vvEPA
United States
Environmental Protection
Agency
Office of Research and
Development
Washington DC 20460
EPA/600/R-97/099
September 1997
Michigan Soil Vapor
Extraction Remediation
(MISER) Model
A Computer Program to
Model Soil Vapor
Extraction and Bioventing of
Organic Chemicals in
Unsaturated Geological
Material
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EPA/600/R-97/099
September 1997
MICHIGAN SOIL VAPOR EXTRACTION
REMEDIATION (MISER) MODEL:
A COMPUTER PROGRAM TO MODEL SOIL VAPOR EXTRACTION AND
BIO VENTING OF ORGANIC CHEMICALS IN
UNSATURATED GEOLOGICAL MATERIAL
by
Linda M. Abriola, John Lang, and Klaus Rathfelder
Department of Civil and Environmental Engineering
The University of Michigan
Ann Arbor, Michigan 48109
Cooperative Agreement CR-822017
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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DISCLAIMER
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-822017 to the
University of Michigan. 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
endorsement or recommendation for use.
When available, the soft ware in this document is supplied on an "as-is" basis without guarantee or
warranty of any kind, express or implied. Neither the United States Government (United States Environmental
Protection Agency, Robert S. Kerr Environmental Research Center), the University of Michigan, nor any of
the authors accept any liability resulting from use of this software.
11
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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.
Soil vapor extraction (SVE) and bio venting (BV) are effective and widely used in-situ remediation
techniques for unsaturated soils contaminated with organic compounds, primarily petroleum hydrocarbons.
Despite the effectiveness and flexibility of SVE and BV technologies, the efficiency and degree of success of
those systems is controlled by a combination of physical, chemical, and biological factors. The dynamics of
those interrelated processes is often incompletely understood, and consequently the performance and efficiency
of specific SEE/BV systems is generally difficult to predict. This report describes the development of a
numerical model for the simulation of physical, chemical, and biological interactions occurring in SVE and
BV systems. The model can be used as a research tool for studying and elucidating dynamics in SVE and BV
systems.
L
:u
Clinton W. Hall, Director
Subsurface Protection and Remediation Division
National Risk Management Research Laboratory
in
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ABSTRACT
This report describes the formulation, numerical development, and use of a multiphase,
multicomponent, biodegradation model designed to simulate physical, chemical, and biological interactions
occurring primarily in field scale soil vapor extraction (SVE) and bioventing (BV) systems. The model is
entitled the Michigan Soil Vapor Extraction Remediation Model, or MISER. MISER solves the governing
flow and transport equations in two space dimensions - either a cross sectional x-z domain, or an
axisymmetrical r-z domain for simulating radial flow to a single well. A standard Galerkin finite element
approach with linear triangular elements is employed. The coupled nonlinear equations are solved using a
modular, set-iterative solution algorithm. In this approach the sets of flow, transport, and biodegradation
equations are decoupled within the simulator and solved separately. The set-iterative approach substantially
reduces the size of solution matrices and provides increased flexibility. Features of the model include: the
ability to simulate multiphase flow, including water table coning; the simulation of multicomponent transport
processes, incorporating fate-limited interphase exchange in processes of volatilization and dissolution of an
entrapped organic liquid, interphase exchange between the mobile gas and aqueous phases, sorption, and
biophase update; and the simulation of multicomponent biodegradation kinetics and microbial population
dynamics.
This report is divided into 6 sections. Section 1 provides an overview of SVE and BV systems and
a review of existing models. Section 2 presents the conceptual formulation of MISER and the associated
mathematical representation for flow, transport and biotransformation processes. Section 3 describes the
numerical solution approach and Section 4 presents the results of model verification analyses. Description and
usage of the model is provided in Section 5, and example SVE and BV simulations are described in Section
6.
This report was submitted in fulfillment of CR-822017 by the University of Michigan under the partial
sponsorship of the U.S. Environmental Protection Agency. This report covers a period from September 1993
to March 1996 and work was completed as of March 1996.
IV
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CONTENTS
DISCLAIMER ii
FOREWORD iii
ABSTRACT iv
LIST OF FIGURES x
LIST OF TABLES xiii
LIST OF ABBREVIATIONS AND SYMBOLS xv
1 INTRODUCTION 1
1.1 OVERVIEW AND PURPOSE 1
1.2 BACKGROUND AND LITERATURE REVIEW 2
1.2.1 Limits of Applicability 2
1.2.2 Rate Limited Mass Transfer 3
1.2.3 Biodegradation Rates 3
1.2.4 Temperature 4
1.2.5 Previous Models 5
1.3 MODEL FEATURES 6
2 MODEL FORMULATION AND THEORETICAL DEVELOPMENT 8
2.1 CONCEPTUAL MODEL 8
2.2 PHASE MASS BALANCE EQUATIONS 11
2.3 COMPONENT MASS BALANCE EQUATIONS 13
2.4 INTERPHASE MASS TRANSFER 15
2.4.1 Equilibrium Partitioning 15
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2.4.2 Rate Limited Interphase Mass Transfer 17
2.4.3 Biotransformations 19
2.5 CONSTITUTIVE RELATIONS 21
2.5.1 Capillary Pressure 21
2.5.2 Relative Permeability 23
2.5.3 Gas phase density 23
2.5.4 Liquid Phase Density 23
2.5.5 Gas phase viscosity 24
2.5.6 Aqueous Phase Viscosity 24
2.5.7 Hydrodynamic Dispersion 24
2.5.8 Matrix Compressibility 25
3 NUMERICAL DEVELOPMENT 26
3.1 FINITE ELEMENT APPROACH 26
3.2 SOLUTION OF THE PHASE MASS BALANCE EQUATIONS 28
3.2.1 Pressure Based Formulation 28
3.2.2 Trial Functions and Weighted Residual Equations 29
3.2.3 Capacity Coefficients 31
3.3 MATERIAL PROPERTIES 31
3.4 VELOCITY EQUATIONS 32
3.5 COMPONENT MASS BALANCE EQUATIONS 34
3.5.1 Weighted Residual Equations in Cartesian Coordinates 35
3.5.2 Mass Exchange Terms 38
3.6 BIOLOGICAL REACTIONS 39
3.7 NAPL SATURATION 40
3.8 AXISYMMETRIC COORDINATES 40
3.9 TIME DISCRETIZATION 41
3.10 TIME STEP CONTROL 41
3.11 BOUNDARY CONDITIONS 42
3.11.1 Phase Mass Balance Boundary Conditions 42
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3.11.2 Component Mass Balance Boundary Conditions 43
3.11.3 Extraction Wells 44
3.11.4 Treatment of Injection Wells 45
3.12 ITERATION SCHEME 46
3.13 SOLVER 46
4 MODEL VERIFICATION 49
t
4.1 MATERIAL BALANCE CALCULATION i 49
4.1.1 Phase Material Balance 49
«
4.1.2 Component Material Balance 50
4.1.3 Calculation of Mass Balance Error . 50
4.2 VERIFICATION OF THE PHASE MASS BALANCE SOLUTIONS 52
4.2.1 Comparison with One Dimensional Richards Equation 52
4.2.2 Comparison with Two Dimensional Richards Equation 54
4.2.3 Comparison with Quasi Analytical Solutions for Unsteady Radial Flow of Gas ... 57
4.3 VERIFICATION OF THE COMPONENT MASS BALANCE SOLUTIONS 60
4.3.1 Comparison with One Dimensional Analytical Solutions 60
4.3.2 Comparison with Two Dimensional Analytical Solutions 61
4.3.3 Verification of Biokinetics 62
4.3.4 Verification of Interphase Exchange 64
4.4 VERIFICATION OF THE COUPLED PHASE AND COMPONENT MASS BALANCE
SOLUTIONS 65
5 PROGRAM DESCRIPTION AND SIMULATION SETUP 68
5.1 CODE DESCRIPTION 68
5.2 PROGRAM MODULES 68
5.3 ARRAY DIMENSIONS AND PROGRAM VARIABLES 68
5.4 DESCRIPTION OF INPUT FILES AND INPUT DATA 69
5.4.1 Data Block A - Input/Output Files and Control Options 69
5.4.2 Data Block B - General Model Control Options 69
5.4.3 Data Block C - Time Step and Iteration Control Parameters 69
VII
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5.4.4 Data Block D - Grid Information and Control Options 69
5.4.5 Data Block E - Component Chemical Properties 70
5.4.6 Data Block F - Mass Transfer Coefficients 70
5.4.7 Data Block G - Material Property Block Information 70
5.4.8 Data Block H - Sorption Parameter Data 70
5.4.9 Data Block I - Biological Parameter Data 71
5.4.10 Data Block J - Phase Parameter Data 71
5.4.11 Data Block K-Temperature Parameter Data 71
•»
5.4.12 Data Block L - Output Control Parameters 72
5.4.13 Data Block M - Restart Identifier 72
5.4.14 Data Block N - Initial Pressure Conditions 72
5.4.15 Data Block O - Velocity Computation 73
5.4.16 Data Block P - Organic Liquid Saturation and Composition 73
5.4.17 Data Block Q - Oxygen and Nutrient Initial Conditions 73
5.4.18 Data Block R - Boundary Conditions 73
5.4.19 Data Block S - Extraction/Injection Well Conditions 74
5.4.20 Data Block T-Velocity Boundary Conditions 74
5.5 DESCRIPTION OF OUTPUT FILES 74
5.5.1 Main Output File - 'Outpre.out' 74
5.5.2 Convergence History and Runtime Information Output File - 'Outpre.cnv' 75
5.5.3 Error Message Output File -'Outpre.err' 75
5.5.4 Mass Balance Output File - 'Outpre.mb' 75
5.5.5 Contour Plot Output File - 'Outpre.con' 76
5.5.6 Time Series Plot Output File - 'Outpre.plt' 76
5.5.7 Restart Output File - 'Outpre.rst' 76
6 DEMONSTRATION OF MISER 105
6.1 SOIL VAPOR EXTRACTION 106
6.2 BIOVENTING 107
6.3 FIELD SCALE BIOVENTING 109
vm
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A ELEMENT MATRICES FOR THE SIMULTANEOUS SOLUTION OF THE PHASE MASS
BALANCE EQUATIONS ii
B ELEMENT MATRICES FOR THE SOLUTION OF DARCY'S LAW EQUATION
C ELEMENT MATRICES FOR THE SEQUENTIAL SOLUTION OF THE COMPONENT
MOLE BALANCE EQUATIONS
D ELEMENT MATRICES FOR THE SOLUTION OF THE ORGANIC PHASE MASS BAL-
ANCE EQUATION 129
E Description of Major Variables
F EXAMPLE MAKE FILE
13J
139
G EXAMPLE DATA FILES
H SOURCE CODE LISTING
REFERENCES
140
151
230
IX
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LIST OF FIGURES
1.1 Basic SVE/BV system configuration 2
2.1 Conceptual model of the soil system composition 9
2.2 Conceptual model of interphase mass transfer pathways 10
3.1 Triangular element in global and transformed coordinates (after Lapidus and Finder, ,1982). 27
3.2 Variable representation in MISER 32
3.3 Representation of an extraction well in the discretized domain 44
4.1 Computational grid used for the numerical solution of the one dimensional Richards equation. 53
4.2 Comparison of numerical and analytical solutions for the one dimensional Richards equation.
Simulation time = 6 hours; convergence tolerance = 1 x 10~4 54
4.3 Domain configuration used in two dimensional (2D) flow simulations for comparison to
SWMS_2D 55
4.4 Numerical grid used in two dimensional flow simulations for comparison to SWMSJ2D. . . 56
4.5 Simulated volumetric moisture content in the homogeneous domain at time 12 hrs (MISER
= solid line; SWMS-2D = dashed line) 56
4.6 Simulated volumetric moisture content in the layered domain at time 6 hrs (MISER = solid
line; SWMS_2D = dashed line) 57
4.7 Simulated volumetric moisture content in the layered domain at time 12 hrs (MISER = solid
line; SWMS.2D = dashed line) 57
4.8 Domain configuration used in two dimensional flow simulations for comparison to quasi
analytical solutions for radial gas flow. 58
4.9 Comparison of quasi analytical and numerical solutions for two dimensional radial gas flow
in a uniform soil with fc = 1 x 10~u m2 59
4.10 Comparison of quasi analytical and numerical solutions for one dimensional radial gas flow
in a uniform soil with k = 1 x 10~~I4m2 59
4.11 Computational grid used for the numerical solution of the one dimensional transport equation
with and without advection 60
4.12 Comparison of MISER with the one dimensional analytical solution for diffusion driven
transport 61
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4.13 Comparison of MISER with the one dimensional Ogata and Banks analytical solution for
transport with dispersion and constant advection 61
4.14 Comparison of MISER (solid lines) with a two dimensional analytical transport solution
(dashed lines) at 4000 sec. Contours of normalized concentration are from left to right: 0.8,
0.6,0.4, 0.2,0.1, and 0.01 62
4.15 Comparison of MISER (solid lines) with a 2D analytical transport solution including first
order decay (dashed lines) at 4000 sec. Contours of normalized concentration are from left
to right: 0.8, 0.6, 0.4,0.2,0.1, and 0.01. . ; 63
4.16 Comparison of substrate profiles along a one dimensional column by MISER (lines) and a
one dimensional numerical solution (discrete points) for biodegradation by Moltz et al, [1986]. 64
4.17 Comparison of MISER (solid lines) with a two dimensional analytical solution including
linear equilibrium sorption (dashed lines) at 4000 sec. Contours of normalized concentration
are from left to right: 0.8, 0.6, 0.4,0.2, 0.1, and 0.01 65
4.18 Comparison of MISER (lines) with a one dimensional column experiment (discrete points)
for multicomponent organic liquid (benzene, TCE, toluene) volatilization under equilibrium
conditions 65
4.19 Comparison of predicted solute concentrations at time 6 hrs (MISER = solid line; SWMS_2D
= dashed line) 66
4.20 Comparison of predicted solute concentrations at time 12 hrs (MISER=solid line; S WMS _2D
= dashed line) 67
6,1 Problem depiction used in example simulations. Contours show the initial organic liquid
distribution. The contour interval is 0.005 with levels increasing inward 105
6.2 Predicted organic liquid saturation distribution in SVE simulations with intermediate mass
transfer rates. The contour interval is 0.005 with levels increasing inward 107
6.3 Toluene sorbed (ppm) at 20 and 100 days 107
6.4 Toluene removal versus time 108
6.5 Predicted organic liquid saturation (%) at selected times in the example BV simulation. . . . 109
6.6 Predicted biomass distribution (g/1 x 10~3) at selected times in the example BV simulation. 109
6.7 Simulation domain used in the field scale bioventing demonstration simulation 110
6.8 Initial conditions used for the field scale bioventing demonstration simulation 113
6.9 Predicted organic liquid distributions at specified times for the field scale bioventing demon-
stration simulation 114
6.10 Predicted benzene substrate distributions at specified times for the field scale bioventing
demonstration simulation 115
6.11 Predicted biomass distributions at specified times for the field scale bioventing demonstration
simulation 116
XI
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6.12 Predicted oxygen distributions at specified times for the field scale bioventing demonstration
simulation H7
XII
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LIST OF TABLES
3.1 Summary of mass transfer expressions 35
3.2 Summary of lumped mass exchange and bioreaction coefficients 37
3.3 Summary of numerical scheme in MISER ;. 47
4.1 Comparison of global mass balance errors from numerical solutions of the one dimensional
Richards equation at time 6 hrs 54
4.2 Soil properties used in two dimensional flow simulations for comparison to SWMS_2D. . . 55
4.3 Soil properties used in two dimensional flow simulations for comparison to quasi-analytical
solutions for radial gas flow 58
5.1 MISER program modules . 77
5.2 Selected parameter variables defined in the include file'dimen.inc.' 79
5.3 Description of input and output files 80
5.4 Input Data in Block A - Input/Output Files and Control Options 81
5.5 Input Data in Block B - General Model Control Options 83
5.6 Input Data Block C - Time Step and Iteration Control Information 84
5.7 Input Data Block D - Grid Information and Control Options Information 85
5.8 Input Data Block E - Component Chemical Properties 86
5.9 Input Data Block F - Mass Transfer Coefficients 87
5.10 Input Data Block G - Material Property Block Information 88
5.11 Input Data Block H - Sorption Parameter Data 89
5.12 Input Data Block I - Biological Parameter Data 90
5.13 Input Data Block J - Phase Parameter Data 91
5.14 Input Data Block K - Temperature Parameter Data 92
5.15 Input Data Block L - Output Control parameters 93
5.16 Input Data Block M - Restart Identifier. 96
5.17 Input Data Block N - Initial Pressure Conditions 97
5.18 Input Data Block O - Velocity Computation 98
xm
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5.19 Input Data Block P - Organic Liquid Saturation and Composition 99
5.20 Input Data Block Q - Oxygen and Nutrient Initial Conditions 100
5.21 Input Data Block R - Boundary Conditions 101
5.22 Input Data Block S - Extraction/Injection Well Conditions 103
5.23 Input Data Block T - Velocity Boundary Conditions 104
6.1 Soil properties used in example SVE and BV simulations 106
6.2 Mass transfer coefficients used to simulate an SVE system 106
6.3 Biotransformation parameters used in an example BV simulation 109
6.4 Soil parameters used in the field scale bioventing demonstration simulation Ill
6.5 Fluid properties used in the field scale bioventing demonstration simulation. All values are
for20°C Ill
6.6 Mass exchange and biokinetic parameters used in the field scale bioventing demonstration
simulation 112
xiv
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LIST OF ABBREVIATIONS AND SYMBOLS
aap specific contact area between the a and ft phases
A general mass matrix
Ae area of a triangular element [L2]
AXl cross-sectional area associated with node i [L2]
A; subarea of a triangular element [L2]
b Klinkenberg parameter [ML"1 T~2]
B general stiffness matrix
#1,2,3 material balance error measures [%]
Ba net mole biological transformation rate in phase a
per medium volume [mole L~3Z"~1].
Bac mole biological transformation rate of component'
c in phase a. per medium volume [mole L"3 T"1 ].
B* net mass biological transformation rate in phase a
per volume of phase a [ML~3T~1].
B*c mass biological transformation rate of component
c in phase a per volume of phase a [ML~3T~1].
