
IPRF(ID) - Flag indicating if partial completion of the well is considered.
Possible Values:
0 - The well is fully completed
1 - The well is partially completed
4.6.16.b KPRF(ID,IWB), for IWB = 1, NWBC (This line is read only if IPRF = 1)
KPRF(ID,IWB) - Flag indicating if the IWB* well block of the ID* well is perforated or not.
Possible Values:
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0 - The well block is not perforated
1 - The well block is perforated
4.6.16.C WELNAM(ID)
WELNAM(ED) - Name of the IDth well.
Note: The name can consist of any combination of up to 18 alphanumeric characters. This
information will be printed—along with the well ID. number, IDW(ID)—at the
beginning of the history output files.
4.6.16.d ICHEK, PWFMIN(ID), PWFMAX(ID), QTMIN(ID), QTMAX(ID)
ICHEK(M) - The flag to specify whether to check the rate or pressure caps for the Mth well.
Possible Values:
0 - There will be no check on the rate or pressure limits and no automatic shut in for
the pressure constraint injector
1 - There will be no automatic shut in for the pressure constraint injector but the user
specified pressure or rate limits are checked
2 - There will be both the automatic shut in and the check on the user specified
pressure or rate limits
PWFMIN(ID) - Minimum flowing bottom hole pressure (specified at the top layer) for the IDth
well.
Units: psi (IUNIT=0) or kPa (IUN1T=1)
PWFMAX(ID) - Maximum flowing bottom hole pressure (specified at the top layer) for the IDth
well.
Units: psi (IUNIT=0) or kPa (IUNIT=1)
QTMIN(ID) - Miriimum total flow rate (specified at the top layer) for the IDth well.
Units: ft3/day (IUN1T=0) or m3/day (IUNIT=1)
QTMAX(ID) - Maximum total flow rate (specified at the top layer) for the IDth well.
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
Note: See the note for input line 4.6.6.d.
4.6.17 NWEL2, (ID(J), for J = 1, NWEL2)
NWEL2 - Number of wells with changes in rate, concentration or bottomhole pressure.
ID(J) - ID number for Ith well with changes.
4.6.18 The data on input lines 4.6.18.a through 4.6.18.d are repeated for M= 1 to NWEL2 times.
4.6.18.a ID, (QI(ID,L), for L = 1, MXP), (C(ID,KC,L), for KG = 1,N), for L =1, MXP (This set of data is
read only if EFLAG(ID) = 1 or 3)
ID - Well ID number with changes from the previous slug injection period.
QI(ID,L) - Injection rate of Lth phase in ID* well (see note for input line 4.6.7.a).
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
C(ID,KC,L) - Concentration of KCth component in Lth phase for IDth well.
Units: vary according to component (see note for line 4.6.7.a)
Note: If IGAS = 0, then MXP = 3. If IGAS = 1, then MXP = 4.
4.6.18.b ID(ID), PWF(ID) (This line is read only if IFLAG(ID) = 2 or 3)
ID(ID) - Well ID number with changes from the previous slug injection period.
PWF(ID) - Flowing bottom hole pressure for the IDth well.
Units: psia (IUNIT=0) or kPa (IUNIT=1)
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4.6.18.c ID(ID), TEMINJ(ID) (This line is read only if ffiNG = 1 and IFLAG(ID) = lor 3)
ID(ID) - Well ID number with changes from the previous slug injection period.
TEMINJ(ID) - Injection temperature for the IDth well.
Units: °F (IUNIT=0) or °C (IUNIT=1)
4.6.18.d ID(ID), QI(ID,1) (This line is read only if IFLAG(ID) = 4)
ID(ID) - Well ID number with changes from the previous slug injection period.
QI(ID, 1) - Total production rate for ID* well.
Units: ft3/day (IUNIT=0) or m3/day (IUNIT=1)
Note: This value needs to be input as a negative number.
4.6.19 TINJ, CUMPR1, CUMHI1, CUMHI2, WRHPV, WRPRF, RSTC
TINJ - Cumulative injection time.
Units: days or pore volumes (dependent on value of ISTOP flag on input line 4.2.1)
CUMPR1 - Indicates interval at which profiles should be written to UNIT 4.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
CUMHI1 - Indicates interval at which production data should be written to UNIT 4.
- Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
CUMHI2 - Indicates interval at which production data should be written to UNIT 3.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
WRHPV - Indicates interval at which production histories should be written to output file(s) for
history plotting.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
Note: If WRHPV > total pore volume injected or maximum simulation time, the data will
not be printed. The unit number of the file to be written to starts at 19 and continues
upward. For example, for a run with three producers, UNITS 19, 20, and 21 would
be used. The history of reservoir properties and the total rate from all the producing
wells is written to UNIT 9.
WRPRF - Indicates interval at which concentration, pressure, saturation, tracer phase concentration,
capacitance property, pressure difference, gel property, alkaline property , and temperature
profiles should be written to UNITS 8, 11,12, 13, 14, 10, 15 and 18 respectively.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
Note: If WRPRF > total pore volume injected or maximum simulation time, the data will not
be written.
RSTC - Indicates the interval at which restart data should be written to UNIT 7.
Units: pore volumes or days (dependent on value of ICUMTM flag on input line 4.2.1)
4.6.20 DT (This line is read only if IMES = 1 and ITIME = 0)
DT - Time step size for constant time step option.
Units: days
4.6.21 DT, DCLIM, DTMAX, DTMIN (This line is read only if IMES = 2 and ITIME = 0)
DT - Initial time step size, Ati.
Units: days
DCLIM - Tolerance for concentration change for the first three components, AQim.