Cai. mass concentration of component c in phase a
[ML"3]
Cp capacity coefficient dS^/dPc [M~1LT2]
D^c hydrodynamic dispersion tensor of component c
in phase a [L27"~:]
L>™ binary molecular diffusion coefficient of compo-
nent c in phase a [L2T-1]
E general RHS vector
Ea net interphase mole transfer rate to phase a from
all contiguous phases per pore volume [mole
Eac netinterphase mole transfer rate to phase a of com-
ponent c from all contiguous phases per pore vol-
ume [mole L"3?1"1]
Eapc interphase mole transfer rate of component c to
phase a, from phase ft per pore volume [mole
E* net interphase mass transfer rate to phase a.
from all contiguous phases per pore volume
net interphase mass transfer rate of component c
to phase a from all contiguous phases per pore
volume [ML~3T~l]
interphase mass transfer rate of component c
to phase a from phase ft per pore volume
/, F general RHS vectors
Fci use coefficient of component c with substrate /
degradation [-]
foe soil organic carbon fraction [-]
Fb boundary flux in material mass balance calculation
Fr
g
gx
gz
Ga
hgj
7C
7™
J«c
exchange flux in material mass balance calculation
[ML~3T~l]
source/sink in material mass balance calculation
rate of change in material mass storage for balance
calculation [ML~3T~l]
biological reaction rate in material mass balance
calculation [ML"3?7-']
lumped RHS mass transfer coefficient for compo-
nent c in phase a [mole L"3?""1]
gravitational acceleration vector [LT~2]
horizontal component of g [LT~2]
vertical component of g [LT"2]
a phase compressibility factor [-]
equivalent gas phase head [L]
component c inhibition function [-]
„ biomass inhibition functions [-]
saturation inhibition function [—]
mass flux of component c in phase a by kinematic
dispersion [ML"2?1"1]
mass flux of component c in phase a by molecular
diffusion [ML"2?7"1].
intrinsic permeability tensor [L2]
biomass decay rate [T~l]
effective gas phase permeability [L2]
maximum substrate / use rate [mole M~lT~l]
relative permeability of phase a [—]
half saturation constant for substrate / [-]
overall mass transfer coefficient for component c
controlled by phase a [LT~l]
xv
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gas phase permeability at a high pressure; equiva-
lent to the liquid permeability [L2]
Henry's Law constant for component c
K,
oc,
Ka
L(H)
Lj
Lar
m
Ma
Mc
71
N*
M-
PC
Pgf
"nw
P*
Pw
Pa
9
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p*o
PC,
p*a
e
0>Se
mass density of the uncontaminated gas phase
[ML-3]
bulk solid phase mass density [ML~3]
molar density of phase a [mole L~3]
mass density of phase a [ML~3]
element average phase mass density [ML~3]
tortuosity of phase a [-]
porosity [-]
gas phase viscosity parameter [-]
variable time weighting factor [-]
adsorbed mass of component c per mass of soil [-]
computational domain
subscripts
a aqueous phase
A nutrient
b biophase
c component
g gas phase
i, j nodes
k direction
/ degradable substrate; direction
L longitudinal direction
N2 nitrogen
o organic phase
Oi oxygen
r radial direction
s solid phase
t total
T transverse direction
x horizontal direction
to water
z vertical direction
a, ft phase (aqueous, gas, organic, solid)
y components of the organic liquid
superscripts
d kinematic dispersion
e element
h hydrodynamic dispersion
k iteration counter
L mass lumped
m molecular diffusion
o initial time, conditions in contacting fluid, uncon-
taminated gas phase
t time
* mass based variable
abbreviations
BV bioventing
LEA local equilibrium assumption
LHS left hand side
RHS right hand side
SS simultaneous solution method
SVE soil vapor extraction
xvu
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Section 1
INTRODUCTION
1.1 OVERVIEW AND PURPOSE
The migration and fate of nonaqueous phase liquid (NAPL) organic contaminants in the subsurface has
been the subject of intensive investigation in the past few years. It is now generally recognized that the
prevalence of NAPLs at contaminated sites is a significant impediment to aquifer restoration [Mackay and
Cherry, 1989]. As a NAPL migrates through a porous formation a portion of the organic liquid is retained
within the pores due to the action of capillary forces. Residual NAPL can vary from 5-40% of the pore
volume, or on a volume basis, from 3-5 1/m3 in permeable soils up to 30-50 1/m3 in low permeable soils
[Schwille, 1984; Hoag and Marley, 1986; Wilson et al., 1990]. These entrapped residuals cannot be
mobilized by simple hydraulic flushing, and thus due to the low aqueous solubility of the NAPLs, the
residuals may serve as long term sources of groundwater contamination. Conventional pump and treat
remediation technologies have proven to be an ineffective and costly approach to aquifer restoration when
NAPLs are present [Mackay and Cherry, 1989; Haley et al., 1991; National Research Council, 1994].
Based upon the limitations of conventional pump and treat methods, considerable effort is currently
focused on the development of alternative remediation technologies. Soil vapor extraction (SVE) is an
alternative remediation approach which targets the removal of volatile organic contaminants (VOCs) from
the unsaturated zone. SVE involves the generation of advective vapor fluxes through the pores of the
contaminated soil to induce transfer of VOCs to the air stream. Air flow is established by pumping from a
system of vadose zone wells through which contaminant vapors are collected and transported above ground
where they are treated if required, and discharged to the atmosphere (Figure 1.1). Since its development in
the late 70's and early 80's [Texas Research Institute, 1980, 1984; Thornton and Wootan, 1982; Marley and
Hoag, 1984; Crow et al., 1985, 1987] SVE applications have become widespread, with SVE now
comprising up to 18% of selected remedies at Superfund sites [Travis andMacinnis, 1992]. The popularity
of SVE technologies stems from their proven effectiveness for removing large quantities of VOCs from the
soil, their cost competitiveness, and their relatively simple nonintrusive implementation. Numerous articles
and reports document and describe SVE applications [e.g. Hutzler et al., 1989; Downey,and Elliott, 1990;
Gerbasi andMenoli, 1994; McCann et al., 1994].
The ability of SVE systems to enrich the unsaturated zone with oxygen and stimulate indigenous
microorganisms to biodegrade organic contaminants was recognized in early feasibility studies [Thornton
and Wootan, 1982; Texas Research Institute, 1984]. Enhanced biodegradation in the unsaturated zone was
subsequently evaluated in laboratory treatability studies [Hinchee and Arthur, 1991; Kampbell and Wilson,
1991] and in monitored field applications [Miller, 1990; Hinchee et al., 1991; Dupont et al., 1991]. These
studies helped spawn the development of engineered systems referred to as bioventing (BV) (Figure 1.1).
BV is similar to SVE in that remediation is facilitated by advective vapor fluxes established through vadose
zone wells. BV, however, differs fundamentally from SVE in that it designed to maximize soil remediation
by in situ biodegradation and to minimize contaminant volatilization and above ground recovery [Dupont,
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SVE System
BV System
Figure 1.1: Basic SVE/BV system configuration.
1993; Hinchee, 1994]. BV is now recognized to be a highly effective and cost-competitive remediation
alternative [Miller et al, 1994] especially when treatment of off-gas is required [Reisinger et al., 1994] ;
Because of the complexity of the processes influencing the performance of SVE/BV technologies,
design and operation guidelines are frequently qualitative in nature based on experience or simple design
rules [Hutzler et al, 1989; Dupont, 1993; Johnson etal, 1990,1995]. Mathematical models are recognized
as powerful tools that can be used to integrate and quantify the interaction of physical, chemical, and
biological processes occurring in field scale SVE/BV systems. In addition to predicting potential mass
removal, mathematical models can be used to explore alternative system designs and to investigate factors
limiting successful remediation. This report describes the development of a comprehensive SVE/BV
simulator, entitled the Michigan Soil Vapor Extraction Remediation Model, or MISER.
1.2 BACKGROUND AND LITERATURE REVIEW
1.2.1 Limits of Applicability
Reviews of SVE technologies indicate success of SVE is strongly correlated with contaminant volatility
and the ability to generate advective gas fluxes through the contaminated soil [Hutzler et al., 1989; U.S.
EPA, 1991; Pedersen and Curtis, 1991; Johnson etal., 1995; Rath/elder et al., 1995]. SVE has been
effectively applied for the removal or mass reduction of a wide variety of halogenated and nonhalogenated
volatile and semivolatile organic compounds. It is not considered effective for organic compounds of low
volatility, inorganic compounds, polychlorinated biphenyls (PCB), dioxins, organic pesticides, cyanides,
and corrosives [U.S. EPA, 1991]. SVE is generally most effective in uniform soils with good conductivity,
low moisture content, and low organic carbon content [Fine and Yawn, 1993]. Soils with low air
permeability are more difficult to remediate [U.S. EPA, 1991], although applications in low permeability,
fractured media have been reported [Agrelot et al., 1985; Gibson etal., 1993].
Reviews of BV design and applications [Thomas and Ward, 1992; Dupont, 1993; Miller et al., 1994;
Litchfield, 1993; Hinchee, 1994] indicate BV is most applicable for the removal of petroleum
hydrocarbons. Chlorinated organic compounds have not been considered appropriate for BV due to their
resistance to direct biodegradation, however, potential exists that these compounds can be cooxidized
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during microbial growth on other hydrocarbons [English andLoehr, 1991; Speitel and Alley, 1991; Barbee,
1994; Wilson, 1994; Fuller et al, 1995]. In contrast to SVE, BV is not constrained by contaminant
volatility and is therefore applicable to contaminants with moderate to low volatility [Hinchee, 1994].
Moreover, biodegradation rates are slower than volatilization processes for many hydrocarbons, and
therefore BV may be well suited for application during the periods of long term, low level removal
efficiency observed in traditional SVE systems. Consequently, integrated systems have been designed
which employ SVE for rapid VOC recovery during early stages, followed by low cost, long term BV
operations [Dupont et al., 1991; Nelson et al., 1994].
I
1.2.2 Rate Limited Mass Transfer
SVE systems characteristically exhibit large initial VOC recovery rates followed by a rapid drop in exhaust
VOC concentrations and long term, low level removal efficiency [Crow etal, 1987; DiGiulio, 1992; Travis
and Macinnis, 1992; McClellan and Gilham, 1992]. Diminished removal efficiency is attributed to several
mechanisms which decrease the rate of VOC mass transfer to the mobile gas stream. Lighter, more volatile
contaminant fractions are preferentially removed, leaving the heavier, less volatile components and
decreasing remediation efficiency [Hoag etal., 1984; Fine and Yaron, 1993]. Secondly, removal efficiency
decreases due to preferential removal of contaminants that are most accessible to the advective gas stream,
leaving behind contaminants that have poor accessibility to the gas stream due to occlusion in
intraaggregate or intraparticle regions [Brusseau, 1991; Gierke et al, 1992], or due to flow by passing of
zones of low permeability [Kearl et al., 1991; Ho and Udell, 1992]. Diffusion controlled, rate limited
interphase mass transfer, including processes of volatilization, dissolution, sorption and biotransformation,
are also a potentially critical factor affecting removal efficiency [Brusseau, 1992; Armstrong et al, 1993,
1994; Wilkins et al, 1995].
Several studies indicate the rate of NAPL volatilization can be adequately modeled with the assumption
of instantaneous local equilibrium [Hoag et al., 1984; Baehr et al., 1989; Berndtson andBunge, 1991;
Bloes et al., 1992; Hoyden et al., 1994; Ho etal., 1994]. Other studies, however, have shown the rate of
NAPL volatilization to be limited, even in relatively homogeneous materials, at high pore velocities
[Rainwater et al, 1989; Kearl et al., 1991; Hoffman etal., 1993; Wilkins et al., 1995], or low constituent
mole fractions [Haydenetal., 1994]. Hoffman et al. [1993] and Wilkins et al. [1995] found that measured
effective mass transfer coefficients in sandy media could be well correlated with dimensionless parameters
incorporating the vapor flux and mean grain size. Laboratory and field studies have also documented rate
limited interphase mass transfer of VOCs between the soil water and mobile gas phases [Cho andJaffe,
1990; Berndtson and Bunge, 1991; Gierke et al., 1992; McClellan and Gilham, 1992], and between the
water and organic liquid phases [Powers et al., 1991, 1992,1994]. Rate limited sorption/desorption on soil
particles also plays an important role in the transport and retention of VOCs [Brusseau and Rao, 1989;
Weber et al., 1991], and may limit bioavailability of organic substrates [Pignatello and Xing, 1996]. Recent
experimental studies suggest that unsaturated zone sorption is more complex than that in the saturated zone,
due to the presence of gas-liquid interfaces [Pennell et al., 1992].
1.2.3 Biodegradation Rates
Biodegradation rates in field BV systems have been assessed by the measurement of: carbon dioxide
production [Hinchee and Arthur, 1991; Huesemann and Moore, 1994; van Eyk, 1994]; hydrocarbon
-------
consumption rates [Kampbell and Wilson, 1991]; and oxygen consumption [Baehr et al, 1991; Ong et al.,
1991; Hinchee, 1994; Huesemann and Moore, 1994]. Oxygen consumption is generally considered a more
reliable measure of biodegradation and is typically measured by in situ respirometry tests [Hinchee, 1994].
Biodegradation rates in unsaturated soils have been observed in field and laboratory studies to be linked
to the soil moisture content. The reason for this linkage is poorly understood. Results from laboratory
studies generally show that higher rates of biotransformation occur at higher levels of soil moisture content
[Fan and Scow, 1993] and that this dependence may be compound specific [Holman and Tsang, 1995].
Moisture addition in field BV applications has similarly produced an increase in degradation rates [Hinchee
andArthur, 1991; Zwick etal., 1995]. At other sites, moisture addition has been found to reduce
degradation rates due to the constriction of air permeability and the resulting decrease in oxygen transport
[Miller et al., 1994] or was reported to have no affect on biodegradation rates [Miller, 1990].
Enhanced biodegradation rates have also been observed in laboratory experiments following nutrient
additions (e.g. nitrogen or phosphorus) indicating that nutrient limitations can constrain biodegradation rates
[Hinchee andArthur, 1991; Dupont, 1993; Baker et al., 1994; Fuller et al., 1995; Breedveld et al, 1995].
Nutrient addition in field applications is typically accomplished by water flooding [Nelson etal, 1994;
Norris et al., 1994]. However, it is not clear whether there is substantial enhancement of biodegradation
after nutrient addition in field studies [Miller, 1990; Miller etal., 1994; Leeson etal., 1995], partly because
it is difficult to separate the effects of nutrient addition from moisture addition [Dupont et al., 1991].
Inhibition of biodegradation at high concentrations of inorganic nutrients [Baker et al., 1994] or high
concentrations of organic substrates [Speitel and Alley, 1991; Huesemann and Moore, 1994; Mu and Scow,
1994] has been observed in laboratory studies. The significance of inhibition in field operations, however,
has received limited attention. One study noted the possibility of observed substrate inhibition at low flow
rates [Moore etal., 1995]. Thus inhibitory effects, if important, could be strongly linked to system
operation and design.
Degradation rates in field conditions depend not only on the metabolic properties of the microbes, but
also on the availability of substrates to the microorganisms. A host of laboratory and theoretical studies
provide substantial evidence that diffusion controlled desorption of organic substrates can control the
overall rate of biodegradation [Molz etal., 1986; Scow and Alexander, 1992; Scow andHutson, 1992;
Novak et al., 1993; Scow, 1993]. Thus, relatively slow rate limited desorption processes can in effect
control bioremediation of subsurface systems [Mueller etal., 1989; Rijnaarts etal., 1990]. Exposure time
and aging of the spill enhance the resistance to desorption and biodegradation [Novak et al., 1993;
Pignatdlo and Xing, 1996; Fuller etal., 1995]. Consequently, modeling of biodegradation processes
requires an accurate understanding and representation of sorption kinetics [Scow and Hutson, 1992;
Pignatello and Xing, 1996].
1.2.4 Temperature
Subsurface temperature is an important environmental variable in SVE remediation processes. The
efficiency of SVE remediation is strongly linked to the vapor pressures of the target compounds with a
suggested lower limit on vapor pressure of approximately 1000 Pa [Pedersen and Curtis, 1991; Johnson et
al., 1990]. Vapor pressures of organic compounds increase by a factor of approximately 3 or 4 with every
10"C rise in temperature. Experimental evidence also suggests that vapor sorption is inversely proportional
to temperature [Goss, 1992]. Methods to increase SVE efficiency by increasing the subsurface temperature
-------
have been attempted by heating and injection of ambient air [Sittler et al., 1993] or by methods of steam
injection [Falta et al., 1992; Wilson and Clarke, 1992]. Several other novel approaches which integrate
SVE with methods for soil heating have been considered {Downey and Elliott, 1990].
The effect of subsurface temperature on the design and operation of B V remediation efforts has
received little attention [Sayles et al., 1993,1995]. It is generally accepted that soil temperatures at most
sites are within the limits for microbial growth [Litchfield, 1993]. In Alaska, where soil temperatures are as
low as 1°C, respiration rates comparable to those in temperate and subtropical regions were observed
during summer months [Ong et al., 1994; Kellems et al., 1994]. The observed rates dropped slightly during
the winter months with less effect noted at sites with either active or passive soil wanning.
1.2.5 Previous Models
A number of mathematical models have been presented in the literature for the description of the SVE
process. These vary greatly in level of complexity and in the processes included. The simplest models are
analytical solutions for gas flow, intended to aid in the analysis of pneumatic pump tests and the design of
SVE applications [Massmann, 1989; Johnson etal, 1990; McWhorter, 1990; Baehr and Hult, 1991; Cho
andDiGiulia, 1992; Massmann and Madden, 1994; Beckett and Huntley, 1994; Baehr etal., 1995].
Numerical models of gas phase advection have also been developed for analysis of SVE systems [Welty et
al., 1991; CroiseandKaleris, 1992; Edwards and Jones, 1994] and BV systems [Mohr an d Merz, 1995].
Because only the gas phase flow field is considered in this group of models, they are not capable of
describing contaminant partitioning and migration, nor are they suitable when water movement is
important. These models are generally applicable for screening purposes and simple design analyses.
A more complex group of models are those which combine constituent transport and steady state gas
phase flow. Although transport processes are considered in this group of models, their applicability is
restricted by assumptions on the flow field, partitioning mechanism, or domain configuration. They are, in
general, not adequate for comprehensive simulation of field scale SVE/BV system, but are suitable for
behavior assessment and screening purposes. The simplest models in this group couple steady state flow
fields with analytical transport models [Roy and Griffin, 1991; Zaidel andRusso, 1993]. Other models
incorporate steady state flow fields and the numerical solution of transport equations [Massmann and
Farrier, 1992; Johnson et al., 1990; Wilson etal., 1988]. The model by Wilson et al. [1988] is extended in
a series of papers to explore: the effects of impermeable caps, permeability and evaporative cooling
[Gannon and Wilson, 1989]; anisotropic permeability [Mutch and Wilson, 1990]; variable permeability and
soil moisture content [Gomez-Lahoz etal., 1991]; system geometry [Rodriguez-Maroto etal, 1991]; and
spatially variant permeability [Roberts and Wilson, 1993]. Other modifications to this model have enabled
the consideration of: rate limited mass transfer from fractured bedrock [Wilson, 1990] or areas of low
permeability [Rodriguez-Maroto and Wilson, 1991; Osejo and Wilson, 1991]; Raoult's Law behavior of
organic contaminant mixtures [Kayano and Wilson, 1992]; and departures from Darcy's Law [Clarke et al.,
1993]. Other models coupling steady state flow fields and numerical transport solutions have been extended
to include complexities introduced by soil heterogeneities [Baehr etal., 1989; Benson etal., 1993; Joss,
1993].
Several numerical models incorporating transient single phase gas flow and constituent transport have
been developed. Two dimensional finite element models with transport of a single volatile organic species
have been developed [Metcalfand Farquhar, 1987; Stephanotos, 1988]. More complex one dimensional
models encompassing single phase gas flow have been developed for analysis of nonequilibrium interphase
-------
exchange [Brtisseau, 1991; Armstrong etal., 1994] and multicomponent, nonisothermal conditions
[Lingineni and Dhir, 1992]. A one dimensional model developed by Gierke et al. [1990] includes both
mobile gas and mobile aqueous phases. A two dimensional numerical model incorporating transient single
phase gas flow and multi component compositional transport was developed by Rath/elder et al. [1991].
Nonequilibrium mass transfer was also explored.
Few models have appeared in the literature which can simulate multiphase flow, including gas and
aqueous phase advection, multicomponent transport, and interphase mass exchange [Abriola, 1984, 1988;
Abriola and Finder, 1985];. A two phase (air-water) two dimensional finite element simulator was
presented by Stephamatos [1988] for the transport of a single volatile organic species. Baehr et al. [1989]
presented a one dimensional multicomponent transport model which could predict vapor flux in a three
phase (air-NAPL-water) system. Both of these models assumed equilibrium mass transfer between phases.