Units: volume fraction
DTMAX - Maximum time step size, Atmax.
Units: days
DTMIN - Minimum time step size, Atmin.
297
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Units: days
Note: See note for input line 4.6.10.
4.6.22 DT, DCLIM, CNMAX, CNMIN (This line is read only if IMES = 2, ITIME = 1, and at least one
well is not shut-in.)
DT - Initial time step size, Ati.
Units: days
DCLIM - Tolerance for concentration changes for the first three components.
Units: volume fraction
CNMAX - Maximum Courant number.
Units: dimensionless
CNMIN - Minimum Courant number.
Units: dimensionless
Note: See note for input line 4.6.11.
4.6.23 DT, (DCLIM(KC), for KC = 1, N), DTMAX, DTMIN (This line is read only if IMES = 3 or 4 and
ITIME = 0)
DT - Initial time-step size, Ati.
Units: days
DCLIM(KC) - Tolerance for concentration change, ACiim>K, of KCth component (IMES = 3) or
relative tolerance for concentration change, Riim,io of KCth component (IMES = 4).
Units: IMES = 3: volume fraction, weight percent, meq/ml, or ppm (depending on which
component the tolerance is for—see note for input line 4.6.7.a)
IMES = 4: dimensionless
DTMAX - Maximum time step size, Atmax.
Units: days
DTMIN - Minimum time step size, Atmin.
Units: days
Note: See note for input line 4.6.12.
4.6.24 DT, (DCLIM(KC), for KC = 1, N), CNMAX, CNMIN (This line is read only if IMES = 3 or 4,
ITIME = 1, and reservoir is not shut-in.)
DT - Initial time step size, Atj.
Units: days
DCLIM(KC) - Tolerance for concentration change, ACnm;1o of KCth component (IMES = 3) or
relative tolerance for concentration change, Riim,K, of KCth component (IMES = 4).
Units: IMES = 3: volume fraction, weight percent, meq/ml, or ppm (depending on which
component the tolerance is for—see note for input line 4.6.7.a)
IMES = 4: dimensionless
CNMAX - Maximum Courant number.
Units: dimensionless
CNMIN - Minimum Courant number.
Units: dimensionless
Note: See note for input lines 4.6.11 and 4.6.12 for time step calculation information.
B.5 NOMENCLATURE
The nomenclature consists of the names of the variables as they appear in equations in this text
(and related reports) and descriptions of those variables. FORTRAN names of the variables as they
appear in the UTCHEM simulator appear in parenthesis where applicable.
298
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Appendix B - UTCHEM Local Grid Refinement User's Guide
aT
as
asi
34 =
342
aK
Api
AP2
AP3
Bis =
b3 =
b4 =
bK =
CpC =
C =
Q.K =
ACi>K =
C0
CSE
CSEL
CSEP
CSEU
CTI
Co
6
CK =
CK =
CKO =
CKW =
CNMAX
CNMIN
Ds
k
k
a
Adsorbed tracer amount per unit mass of rock.
Surfactant adsorption parameter
Surfactant adsorption parameter (AD31)
Surfactant adsorption parameter (AD32)
Polymer adsorption parameter
Surfactant adsorption parameter (AD41)
Polymer adsorption parameter (AD42)
Adsorption parameter for Kth component (A14D, A15D)
Polymer viscosity parameter (API)
Polymer viscosity parameter (AP2)
Polymer viscosity parameter (APS)
Permeability reduction parameter for Langmuir correlation with gel concentration (AGK)
Permeability reduction parameter for Langmuir correlation with gel concentration (BGK)
Surfactant adsorption parameter (BSD)
Polymer adsorption parameter (B4D)
Adsorption parameter for Kth component (B14D, B15D)
Capillary pressure parameter (CPC)
Shear rate coefficient
Total concentration of component K in gridblock i
Change in total concentration of component K in gridblock i over the current time-step
Tolerance for concentration change of component K
Initial condition for tracer used in radioactive decay equation
Effective salinity for phase behavior and surfactant adsorption
Type II(-)/III phase boundary or effective salinity limit (CSEL7 for Alcohol 1—Component 7
and CSEL8 for Alcohol 2—Component 8)
Effective salinity (ion strength) for polymer properties
Type HI/II(+) phase boundary or effective salinity limit (CSEU7 for Alcohol 2—Component
7 and CSEU8 for Alcohol 2—Component 8)
Concentration of tracer in phase 1
Concentration of free calcium cations
Concentration of free sodium cations
Permeability reduction parameter for gel (CRG) .
Overall concentration of component K in the mobile phases
Adsorbed concentration of component K
Concentration of tracer component K in oil
Concentration of tracer component K in water
Overall concentration of component K in the mobile and stationary phases
Concentration of component K in phase I
Maximum Courant number
Minimum Courant number
Retardation factor for tracer (RET)
Relative permeability exponent for phase I
Relative permeability exponent for phase I at low interfacial tension (E13C, E23C, and E31C)
Relative permeability exponent for phase I at high interfacial tension (E1W, E2W, and E3W)
Amount of component K associated with surfactant
Permeability at 100% brine saturation
Apparent permeability used in capillary pressure calculations
299
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Relative permeability of phase t
End point relative permeability of phase t
End point relative permeability of phase I at low interfacial tension (P1RC for phase 1, P2RC
for phase 2, and P3RC for phase 3)
End point relative permeability of phase I at high interfacial tension (P1RW for phase 1,
P2RW for phase 2, and P3RW for phase 3)
Absolute permeability in the x-direction (PERMX)
Absolute permeability in the y-direction (PERMY)
Absolute permeability in the z-direction (PERMZ)
Tracer K partition coefficient (TK)
Length of the core, or reservoir length
Molecular weight of chromium component
Molecular weight of polymer component
Cr3+/polymer mass stoichiometric ratio
Capillary pressure exponent (EPC)
Capillary number of phase t
Viscosity number
Dimensionless number representing the reduction of the pore radius due to adsorption of gel
Capillary pressure between phases i and K
Exponent for calculating shear rate dependence of polymer viscosity (POWN)
Maximum injection/production flow rate in well block i
Cation exchange capacity of clay (QV)
Permeability reduction factor
Residual resistance factor for gel
Maximum residual resistance factor for gel
Normalized mobile saturation of phase i used in relative permeability and capillary pressure
calculations
Exponent for calculating salinity dependence of polymer viscosity (SSLOPE)
Saturation of phase i
Residual saturation of phase £
Residual saturation of phase K at low interfacial tension (S1RWC, S2RWC, and S3RWC for
phases 1, 2 and 3)
Residual saturation of phase £' at high interfacial tension (S1RW, S2RW, and S3RW for
phases 1,2 and 3)
Stoichiometric ratio between Cr3+ and polymer
A time variable in the radioactive decay of tracer equation
Initial time-step size (DT)
Maximum time-step size (DTMAX)
Minimum time-step size (DTMIN)
Time-step size at nth time level
Time-step size at n+lth time level
An initial time at which the tracer concentration C0 is known; used in the radioactive decay
equation
Capillary desaturation parameter for aqueous phase (Til)
Capillary desaturation parameter for oleic phase (T22)
Capillary desaturation parameter for microemulsion phase (T33)
kx
ky
kz
KK
L
MCrs+
Mpolymer
n
Nv
N5
Pcet
Pa
Qi
Qv
Rk
RRF
RRFmax
S =
Sfrw
SGR
t
Ati
Atn
l
to
T2
T3
300
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Appendix B - UTCHEM Local Grid Refinement User's Guide
T4
u
Axj
Ayi
AZJ
as
0x4
0:5
Pc
= Capillary desaturation parameter for gas phase (T44)
= Flux
= Tracer velocity
= Size of gridblock i in x direction
= Exponent used in gelation reaction
= Exponent used in gelation reaction
= Exponent used in gelation reaction
= Size of gridblock i in y direction
= Size of gridblock i in z direction
Greek Symbols
(Xi = Compositional microemulsion phase viscosity parameter (ALPHA1)
«2 = Compositional microemulsion phase viscosity parameter (ALPHA2)
= Compositional microemulsion phase viscosity parameter (ALPHAS)
= Compositional microemulsion phase viscosity parameter (ALPHA4)
= Compositional microemulsion phase viscosity parameter (ALPHAS)
= Cation exchange constant for clay (XKC)
pp = Effective salinity parameter for polymer viscosity (BETAP)
Ps = Cation exchange constant for surfactant (XKS)
Pe = Effective salinity parameter for calcium — Component 6 (BETA6)
Py = Effective salinity parameter for Alcohol 1 — Component 7 (BETA?)
= Effective salinity parameter for Alcohol 2 — Component 8 (BETAS)
= Equivalent shear rate for porous medium
= Coefficient in equivalent shear rate equation (GAMMAC)
= Shear rate at which polymer viscosity is one-half the polymer viscosity at zero shear rate
(GAMHF)
= Specific weight of brine — Component 1 (DEN 1)
= Specific weight of oil — Component 2 (DEN2)
= Specific weight of surfactant — Component 3 (DENS)
= Specific weight of Alcohol 1 — Component 7 (DEN7)
= Specific weight of Alcohol 2 or gas — Component 8 (DENS)
= Radioactive decay coefficient for K* tracer (RDC)
= Intrinsic viscosity of a gel solution . ,
= Polymer viscosity at zero shear rate
= Polymer viscosity
= Water viscosity
= Viscosity of phase t (VIS 1 for phase 1, VIS2 for phase 2, and VIS4 for phase 4)
= Viscosity of gas phase at reference pressure
= Slope of gas viscosity function
= Viscosity at infinite shear rate
= Rock density
= Solution density
= Density of phased
= Interfacial tension between oil and water
= Interfacial tension between phases i and I'
= Porosity (POR)
= Porosity of gridblock i
= Potential
7eq
7C
Y 1/2
Yl
72
73
77
78
A,K
[|i]
|Ho
|0,p
H4)S
(loo
pg
ps
p£
awo
301
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Qo = Relaxation time coefficient
Subscripts
K = Component number
For all values of IREACT:
1 = Water
2 = Oil
3 = Surfactant
4 = Polymer
5 = Chloride
6 = Calcium
7 = Alcohol 1
8 = Alcohol 2 or Gas
9 = Tracer 1
10 = Tracer 2
11 = Tracers
For IREACT = 0:
12 = Tracer 4
13 = TracerS
20 = Tracer 12
21 = Tracer 13
For IRE ACT = 1:
12 = Sodium dichromate (
13 = Thiourea (CSN2H4)
14 = Trivalent chromium (Cr3+)
15 = Gel
16 = Hydrogen
For IREACT = 2, 3,4, 5, or 6:
12 = Sodium
13 = Hydrogen
14 = Magnesium
15 = Carbonate
For IRE ACT = 3:
16 = Acid component of crude oil
For IREACT = 4, 5, or 6:
16 = Aluminum
17 = Silica
For IREACT = 5:
18 = Acid component of crude oil
For IREACT = 6
18 = Sodium dichromate (
19 = Thiourea (CSN2H4)
20 = Trivalent chromium (Cr3+)
21 = Gel
302
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Appendix B * UTCHEM Local Grid Refinement User's Guide
B.6
i = Phase number
1 = Aqueous
2 = Oleic
3 = Microemulsion
4 = Gas
r = Residual
w = Low capillary number values
c = High capillary number values
OUTPUT FILES AND REACTIONS
The following sections describe: (1) data that is automatically written to the profile data file,
(2) restart run procedure, (3) data written to stored restart data file, (4) data written to history files for
each well, (5) data written to history of reservoir properties and overall injection and production rates
from all the wells, (6) data written to aqueous phase tracer concentration data files, (7) list of elements
and reactions for IREACT=2, (8) list of elements and reactions for IREACT=3, (9) list of elements
and reactions for IREACT=4 or 6, and (10) list of elements and reactions for IREACT=5.