Several more advanced models incorporate the effects of rate limited interphase mass exchange [Reeves
and Abriola, 1988, 1994; Sleep andSykes, 1989; Falta etal., 1989], however, these models have not been
extensively applied to SVE. Additionally, none of these models incorporates biotransformations of
contaminants.
Existing models capable of simulating bioremediation processes have focused primarily on
transformations and transport in the saturated zone [e.g. Chiang et al., 1989]. For saturated transport
models which incorporate microbial growth and transport and uptake of contaminants, nutrients, and
electron acceptors, two general approaches have been used to represent microbial activity. In the first
approach kinetic expressions describing the microbial consumption of a component are incorporated
directly into the transport equation as a macroscopic sink term [e.g. Sykes etal., 1982; Borden and Bedient,
1986; Frind et al., 1990; Sleep and Sykes, 1991]. Here the bulk phase concentration of a component
controls microbial consumption. In the second approach, the potential for diffusion limited transport to the
biophase is accounted for by employing a macroscopic Pick's Law expression to represent the sink term
[Molzetal., 1986; Widdowsonetal., 1988; Baveye and Valocchi, 1989; Kinzelbach et al, 1991; Chen etal,
1992]. Of the models presented above, only Chen etal, [1992] includes interphase mass transfer and
transport within the gas phase. However, in this model, equilibrium interphase partitioning is assumed,
residual NAPL is not considered, and transport in the gas phase is by diffusion only. The model of Sleep
andSykes [1991] includes advective flow of three fluid phases, however, no mass transfer limitations are
considered, including mass transfer to the biophase.
1.3 MODEL FEATURES
A review of the relevant literature indicates that SVE/BV performance is influenced by a variety of
interrelated and spatially dependent physical, chemical, and biological processes. It points to the need for a
flexible simulator which can accommodate multiphase multicomponent transport and potential mass
transfer limitations. Such a model must link microbial degradation with a microbial population and
availability of substrates, electron acceptor, and nutrients.
The overall objective of this project is the development of a comprehensive numerical model for the
simulation of multiphase flow, compositional transport, and biodegradation processes, occurring primarily
in SVE and BV systems. Features in MISER include:
• the simulation of both cross sectional x-z and axisymmetric r-z domains;
-------
• the ability to simulate the simultaneous flow of aqueous and gas phases resulting from natural and
induced processes, such as: applied stresses at vadose zone extraction/injection wells, natural and
artificial moisture infiltration, and density driven gas phase advection;
• the simulation of multicomponent transport processes including multicomponent organic substrates, an
electron acceptor, and a limiting nutrient;
• the incorporation of rate limited interphase exchange including processes of volatilization, dissolution,
sorption, and biophase uptake; and
• the simulation of multicomponent biodegradation kinetics and microbial population dynamics.
While MISER has the capability to consider both the unsaturated and saturated zones, it is not designed
to simulate remediation processes primarily directed at the saturated zone such as pump and treat or air
sparging. MISER is also not capable of simulating organic liquid migration nor is hysteresis considered in
the movement of the gas and aqueous phases. MISER is designed to simulate aerobic microbial processes
by a single population which can metabolize multiple substrates.
-------
Section 2
MODEL FORMULATION AND THEORETICAL
DEVELOPMENT
2.1 CONCEPTUAL MODEL
The following conceptual model is formulated and used as the framework for development of MISER.
Three fluid phases are modeled: (1) an entrapped organic liquid; (2) a mobile gas phase; and (3) a
mobile aqueous phase. Because the organic liquid is assumed to be immobile, only the chemical and
physical processes affecting the disappearance of the entrapped organic are modeled in this approach. The
initial spatial distribution and composition of residual organic liquid are user defined inputs. The gas and
aqueous phases are considered mobile and can flow simultaneously in response to applied stresses at
extraction/injection wells, and to density gradients arising from spatial variation in phase composition.
A compositional modeling approach is employed. The transport and transformation of the following
chemical species are modeled: the components comprising the organic liquid contaminant; one electron
acceptor (oxygen); nitrogen (the major component of air); water (including water vapor); and one limiting
nutrient (e.g. ammonia). A schematic of the conceptualized composition of the soil system is shown in
Figure 2.1.
The organic liquid contaminant is considered as a mixture of y components. Partitioning of gas and
aqueous phase constituents into the organic liquid is assumed negligible. The composition of the organic
liquid can vary in space and time due to mass exchange into adjacent phases. The components of the
organic liquid may dissolve into the aqueous phase, but are assumed to be sparingly soluble. This
assumption is valid for a wide variety of organic components at typical environmental conditions
[Scliwanenbach etal., 1993]. Oxygen and the limiting nutrient may also partition into the aqueous phase.
Based upon available laboratory information, it is assumed that the microbes can metabolize only from the
aqueous phase. To account for possible rate limited uptake by the microbes, the biophase is envisioned as a
subset of the aqueous phase as depicted in Figure 2.1. The gas phase is assumed to be comprised of
nitrogen and oxygen (i.e. the two major components of air), water vapor, the volatile components of the
entrapped organic liquid, and the limiting nutrient. Water vapor is included so that drying effects caused by
the application of S V, can be predicted. Although carbon dioxide has been monitored as an indicator of
biological activity [Dupont et al, 1991], this component is not modeled due to the complex geochemical
considerations which impact the concentration of carbon dioxide in a soil systems. Sorption to the solid
phase is limited to components of the organic liquid.
Mass transfer expressions are incorporated into the model to simulate rate limited mass exchange
between phases. These expressions are used to model volatilization and dissolution of the entrapped
organic liquid, mass exchange between the aqueous and gas phases, rate limited sorption, and rate limited
transport to the biophase. This modeling approach is schematically illustrated in Figure 2.2.
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gas phase
nitrogen
oxygen
water vapor
NAPL components
limiting nutrient
organic phase (NAPL)
NAPL components
— ass&ssa-
solid phase
NAPL components
^ attached
micro-colonies
water
organic substrates
oxygen
limiting nutrient
aqueous phase
water
NAPL components
oxygen
limiting nutrient
Figure 2.1: Conceptual model of the soil system composition.
The conceptual distribution of fluids in the soil system is shown in Figure 2.1 and is based on following
assumptions: water is the preferential wetting fluid; gas is always the non-wetting fluid; and the organic
liquid has intermediate wettability [Mercer and Cohen, 1990; Wilson, 1992]. Complete drying of the
aqueous phase is not considered. Thus, the soil grains remain in continuous contact with the aqueous
phase. Correspondingly, solid phase sorption occurs only through the aqueous phase. Adsorption from the
vapor phase, which can be significant in dry systems [Pennell et al, 1992], is neglected.
Quantification of the biotransformation processes follows the conceptual approach of Chen et al.
[1992]. Biodegradation is assumed to occur only within the aqueous phase by an indigenous, spatially
homogeneous, mixed microbial population which is present as attached microcolonies. Monod-type kinetic
expressions are used to model biophase utilization of substrates, electron acceptor, and limiting nutrient, as
well as growth of the microbial population. Under zero substrate conditions, the microbes are not permitted
to die off completely, but are maintained at a minimum concentration representative of the background
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Phase Interrelationships
organic components,
oxygen, limiting
nutrient, biomass
organic components
Solid Phase
Aqueous Phase
VOLATILIZATION / DISSOLUTION
SORPTION
organic components,
water, oxygen, limiting
nutrient
DISSOLUTION
Gas Phase
organic components,
oxygen, nitrogen,
limiting nutrient
organic components
VOLATILIZATION
Figure 2.2: Conceptual model of interphase mass transfer pathways.
microorganism populations that are found in nearly all vadose zone environments. It is further assumed that
biomass growth does not affect soil permeability and that there is no biomass transport. These two
assumptions are consistent with the dominant influence of gas phase mobility during SVE and BV
remediation, as well as the generally low mobility of the aqueous phase in the vadose zone. Due to the large
number of required microbial transformation parameters, the number of biodegradable components is
limited to three. A detailed discussion of many of the concepts mentioned above can be found in Brock et
at. [1984].
10
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Interphase partitioning and biological degradation processes are strongly temperature dependent. The
prediction of transient temperature effects requires the solution of an energy balance equation, which
substantially increases model complexity and computational requirements. To limit model complexity and
computational requirements, temperature dependence is incorporated in the SVE simulator by the
specification of a known (steady state) spatial distribution of temperature. This nonuniform temperature
distribution is allowed to be a function of depth only.
2.2 PHASE MASS BALANCE EQUATIONS
Description of multiphase fluid movement is based on the numerical solution of phase mass balance
expressions (i.e., flow equations). A general mass balance equation for a fluid phase, a, which is composed
of multiple components, c, is expressed as [Abriola, 1989],
9
VI i *c T7- \ i v^ V^ F* i V^ D*
• I (DO , Jni V nl — 0 7 7 Hi ,a + / tf
\rrct a a; v / ^ / , ap'c / j ac
(2.1)
where:
a = g,a, o, s, b
denotes the phases comprising the porous medium (g=gas, a=aqueous, o=NAPL;
5=solid; &=biophase);
c denotes components of the phase a;
(j) is the matrix porosity [-];
p* is the mass density of phase a. [ML~3];
8^ is the saturation of phase a [-];
Va is the pore velocity of the phase a[LT~1];
is the rate of interphase mass transfer of component c to the a -phase from the ft
phase, per unit pore volume; [ML~3T~1];.
is the net rate of biological transformation of component c in the phase a per unit
aquifer volume [ML~3r~!]; and
Ra are the internal source/sinks of phase a - volume of a. phase produced per unit
aquifer volume per unit time IT""1].
E*p
B*
The fluid saturations in (2.1) are subject to the constraint,
Sa + S0
Sg =
(2.2)
Note that Sb is neglected in 2.2. This is a consequence of the assumption that biomass growth does not
affect the flow field. For mass balance purposes Sb is included in Sa.
The phase velocity is typically evaluated with an extended form of Darcy's Law which accounts for the
simultaneous flow of more than one fluid [Abriola, 1989],
qa = SaVa = -k- (VP« - p*ag) = -\a
(2.3)
where:
11
-------
A* =
qa is the specific discharge of phase a [LT *];
k is the intrinsic permeability tensor of the medium [L2];
kra is the relative permeability of the a phase [-];
Ha is the a phase dynamic viscosity [ML"1 T~1];
Pa is the a phase pressure [ML"1 T~2];
p is the gravitational acceleration vector [LT~2]; and
:^* is the mobility tensor of phase a [M"1 L3T].
Darcy's Law is applicable when average water and gas velocities are within an accepted laminar flow
range. For groundwater flow the upper range of validity is generally not violated except for possibly near
wells [Bear, 1972]. Similarly, gas fluxes generated in SVE systems are known to diminish fdpidly at short
distances from the extraction well and are generally within the upper range for laminar flow [Cho and
DiGiulio, 1992; Beckett and Huntley, 1994]. Gas phase velocities are therefore also assumed to be within
the upper range of validity, or that deviations are localized near the extraction well.
The lower range of validity of Darcy's Law becomes significant for gas flow when the mean free path
approaches the diameter of the pores resulting in a gas slippage which increases the effective gas
conductivity. Klinkenberg [1941] observed that gas permeability decreases with increasing pressure until it
approaches the liquid permeability. Slip flow, which is also known as the Klinkenberg effect in porous
media, is most significant at low air pressure in fine textured material [Corey, 1986]. Comprehensive error
analyses have been conducted by several researchers [Massmann, 1989; McWhorter, 1990; Baehr and Huh,
1991 ] and all have found that the Klinkenberg effect is significant only in fine sands and silts at low
pressures. However, a Klinkenberg correction factor which accounts for the pressure influence on gas
permeability is included in MISER for two reasons: first SVE systems are being increasingly applied in
fine textured materials; and secondly implementation of the correction is relatively simple with minimal
effect on overall computational requirements. The correction factor has the form,
(2.4)
where:
2
is the effective gas phase permeability [L2];
is the gas phase permeability at a high pressure and is equivalent to the liquid permeability
[L2]; and
b is a parameter of the porous medium referred to as the Klinkenberg parameter [M L T ].
An empirical relation for b was developed by Held et al. [1950],
b = (3.98 x 10~5)fc-°-39
(2.5)
where b is in atmospheres and fcoo is in cm2. This correlation is based on experimental measurements of air
permeability in consolidated soils of 11 synthetic cores and 164 natural cores from various oil fields in the
12
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United States. Abu-El-Sha'r [1993] measured air permeability in a variety of unconsolidated soils and
compared them with predicted values from (2.5). He found that measured values of b from unconsolidated
soils were generally within the envelope containing the measurements of Held et al. [1950], with the
exception of an Ottawa sand which was slightly greater than the upper limits. This finding is consistent
with an analysis by Baehr and Hult [1991 ]. These researchers conclude that the correlation of Held et al
[1950] may underestimate b for some unconsolidated soils, but in general can be used to approximate the
Klinkenberg effect over a range of soil types.
Substituting Darcy's Law (2.3) into (2.1), the aqueous and gas phase mass balance equations are
expressed as,
d_
~ai
- (faZSa) - V • [p*\u (VPa -
a=a,g
(2.6)
where E* = ]TC ^ E*pf. Here it has also been assumed that biodegradation of the organic components
has no appreciable effect on the aqueous flow field. These constituents comprise a small fraction of the
aqueous phase mass and the rate of their biodegradation is comparatively slow.
Changes in the NAPL saturation result solely from interphase mass transfer processes because the
NAPL is assumed to be immobile and there are no internal sources and sinks of organic liquid. The NAPL
mass balance equation is thus expressed as,
ts,) =£,
(2.7)
Changes in the solid phase bulk density due to sorption and desorption are considered negligible and
ignored. Also, the biophase volume is considered constant with the same properties as the aqueous phase.
Therefore, phase mass balances are not required for the solid and biophases.
2.3 COMPONENT MASS BALANCE EQUATIONS
A general mass balance equation of component c within phase a. (i.e. transport equation) is expressed as,
where:
Cac is the mass concentration of component c in phase a [ML~3];
J%c is the mass flux of component c in phase a by kinematic dispersion [ML~2T~1]; and
J™ is the mass flux of component c in phase a by molecular diffusion [ML~2T~1].
The dispersive and diffusive mass fluxes are typically combined and expressed in a Fickian form, e.g.
(2.9)
13
-------
where JDJJC is the hydrodynamic dispersion tensor of component c in phase a [L2T ']. The validity of the
Fickian approach for gas transport in the subsurface was rigorously studied by Fen [1993] through
comparisons with a dusty gas model. The latter model is considered to be more general because it
integrates a number of flux mechanisms for multicomponent gas transport which are not captured in the
Fickian approach. Fen [1993] found the Fickian approach is generally valid when advection is the
dominant mass flux mechanism. In systems where diffusive fluxes are significant the Fickian approach
coupled with the flow equations was found to inaccurately represent induced pressure gradients due to
nonequimolar effects. Errors were found to be reduced when the mass balance equations were expressed in
molar form, and when the organic contaminants were of low volatility or their molecular weights were
similar to the ambient gases.
Dispersive and diffusive mass fluxes are evaluated in MISER with the Fickian approach expressed by
(2.9). This approach is used for several reasons. The Fickian approach is simpler and more expedient to use
because the dusty gas model is conceptually complex and numerically difficult to implement. Secondly,
advective fluxes of equal magnitude to diffusive fluxes are obtained from very small pressure gradients
[Thorstenson and Pollock, 1989]. Thus, advection dominance can be reasonably expected throughout a
majority of the domain during SVE/BV operations in typical systems. Diffusive fluxes are expected to
become significant only at large distances from the extraction/injection wells, in tight formations, or during
shut down periods.
To reduce possible errors in the modeling of nonequimolar fluxes in regions of diffusion dominance,
the component mass balance equations are converted to molar form [Fen, 1993]. Mass concentration may
be expanded as,
Cac = paMcxac (2.10)
where pa is the phase molar density [mole L~3]. Substituting (2.9) and (2.10) into (2.8), and defining
McEai = £0 E%p and McBUc = E/? B*pc, the general molar based transport equation is expressed as,
—
• (t>Sa (paxacVa -
= (/>Eac + B
ac
(2.11)
where:
B,
Cte
is the mole fraction of component c in phase a [-];
is the net rate of moles of component c transferred to the a phase from all contiguous
phases per unit pore volume [mole L~^T~1]; and
is the net rate of biological transformation of moles of component c in phase a per unit
aquifer volume [mole L~3T-1].
The component mole fractions in (2.11) are subject to the constraint,
(2.12)
Five equations of the form (2.11) are developed for each component - one for each fluid phase, one for the
solid phase, and one for the biophase.
Constituents of the gas and aqueous phases are subject to transport by advective and dispersive
processes. Constituents of the aqueous phase may also be subject to biotransformation when a separate
14
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biophase is not considered. The constituent mass balance equations for these phases are expressed as,
—WSgpgXgJ
V •
(pgxgi.Vg -
8_
a7
O2, A
c = y, 02, A
(2.1 3a)
(2.13b)
where the denoted components are: y = organic liquid constituents; w = water or water vapor; Oi =
oxygen; A = nutrient. Note that constituent mass balance equations are not needed for nitrogen (N2~) in the
gas phase and water in the aqueous phase due to use of the mole fraction constraint (2.12).
Constituents in the organic phase, solid phase, and biophase are not subject to transport by advection. It
is further assumed that diffusion in these phases is negligible. Diffusion in the organic liquid is restricted by
the assumed disconnected nature of entrapped residuals. In the solid phase, surface diffusion of sorbed
components is considered negligible. The transport equations for the organic and solid phases are then
given by:
<\
= 4>E0t c = y (2.14)
a_
~di
d_
a?
c = y
(2.15)
where a)sc is the sorbed mass of component c per mass of soil, and p* is the bulk solid phase mass density.
Diffusion is similarly neglected in the biophase because the constituent distribution is assumed to be
dominated by exchange with the aqueous phase and by biotransformation. Due to difficulties in calculating
the molar density of subsurface microorganisms, the biophase density is assumed to be equal to the aqueous
phase molar density. The transport equation for the biophase is,
d_
Tt
= Ebc + Bbc
= Y, O2, A
(2.16)
where Sb is the biophase saturation. Since aqueous flow is assumed to be unaffected by biomass growth, Sb
is considered constant, representing the fraction of pore volume suitable to microbial growth. It is evaluated
by,
-^
(2.17)
P*a
where Xmax [M L 5} is the maximum biomass concentration.
2.4 INTERPHASE MASS TRANSFER
2.4.1 Equilibrium Partitioning
In the absence of phase partitioning rate data the local equilibrium assumption (LEA) has been employed in
SVE models to simplify the description of phase partitioning. The LEA enables the use of partition
coefficients to relate constituent phase concentrations. These partitioning coefficients are typically
developed under the assumption of ideal fluid behavior. Detailed developments of the partition coefficients
are found in: Lyman et al. [1982]; Baehr [1984]; and Schwarzenbach et al. [1993].
15
-------
Equilibrium partitioning between the organic and gas phases is expressed with Raoult's Law, which
states,
P,, = Yo,x0rP^ (2.18)
where:
is the partial pressure of the component c
~ ' ~2
T~2];
y0f is the activity coefficient of component c in the organic phase [-]; and
PV(, is the vapor pressure of component c as a pure substance [ML~1T~2].
The activity coefficient is a relative measure of nonideal behavior due to interactions of dissimilar
molecules. Ideal behavior of the organic phase (i.e. y0c = 1) can be readily assumed for pure NAPLs and
many common mixtures of hydrocarbons which are composed of chemically similar components (e.g.
gasoline and petroleum hydrocarbons) [Baehr, 1984; Schwarzenbach et al., 1993; Adenekan et
-------
which can be expanded as,
Pi,. =•
(2.24)
Equation (2.24) is a statement of Henry's Law where KH = PVc/x™} is the Henry's Law constant. There is
substantial evidence that KH is unaffected by solute-solute interactions for slightly, or even, moderately
soluble organic compounds [Schwarzenbachetal, 1993].
Equilibrium sorption capacity is commonly related to the aqueous concentration by a Freundlich
isotherm [Weber et al, 1991],
where:
Kfa
(2-25)
is the aqueous/solid equilibrium partition coefficient [(mass adsorbed / mass soil) / (mass
solute / volume solution)]" [(Z^M"1)")]; and
n is an empirically derived constant [-].
In the case where n = 1, a retardation factor may be defined as,
/ n* W \
/1+p^\
(2.26)
where rc is then inserted directly into (2.1 1) for the aqueous phase,
— (rcSapaxac) + V • (j)Sa
at
ac = Eac
(2.27)
Sorption is assumed to be both linear and at equilibrium when using retardation for a given component, c.
Retardation can be considered for all the components of the aqueous phase.
In the absence of measured data, AT® 'can be estimated from commonly used correlations with the soil
organic content [Lyman, 1982],
y& sc f f //-> oo\
Ksac — 7T~ — it-ocjoc (2.2S)
where:
Koc is the organic carbon - normalized partition coefficient (mass sorbed / (mass organic
carbon) / (mass) / volume solution); and
foe is the fraction of organic carbon in the soil [-].
Additionally, n = 1 is assumed when this correlation is used.
2.4.2 Rate Limited Interphase Mass Transfer
Nonequilibrium interphase mass transfer processes are often represented by the dual resistance model
[Weber and DiGiano, 1996]. This model assumes: (1) mass transfer is controlled by the rate of diffusion on
each side of the interface, and (2) no resistance is encountered at the interface. The diffusional resistance on
17
-------
one side of the interface is frequently considered dominant such that the mass transfer rate can be described
with an overall mass transfer coefficient [Weber and DiGiano, 1996}. Generally, use of overall mass
transfer coefficients are strictly applicable for the measured system only and should, be extended to other
systems with caution.
The rate of organic phase volatilization is assumed, to be controlled by gas phase resistance, and is
evaluated with a linear driving force expression [Weber and DiGiano, 1996],
ES°c —
c \xgoc ~ X8c)
(2.29)
where:
Kgo<. is the lumped gas-organic mass transfer coefficient [T !]; and
xca is the gas phase mole fraction of component c in equilibrium with the prganic phase mole
fraction of component c [-].
The lumped mass transfer coefficient is a function of the fluid saturation, phase velocity, and properties of
the porous media. It can be expressed as,
Ken =ke,.aeo (2-30)
where:
is the overall mass transfer coefficient based on gas phase control (moles transferred /
(time)(interfacial contact area)(Apgx)) [LT~1]; and
a
go is the gas phase specific contact area with the organic phase (gas-organic interfacial contact
area / pore volume) [L~ l ] .
The linear driving force model is completed by relating the equilibrium gas phase mole fraction of
component c in (2.29) with the corresponding organic phase mole fraction concentration by (2.21),
(2.31)
A similar linear driving force model is used for the rate of nonequilibrium organic phase dissolution. In
this case, the mass transfer resistance is assumed to be contained within the aqueous phase. Equation (2.22)
completes the expression by relating the equilibrium aqueous phase mole fraction of component c to the
corresponding organic phase mole fraction,
Ean, —
(2.32)
Mass transfer across the aqueous-gas interface is commonly assumed to be controlled by resistance in
the aqueous phase. This assumption is generally valid for sparingly soluble organic compounds, however,
gas phase resistance becomes more significant for moderately soluble compounds [Munz and Roberts,
1984; Roberts et al, 1985]. The aqueous/gas transfer term is expressed as,
x"
0
(2.33)
18
-------
Here the equilibrium aqueous phase mole fraction of component c is related to the corresponding gas phase
mole fraction with (2.23).
The rate of mass transfer between the aqueous and solid phases is also assumed to be controlled by
resistance in the aqueous phase,
(2.34)
where x%s . is the aqueous phase mole fraction in equilibrium with the solid phase loading as computed by
(2.25).
Rate limited mass transfer into the biophase is assumed to occur through an immobile liquid film
adjacent to the biomass. Diffusional mass transfer resistance into the biophase can be represented with,
Eabc = PaKabc (xbc ~ -V) (2.35)
where Kabc is a lumped biophase/aqueous phase mass exchange coefficient for component c.
2.4.3 Biotransformations
The biodegradation module of MISER can model up to six spatially heterogeneous variables; three
biodegradable organic substrates (contaminants), oxygen as the electron acceptor, a limiting nutrient, and
the biomass. Monod-type kinetics are used to describe the microbial consumption and growth processes.
s approach assumes that the conversion of contaminant into biomass is not instantaneous. Additionally,
icrobial activity may be limited by the diffusional mass transfer resistance described with (2.35) above. In
is approach biotransformation is coupled to the aqueous phase component balance equations (2.13b), by
e exchange term Eabc.
microbial activity may be limited by the diffusional mass
this approach biotransfo
the exchange term Eabc.
No mass transfer resistance internal to the biophase is considered due to a lack of information and the
difficulty in determining the additional parameters needed to represent such processes. The biophase mole
fraction profiles of the contaminants, oxygen and the limiting nutrient are therefore assumed to be uniform
within the biophase. This assumption is based on two concepts. First, that microbial populations in the
subsurface are generally low and hence that microcolonies can be modeled as fully penetrated biofilms.
Secondly, that microbial kinetics within the biofilm are fast relative to the time scales of the physical
processes in bioventing and thus biophase concentration profiles can be considered to be at "pseudo-steady
state" during a time step. By assuming a uniform concentration within the biophase (i.e. a fully penetrated
biofilm or a quasi steady state consumption of the substrate /) the mass transfer expression (2.35) can be
related to biophase utilization by a Monod-type kinetics expression [Williamson andMcCarty, 1976] as,
— (Sbpaxbc) =
at
c - FdkiX
(2.36)
where:
Fci is the use coefficient of component c with substrate / degradation [(mole c)(mass /)~1],
Fci = Mc~l when c — I. Note that Fci is input in units of gm c/gm / and is converted
internally;
ki is the maximum specific substrate utilization rate of substrate / [(mass /)(biomass 71)"1];
X is the active biomass concentration [ML~3] expressed on a media volume basis;
19
-------
Kst is the half-saturation coefficient of component / [(mole /)(mole biophase) *]. Note that
KSI is input in units of gm //liter and is converted internally;
// is a substrate inhibition function described below [-];
/02 is an oxygen inhibition function described below [-];
I A is a nutrient inhibition function described below [-]; and
Is is a saturation inhibition function described below [-].
When c = Oz or A, the Monod expression on the right hand side of (2.36) must be summed over all the
substrates, /. Equations of the form (2.36) comprise a system of coupled nonlinear equations.
A second approach used to model biodegradation is to assume that constituents in the aqueous and
biophases are in equilibrium. The biotransformation sinks are then directly inserted into the aqueous phase
component balance equations (2.l3b) using,
Bac = -
(2.37)
Because the organic substrates may potentially have inhibitory effects on biodegradation at high
concentrations [Speitel and Alley, 1991; Huesemann and Moore, 1994; Mu and Scow, 1994], equations
(2.36) and (2.37) are modified to include inhibition kinetics. The following expressions for inhibition are
currently used,
/i = 1 -
1 -
XI
..max
Xl .
(2.38)
where x"tin represents the minimum detectable mole fraction of / (currently 1 ppb on a mass basis) and
xfax is the inhibitory mole fraction of substrate /. In the presence of several substrates, inhibition may be a
function of the total substrate mole fraction. In this case, xi in (2.38) is the sum of all the substrate mole
fractions. Jtf"'" remains the same and x™ax can have different values for each substrate. Equation (2.38) is
also used to represent nutrient inhibition by replacing / with A and setting xfn = 0.
Microbial activity is assumed to be restricted by a threshold oxygen concentration below which aerobic
metabolism ceases. This effect is modeled with an inhibition function of the form,
I
-------
Both the equilibrium and nonequilibrium descriptions of biotransformation discussed above require
additional expressions describing the growth and decay of the attached biomass. Here, an ordinary
differential equation based on Monod kinetics is used,
dX
~dt
where:
&02
Kso2 + xb
02
KSA + xbA
X
(2.41)
is the biomass yield coefficient for the metabolism of substrate / [(biomass)(mole /)"'].
Note that F/ is input in units of (biomass)(gm /)"' and is converted internally;
is the microorganism decay coefficient [T ];
is a function which prevents the biomass from exceeding a maximum concentration given
by,
(2.42)
Xmax is the maximum allowable biomass concentration
Imin is a function which maintains a minimum concentration reflecting the indigenous
population present in uncontaminated subsurface environments,
Imin = (1 ^- } ; and
V A /
X/n;n is the background or indigenous concentration of biomass.
(2.43)
The detachment or sloughing of the attached biofilm is not considered in this equation due to a lack of
information regarding the necessary parameters to model this process.
2.5 CONSTITUTIVE RELATIONS
2.5.1 Capillary Pressure
Capillary pressure is defined as,
P — P — P
* c. — I nw in.
(2.44)
where Pnw and Pw are the phase pressure in the non-wetting and wetting fluids, respectively. In soil
systems containing only two fluid phases (e.g. gas and aqueous), capillary pressure data is routinely
measured and related to fluid saturation. A common fitting function for such two phase gas-aqueous
capillary retention data was developed by van Genuchten [1980],
(2.45)
where:
21
-------
Sa = sf fr is the normalized aqueous saturation [-];
1—-Vo
Sra is the residual aqueous saturation [-];
asa fitting variable [LT2M~' ]; and
n, ;n = 1 — 1/n are additional fitting variables [-].
Here, the wetting fluid is the aqueous phase and gas phase is the nonwetting fluid.
In contrast to two phase systems, capillary pressure behavior in a porous medium containing three fluid
phases (gas, aqueous, and organic) is difficult to measure. Consequently, three phase behavior is typically
estimated from two phase capillary pressure data. A parametric model developed by Parker et al. [1987] is
frequently used to estimate three phase capillary pressure. This model assumes the aqueous phase is the
preferential wetting fluid, gas is the nonwetting fluid, and the organic phase retains intermediate wettability
and completely separates the gas and aqueous phases. Thus, gas-aqueous interfaces do not occur in the
three phase system. Under such conditions the two phase organic-aqueous relation is assumed to control
the aqueous phase saturation, and the two phase gas-organic relation is assumed to control the total liquid
saturation regardless of the proportion of aqueous and organic liquids. Extensions of the three phase
estimation model have been developed for hysteretic behavior and capillary entrapment of organic liquid
and gas \Kaluarachchi and Parker, 1992].
The parametric model described above is mathematically expedient, but requires the explicit evaluation
of an organic liquid pressure. Tracking the pressure of an organic liquid which is assumed to be at
immobile residual saturation is a difficult prospect that is complicated by limitations of the three phase
parameteric model. The parametric model predicts organic liquid entrapment by the water phase, but not by
the gas phase. Thus, evaluation of the residual organic liquid pressure is uncertain in a system containing
residual water, and can only be exacerbated by the effects of volatilization from the organic phase . The
parametric model also predicts a discontinuity in capillary pressure due to the appearance and
disappearance of the organic phase which can potentially lead to numerical difficulties. Lastly, the
assumption that the organic phase completely partitions the gas and aqueous phases may be invalid for
nonspreading organic liquids [McBride etai, 1992; Wilson, 1992], leading to further difficulties in the
tracking of organic liquid pressures.
Due to the conceptual difficulty of tracking the pressure of an organic liquid which is assumed to be at
immobile residual saturation, MISER assumes that all capillary behavior is independent of the organic
liquid pressure. The aqueous phase saturation is related to the two phase gas-aqueous capillary pressure
data (2.45), regardless of the proportion of aqueous and organic phase, or the spreading characteristic of the
organic phase. Hysteretic behavior in this relation is also neglected. Under this assumption of effects of air
entrapment on fluid distribution is neglected. While these effects may be significant under some conditions,
neglecting hysteretic behavior due to air entrapment should not pose a significant limitation in modeling
field scale SVE/BV systems due the typically large uncertainty in quantifying distributed capillary and
relative permeability parameters.
With the assumptions described above, eq. (2.45) is used to determine aqueous saturation from
predicted gas and aqueous pressures. Subsequently, gas phase saturation is calculated from (2.2). In the
case when the total liquid saturation is greater than one, then Sg is set to zero and Sa = 1 — $„.
22
-------
2.5.2 Relative Permeability
Relative permeability expressions for the three phase system are obtained from the model of Parker et al.
[1987]. This model employs correlations developed by Mualem [1976] to relate effective permeability with
Pc (5) data. The functional forms for the aqueous and gas phases are,
L. — ~c1/2n _ n ~?l/
-ra — oa U U — Ja
(2.46a)
(2.46b)
where St = Sa + S0. Because the organic phase is assumed immobile throughout SVE operations,
kro = 0 (2.47)
As discussed above, hysteretic behavior in the relative permeability relations due to gas entrapment is
neglected.
2.5.3 Gas phase density
At common environmental conditions (0-50 °C, & I atm.), the gas phase molar density can be accurately
estimated with the ideal gas law [Lyman, 1982],
_Pg_
- RT
(2.48)
The gas phase mass density is then given by,
(2.49)
2.5.4 Liquid Phase Density
Compressibility of the aqueous and organic phases is considered negligible for environmental pressures
expected during typical venting operations. Liquid density is computed as a function of composition and
temperature.
The molar density of liquid mixtures at constant temperature and pressure is estimated with Amagat's
Law [Reid et al., 1977],
P« =
(2.50)
where p* is the mass density of pure component c at the mixture temperature [ML~3]. Amagat's Law
assumes the volumes of the mixture components are additive. This assumption is valid for mixtures of
similar components which are at low to moderate pressures and temperatures not close to the critical point
of the mixture. These conditions are readily met for common organic contaminants in typical
environmental settings.
23
-------
2.5.5 Gas phase viscosity
Gas viscosity is independent of pressures at the relatively low pressure encountered in environmental
settings (below 10 atmospheres) [Welty et al., 1984]. Under these conditions the gas phase mixture viscosity
can be estimated as a function of composition using the semi-empirical formula [Reid et al., 1977],
V-R = V, T-/fe^l (2.51 a)
(2.5 Ib)
where fjLc and IJL ; are the viscosity of components c and j in the pure state at the system temperature.
2.5.6 Aqueous Phase Viscosity
The aqueous phase viscosity is assumed to be independent of composition and pressure. For steady state
temperature conditions the aqueous phase viscosity is constant in time.
2.5.7 Hydrodynamic Dispersion
Dispersive fluxes are assumed to be significant in the mobile aqueous and gas phases only; diffusion within
the immobile NAPL and biophase is neglected, as is surface diffusion within the solid phase. A traditional
groundwater modeling approach is used in applying Pick's Law to evaluate combined processes of
mechanical dispersion and molecular diffusion. For an isotropic medium the dispersion tensor is evaluated
by [Bear, 1972],
= cti\qa\Ski + (SaTaD™f&L.T (2.52)
LT
via \
where:
-------
2.5.8 Matrix Compressibility
Changes in the soil porosity are assumed to be negligible under pressure changes induced in typical
SVE/BV systems. Thus,
JP =°
(2.54)
25
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Section 3
NUMERICAL DEVELOPMENT
The mathematical model of SVE/BV processes developed in the preceding section consists of a number
of coupled nonlinear partial differential equations. A numerical solution of these equations is developed
using the Galerkin finite element method. This approach is well suited for the simulation of SVE/BV
scenarios and has advantages over other methods in the ability to accurately represent boundary conditions
and source/sinks, as well as flexible discretization of irregular and heterogeneous domains. The governing
equations are solved in two space dimensions; either a cross sectional x-z domain, or an axisymmetrical r-z
domain. This section describes details of the numerical algorithm implemented in MISER.
3.1 FINITE ELEMENT APPROACH
The Galerkin finite element method has been widely used to solve groundwater flow and transport
equations. Detailed descriptions of this method are found in several reference texts (Strang and Fix, 1973;
Lapidus and Finder, 1982; Huyakorn and Finder, 1983; Zienkiewicz and Taylor, 1991].
The finite element method is based on a weighted residual technique to approximate the solution, u, of
the general differential equation represented by,
L(«) - / = 0 (3.1)
The solution domain, £2, is first discretized into a network of elements which are connected at discrete
nodal points. Within each element the dependent variable u is approximated by a trial function u,
(3.2)
J=l
where Nj are the basis functions; iij are values of the dependent variables at nodes of the element, and ne is
the number of nodes in the element. Substituting u into (3.1) results in an error or residual. This residual is
weighted and integrated over the domain, £2, developing the weighted residual equations as,
f (L(u) - /)
Jo.
= 0
(3.3)
where VV/ is an arbitrary weighting function. In the Galerkin finite element method the weighting functions
are chosen to be the basis functions. Combining (3.2) and (3.3) leads to a system of n simultaneous
equations which are solved for the all the unknowns, M,-, at the n nodes in £2.
Application of the Galerkin finite element method in MISER employs triangular elements for spatial
discretization and linear basis functions. Triangular elements are advantageous for the discretization of
irregular and heterogeneous domains. They also simplify the evaluation of integrals in the weighted
26
-------
Xi.Z,
x3.z3
X2,Z2
x,,z,
X2.Z2
L2=1
Figure 3.1 : Triangular element in global and transformed coordinates (after Lapidus and Finder, 1982).
residual equation by the use of local area coordinates. Figure 3.1 shows an arbitrary triangular element in a
two-dimensional Cartesian domain and the transformed element in local area coordinates.
Linear basis functions for triangular elements may be developed in global coordinates as [Lapidus and
Finder, 1982; Huyakorn and Finder, 1983],
(3.4)
where,
= 3*2 — w, y\ = *3 —
(3.5)
and,
j.
2'
z\
Z2
= area of the triangle
(3.6)
Transformation from the global coordinates (xy,zy) to the local area coordinates (Ly) is obtained by,
A,-
LJ = -fe (3-7)
where the subarea Ay is defined by the point of interest within a given element and the element vertices
(Figure 3.1). Since A\ + A2 + A3 = A then LI + L2 + L3 = 1.0, and it can be shown that the local
coordinate variables Ly are equivalent to the basis function Nj [Lapidus and Finder, 1982; Huyakorn and
Finder, 1983]. The advantage of using the local area coordinates is that simple integration formulas have
been developed for linear basis functions [Lapidus and Finder, 1982],
(mi + m2+m3+'2)!
2A
(3.8)
27
-------
where £2C is the domain occupied by element e. Differentiation of the basis function yields,
dx
dx 2Ae
dN, 9L,-
Yj
(3.9a)
(3.9b)
3z 9z 2Ae
After transformation to local area coordinates the weighted residual equation (3.3) can be expressed as,
= 0 (3.10)
e=l
where Ne is the number of elements in £2.