B.6.1 Default Data Written to Profile Data File
The information in the following lists is always written to the profile data file (PROFIL) and is
not controlled by the various print control flags in the input files.
Printed at each CUMHI1 interval:
Time, number of time steps
Time step size
Courant number
Cumulative pore volume injected
Original in place for each component
Cumulative injection for each component
Cumulative production for each component
Amount retained for each component
Relative error for each component
Fraction of oil recovered
IfIREACT>2:
, Average number of iterations, computation time
For each well:
Position of the well, first and last well block completed
Cumulative injection/production
Bottomhole pressure for each well block
All well related information (such as pressure for each phase, phase concentration,
phase cut, etc.)
Producer wellbore temperature and phase cut and concentration
Printed at each CUMPR1 interval:
Reservoir temperature if IENG = 1
Phase saturation profile for each phase
Aqueous phase pressure profile
Concentration of each component in the fluid
If tracers are present.and ICAP^O:
Flowing concentration
Dendiritic concentration
303
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Flowing saturation
Dendiritic saturation
Restart Run Procedure
The restart procedure is available with UTCHEM. This enables a user to continue a run past
the initial time period or to break a large run up into smaller segments. Each time you run UTCHEM,
a file called RESTAR is created. This file (described in section 6.3 of this appendix) contains all the
information necessary to continue the run at a later time. In order to do so, the user needs to:
B.6.2
B.6.3
1.- Rename the output file RESTAR from the previous run to INPUT2
2.- Set the variable IMODE equal to 2 on line 4.1.3 of input file INPUT
3.- Change the value of TMAX on input line 4.3.1 of file INPUT to the new injection period being
simulated in the restart run
4.- Change the value of TINT on input line 4.5.8 of file INPUT if appropriate
5.- Add additional information for input lines 4.5.14 through 4.5.24 of file INPUT if the well
conditions are different for the new injection period
Note: Make sure the source code you run the restart problem (IMODE=2) has the same values for
the array sizes in the parameter statement as the one used in original ran (IMODE=1).
Data Written to Stored Restart Run Data File
The information in the following list is always written to the stored restart data file (RESTAR).
If the user is running a RESTART run, this data file needs to be renamed to correspond to the
INPUT2 input file. The values in parentheses are the FORTRAN variable names as they appear in the
code.
Printed at the end of each run:
Time (T), injection time (TINT), time step size (DT), number of time steps (ICNT)
New slug injection or restart flag (IINJ), number of time step reduction (INEC), cumulative
pore volume injection (CUMPV), number of blocks in X-direction minus 1 (NXM1)
Cumulative injection (CUMI), cumulative production (CUMP), original in place (OIP) for
each component
Cumulative injection/production (CUMQ) for each well
Phase concentration (C), phase saturation (S), effective salinity (CSE), overall concentration
(CTOT), number of phases (NPHASE)
IfICOORD=2:
Boundary concentration (CE), boundary pressure (PE)
Viscosity (VIS), relative permeability (RPERM), injection rate (QI), total rate for each well
(QT), phase rate (Q), bottomhole pressure (PWF)
Pressure (P)
Surfactant adsorption (C3ADSS), surfactant adsorption parameter (A3DS), polymer
adsorption (C4ADSS)
Permeability reduction factor (RKF), calcium concentration (C6JO), calcium adsorbed by clay
(C6ADSS), calcium adsorbed by surfactant (C6HATS)
Alcohol 7 partitioning coefficient (X7OLD), alcohol 8 partitioning coefficient (X8OLD)
Variables for writing profiles to UNIT 4 (CUMPRO), histories to UNIT 4 (CUMHIS),
histories to UNIT 3 (CUMHCP)
Oil breakthrough (BTO), tracer breakthrough (TBT), tracer injection concentration (CINJT),
tracer retardation factor (TRD)
Lower effective salinity (CSEL), upper effective salinity (CSEU)
Density (DEN), capillary pressure (PRC)
Total surfactant (TSURF)
304
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Appendix B - UTCHEM Local Qrid Refinement User's Guide
IfICAP>0:
Dendiritic concentration (CD), dendiritic saturation (SD), flowing saturation (SF), total
flowing concentration (CTF)
IfNG^O:
Chromium adsorption (C14ADS), gel adsorption (C15ADS), cation exchange capacity
of clay (QW)
If IENG = 1
Cum. heat inj. (CUMHI), cum. heat prod. (CUMHP), temperature (TEM), total
volumetric heat capacity (TVHC)
If IENG = 1 and IHLOS = 1
Cum. heat loss (TQLOS), integral for overburden and underburden heatloss
calculations (RING, RINU), time of change of overburden temp, from the reservoir
block (TTCHG), overburden temperature (TEMPOS), underburden temperature
(TEMPUB) F
If IENG =1 and ICOORD =2
Boundary enthalpy (ENTHE)
IfIREACT>l:
Solid concentration (CSLDT), adsorbed concentration (CSORBT), species
concentration (CAQSP), surf, associated cation concentration (CACATT) cation
concentration (CACAT)
Cumulative no. of iteration for geochem option (ITCUM)
B .6.4 Data Written to Well History Plotting Data File(s)
The information in the following list is always written to the well history plotting data files
(HIST01-HISTO for each production well.