3.2 SOLUTION OF THE PHASE MASS BALANCE EQUATIONS
The aqueous and gas phase flow equations (2.6) are solved by the simultaneous solution (SS) method [Aziz
andSettari, 1979]. In this approach fluid pressures are selected as the primary dependent variable, and the
flow equations are solved simultaneously for Pa and Pg. Saturations are subsequently updated from
capillary pressure-saturation relations (2.45).
3.2.1 Pressure Based Formulation
The simultaneous solution scheme is developed by first recasting the flow equations in terms of the primary
pressure variables. The time derivatives in (2.6) are expanded as,
The first term on the right hand side (RHS) is the change in mass storage due to matrix compressibility,
which is assumed to be negligible.
The middle term represents the temporal change in phase density. Density of the aqueous phase is
assumed to depend on composition only. Moreover, the temporal change of this term is assumed to have a
minor influence on the aqueous flow field such that it can be lagged by a single time step and moved to the
RHS. The density of the gas phase, however, depends on composition and pressure. The temporal change
of gas density may be expanded as,
a r ji/f D n fl/f a D D a KA
(3.12)
8 RT dt
Similar to the aqueous phase, changes in the gas phase density due to temporal changes in composition (i.e.
the last term in (3.12)) are assumed to be small such that they can be lagged by a time step.
The last term on the RHS of (3.11) accounts for change in phase mass storage due to change in fluid
saturation. This term is expanded in terms of capillary pressure, obtaining,
P \
(3.13)
28
-------
where C,,a = dSa/dPc is the capacity coefficient. Note Cp = Cpa = dSa/dPc = -dSg/dPc.
The pressure based aqueous and gas flow equations are developed in two dimensional coordinates by
substituting (3.12) and (3.13) into (2.6), dividing through by p*, and expanding the spatial derivatives,
- Pa8x -
-^, ~
dx
-g»
dp*
dp*
-A*
dz
(3.14a)
dz
(3.14b)
where gx and gz are components of the gravitational acceleration vector. Division by the phase density is
performed to simplify the specification of boundary conditions.
3.2.2 Trial Functions and Weighted Residual Equations
Standard trial functions are employed for the primary variable, Pa, and for secondary variables p*, Ea, and
^•a» :
3
Pa(x, y, 0 -
(3.15a)
(3.15b)
(3.15c)
(3.15d)
7 = 1
Based on the work ofAbriola and Rath/elder [1993] and Rath/elder andAbriola [1994], nontraditional
finite element approaches are used in defining trial functions involving products of dependent variables and
coefficients. In this work it was found that computational efficiency and material balance properties are
29
-------
enhanced when products are expanded collectively with a single basis fimction. The following trial
functions for the terms in (3.14) are defined,
(i)Sg 3P8 ~, ^ V^ SSj dPgj ,r
RTpg dt
dt
dt
3
E
w=i
i
J — 1
y=l
(3.16a)
(3.16b)
(3,16c)
(3.16d)
(3.16e)
(3.16f)
where (j>e is the porosity in element e.
Substituting the trial functions (3.15) and (3.16) into (3.14) and applying Galerkin's method and
Green's theorem leads to the weak form of the weighted residual equations. For the aqueous and gas
phases, respectively, the weak form is expressed as,
dN;
(3.17a)
= E /ff
aj
_RTJPgj
j?j Sj_XT /-* / ffy ^j \
/p-f, a? y~ Pj\ dt dt )
dNi
30
-------
9Ni
(3.17b)
Sj
"Sj
where the summation convention is used for the repeated subscript j, Ye is the domain boundary of domain
associated with element e, and n is an outward unit normal vector.
Performing the integration over each element and assembling the resulting equations yields a global
system of time dependent ordinary differential equations with nonlinear coefficients,
[A]
+ [B] {P} = {F} + {E} + {Q}
(3.18)
where {P} is the vector of pressures at all nodes and is ordered with alternating aqueous and gas pressures,
[A] is the mass matrix, [B] is the stiffness matrix, and {F}, {E}, and {Q} are the RHS matrices. MISER
also includes an option to lump the mass matrix. Detailed development of the element matrices is given in
Appendix A.
3.2.3 Capacity Coefficients
Treatment of the capacity coefficient is based on the work ofAbriola and Rath/elder [1993] who
investigated mass balance accuracy in two-phase flow problems. They showed that finite element solution
with the SS scheme is mass conservative when the accumulation term is approximated with the
nontraditional trial function in (3.16b) and the capacity coefficient is evaluated with the standard chord
slope approximation,
0*,f+I I Of
- "' +S" (3-19)
P'c;
where k is an iteration counter. Cpi is set to a dummy minimum value (1 x 10~7) at the first iteration
(k = 1), and additionally if the calculated value of CP! is less than the minimum value.
3.3 MATERIAL PROPERTIES
The representation of heterogeneous soil properties is essential for accurate representation of field
processes. Discontinuities in soil properties produce discontinuities in dependent variables such as
saturation, mobility, and mass exchange. Since these parameters influence transport and degradation
processes, the method used to represent discontinuous material properties can influence simulation results
and interpretation. Discontinuities are typically handled by averaging adjacent, but different material
properties [Voss, 1984; Simunek et al., 1994]. This can introduce a smearing or dispersion effect that
31
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Element Properties
porosity
permeability
soil density
organic carbon
dispersiyity
tortuosity
Freundlich parameters
van Genuchten> parameters
element average velocity
media 1
S«W«IS
media 2.
Stacked Modal Properties
saturation
Interphase exchange (computed)
mobility
Domain Properties
mass transfer coefficients (input)
biological parameters
retardation-
Klinkenberg parameter
aqueous viscosity
media 3
«ffiS«»CS
media 4
Nodal Properties
pressure
mole fractions
biomass
density
gas viscosity
nodal Darcy velocity
Figure 3.2: Variable representation in MISER.
necessitates grid refinement for the accurate representation of interfaces. Such refinement, however, may
not always be possible for the simulation of large and/or strongly heterogeneous domains. MISER
incorporates a unique data structure for the representation of discontinuous properties at soil interfaces.
MISER maintains and numerically tracks discontinuous variables at material property interfaces, including:
saturation, mobility, and interphase exchange. These variables are termed 'stacked nodal variables' (Figure
3.2) because multiple values can exist at a single node. A maximum of four material property blocks may
be contiguous at a given node.
Other variables are treated as either continuous nodal properties (material independent), element
constant variables (material dependent), or domain properties (spatially invariant). Figure 3.2 identifies
variables in each group.
3.4 VELOCITY EQUATIONS
MISER includes two optional approaches for evaluating aqueous and gas phase specific discharges from
Darcy's Law (2.3). The first approach generates element wise constant fluxes by solving (2.3) directly,
(3-.20a)
(3.20b)
where:
32
-------
q^x is the element constant specific discharge of phase a in the x direction [LT~1];
q#z is the element constant specific discharge of phase a in the z direction [LT~l}\
Xeaxx is the element averaged mobility of phase a in the x direction [M~1L3T];
Xea^ is the element averaged mobility of phase a in the z direction [M~ l L3 T] ; and
pea is the element averaged phase mass density [ML~3].
The element averaged mobilities are computed from,
2-,
(3.21)
Averaging of the phase density is done in a manner that is consistent with the spatial variability of the
pressure term [Voss, 1984],
'3 l EL
•7=1 I 3z
(3.22)
The second option is the calculation of nodal specific fluxes by solving Darcy's Law (2.3) with the finite
element method. This approach eliminates discontinuities in the velocity field that are present when using
element average velocities. The use of a continuous nodal velocity field has been shown to yield significant
improvements in mass balance for the transport equation [Yeh, 1981]. After substituting the trial functions
and applying Galerkin's method to (2.3), the weighted residual equations for the aqueous phase are,
N
E
e
f q^NjNtdOT = -E
=l " e=l
Nj
?^-Pl1**Nj)WV
JV f
EI 9«w
7=1 J «e '
where the summation convention is used for the repeated subscript j.
(3.23a)
(3.23b)
For the gas phase, a modified version of (2.3) is used which is expressed in terms of the equivalent head
[Mendoza and Frind, 1990]. The weighted residual equations for the gas phase are,
N' f
5/,
Ne
(3.24a)
(3.24b)
where the summation convention is used for the repeated subscript j, p*0 is the mass density of the
uncontaminated gas phase, and the equivalent head hgj is defined by,
Pg.
h — 8j 4- 7 •
' — o* p
Additionally, nodal gas phase velocity is set to zero when the gas phase saturation is less than a user
specified value, currently set at 5%.
(3.25)
33
-------
3.5 COMPONENT MASS BALANCE EQUATIONS
The transport equations are solved in sequence [Reeves, 1993; Reeves andAbriola, 1994]. They are first
modified to eliminate the divergence of velocity which is not defined when using a linear interpolation
space to approximate the pressure field.
c) + V • Sa (paxac Va -
ac = Eac + Bac
The general form of the component balance equation from Section 2, eq. (2. 1 1) in molar form is,
r\
—
The first two terms in (3.26) are expanded using the chain rule,
f\ O
Xa—tySapd) + (j>Sapa —
at at
V - (SapaDhac V xac) = Eac + Bac
Equation (3.26) is next summed over all the components c in phase a and multiplied by xac,
(3.26)
ttc V (SapaVa) + 4>SapaVa- V (xac) -
(3.27)
= xa
Btt)
a ac • aaa ac
at
Substituting (3.28) into (3.27), the divergence in velocity term is eliminated, obtaining,
#\
— (XaJ + 4>SapaVa- V (*«,) - V •
- xac (Ea + Ba)
(3.28)
(3.29)
The nonequilibrium mass exchange terms are evaluated with the linear driving force expressions
described in the preceding chapter. These expressions have the general form,
(3.30)
where Eapc is the rate of moles of component c transferred to the a-phase from the ft phase per pore volume,
and K%p is the equilibrium phase partitioning coefficient for the a phase in contact with the /3 phase.
The nonlinear biotransformation reaction terms, Bac, are developed in detail in Section 3.6. Presently
these terms are represented by,
Bac = (Jiacxac (3.31)
where tiUe represents aMonod-type nonlinear reaction coefficient [mole L~3r~1].
The foregoing expressions are used to develop a general form of the transport equation. Substituting
(3.30) and (3.31) into (3.29) and rearranging, the general form of the transport equation is,
SaPa—(xac)
- V •
Uc I Pa ^2 Kctflc
(3.32)
34
-------
Note that the last term on the right hand side of (3.32) reflects those mass transfer terms for which the mass
transfer resistance is assumed to be present in the ft phase. In (3.32) the coefficients included in the mass
exchange terms reflect which phase controls the equilibrium partitioning and nonequilibrium mass
exchange. To simplify notation and to facilitate the development of general finite element equations, the
following lumped coefficients are defined,
— P<*
(3.33a)
(3.33b)
These terms contain the mass exchange and bioreaction information and may be different for each phase
and component. Tables 3.1 and 3.2 summarize the phase and component dependencies of these lumped
coefficients. Substituting (3.33) into (3.32), the final form of the general transport equation in molar form is,
O
—
V •
(3.34)
Equation (3.34) is used to model transport of component c in the two mobile phases. The transport
equation for the immobile phases (organic, solid, biophase) is derived directly from (3.34) by neglecting the
advective and dispersive terms, obtaining,
— (Xac) +
a — O, S, b
(3.35)
Note that for the solid phase, the principal variable is the mass loading, a>Sc, the bulk solid phase mass
density, p*, is used on the LHS in place of
-------
Component
organic
water
oxygen
nutrient
Phase pair
gas-organic
aqueous-gas
aqueous-organic
aqueous-solid
aqueous-biophase
all others
aqueous-gas
all others
aqueous-gas
aqueous-biophase
all others
aqueous-gas
aqueous-biophase
all others
Mass exchange expression ;
£:;=P!W'">
17 _ #•• / z^e v \- \
'J-'aSy — Pa^asy vjv«^ YASy ^ay)
^--M^J
Jj1 f\
\:^Kf
Table 3.1: Summary of mass transfer expressions.
After applying Green's Theorem the weak form of the weighted residual equation (3.36) is,
±dQ.e
= E /Q, 7'., NiN'dff + E /r, {*'«., A.,
"'
(3.37)
When retardation is considered in the aqueous phase, the time derivative term in (3.37) becomes,
(3.38)
Retardation may be considered for any component of the aqueous phase. When retardation is included,
nonequilibrium mass exchange to the solid phase is not allowed for any aqueous phase component.
36
-------
Phase
organic
Aqueous
Gas
Solid
Biophase
Component
organic
organic
02
water
nutrient
organic
water
nutrient
organic
organic
oxygen
nutrient
Lumped Mass Exchange and Bioreaction Terms
F°Jy =
Kay =
^ -
K002 =
~Fa02 =
J_am =
I1 I
FJY =
f£ =
FgA =
"F*
r; :
SY
Kby ' =
F_by =
£bA =
E0
-Ea0y - 4>Eg0y
Ea+ Ba+4>Pa (KaoY + Kagy + Kaby + KaSy)
*r^^ + V^, + ^r
Ea + Ba+ (t>pa \Kag02 + Kabo2) ~ f^ao2
pa (Kag02Keagofg02 + KabQ2xbo^
Ea
fiEa + Ba + 4>pa \KagA "h Kabfj — fJ,aA
Eg + (j)pgKg0
Eg
4>Eg
0
— (j)E
f^by
—Eaby
=*c
Table 3.2: Summary of lumped mass exchange and bioreaction coefficients.
Equation (3.37) applies to the mobile aqueous and gas phases. The weighted residual equations for the
immobile phases are developed from (3.37) by dropping the advective and dispersive terms. For the organic
phase the weak form of the weighted residual equation is,
(3.39)
/• f dx»c- ;— - } ^ r -
/ ^S0jp0jNj—-^Nj + K0 NjXoc NJ Nidtf = E / FOCJ NjNidQ
=\ jQ'e I at } e=\ Ja'
A similar equation can be developed for the solid phase. Note that since mass exchange is assumed to be
37
-------
negligible compared to the mass of the solid phase, E* = 0,
N' r { 9
-------
restriction applies to a single element. Over several elements a much closer approach to equilibrium
is possible with MISER (see Section 4,3.4).
2. When the organic phase is present in a given element, organic mass exchange is not considered
between the aqueous and gas phases, the aqueous and solid phases, or between the aqueous and
biophase. ,
3. Exchange into the gas phase from the organic phase is not allowed when the gas phase saturation
falls below a specified value, (currently 0.05)..
4. The exchange terms for organic phase volatilization are;adjusted downward when the predicted
exchanged component mass for an element is greater than the organic phase component mass present
in the element. The exchange terms are reduced by the ratio of the total component mass present in
the element to the original predicted component exchange mass.
5. Mass is not allowed to partition from the aqueous or gas phases into the organic phase when only one
organic component is present.
6. Oxygen mass transfer from the aqueous phase to the biophase is allowed only when the aqueous
phase oxygen mole fraction is positive.
7. Nutrient mass transfer from the aqueous phase to the biophase is only allowed when the aqueous
phase nutrient mole fraction is positive.
3.6 BIOLOGICAL REACTIONS
Biological activity is described with Monod-type kinetic expressions. As shown in Table 3.2 these
expressions can be inserted directly into the aqueous phase component transport equations or into a
separate biophase component transport equations when mass transfer rate limitations to the biomass are to
be considered. The nonlinear rate coefficient /j,ai takes three forms as follows, one form for the degradation
of organic substrates, one for the utilization of oxygen, and the last for the utilization of nutrient,
1
•or;
*-cto2
>'O
*-ctA
Biomass growth, maintenance, and decay is governed by an ordinary differential equation,
,]V / \
—77 — I 2_/ (^l^a,Xa,Imax} — ^-dlmin I X
at \ I /
(3.43b)
(3.43c)
(3.44)
In order to reduce negative mole fractions in either the biophase transport equations when considering a
separate biophase, or in the aqueous phase transport equations when they have the bioreaction term inserted
39
-------
directly, the size of the bioreaction term is limited in some cases. If the calculated bioreaction term over the
course of the current time step will consume more of the component to which it applies than is available,
the bioreaction term is reduced by the ratio of available component rnass to projected required component
mass. The available component mass is defined as the mass of component present in the appropriate phase
plus the projected amount of component to be delivered to the appropriate phase through interphase mass
exchange. Other affected bioreaction terms are also reduced. For instance, if a organic component reaction
rate is reduced, that component's contribution to oxygen and nutrient usage, as well as to biomass
production, must be accounted for. A reduction in oxygen or nutrient reaction rate affects all the organic
components and biomass production. In addition, Monod terms are zero when the corresponding
component is below a preselected minimum detectable value, currently set to 1 ppb by mass.
3.7 NAPL SATURATION
The numerical formulation is completed with an expression describing the change in organic phase
saturation. Since the organic phase is assumed to be immobile, changes in organic saturation result solely
from interphase mass transfer as indicated in (2.7). Expanding the time derivative term of this equation and
substituting the summation over the phase exchange terms as previously defined gives,
dt
dt
(3.45)
Because the organic phase is assumed to be incompressible, -jf- is strictly a function of composition.
Furthermore, since the organic phase saturation is updated after convergence of the phase compositions, the
density derivative term is known and can be moved to the right hand side along with the exchange terms,
(3.46)
(3.47)
The weighted residual equation for (3.46) is then developed as,
2* = E £ * \f0iN, - SojNj^Nj} N,
The solution of (3.47) is obtained by mass lumping the left hand side. When the organic phase consists of
only one component, the resulting finite element equation is explicit in organic phase saturation since the
density derivative term is zero. When more than one organic phase component is present, (3.47) is solved
iteratively because the organic phase saturation appears on both sides of the equation. Additionally, the
organic phase saturation is never allowed to fall below zero.
3.8 AXISYMMETRIC COORDINATES
An axisymmetric coordinate system (r-z) is simulated by multiplying the element matrices by [Huyakorn
and Finder, 1983],
27T
re = — (n + /-2 + rs) for (r-z) (3.48)
40
-------
where r/ is the radial coordinate of node /.The horizontal coordinate x is then taken to represent the radial
distance r. When simulating a cross sectional (x-z) domain, 7e is set to unity,
for (x-z)
(3.49)
3.9 TIME DISCRETIZATION
Consider the following generic finite element equation,
I- J f\ , ' t- J 1 J
A standard finite difference approach is used to discretize the time derivative in all the finite element
equations developed above [Huyakorn and Finder, 1983],
9/1,1 f,.lk+l,t+l
\ul W
(3.50)
(3.51)
where k is an iteration counter; A? is the time step; and the superscript t + I represents the t + A? time
level. A variable time weighting factor, 9, is included in MISER and is defined as,
[u}k+l't+l = 0 {u}k+l't+l + (1-6) {«}'
where 0 — 1 is used for fully implicit time stepping and 6 = 1/2 is used for Crank-Nicholson time
stepping. Substituting (3,51) and (3.52) into (3.50) yields,
(3.52)
] {u]
[A] + e[B]
To reduce potential errors due to limited computer precision, the dependent variable is expressed as a
difference over the time step, Aut+l,
= {uy
and substituting (3.54) into (3.53) yields,
-±-[A]+9[B]}
it j
= -[B] {u}1 + {F}k't+l
(3.54)
(3.55)
Equation (3.55) is not used for the calculation of the velocities when (3.23) and (3.24) are solved. In this
case difference equation (3.53) is employed.
3.10 TIME STEP CONTROL
The time discretization starts with a prescribed time step size. This time step is adjusted automatically in
accordance with the following set of rules:
1. The time step size cannot be smaller than a prescribed minimum value.
41
-------
2. The time step size cannot be larger than a prescribed maximum value.
3. During a given time step, if the number of iterations required for convergence of the flow equations
and for convergence of the transport equations is less than prescribed numbers, the time step is
increased by multiplying the current time step by a prescribed constant (> 1). Different values of the
prescribed number of iterations may be specified for the flow and transport equations.
4. During a given time step, if convergence of the flow equations or of the transport equations is not
attained within a specified maximum number of iterations, the time step is decreased by multiplying
the current time step by a constant (< 1). Different values of the maximum number of iterations may
be specified for the flow and transport equations. If convergence is repeatedly not attained, the
simulation will terminate when a minimum time step size is reached.
5. Solution of the flow equations may be skipped for a specified number of time steps. The transport
equations are always solved on every time step. Adjustment of the time step size proceeds as
described above, however, the use of small multipliers for increasing the time step size is advised
(< 1.1).
3.11 BOUNDARY CONDITIONS
3.11.1 Phase Mass Balance Boundary Conditions
Boundary conditions must be specified for the aqueous and gas phase mass balance equations as either
constant specified pressure (type I) or constant specified flux (type II).
Constant pressure conditions may be specified at any node in the computation domain. This condition
is implemented by modifying the appropriate row in the global matrix equation (3.18) to,
•] = 0 (3.56)
where / is the node at which constant pressure conditions are specified.
Specified boundary fluxes are introduced through the source/sink terms. The flow across a boundary
segment of element e is represented by the surface integrals on the RHS of (3.17) and is expressed as,
N* r N* A
= -E a* AWr'= -!>««,-f-
e=l •T' e=i *
(3.57)
where qa, is the boundary flux [LT~l] of phase a at the boundary node i and Qai is the total discharge at
node / [L3T~']. No flow boundaries (qa = 0) are the natural finite element boundary condition. The
boundary flux is assumed to be uniform over the cross sectional area, Ax., associated with the boundary
node i. This cross sectional area depends on the coordinate system and thus the specified flow must
properly reflect the cross sectional area.
Due to compressibility effects the specified volumetric flux of the gas phase is referenced to free
surface conditions (fs) conditions which are assumed to 1 atmosphere of pressure at 20 °C. The free surface
42
-------
conditions are related to the reservoir conditions (re) by a compressibility factor, G8 [-], which is evaluated
from the ideal gas law (2.49),
/P*rTK\
Qg« = QgfsGg = Qg(s —V (3.58)
3.11.2 Component Mass Balance Boundary Conditions
Boundary conditions are required for the gas and aqueous phase component balance equations. These may
be specified as either: constant specified mole fraction (type I); specified diffusional flux (type II),
. _
~
(3.59)
where Lar is the thickness of the stagnant boundary layer in the contacting a phase fluid and x° is the
specified value of the component mole fraction in the contacting fluid; or mixed (type III) where'the
composition of an incoming fluid is specified along a boundary section,
(3.60)
•~ ~ \j j\t i
When the boundary is impermeable or water flow is directed out of the domain, (3.60) reduces to (3.59).
Eqs. (3.59) and (3.60) are expressed at all nodes to which a given boundary condition applies.
Constant mole fraction boundary conditions may be specified at any node in the computational domain.
This condition is implemented by modifying the appropriate row in the global matrix equation (3.55) to,
(3.61)
where i is the node at which constant mole fraction conditions are specified.
Zero diffusive flux type n boundaries are the natural finite element boundary condition for the transport
equation, i.e.,
*"<-•-" • (3.62)
dx.
=0
This boundary condition corresponds to setting the surface integral term on the RHS of (3.37) to 0. This
condition is used to represent those boundaries where advective transport is directed outward and there is
no mole fraction gradient at the boundary. Since the NAPL, solid, and biophase component transport
equations do not consider advective or diffusive flux no additional specification of boundary conditions is
required beyond the natural condition. This is also true for the NAPL saturation equation.
Nonzero type II and type III boundary fluxes are introduced through the surface integral on the RHS of
(3.37). For type III boundaries, (3.60) becomes,
= QajnjXae -
(3.63)
The first term on the RHS of (3.63) represents the advective flux and is inserted into the matrix [B] in
(3.55). The second term is the total material flux and is added to the vector {F} in (3.55). The boundary
flux is evaluated in two ways. When the flow equations are solved, the boundary flux calculated for the
43
-------
well screen
interval
k+1
Figure 3.3: Representation of an extraction well in the discretized domain.
phase material balance calculation, or imposed as a boundary condition for the flow equations is used to
evaluate Qa. Otherwise the boundary flux is evaluated using the Darcy flux in the following fashion. The
boundary flux is assumed to be uniform over the cross sectional area, AXi, associated with the boundary
node i. The cross sectional area depends on the coordinate system and is evaluated by,
AX! = k
AX =
for (x-z)
for (r-z)
(3.64a)
(3.64b)
Here // = |(/ei + lez) is the length of the boundary segment associated with node i and le\ and Ie2 are the
lengths of the boundary segments of elements el and el which are connected at node /. The average radius
of the boundary segment associated with node i is r/ = |(r/_i + In + r/+i). Here r/_i, n, and ri+\ are the
radii of the three nodes spanning e 1 and el. Nonzero type II boundaries are treated in the same manner as
nonzero type HI boundaries with the RHS of (3.63) being replaced by the RHS of (3.59) after evaluation of
the surface integral.
3.11.3 Extraction Wells
MISER incorporates the option to simulate radial flow to an extraction well positioned in the center of
axisymmetric (r-z) domains. Consider the problem of simulating an extraction well along the left boundary
of the domain shown in Figure 3.3. The well screen spans k elements and k + 1 nodes, and is assumed to be
parallel to the z-coordinate.
Vadose zone extraction wells operate in regions of variable saturation and therefore typically remove
both aqueous and gas phases during operation. MISER requires the specification of the total combined
(aqueous and gas) extraction rate and then apportions the flow of each phase at each node along the well
44
-------
screen. The flow of each phase is apportioned along the well screen by [Aziz and Settari, 1979],
E
k 2
yyj
2-/Z^;
£»fs
(3.65)
where Qt(fs is the specified combined discharge at free surface conditions, and j denotes the nodes along
the well screen in element e. The cross sectional area associated with each node along the well screen is
computed by,
Ax. = 2jrrweii// (3.66)
where rwell is the radius of the well, // = i(lei + Ie2) is the vertical length of well segment associated with
node i, and le\ and Ie2 are the lengths of the element el and el which are connected at node i. Here it is
assumed that well is parallel with the z-coordinate.
Further simplification is made by assuming that the potential gradient for each phase is the same in all
layers. The flows may then be apportioned solely by mobility,
E
e=l
Q
ttfs
(3.67)
where the aqueous compressibility is set to 1, and the gas phase compressibility is computed from (3.58).
This 'transmissibility allocation' method is generally valid when variation in permeability along the well is
small. However, the method "may give erroneous results in the case of large vertical heterogeneity and
especially when non-communicating layers exist" [Aziz and Settari, 1979].
The appropriate boundary condition for the transport equations at an extraction well is type II with zero
diffusive flux.
3.11.4 Treatment of Injection Wells
Presently MISER is configured to consider the injection of gas phase only. Thus, under injection conditions
the specified total discharge, Qtt(s, is comprised solely of gas phase which is similarly apportioned along
the well screen by the transmissibility allocation methods, using,
= E
2_,e=l 2^;=1
Q
gtfs
(3.68)
In the case when the denominator in (3.68) is zero (i.e. injection below the water table), then Qtt!s is
distributed uniformly over the well screen.
The appropriate boundary condition for the transport equations at an injection well is type in which
specifies the composition of the incoming fluid.
45
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3.12 ITERATION SCHEME
An iteration scheme is necessary to update secondary variables that are functions of the primary solution
variables. A Picard iteration approach is employed in MISER [Huyakorn and Pinder, 1983]. This approach
is implemented by simply lagging the secondary variables and iterating within a time step until a
convergence criterion is satisfied.
A relative maximum differential is used to test convergence. For the flow equations convergence is
established by the change in pressure, evaluated by,
max/\P5
•k+l
(3.69)
maxy|P*+M - 7
where e/ is the convergence tolerance for solution of the flow equations.
Mole fractions, *<*,., are used to control convergence of the transport equations. The transport equations
for the gas, aqueous, organic, solid and biophases are solved sequentially until convergence is achieved for
each equation. Two values of the convergence criteria are used, one for the gas and aqueous phase transport
equations, em, and one for the immobile phase transport equations, e,-. Convergence is measured by,
max,-
max,- be:
•fc+ii
< Cm Or €/
(3.70)
't*c,
For the solid phase, convergence is measured using solid phase mass loadings, coSc, otherwise the
expression is the same as (3.70).
After convergence has been obtained for all the transport equations (3.47) is solved for the organic
phase saturations. An iterative solution is not required if the organic phase is composed of only a single
component. When more than one organic phase component is present, convergence is measured using the
organic phase saturations,
max
-.S*|
(3.71)
max;
were e0 is the convergence criterion for the organic phase saturation. When a nodal organic phase mole
fraction falls below a user specified value (currently 10~3), convergence is not measured for that nodal mole
fraction.
Table 3.3 summarizes the numerical iteration scheme employed in MISER.
3.13 SOLVER
The nonlinear discretized flow and gas and aqueous phase transport equations are solved using the Harwell
Sparse Matrix Package [Duff, 1979]. The specific flux equations are solved directly when calculating
element fluxes. When calculating nodal velocities the Harwell package is used, unless the mass matrix is
lumped. In that case, the specific fluxes are solved for directly. The NAPL and solid phase transport
equations can also be solved using the Harwell Sparse Matrix Package. The NAPL and solid phase
46
-------
Numerical Solution Scheme
Sequence
Description
Section Reference
1.
2.
3.
Problem Setup
Read input files and initialize variables as needed.
Calculate element areas.
Calculate initial mass in domain.
5.4
3.1
4.1
4.
Begin Iteration Over Time
Update phase molecular and mass densities.
2.5.3 and 2.5.4
Solve Flow Equations
5. Update gas phase viscosity.
6. Begin iterative solution of flow equations.
6a. Update capacity coefficients and mobilities.
6b. Update well terms.
6c. Solve flow equations after imposing boundary conditions.
6d. Update gas and aqueous phase saturations.
6e. Update gas phase mole and mass density.
6f. Check convergence. Iterate to 6. if not converged.
7. Update boundary fluxes for material balance and
transport equation boundary conditions
Update phase material balance.
2.5.5
3.2
3.2.3, 2.5.2
3.11.3,3.11.4
3.11.1
2.5.1
2.5.3
3.12
4.1.1
4.1
Solve Transport Equations
9. Update velocity field.
10. Update bioreaction terms and biomass.
Only when a separate biophase is not present.
11. Begin iterative solution of transport equations.
11 a. Update biophase mole fractions and biomass.
Only when a separate biophase is present.
lib. Update phase molecular and mass densities.
lie. Update mass exchange terms. >•
1 Id. Update dispersion coefficients.
lie. Solve gas and aqueous phase transport
equations after imposing boundary conditions.
1 If. Solve organic phase transport equations.
1 Ig. Solve solid phase transport equations.
1 Ih. Solve organic phase saturation equation.
Hi. Update gas and aqueous saturations
if the flow equations are not included.
1 Ij. Check convergence. Iterate to 11. if not converged.
3.4
3.6
3.5
3.6
2.5.3 and 2.5.4
3.5
2.5.7
3.5.1 and 3.11.2
3.5.1
3.5.1
3.7
3.12
Increment to Next Time Level
12. Update component material balance.
13. Print output if desired.
14. Adjust time step if indicated and proceed to next time level.
4.1.2
3.10
Table 3.3: Summary of numerical scheme in MISER.
47
-------
transport equations only have the thrie derivative term on the left hand side arid are solved directly when
mass lumped. In contrast, when considering a separate biophase, the biophase transport equations have
exchange and bioreaction terms oh the left hand side arid hence ate not diagonal after mass lumping. Thus,
the biophase transport equations ate always solved using the Harwell package. The &APL saturation
equatibn is always mass lumped and solved directly.
48
-------
Section 4
MODEL VERIFICATION
4.1 MATERIAL BALANCE CALCULATION
A material balance calculation is included as an option in MISER. This option calculates a mass balance
error as a measure of the material balance in the numerical solution of the flow and transport equations. The
mass balance error is calculated over the entire computational region £2.
4.1.1 Phase Material Balance
Mass balance error in solutions to the flow equations is obtained by integrating (2.6) over £2 and applying
the divergence theorem,
f — (p*Sa) dQ, + f [p*Aa (VPa - p*gVz)} • ndF - f E*d& - f RadQ, = 0 (4.1)
J& at Jr JQ Jo.
where F is the boundary of £2.
If the numerical solution is substituted into (4.1) then the mass balance residual of phase a. may be
calculated by,
e« = FSa + Fba + Fea + Fra " (4.2)
where,
3
" " "" (4.3a)
= Li
ba = f [p*Aa (VPa - p*
Jr
Fe = -
ra = - f Ra
J Q
(4.3b)
(4.3c)
(4.3d)
Here mass lumping is employed to evaluate the volume integrals. The boundary integrals are evaluated by
back substitution of the predicted pressures into the finite element equations [Huyakorn and Finder, 1983].
49
-------
4.1.2 Component Material Balance
Mass balance error in solutions to the transport equations is obtained by integrating (2,1 1) over Q, applying
the divergence theorem, and substituting iJiacxac for Bac. The resulting equation is summed over the phases
giving,
f ^ (PaSarcxac
JQ Of
-Mc^L
H J ifi
= 0
(4.4)
where Mc is the component molecular weight. Retardation (rc =^ 1) is included only when a = a and
nonequilibrium sorption is not considered.
If the numerical solution is substituted into (4.4) then the component residual for the entire domain may
be calculated by,
where,
r ft
sc = McJ2 -^ ( for r«- = Typ6 n
III f
E E / A*, J2S'^, Ni for T,- = Type HI
a f=i Jy
(4.6b)
(4.6c)
The type I boundary integrals are evaluated by back substitution of the predicted mole fractions into the
finite element equations [Huyakorn and Finder, 1983]. When rc ^ 1, the change in component mass
determined with (4.6a) includes the change in sorbed mass.
4.1.3 Calculation of Mass Balance Error
The accuracy of the numerical scheme is evaluated by three measures of mass balance error. The first two
are relative errors, and the third represents an absolute error. The expressions used to calculate these errors
50
-------
are respectively,
At
100
Ne ^ ,
\e=l ^!
#At inn i
Da'i 1UU 1 max|Y| p
oAt
Da3
J?Af -inn
100
A
I
+
eaA?|
*
\ea
Fea
=^
+
N^
Fra|)
P i p i p
^ £>a T fga T /^ra
.^.
/
N<
€CA
/„'
t\
>J 5
°Af
^C2 = 100
\Sc\
= 100 11 -
(4.7e)
(4.7f)
where the denominators in (4.7a) and (4.7d) are the mass storages of phase a and component c respectively
at the start of the simulation. Ba\, Ba2, #0-3, Bc\, 5C2,and B& are set to zero if the denominator is zero.
The error measures above represent the percentage mass balance error over a single time step.
Cumulative mass balance errors are also computed using,
5f,, = 100
At
^' /"
\e=l •*&
(4.8a)
= 100
(4.8b)
(4.8c)
B'd = 100
f f piailxlK
=i JV
(4.8d)
51
-------
B'c2 = 100
B'c3 = 100 | 1 -
(4.8e)
(4.8f)
4.2 VERIFICATION OF THE PHASE MASS BALANCE SOLUTIONS
4.2.1 Comparison with One Dimensional Richards Equation
Numerical solutions of the flow equations were compared with analytical solutions of the Richards
equation. This equation describes the movement of a constant density aqueous phase in variably saturated
media under the assumption that the gas phase does not impede the liquid migration; i.e. the gas pressure is
static. Thus, comparisons with solutions of Richards equation provides verification for the solution of the
aqueous flow equation only, even though both aqueous and gas flow equations are solved.
The one dimensional vertical form of Richards equation is expressed as,
. 8Sa 9 rkkr.
(4.9)
Semi-analytical solutions of (4.9) developed by Philip [1969] were compared to MISER. The test problem
considered is for vertical moisture infiltration under constant surface ponding into a soil with an initial
moisture content close to residual. Conditions of the test problem were obtained from Celia et al., [1990].
The asymptotic characteristic of the capacity coefficient in the region of residual water saturation creates
computational difficulties for numerical simulators. Therefore, this test problem provides a rigorous test of
MISER for typical moisture infiltration conditions in the unsaturated zone. The hydraulic properties of the
test problem are,
1 ~ ^ ! + Sra (4.10)
—-—— (4.11)
where 0 = 0.368; Sra = 0.2772; n = 2; m = 0.5; a = 3.415 x 10~4 Pa"1; and k = 9.43435 x 1Q-'2 m2.
The initial and boundary conditions are:
Pa(jc,z,f = 0) = -1000 cm = -98071 Pa Pg(x,z, t = 0) = OPa (Sa = 0.299)
Pa(x,z = 0,0 = -75 cm = -7355.325 Pa Pg(x, z = 0, t) = OPa (Sa = 0.544)
Pa(jc,z = Z,,0 =-1000 cm =-98071 Pa Pg(x, z = L, t) = OPa (Sa = 0.299)
3 pa (x = 4 cm, z, t)/dx = 0
dPg(x = 4cm,z,t)/dx = 0
52
-------
40cm
2cm
101 102 103
2cm
Figure 4.1: Computational grid used for the numerical solution of the one dimensional Richards equation.
Numerical simulation of the moisture infiltration problem was obtained on a symmetric "union jack"
grid consisting of 160 elements and 103 nodes (Figure 4.1). Nodes were uniformly spaced in the x and z
directions at 2 cm. The gas phase was simulated with three components: nitrogen, oxygen, and water.
Since transport equations were not solved, the gas phase composition was fixed, with a mass density of 1.24
g/1. To reduce the effect of gas pressure transients on aqueous migration, the vapor viscosity of the three
components were reduced to an artificially small value of 1 x 10~7 Pa-s. The aqueous phase was simulated
as pure water.
Figure 4.2 compares the predicted and analytical solutions at time 6 hrs. Close agreement was
generally obtained for pressure and saturation distributions. Pronounced oscillations at the toe of the sharp
front are evident in the pressure distribution when the consistent form of the mass matrix is used. The
oscillations are eliminated when the mass matrix is lumped. This behavior is consistent with that
commonly observed in the numerical solution of Richards equation [Milly, 1985; Celia etal, 1990;
Rath/elder and Abriola, 1994]. The magnitude of oscillations increases as Ca = dSa/dPc approaches zero
(i.e. as Sa approaches Sra), and the effect of the oscillations can be to severely limit computational
efficiency and numerical accuracy. Therefore, mass lumping is frequently recommended to eliminate
oscillatory behavior [Milly, 1985; Celia et al., 1990;], at the expense of some loss in numerical accuracy
[Huyakorn and Finder, 1983; Zienkiewicz and Taylor, 1991].
Global mass balance errors at varying convergence tolerances are listed in Table 4.1. Small mass
balance errors further confirm the accuracy of the numerical solutions. Mass balance errors increase
slightly with increasing convergence tolerance.
No grid effects were observed in that all solutions were identical along nodes in the horizontal plane.