Printed at each WRHPV interval:
Cumulative pore volume, time in days, cumulative production (ft3, m3, or STB), water oil
ratio, cumulative oil recovery, total production rate (ft3/day, m3/day, or STB/day)
Water cut, oil cut, microemulsion cut, gas cut (only if IGAS = 1)
Wellbore pressure for each well block (psi or kPa)
Wellbore temperature (°F or °C) (only if IENG=1)
Forl= 1,N:
If ICF(I) = 1: phase concentration for component N. (C(I,L), L=1,MXP), total
concentration of component N (CTOT(I))
Lower effective salinity, upper effective salinity, effective salinity (only if ICSE = 1)
ForIREACT>l J^ 3 '
Independent species concentration, mole/liter of water (CAQSP(KK), KK = 1, NIAQ)
Dependent species concentration, mole/liter of water (CAQSP(KK) ' KK -
NIAQ+l,NFLD)(onlyifIRSPS>0) ~
Phase Concentration of (inj.+genereated) surfactant (PSURF(I,L), L = 1,3), total
concentration of (inj.+ generated) surfactant (TSURF) (only if IREACT = 3 or'5)'
Concentration of solid components, mole/liter of pore volume (CSLDT(KK) KK = 1
. NSLD)(onlyifNSLD>0)
Logio of interfacial tension between water/microemulsion and oil/microemulsion
(XIFT1, XIFT2) (only if ICNM>0) (dyne/cm)
. The information in the following list is always written to the well history plotting data files for
each injection well. &
305
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Printed at each WRHPV interval:
Cumulative pore volume, time in days, cumulative injection (ft3, m3, or STB), injection rate
(ft3/day, m3/day, or STB/day)
Wellbore pressure for each well block (psi or kPa)
Pressure drop between the wells (for the specific case of one injector and one producer only)
or pressure drop between the pressure tabs (when NG>0, NY=1, NZ=1, see line 4.4.93) (psi
orkPa)
B .6.5 Data Written to Overall History Plotting Data File
The information in the following list is always written to the overall history plotting data file
(OVERAL).
Printed at each WRHPV interval:
Cumulative pore volume, time in days, volumetric averaged reservoir pressure (psi or kPa),
cumulative oil produced (%OOIP), cumulative oil produced (bbls or m3), volumetric
averaged reservoir temperature (°F or °C) (only if IENG= 1 )
Total injection rate (B/D or m3/day), total production rate (B/D or m3/day), total fluid injected
(1000 bbls or m3), total fluid produced (1000 bbls or m3)
Overall production rate for each phase (QBAR(L) for L = 1, MXP where MXP=3 if IGAS=0
and MXP=4 if IGAS =1) (B/D or m3/day)
Average cut for each phase (FBAR(L) for L = 1, MXP where MXP=3 if IGAS=0 and
MXP=4 if IGAS =1)
Average saturation for each phase (SBAR(L) for L = 1, MXP where MXP=3 if IGAS=0 and
MXP=4ifIGAS=l)
If ICF(3) = 1: Cumulative surfactant injected (bbls or m3), Cumulative surfactant produced
(bbls or m3), adsorbed surfactant (bbls or m3), retained surfactant (bbls or m3)
If ICF(4) = 1: Cumulative polymer injected (wt%), Cumulative polymer produced (wt%),
adsorbed polymer (wt%), retained polymer (wt%)
B.6.6 List of Elements and Reactive Species for IREACT = 2
Elements or pseudo-element:
Hydrogen (reactive), Sodium, Calcium,
Magnesium, Carbonate, Chlorine, Oxygen, S
(inj. surfactant)
/y
Independent aqueous or oleic species: H+, Na+,Ca2+, Mg2+,CO 3 , Cl~, S~, H2O
Dependent aqueous or oleic species: Ca(OH)+, Mg(OH)+, Ca(HCO3)+,
Mg(HCO3)+, OH-, HCOg , H2CO3,
Solid species:
Adsorbed cations:
CaCO3 (Calcite), Ca(OH)2 (Calcium
hydroxide), MgCOs (Magnesite), Mg(OH)2
(Magnesium hydroxide)
W + , Na + , Ca 2+, Mg 2+
306
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Adsorbed cations on micelles:
Aqueous reactions
H20 <4 H
H+ + C0; HC0
Na + , Ca 2+, Mg 2+
Equilibrium constant
Ke!q =[H+] [OKI
T,eq [HCOJ]
Ca(OH)+
+ +
H20 <3 Mg(OH) + H
Ca2+ + H+.