Furthermore, identical solutions were obtained when the vertical direction was numerically reversed (i.e.
the grid was rotated by 90 degrees and gravity components were set to gz=Q and gx=9.81 m/s2).
Collectively these results indicate MISER is correctly solving the aqueous phase mass balance equation in
cartesian coordinates.
53
-------
pressure distribution
0
5
10
15
20
25
30
35
40
-1200 -1000 -800 -600 -400 -200
aqueous pressure (cm)
saturation distribution
1 1
- o- -lumped r
—•a— conslste
'" '•&
[
i
I
i
i
i
— i r •— i
1 solution
nass matrix
it mass matrix '
i
i i i
analytical solution
- lumped mass matrix
consistent mass matrix
0 0.25 0.3
0.35 0.4 0.45
aqueous saturation
0.5
Figure 4.2: Comparison of numerical and analytical solutions for the one dimensional Richards equation.
Simulation time = 6 hours; convergence tolerance = 1 x 10~4.
convergence
tolerance
l.Ox 10-2
1.0 x 1CT2
1.0 x 1Q-3
1.0 x 10-3
l.Ox 10~4
1.0 x 10~4
mass
matrix
consistent
lumped
consistent
lumped
consistent
lumped
residual
ea (kg)
2.66 x 10~4
1.76xlO-4
-4.64 x 10~5
-4.58 x 10~6
5.35 x 10-7
-5.70 x 10~6
B\a W
3.00 x 10-3
1.98 x 10-3
5.21 x 10-4
5.14x 10~5
6.02 x 10~6
6.41 x 10~5
*L (%)
5.77 x 10~2
3.81 x 10~2
1.00 x 10~2
9.93 x 10-4
1.16 x 10~4
1.23 x 10-3
Table 4.1: Comparison of global mass balance errors from numerical solutions of the one dimensional
Richards equation at time 6 hrs.
4.2.2 Comparison with Two Dimensional Richards Equation
The capability of MISER to simulate a two dimensional variably saturated axisymmetric flow was tested by
comparison to numerical solutions of the two dimensional Richards equation obtained from the SWMS-2D
model [Simimek et al., 1994]. The scenario under consideration is described as example problem 4 [Section
7.4, Sinntnek et al., 1994] and involves moisture infiltration from a single-ring infiltrometer. The
axisymmetric domain is shown in Figure 4.3 and the associated soil properties are listed in Table 4.2. The
radius of the ring infiltrometer is 20 cm.
SWMS_2D numerically solves the two dimensional Richards equation using the Galerkin-type linear
finite element scheme. For comparisons presented herein, SWMS_2D was run using quadrilateral elements.
The grid, shown in Figure 4.4, consists of 342 elements and 380 nodes; it is identical to that described in
the users manual [Section 7.4, Simunek et al., 1994]. No flow conditions were prescribed along all
boundaries, except at the five nodes along the top left boundary where constant pressure conditions were
54
-------
40
§
§-80
T3
120
130
layer 1.
layer 2
0.84-
0.91-
-—0.98 • —
radius (cm)
125
radius (cm)
125
Figure 4.3: Domain configuration used in two dimensional (2D) flow simulations for comparison to
SWMS_2D.
Parameter
kx — kz (m2)
^>rw
n
a (I/Pa)
Layer 1
0.399
3.9598xlO~13
2.51xKT4
1.376
1.77xlO~4
Layer 2
0.339
6.0327xlQ-13
2.95 xlO~4
1.603
1.42xlO~4
Table 4.2: Soil properties used in two dimensional flow simulations for comparison to SWMSJ2D.
specified (Pa — 1 atm; Sw = I).
The two dimensional moisture infiltration problem was simulated with MISER using the same nodal
structure as in'Figure 4.4. Each quadrilateral element was subdivided into two triangular elements resulting
in 684 elements and 380 nodes. Boundary conditions for the gas phase were specified as first type, constant
atmospheric gas pressure along the entire top boundary and no flow conditions on remaining boundaries.
Other specifications required to conform to assumptions inherent in Richards equation were identical to
those used in the one-dimensional comparisons: the transport equations were not solved; the gas phase
composition was fixed; and the vapor viscosity was set to an artificially small value to eliminate effects of
gas pressure transients on aqueous migration.
Intermodel comparisons were initially made for a homogeneous problem, employing the soil properties
for layer 1 over the entire domain. Very close agreement was obtained in numerical predictions of moisture
content, as demonstrated by near indistinguishable contour lines shown in Figure 4.5. Mass balance
computations from MISER were on the order of 10~6 and 10"3% for the relative and absolute error
measures, respectively, at a convergence tolerance of 10~3. Collectively, these results indicate MISER is
correctly solving the aqueous phase flow equation in a two dimensional axisymmetric domain.
The second comparison was for the layered domain shown in Figure 4.3. Results shown in Figures 4.6
and 4.7 show very close agreement in the upper layer and moderate discrepancies near the region of the soil
interface (depth = 40 cm). These discrepancies are attributed to differences in the way that discontinuities
55
-------
constant head nodes
i * * >
Or
40
_o_
I 80
T3
120-
130L
radius (cm)
125
Figure 4.4: Numerical grid used in two dimensional flow simulations for comparison to SWMS_2D.
0.5 0.8
radius (m)
Figure 4.5: Simulated volumetric moisture content in the homogeneous domain at time 12 hrs (MISER =
solid line; SWMS_2D = dashed line).
at the material property interface are treated in the two numerical models. In MISER, discontinuities are
preserved numerically by tracking separate nodal material property parameters and saturation values within
contiguous elements spanning the interface. Moisture profiles from MISER exhibit a sharp contrast at the
interface (depth = 40 cm). In SWMS.2D, the nodal material property parameters are averaged. Moisture
profiles from SWMS.2D exhibit a sharp contrast at depth of approximately 45 cm, or approximately the
distance of one-half element below interface. Despite discrepancies near the interface, moisture profiles in
Figure 4.7 show good agreement at depth below the interface.
56
-------
u.u-
0.1 -
0.3-
0.4-
0.5-
1 0.6-
t °-7:
0.8-
0.9-
1.0-
1.1 -
1.2-
1.3-
^JJJ L
~^Ml L ^
0.00
0.25
0.75
radius (m)
1.00
1.25
Figure 4.6: Simulated volumetric moisture content in the layered domain at time 6 hrs (MISER = solid line;
SWMS_2D = dashed line).
1.3
0.00
0.50 0.75
radius (m)
1.00
1.25
Figure 4.7: Simulated volumetric moisture content in the layered domain at time 12 hrs (MISER = solid line;
SWMSJ2D = dashed line).
4.2.3 Comparison with Quasi Analytical Solutions for Unsteady Radial Flow of Gas
The capability of MISER to simulate axisymmetric flow of gas to vadose zone extraction or injection wells
was tested by comparison to quasi analytical solutions developed by McWhorter [1994]. The quasi
analytical solutions represent unsteady one dimensional radial gas flow and account for nonlinearities
stemming from pressure dependent density (compressibility) and permeability (Klinkenberg effect). To
conform with conditions of the analytical solution, MISER was used to simulate confined radial gas flow to
57
-------
Q
-no flow boundary
1m
.'uniform soil conditions -;;'•:"•;-••
= 0.25m
constant atm
pressure
-*-r,
max
Figure 4.8: Domain configuration used in two dimensional flow simulations for comparison to quasi analytical
solutions for radial gas flow.
Parameter
kx = kz (m2)
"Viu
n
a (I/Pa)
b (atm)
Casel
0.33
IxlQ-11
0.12
7.0
0.002
0.0
Case 2
0.33
IxlO"14
0.12
7.0
0.002
0.316
Table 4.3: Soil properties used in two dimensional flow simulations for comparison to quasi-analytical
solutions for radial gas flow.
a fully penetrating extraction/injection well (Figure 4.8). All soil properties were homogeneous (Table 4.3),
with water present at the immobile residual level. Properties of nitrogen gas were used to represent the gas
phase in both the numerical and analytical solutions.
Comparisons were made for varying conditions of gas injection and extraction using two values of
intrinsic permeability. The first case involves a relatively conductive soil under conditions in which slip
flow phenomena are negligible. For this problem the domain was discretized into 505 nodes (5 vertical by
101 horizontal) and 800 elements. Nodal spacing was uniform in the vertical direction and nonuniform in
the radial direction, evaluating nodal coordinates from [Aziz and Settari, 1979],
(4 12)
n Well/
where n = 101 is the number of nodes in the radial direction, and rmax = 1000 m is the radial coordinate of
the right boundary. Comparisons of predicted pressure distributions are shown in Figure 4.9 for a extraction
rate of 10 scfm and an injection rate of 1 scfm. Close agreement between MISER and the quasi analytical
solutions is observed, indicating MISER is correctly solving the axisymmetric gas phase flow equation with
specified well conditions. Figure 4.9 also shows an extensive radius of influence, indicating that accurate
representation of the flow field requires a large grid structure under conditions of confined gas flow in a
conductive soil.
The ability to simulate slip flow phenomena based on the Klinkenberg correction factor (2.4) was
examined in a second problem involving extraction from a less conductive soil. For this problem the
domain was discretized into 1005 nodes (5 vertical by 201 horizontal) and 1600 elements, using a uniform
58
-------
Q = -.10scfm
1.01-
Q = 1 scfm
Analytical Solution
--a--MISER, t=1 hr
--e--MISER, t=1 day
MISER, t= 10 days
Analytical Solution
--EJ--MISER, t=1 hr
--e--MISER, t=1 day
--A--MISER, t=10 days
200 400 600
radius (m)
800 1000
100
200 300
radius (m)
400 500
Figure 4.9: Comparison of quasi analytical and numerical solutions for two dimensional radial gas flow in a
uniform soil with k = 1 x 10~n m2.
time = 10 days
time = 30 days
0.2
0
Analytical Solution
.-a-.MISER, with slip flow
--Q-. MISER, no slip flow
5 10
radius (m)
. -a.. MISER, with slip flow
.-0-.MISER, no slip flow
5 10
radius (m)
Figure 4.10: Comparison of quasi analytical and numerical solutions for one dimensional radial gas flow in
a uniform soil with k = 1 x 10~14 m2.
nodal spacing in the vertical direction and (4.12) to compute radial coordinates with rmax = 200 m. The
Klinkenberg parameter (b) was evaluated from (2.5). Comparisons of predicted pressure distributions are
shown in Figure 4.10 for a constant extraction rate of 0.08 scfm. Close agreement between MISER and the
quasi-analytical solutions is observed, indicating MISER is correctly accounting for slip flow phenomena
using the Klinkenberg correction factor.
59
-------
0.5cm
10 cm
61 62 63
0.5cm
Figure 4.11: Computational grid used for the numerical solution of the one dimensional transport equation
with and without advection.
4.3 VERIFICATION OF THE COMPONENT MASS BALANCE
SOLUTIONS
4.3.1 Comparison with One Dimensional Analytical Solutions
The first set of model verifications for the transport section of MISER are comparisons with analytical
solutions of the one dimensional transport equation with and without advection. In all the simulations
discussed in this section, the flow portion of MISER was not operating. Additionally, the component
parameters were normalized for the comparisons with analytical solutions and Sa — 1. These comparisons
were used to verify the ability of MISER to simultaneously simulate transport of multiple components in
two mobile phases. The first analytical solution was of nonadvective transport with constant dispersion
coefficients. The second analytical solution included constant advection [Ogata and Banks, 1961]. Figure
4.11 shows the "herringbone" grid with 63 nodes and 80 elements used for both of these comparisons.
Minor grid effects were observed in that the nodal concentrations were not identical across the axis
perpendicular to the direction of flow. Similar simulations performed using the "union jack" grid did not
show these effects. Both vertical and horizontal orientations were tested for both mobile phases and for two
components in each phase. In all cases, A* = 0.5 cm, Az = 0.5 cm, Ar = 5 sec, D - 0.0003 cm2 sec"1,
and the convergence criteria was 10~8. The component boundary conditions for the analytic solutions were
first type with a value of C = 1.0 at x = 0 cm and second type with a zero solute gradient at x = oo.
Initially the solute concentration was 0.0 throughout the domain. For the numerical solutions, the domain
was large enough so that the second type boundary condition was not violated. For the comparison with the
Ogata and Banks solution, v = 0.0002 cm sec"1. As Figures 4.12 and 4.13 show, MISER and the analytic
solutions closely match at t = 4000 sec. The numerical simulations shown are for oxygen in the aqueous
phase, however good matches were obtained when an additional component was added or when similar
Simulations were performed in the aqueous phase.
60
-------
I
0.8
0.6
1 0.4
0.2
One dimension diffusive transport
analytical solution
numerical solution
D = 0.0003 cm2/sec
t = 4000 sec
246
distance (cm)
10
Figure 4.12: Comparison of MISER with the one dimensional analytical solution for diffusion driven trans-
port.
Advective-dispersive transport
I °'8
c3
1 0.6
.a 0.4
0.2
- Ogata-Banks solution
- numerical solution
D=0.0003 cm2/sec
v=0.0002 cm/sec
t=4000 sec
4 6
distance (cm)
10
Figure 4.13: Comparison of MISER with the one dimensional Ogata and Banks analytical solution for
transport with dispersion and constant advection.
4.3.2 Comparison with Two Dimensional Analytical Solutions
Numerical solutions obtained from MISER were next compared with solutions from a two dimensional
analytical groundwater mass transport model [Cleary and Ungs, 1978]. The analytical solution used
allowed for dispersion and advection in both the x and z directions, as well as first order decay of the solute.
These comparisons demonstrate the ability of MISER to correctly solve the transport equation in two
dimensions. A "herringbone" grid was used for these simulations with 441 nodes and 800 elements. The
61
-------
Q.
0)
TJ
0.000
0.025
0.050-
0.075 -
0.100
0.000 0.025 0.050 0.075
horizontal distance (m)
0.10
Figure 4.14: Comparison of MISER (solid lines) with a two dimensional analytical transport solution (dashed
lines) at 4000 sec. Contours of normalized concentration are from left to right: 0.8, 0.6, 0.4, 0.2, 0.1, and
0.01.
i
grid was square with 21 nodes on each side. In all cases, A* = Az = 5.0 cm, A? = 5 sec,
Dx = Dz = 0.0003 cm2 sec"1, vx = vz = 0.0002 cm sec"1 (where vz is positive upwards), and the
convergence criteria was 10~8. The solute boundary condition for both the analytic and numeric solutions
was first type with a Gaussian distribution along x = 0 cm, centered at z = 5 cm with x = 1.0 at z = 5 cm
and a standard deviation of 1.0. At the other three boundaries the solute concentration gradient was
assumed to be zero (second type boundary) at oo for the analytic solution. For the numerical solutions, the
domain was made large enough so that the second type boundary condition was not violated. The initial
solute concentration was 0.0 throughout the domain at t = 0.0 for both the analytical and numerical
solutions. The close agreement of the analytical and numerical solutions at t = 4000 sec in Figure 4.14
verifies the ability of MISER to correctly solve the transport equation in two dimensions.
4.3.3 Verification of Biokinetics
The ability of MISER to simulate Monod-type biological growth and decay was verified in two ways. First
comparisons were made with the two dimensional analytical solution discussed in Section 4.3.2. The
domain, parameters, boundary conditions, and initial conditions for the analytical solution were the same
with the addition of first order solute decay of k = 0.001 sec"1. MISER was then used to simulate first
order decay by setting the half saturation constant of the degradable solute equal to 1032 and the maximum
solute use rate equal to 1029 resulting in a first order decay rate of 0.001 sec"1 as in the analytic solution.
Otherwise, the grid and parameters were the same as for the previous simulation. MISER required that
oxygen be present in the aqueous phase in order for the biodegradation routines to function properly, but by
setting the oxygen use coefficient equal to zero, any effects of oxygen limitation were eliminated from this
simulation. MISER also allows the biomass concentration to remain constant for the course of a simulation
eliminating any effect of biomass growth. Both oxygen and biomass were set to an initial concentration of
62
-------
0.000
0.025 -
•£ 0.050 -
Q.
CD
T3
0.075 -
0.100-1
0.000 0.025 0.050 0.075
horizontal distance (m)
0.100
Figure 4.15: Comparison of MISER (solid lines) with a 2D analytical transport solution including first order
decay (dashed lines) at 4000 sec. Contours of normalized concentration are from left to right: 0.8, 0.6, 0.4,
0.2,0.1, and 0.01.
1.0 throughout the domain with first type boundary conditions for oxygen at x = 0.0 cm of 1.0. By using
these values for oxygen and biomass, any dependency of the solution from MISER on these terms was
eliminated. For this simulation a separate biophase was not considered and the reaction terms were directly
inserted into the aqueous phase transport equations. The close agreement of the analytical and numerical
solutions at t = 4000 sec shown in Figure 4.15 indicates that the Monod terms are being calculated and
inserted into the appropriate transport equation correctly.
A comparison was also made to the model developed by Moltz et al., [1986] for simulating microbial
growth-degradation processes in porous media where the microorganisms are primarily present in
microcolonies. Modifications were made to MISER to account for the significant differences in the way
Moltz, el al, [1986] handled oxygen usage. Their model also assumed that the transport of substrate and
electron acceptor from the pore fluid to the microcolonies may be dominated by an adjacent diffusion layer
resistance. This concept can be incorporated in MISER by the inclusion of a separate biophase with rate
limited mass transfer. However, for this comparison MISER was operated with the bioreaction terms
inserted directly into the aqueous phase transport equation (i.e., no mass transfer resistance) due to the
differences in the way mass transfer resistance is handled in the two models. The comparison presented in
Figure 4.16 is with Figure 8 from Moltz et al., [1986] and the interested reader is referred to their paper for
all pertinent biokinetic and media parameters. A "herringbone" grid similar to Figure 4.11 was used for
these simulations with 303 nodes and 400 elements. The grid was quasi one dimensional with 3 nodes in
one dimension and 101 nodes in the other dimension. In all cases, Ax = Az = 1.0 cm, the maximum
At = 0.1 day, and the convergence criteria was 10~8. Given the differences between the two models the
comparison at 4 days presented in Figure 4.16 is reasonable and indicates that MISER is incorporating
nonlinear Monod-type biokinetics into the bioreaction terms.
63
-------
16 -
14 -
I 12-
| 10 -
8 8 -
I .-
(a
4 -
2
40 60
Distance (cm)
Figure 4.16: Comparison of substrate profiles along a one dimensional column by MISER (lines) and a one
dimensional numerical solution (discrete points) for biodegradation by Moltz et al, [1986].
4.3.4 Verification of Interphase Exchange
Next the ability of MISER to simulate linear equilibrium sorption was tested. Comparisons were made with
the two dimensional analytical solution discussed in Section 4.3.2. The coefficients of the analytical
solution were modified to incorporate a solute retardation factor of 2.0. This was done by setting
Dx = Dz = 0.00015 cm2 sec"1 and vx — vz = 0.0001 cm sec"1. All the other parameters for the analytical
solution remained the same. For MISER, the parameters and domain configuration discussed in Section
4.3.2 were used with the addition of the sorption parameters Kf — 1.0 and m = 1.0. The mass exchange
coefficient was set to 0.01 sec"1 which was large enough to simulate equilibrium sorption processes using
the nonequilibrium formulation. The other parameters remained the same as in the previous simulations.
As can be seen in Figure 4.17, good comparisons were obtained between MISER and the analytical
solution. The slight differences between the two solutions at the 0.01 contour is consistent with a slight
deviation from equilibrium for MISER. This comparison demonstrates the capability of MISER to simulate
equilibrium exchange processes between mobile and immobile phases. When a retardation factor of 2.0
was incorporated directly into MISER, the match with the analytical solution was nearly exact (not shown).