"e£
Ca(HC03)
Mg(HC03)
H2C03
Mg2++ C0|-§ MgCO§
Dissolution reactions
CaCO. g Ca2+ + CO2,"
-2 -
s =
[Ca(OH)+] [H+
^
iS- =
[Mg(OH)+] [H+]
T-
[Mg2+3
-
5 =
6 =
-7 =
[ca(HC03)+]
[Ca2+] [C02-J[H+]
[Mg(HC03)+]
[Mg2+]
[H2CQ3]
[co|J[H+]:
Keq -•
JVo —
[Ca2+]
_
9 =
[Mg2+][c02-J
Solubilitv product
Ksf=[Ca2+][c02-]
307
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Appendix B - UTCHEM Local Grid Refinement User's Guide
KSP
MgC03 p Mg2+ + C023-
,SP
2+
Ca(OH)2 p Caz+ + 2OH"
Ksp
Mg(OH)2 p Mg2+ + 20H"
Exchange reactions (on clav)
ex
2Na+ + Ca 2+
+ 2+
_ex
Mg
2Na+ + Mg 2+
Na+ + H20
Exchange reactions (on micelle)
2Na + Ca
2+
r,
_
2Na+ + Ca 2+
2Na"t"+Mg
.2+
2Na+ + Mg 2+
Kf = [Mg2+] ^
Ks3p=[Ca2+][H+]-2
KS4P =[Mg2+][H+]'2
Exchange equilibrium constant
PY |c-a2+|[Na+]2
[Ca2+]
|_Mg2+J[Na+]:
[Mg2+]
[Na+]
12
Na+J
w
Na+J[H+]
Exchange equilibrium constant
[Ca2+][Na+]2
exm
K
where
J
[Ca2+]
[S-]
K
exm
2 =
+J2[Mg2+]
exm
where K 2 = P 2
B.6.7 List of Elements and Reactive Species for IREACT = 3
Elements or pseudo-element:
Hydrogen (reactive), Sodium, Calcium,
Magnesium, Carbonate, A (from acid HA),
Oxygen, Chlorine, S (Injected surfactant)
308
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Appendix B - UTCHEM Local Grid Refinement User's Guide
Independent aqueous or oleic species: H+, Na+,Ca2+, Mg2+,CO23" , HA0, Cl', S~,
H20
Dependent aqueous or oleic species: Ca(OH)+, Mg(OH)+, Ca(HCO3)+, HAW,
Mg(HC03)+, OH-, HC03 , A-, H2CO3,
Solid species:
Adsorbed cations:
Adsorbed cations on micelles:
Aqueous reactions
HooS H+ + OH"
CaC03 (Calcite), Ca(OH)2 (Calcium
hydroxide), MgCOs (Magnesite), Mg(OH)2
(Magnesium hydroxide)
H" + , Na + , Ca 2+, Mg 2+
Na +, Ca 2+, Mg 2+
Equilibrium constant
KC!q =[H+] [OH']
Keq _[A'] [H+3
2 ~ tHAw]
-
3 =
+ . TT+
H20 J| Ca(OH)+ + H
[Ca(OH)
+]
[Ca+]
+ . TT+
+ H20 zf Mg(OH)+ + H
Ca(HC03)
Mg(HC03)
[Mg(OH)
+]
[ca(HC03)+]
[Ca2+] |_C02-J[H+]
[Mg(HC03)+]
[Mg2+] [C02-J[H+]
309
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Appendix B - UTCHEM Local Grid Refinement User's Guide
q
H2C03
CaCOo
Mg2+ + CO2' MgCO?
Partitioning of HA
HA0 HAW
Dissolution reactions
sp
CaCO Ca2+ "
MgC03 Jf Mg2+ + C03-
rSP
Ca(OH)2
2+
Mg(OH)2 p Mg^ + 20H'
Exchange reactions (on matrix)
2Na+ + Ca2+
_
+ + Mg2+
ex
_
2Na+ + Mg2+
-
8 =
[H2C03]
|_C023J[H+]
-9 =
[Ca2+] [C023J
[MgCOg]
[Mg2+] [CO2']
Partition coefficient
] Water
D= [HAo]oil
Solubility product
Ksf =[Ca2+]
2+[c023]
KsP=[Mg2+]
[c023]
KS3P =[Ca2+][H+]
2++-2
-+-, -2
Ks4p=[Mg2+][H+]
Exchange equilibrium constant
[Na+]2
[Ca2+]
P
Na+J
[Na+]2
[Mg2+] I Na+
310
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Appendix B - UTCHEM Local Grid Refinement User's Guide
H + + Na+ + OH'^3 Na+ + H20
Exchange reactions (on micelle)
r^exm
= '-+Ca2+ ^ ' " '
ex
K3 -
[Na+]
[Na+J[H+]
Exchange equilibrium constant
[c^+ltNaV
K
exm
[fa+J2[Ca2+]
where KeX1m=pex1m{[A-]+[S-]}
2Na + Mg
2+
,exm
2Na+ + Mg 2+
K
.exm
LMg2+][Na+]2
|_N=a+J2[Mg2+]
where KT=r2{[A-]+[S-]}.
B.6.8 List of Elements and Reactive Species for IREACT = 4 or 6
Elements or pseudo-element:
Hydrogen (reactive), Sodium, Calcium,
Magnesium, Carbonate, Aluminum, Silicon,
Oxygen, Chlorine, S (Injected surfactant)
Independent aqueous or oleic species: H+, Na+,Ca2+, Mg2+, A13+, CO2" , Cl" S"
H4SiO4, H2O
Dependent aqueous or oleic species: Ca(OH)+, Mg(OH)+, A1(OH)2-,A1(OH)2-,
Ca(HC03)+, Mg(HC03)+, OH-, HCOj ,
H3Si04-, H2Si042', HSi2063-, Si2052-,
A1(OH)4-, H2CO3, CaCOg , MgCOg
Solid species: CaCO3 (Calcite), Al2Si2O5(OH)4 (Kaolinite),
MgCO3 (Magnesite), NaAlSi2Oe.H2O
(Analcite), SiO2 (Silica), Mg(OH)2
(Magnesium Hydroxide)
Adsorbed cations on rock surface: if + , Na +, Ca 2+, Mg 2+
Adsorbed cations on micelles: Na +,
-------
Appendix B - UTCHEM Local Grid Refinement User's Guide
Aueous reactions
H
Keq
Keq
HCO
Ca(OH)+
Keq
A13+
A1(OH)2+
Keq
A1(OH)4-
Keq
H4SiO4 £»8 H+ + H3SiO4"
KQq H- 2
H4SiO4 T£ 2H +H2SiO4
K?q
Ca2++ H++ C023~ ^4° Ca(HC03)+
Mg(HC03)+
Euilibrium constant
^ =[H+] [OH']
Kw4
0 —
eq
K3 =
[H+]
[Ca(OH)+][H+]
Mg(OH)+ + H+ K«i =
>]
[A1(OH)2+][H+]
-5 =
Keq eq [Al(OH)2+][H+]2
zt6 A1(OH)2+ + 2H+ ^ q -
req [Al(OH)4-][H+]4
'7 ~ [A13+]
req [H+3[H3SiQ4-]
^8 ~ [H4Si04]
eq [H+]2[H2Si0421
K9 =•
[H4Si04]
req [ca(HC03)+]
'10 ~ [Ca2+] |_C023-J[H+]
req [Mg(HC03)+]
^11=[Mg2+J[c02-][H+]
312
-------
Appendix B - UTCHEM Local Grid Refinement User's Guide
2H4Si04
- < H2C03
Keq
K'q =
+ + HSi206
3"
2H4SiO4 ^44 2H+ + 3H2O + Si2O52'
Solid species
CaCO3
MgCO3
SiO2
Al2Si205(OH)4
NaAlSi2O6.H2O
Mg(OH)2
Keq_[H+]3[HSi2063-]
[H^iO^2
eq_[H+32[Si2052-]
[H4Si04]2
Solubility product
Ksf=[Ca2+][c02-]
Ks2P=[Mg2+]
[c02-]
KS3P =[H4Si04]
Ksp =[H+]-6[Al3+]2[H4Si04]
Ksp
KsP=[Mg2+][H+]
2++-2
Exchange reactions (on matrix) Exchange equilibrium constant
+ Kex
2Na +Ca2+ 2Na+ + Ca2+
ex
Kl -
[Ca2+]
Na
+ Kex
2Na +Mg2+ ^ 2Na+ + Mg2+
_ + Kex +
H + Na"1" + OH" ^ Na + H2O
v
K2 -
[Mg2+] [Na
Ke,X =
313
-------
Appendix B - UTCHEM Local Grid Refinement User's Guide
Exchange reactions Con micelle')
jrexm
Exchange equilibrium constant
+Ca
2+
4- = 9-4-
2Na + Ca /+
.exm
K
where
2Na + Mg
2+
K
.exm
2Na + Mg
K
.exm
[(!a2+][Na+]2
[S-]
[>fa+J2[Mg2+]
exm Rexm
where K 2 = P 2 ^ J
B.6.9 List of Elements and Reactive Species for IREACT = 5
Elements or pseudo-element:
Hydrogen (reactive), Sodium, Calcium,
Magnesium, Carbonate, Aluminum, Silicon,
A (from acid HA), Oxygen, Chlorine, S
(InjectedSurfactant)
n
Independent aqueous or oleic species: H+, Na+, Ca2+, Mg2+, A13+, CO 3 ,
HA0, H20
Dependent aqueous species:
Solid species:
Ca(OH)+, Mg(OH)+, A1(OH)2-, A1(OH)2-,
Ca(HC03)+, Mg(HC03)+, A", OH", HCOj ,
H3Si04-, H2Si042-, HSi2063-, Si2O52-,
A1(OH)4-, H2C03, HAW
CaCO3 (Calcite), Al2Si2O5(OH)4 (Kaolinite),
MgCO3 (Magnesite), NaAlSi2O6-H2O
(Analcite), SiO2 (Silica), Mg(OH)2,
(Magnesium Hydroxide)
Adsorbed cations on rock surface: H + , Na + , Ca 2+, Mg 2+
Adsorbed cations on micelles:
Aqueous reactions
H20
Na +, Ca 2+, Mg 2+
Equilibrium constant
K^ =[H+] [OH-]
314
-------
Appendix B - UTCHEM Local Grid Refinement User's Guide
Keq
w
A" + H2O
C0
2
2+
Keq
Ca + H20 Ca(OH)
+ ,, TT+
Keq
Mg(OH)+ + H+
Keq
A13+ + H2O z±6 A1(OH)2+
Keq
y±7 A1(OH)2+
Keq
A1(OH)4- + 4H+
Keq
H4Si04 ^ H+ + H3Si04"
Keq
H4Si04 2H+ + H2Si042"
Keq
Ca(HC03)
Keq
Mg(HC03)
[H+]
-2 ='
[HAw]
eq [Heps]
T
-------
Appendix B - UTCHEM Local Grid Refinement User's Guide
H2C03
2H4SiO4
+ + HSi206
3-
2H4Si04 <45 2H+ + 3H20 + Si205
2"
Partitioning of HA
HA0 ^ HAW
Solid species
CaCOs
MgCOs
Si02
Al2Si205(OH)4
NaAlSi2O6.H2O
Mg(OH)2
Exchange reactions (on matrix")
_
2Na +Ca2+
_
2Na+ + Ca2+
veq -
K13 -
[C023-J[H+]
[H4Si04]
[+]2[si2o52-]
•-15 ~ 9
[H4Si04]2
Partition coefficient
[ H Aw ] Water
D~ [HAo]oil
Solubility product
Ksp = [Ca2+][c02-]
Ksp =[Mg2+][c02-]
KS3P =[H4Si04]
KS4P =[H+] -6[A13+] 2tH4Si04] 2
Ksp =[H+] -4[Na+][Al3+][H4Si04]
2
KS6P =[Mg2+] [H+] '2
Exchange equilibrium constant
ex
[Ca2+]
Na
Na
316
-------
Appendix B - UTCHEM Local Grid Refinement User's Guide
2Na + Mg2+ ^ 2Na+ + Mg2+
H + Na + OH" ^ Na + H2O
Exchange reactions (on micelle)
_ _
2Na + + Ca2+ 2Na+ + Ca 2+
ex
Mg2+][Na+}
[Mgz+] I Na
ex
Na
+
+
Na
k]
Exchange equilibrium constant
K
exm
2Na + Mg
2+
rr-
2Na
_
+ 2+
where K = {[A-] +[S-]}
K
exm
LMg2+][Na+]2
lfa+J2[Mg2+]
where
317
-------
Appendix C
Discretized Flow Equations
The coordinate system can be either cartesian, radial, or curvilinear. The discretized equations presented here
are for the cartesian coordinate system referred to as (x, y, z). The finite-difference grid is block-centered and
numbered from 1 to NxNyNz, where Nx, Ny, and Nz correspond to the number of gridblocks in the x, y, and
z directions, respectively. The volume of the mth block (i, j, k) is AVm=AxmAymAzm where i, j, and k
correspond to the x, y, and z coordinate directions, respectively. The time increment 8t is from timestep n to
timestep n+1. The delta operator S denotes discrete differences:
fn+l_fn
fm -fm-l'5xfi = f i ~fi-l
* ~~*->"* = * -
(C.I)
m-NxNy
= f ~f-
k-l
Most variables, including pressure, concentrations, adsorbed concentrations, saturations, capillary pressures,
phase properties such as density, viscosity, interfacial tension, and relative permeabilities are calculated and
stored at gridblock centers. Some variables, such as transmissibilities and phase velocities, are evaluated at
the faces between gridblocks. Applying the finite-difference approximations to the species conservation
equations (Eq. C.I) and the pressure equation (Eq. C.10), we obtain a system of finite-difference equations.
For the purpose of simplicity, the system of equations is illustrated for a two-dimensional problem even
though the code is three-dimensional.
The species conservation equation for species K at gridpoint m is
(C.2)
m
The superscript n indicates that the variables are evaluated using both old timestep (n) variables and new
timestep (n+1) variables.
FaK is the accumulation term
(F«c)m = {RAVCK[l + (Cf + C°K)(PR - PRO
FIK is the transport term as
(C.3)
m
318
-------
Appendix C - Discretized Flow Equations
where CXK^, CyK^, Tx^, and Ty^ are defined by
+9m{rxm[(CK,)m]}5x(CK£)m+1/2
m+Nx
(C.4)
m+1
(C.5)
(C.6)
(Tx )m and (Ty)m, given by
(Tx)m =2(AyAz)m/(Axm/km +Axm+1/km+1)
(Ty)m=2(AxAz)m/(Aym/km+Aym+Nx/km+Nx) (C7>
are transmissibilities.
(pm is the flux limiter function defined as follows (Liu et al, 1994):
_ 2(fm+l/2~fm)
fm+1_f (C.8)
The magnitude of the limiting depends on the smoothness of the data, measured by the ratio of consecutive
cell gradients r:
r _
rm -
f _ f
*tn ^m-l
~
rm+l ~ rm
(C.9)
and
-------
Appendix C - Discretized Flow Equations
are the dispersion coefficients defined by
= AymAzm/[(Axm +
)m = AymAzm/[Aym +(Aym_Nx
= AxmAzm/[(Aym +Aym+Nx)/2]((l)RS£KyyK£
= AymAzm/[Axm +(Axm_1
The average specific weight of phase t is calculated from
+(E,Ax)m+1]
+ 8ttnuy//W)m
m
m
where E; is the existence index of phase s> and is defined as
°
FqK is the source and sink term:
-H»RAv[i+(cf +c5
AKS
f=l
1 m
(CIO)
(C.ll)
(C.12)
(C.I 3)
(C.14)
which includes wells constrained by either rate or pressure and the production from chemical reactions.
The pressure equation at gridpoint m is
(C.15)
Fa is the total accumulation
320
-------
Appendix C - Discretized Flow Equations
(Fa)m=(4RAVCtPR)m
Fti is the total transport as a function of reference phase pressure:
ncv
1 + (PR ~ PRO ) X CKCK^
K = l
ncv
I + (PR-PRO)ZC£CK£
(C.16)
m
n
m+1
m+NX
(C.17)
m
Both Ft2, the total transport as a function of capillary pressure and gravity, and Fq, the total source or sink, are
evaluated using values of the old timestep:
(pt2)m = -
"cv
K=l
K=l
•[5x(Pc,R)m+1-(Tx,)m5x(D)m+1]
m
m
(C.18)
m+NX
(Fq) =
^ M/m
ncvnP
-PR -
(C.19)
Coefficients of reference phase pressure PR on the left-hand side of Eq. C.I 5 are concentration-dependent and
are evaluated using values at the old timestep. The equation written for all gridblocks in the spatial domain
results in a system of equations with reference phase pressure PR as the only unknown and is solved
implicitly. The conservation equations (Eq. C.2) are then solved explicitly for overall concentrations. Phase
concentrations and saturations are obtained by phase equilibria calculations. Other phase pressures are
obtained using capillary pressure relations.
321
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