Finally, MISER was compared with a one dimensional multicomponent organic liquid volatilization
column experiment by Bloes et al., [1989]. In this experiment benzene, TCE, and toluene were vented from
a column of glass beads by passing dry nitrogen gas through the column at a constant flow rate. No aqueous
phase was present and the NAPL was at an immobile residual saturation. A analysis of the experimental
results revealed that at the experimental flow rate, the mole fractions of the organic compounds in the gas
phase were approximately at equilibrium with the organic liquid for the duration of the experiment. For this
comparison, MISER was operated with only the gas and organic liquid phases present. All the pertinent
parameters are available in Bloes et al., [1989] and Rath/elder et al., [1991]. A "union jack" grid similar to
Figure 4.9 was used for these simulations with 271 nodes and 480 elements. The grid was quasi one
dimensional with 31 nodes in the x direction and 5 in the z direction. Ax = Az = 1.0 cm, Af = 600 sec,
vx =0.108745 cm sec"', and the convergence criteria was 10"8. The mass transfer coefficients were set to
the arbitrarily large value of 500 sec""1 and eq. (3.42) was used to limit the mass transfer coefficients to a
value sufficient to approximate equilibrium conditions. Figure 4.18 indicates that MISER can simulate
equilibrium multicomponent organic liquid volatilization validating the representation of interphase
exchange between a mobile and an immobile phase, this time for three components.
64
-------
0.000
0.025 H
£ 0.050 -
Q.
•8
0.075 -
0.100-1
0.000 0.025 0.050 0.075
horizontal distance (m)
0.100
Figure 4.17: Comparison of MISER (solid lines) with a two dimensional analytical solution including linear
equilibrium sorption (dashed lines) at 4000 sec. Contours of normalized concentration are from left to right
0.8, 0.6, 0.4, 0.2, 0.1, and 0.01.
200
•B>
6 8
Time (hr)
Figure 4.18: Comparison of MISER (lines) with a one dimensional column experiment (discrete points) for
multicomponent organic liquid (benzene, TCE, toluene) volatilization under equilibrium conditions.
4.4 VERIFICATION OF THE COUPLED PHASE AND COMPONENT
MASS BALANCE SOLUTIONS
In order for the coupled flow and transport portions of MISER to represent transport processes, the phase
pressures must be correctly translated into specific fluxes. Verification of this procedure was done by using
the domain from Section 4.3.1 and running the coupled flow and transport sections of MISER with first
type pressure boundary conditions of 1.001 atm at x — 0.0 cm and 1.0 atm at x = 10.0 cm. Otherwise the
65
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o.o H
0.3-
0.4-
(S O.fe ' ' 0.3 ' 04 ' "0 >
radius (m)
Figure 4.19: Comparison of predicted solute concentrations at time 6 hrs (MISER = solid line; SWMSJ2D
= dashed line).
parameter set remained the same as in Section 4.3.1. The specific fluxes generated by MISER were nearly
identical to specific fluxes calculated using,
Ax
(4.13)
This was done in both directions.
Tests on the coupled flow equations and transport were also conducted by intermodel comparison with
SWMS-2D model [Simunek et al, 1994]. The flow domain was identical to that described in Section 4.2.2.
Water introduced through the ring-infiltrometer contains a solute at the solubility limit. This condition was
simulated with type I (constant concentration) boundary conditions on the aqueous solute. No sorption was
considered in these comparisons. Additional transport parameters are given in Section 7.4 of Simunek et
a/., [1994].
Figures 4.19 and 4.20 compare predicted solute distributions from MISER and SWMSJ2D. Similar
results were obtained with MISER using either element average or nodal velocity computations. Results
show that MISER predicts a slightly more disperse solute front away from the boundaries. There is,
however, relatively good agreement in the location of the center of mass of the solute front (C=0.5), and the
overall agreement is considered reasonably good, given the differences in the type of elements and material
property discretization used by the two models.
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0.1 _
0.3-
—0.1
O.D o'l oi O.B o!4 o)
radius (m)
Figure 4.20: Comparison of predicted solute concentrations at time 12 hrs (MISER = solid line; SWMSJ2D
= dashed line).
67
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Section 5
PROGRAM DESCRIPTION AND SIMULATION SETUP
5.1 CODE DESCRIPTION
MISER is structured in a top down modular format for clarity, to aid in logic tracing, and to simplify code
modification. The modular format also enables the code to be easily programmed to run in different modes
such as: (1) flow solutions only; (2) transport solutions only using a steady state flow field; (3) transport
and biodegradation solutions using a steady state flow field; and (4) full coupling of the transient flow,
transport, and biodegradation equations. The code is liberally annotated with comment lines.
MISER is developed in the FORTRAN 77 programming language with a few standard enhancements
such as 'include' and 'Do-EndDo' statements. Due to the large number of equations being solved and the
complexity of the solution algorithm, the code is intended to be used on work station platforms or main
frame computers. The code has been tested with, and should normally be run using double-precision real
variables.
5.2 PROGRAM MODULES
MISER is comprised of 25 program modules: 1 main program, 23 subroutine files, and 1 include file. Table
5.1 provides a short description of the program modules.
To implement MISER, all program modules must be compiled and linked into an executable code. A
sample make file to compile MISER on an IBM RS6000 workstation is given in Appendix F.
5.3 ARRAY DIMENSIONS AND PROGRAM VARIABLES
Named common blocks are used to dimension all global arrays and to pass information between program
modules. The variable dimensions of all global arrays are defined with parameter statements in a single
'include1 file (dimen.inc). Most array dimensions are calculated from a combination of only a few
parameter variables, such as: the maximum number of nodes; maximum number of elements; maximum
number of components; and maximum number of material property blocks. In this way the dimensions of
most array variables can be easily adjusted by modifying only a few parameter variables in a single
program unit. These parameters should be set greater than or equal to the conditions of the problem to be
simulated. The major user defined parameter variables in 'dimen.inc' are listed in Table 5.2. Other
parameters in 'dimen.inc' include physical constants, constants related to numerical performance, and
control variables. The entire code must be compiled each time changes are made in 'dimen.inc'.
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A description of major program variables is given in Appendix E
5.4 DESCRIPTION OF INPUT FILES AND INPUT DATA
Table 5.3 describes all input and output files that can potentially be used in a single simulation run. A given
simulation may not generate every listed output file depending upon user specifications. Only those files
that are required on the basis of user specifications are opened.
The user supplied input data is contained in the first two input files. The first input file is named
'miser.dl'. 'Miser.dl' must be located in the same directory as the executable code. The name and path of
the second input file (designated as D2 in this documentation) is defined in data block A of 'miser.dl'.
Similarly, a prefix name and path for all output files is defined in data block A of 'miser.dl'.
The input data in 'miser.dl' and D2 are organized into blocks identified by letters A-T. File 'miser.dl'
contains data blocks A-L, and file D2 contains data blocks M-T. Depending on the problem conditions, all
data blocks may not be required for each simulation. The data blocks are further subdivided into fields that
are separated by comment lines designated by a '#' in column 1. An indefinite number of comment lines
can be added between fields, however, there must be at least one. The input data are read using list directed
formatting (free format).
The following sections provide a description of all input data and the organization of the data blocks.
Examples of input data files are shown in Appendix G.
5.4.1 Data Block A - Input/Output Files and Control Options
Input data in block A defines the names and paths of all input and output files used in a particular
simulation. Several optional output files may be generated (Table 5.3) with specified control switches
defined in block A. Table 5.4 describes all input data required in block A.
5.4.2 Data Block B - General Model Control Options
Data block B contains a number of control switches used to specify general model options, such as: the
type of computational domain; the inclusion or exclusion of flow, transport, and biotransformation
processes; and numerical solution control parameters. Table 5.5 describes all data contained in block B.
5.4.3 Data Block C - Time Step and Iteration Control Parameters
Data block C contains parameters that affect time step control, including parameters used for empirical
time step adjustment described in Section 3.10. Table 5.6 describes all data contained in block C.
5.4.4 Data Block D - Grid Information and Control Options
Data block D contains the grid and element information. Input data in this block are described in Table 5.7.
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MISER employs triangular elements to discretize the solution domain. The nodal inpidence list for
each element begins at an arbitrary node and proceeds counterclockwise if the vertical coordinate is
positive downwards, or clockwise if the vertical coordinate is positive upwards. The minimum material
property block size is a quadrilateral containing two elements in the case of a herringbone grid or four
elements in the case of a union jack grid (i.e. a single triangular element cannot be designated with unique
material property information).
User options are provided to either input all nodal coordinates and elements indices, or generate a
regular grid on a rectangular solution domain. Two types of grids can be generated: a symmetric union jack
grid (e.g. Figure 4.1), or a herring bone grid (e.g. Figure 4.11). Material properties in a generated grid are
restricted to horizontal alignments (soil layers).
5.4.5 Data Block E - Component Chemical Properties
Data block E defines the chemical property information for all organic constituents, water, oxygen,
nitrogen, and an optional single limiting nutrient. The ordering of components is important. The organic
components are input first. Subsequently the water, oxygen, nitrogen are defined followed by the nutrient if
present. Each component is identified with a component number starting with 1 for the first organic
component and proceeding in the order that they are input. The organic components, oxygen and nutrient
can be restricted from partitioning into the gas or aqueous phases by specifying negative values for the
vapor pressure and solubility, respectively. Table 5.8 describes all data in block E. Input values required in
this data block are widely available [c.f. Dean (Ed.), 1985].
5.4.6 Data Block F - Mass Transfer Coefficients
Data block F defines the lumped mass transfer coefficients for all the components. The organic liquid mass
transfer coefficients are input first on a line followed by the minimum allowed deviation (See equation
(3.42) from equilibrium for the organic liquid components on a second line. These two lines are repeated
for water, oxygen, nitrogen, and nutrient if present. Note that exchange coefficients for nitrogen are entered
even though nitrogen does not exchange between phases. Table 5.9 describes all data in block F. The user is
referred to several recent studies which have developed correlations for mass transfer coefficients as an
initial point for setting values appropriate for the desired scenarios [c.f. Wilkins et al., 1995; Powers et al,
1991, 1992, 1994; Cho andJaffe, 1990]
5.4.7 Data Block G - Material Property Block Information
Soil property information and dispersion parameters are defined in data block G, and described in Table
5.10. Input values required in this data block are widely available [c.f. Freeze and Cherry, 1979].
5.4.8 Data Block H - Sorption Parameter Data
Sorption parameter data are specified in block H and are described in Table 5.11.
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Sorption can be modeled as either a rate limited or equilibrium process. If rate limited sorption is
modeled, then the solid phase transport equations must be solved as designated by the control switch
lctrl(25) defined in block B, field 2. Under rate limited conditions, sorption can be modeled with either a
single compartment or two compartment model. The two compartment model, however, is restricted to the
case of a homogeneous soil domain and a single component organic liquid. Additionally, the aqueous-solid
exchange coefficients must be nonzero for all organic liquid components. A positive value indicates
sorption is modeled for that organic component. A negative value indicates no sorption is considered for
that organic component and therefore the solid phase transport equation is not solved for the corresponding
component.
Equilibrium sorption processes are modeled by the inclusion of retardation factors. Equilibrium
sorption can only be considered in the absence of nonequilibrium sorptive processes. However, any
component of the aqueous phase can be modeled with retardation. To implement the use of retardation
factors the control switch lctrl(25) must be set to .false., indicating that the solid phase transport equations
are not solved. Sorption isotherm data is widely available in the literature [c.f. Weber et al, 1988, 1991,
1992].
5.4.9 Data Block I - Biological Parameter Data
Biological parameter data are specified in block I and are described in Table 5.12. This data block is read
only if the biotransformation equations are solved, as indicated by the control switch lctrl(3) defined in
block B, field 2. Otherwise the entire block is omitted.
Five options are available to model biokinetics. Option 1 is standard Monod kinetics. Option 2 is
Monod kinetics with substrate inhibition. Inhibition is modeled with hyperbolic functions that impede
microbial metabolism when substrate or nutrient concentrations are greater than specified threshold limits.
Inhibition can also be applied to the electron acceptor, in which case inhibition occurs when the oxygen
concentration is below the specified threshold limit. Option 3 is Monod kinetics with lumped substrate
inhibition. Under this option lumping only applies to the degradable substrates; nutrient and oxygen are
handled as in option 2. Option 4 is Monod kinetics with saturation dependency. Option 5 is Monod kinetics
with saturation dependency and substrate inhibition. Inhibition is handled as in option 2. The user is
referred to several recent studies as a aid to determining the appropriate parameters required by this data
block [c.f. Sleep andSykes, 1991; Chen etal., 1992; Fuller etal., 1995; Chen, 1996].
5.4.10 Data Block J - Phase Parameter Data
Phase parameter data are specified in block J and are described in Table 5.13. On output, the composition
of each phase is identified. Phase parameter data can be found in standard reference texts [c.f. Dean (Ed.),
1985].
5.4.11 Data Block K - Temperature Parameter Data
Temperature parameter data are specified in block K and are described in Table 5.14.
Steady state temperature distributions can be specified as either uniform or nonuniform with depth. The
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latter option can be used only for rectangular domains, and requires input not only for the depth dependent
temperature distribution, but additionally requires the temperature dependencies of the following 6
parameters: vapor pressure, vapor viscosity, Henry's Law constant, aqueous solubility, maximum substrate
utilization rate, and biomass decay rate. Values for the first 5 temperature dependencies are required for all
components present in a given simulation (Note: values may be required for components to which a given
parameter does not apply, i.e. maximum substrate utilization rate for nitrogen. These values are ignored
subsequent to the input section). Values for the temperature dependent parameters are input for each node
along the vertical boundary. Intermediate values are linearly interpolated for the nodes at the center of
"union jack" grids. The user is referred to Dean (Ed.) [1985] for a description of the temperature
dependencies for the first 4 parameters input in this section. Biological parameter temperature
dependencies are typically estimated with the van't Hoff- Arrhenius equation [c.f. Atlas andBartha, 1987;
Chen et al., 1992].
5.4.12 Data Block L - Output Control Parameters
This data block contains control parameters for the three major output files: 'outpre.out', 'outpre.con', and
'outpre.plt', where 'outpre' is the user specified path and file name from data block A, field 2. The user can
specify output variables for printing in the main output file, for printing in a contour plot format, or for
printing as a time series output. A complete description of the input required in this data block is described
in Table 5.15.
5.4.13 Data Block M - Restart Identifier
This data block contains two logical variables; (lctrl(26)) which is set to .true, if initial conditions (pressure,
saturation, and phase composition) are to be read from the restart file and (lctrl(32)) which is set to .true, if
the run is a continuation of a previous run and .false, if the run is a new run using the previous run as initial
conditions. If (lctrl(26)) is .true, data block M also contains the path and name of the file containing the
restart information.
File D2 is read regardless of whether the restart option is used. However, when the restart option is
specified, initial conditions read from D2 are ignored and superseded by those read from the restart file.
Boundary conditions for either case are read from D2.
5.4.14 Data Block N - Initial Pressure Conditions
Initial pressure conditions are specified in block N as described in Table 5.17. Initial pressure conditions at
all nodes can either be input or computed. Computed pressures are assumed to be in hydrostatic
equilibrium, referenced to atmospheric pressure at ground surface for the gas phase, and referenced to the
gas phase pressure at the water table for the aqueous phase. The presence of organic components in the gas
and aqueous phases is ignored in computing the hydrostatic pressure distributions.
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5.4.15 Data Block O - Velocity Computation
This data block provides information indicating the method used to compute aqueous and gas phase
velocity. Table 5.18 describes all data inputs in block O.
User options are provided to compute nodal velocities from the pressure distribution using a finite
element solution of Darcy's Law. Alternatively element velocities may be computed directly from Darcy's
Law using element averages of the nodal mobilities and densities.
Velocity distributions can be unsteady (flow equations are solved) or assumed to be at steady state. This
is controlled by variable lctrl(l) in block B, field 1 (Table 5.5), which indicates if the flow equations are
solved. The velocity field is assumed to be at steady state if flow equations are not solved. A steady state
velocity field can either be input directly, or computed from an input pressure field.
5.4.16 Data Block P - Organic Liquid Saturation and Composition
Data block P contains the initial quantities for the immobile organic liquid saturation distribution and
composition (component mole fractions). All organic liquid saturations and component mole fractions are
input on a element basis and converted to nodal quantities by averaging adjacent elemental values.
Averaging is not performed across boundaries between different material property blocks. This results in
multiple values of NAPL saturation at boundary nodes between different material property blocks.
Components of the organic liquid are partitioned at equilibrium into the gas, aqueous, solid, and biophases
when present. The mass of the organic liquid is not conserved during this process (i.e. organic mass is
generated). This is only done at nodes where organic liquid is present and can lead to sharp discontinuities
in the composition of the contacting phases. The use of smooth initial conditions such as those resulting
from a restart file generated by a diffusion driven problem is recommended. Table 5.19 describes all data
inputs in block P.
5.4.17 Data Block Q - Oxygen and Nutrient Initial Conditions
Initial conditions for oxygen and nutrient are defined in data block Q and described in Table 5.20. Fields
1-3 are for the gas phase, and fields 4-6 are for the aqueous phase. The initial conditions of the biophase
components are identical to those of the aqueous phase. Initial conditions are required only when oxygen is
present in the phase; i.e. if oxygen is omitted from the gas phase and/or the aqueous phase, then no data is
read for the corresponding phase (oxygen can be omitted from the gas and aqueous phases by assigning
negative inputs to the oxygen vapor pressure and solubility, respectively, in block E). No data is read for
nutrient if it is absent (lctrl(9) = .false.). The biodegradation equations must be solved (lctrl(3) = .true,) in
order for nutrient to be present. When water is present in the gas phase the initial conditions are specified
with a relative humidity of 100%.
5.4.18 Data Block R - Boundary Conditions
Boundary conditions for the flow and transport equations are defined in data block R and described in Table
5.21.
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Boundary conditions on the flow field can be either constant pressure or constant flux (Section 3.11.1).
Boundary conditions at nodes not explicitly specified in data block R are treated as second type with no
flow across the boundary. Boundary conditions arising at an injection/extraction well discussed below are
also implemented through flux source/sink terms (Section 3.11.3).
Boundary conditions for the gas and aqueous phase component transport equations include specified
concentration, specified diffusive flux, or mixed third type conditions. Boundary conditions at nodes not
explicitly specified in data block R are treated as second type with no concentration gradient across the
boundary. No boundary information is required for the immobile phases. Sections 3.11.2 and 3.11.3
discuss the transport equation boundary and associated specifications with extraction/injection wells.
5.4.19 Data Block S - Extraction/Injection Well Conditions
An extraction/injection can be defined in an r-z rectangular domain. Data block S contains input data
defining the well conditions (see Table 5.22). The well is positioned along the left vertical boundary; the
nodal coordinates along the left boundary must be equivalent to the specified well radius. A constant
injection/extraction rate is defined for the duration of the simulation (variable pumping rates require the use
of the restart option). The well screen is defined by specifying the minimum and maximum node numbers
along the well screen.
5.4.20 Data Block T - Velocity Boundary Conditions
Data block T contains input data defining the velocity boundary conditions (see Table 5.23). Boundary
conditions for the gas and aqueous velocities must be specified when the velocities are calculated using the
finite element method (lctrl(18) = .true.). When a boundary is specified as impervious, the velocities
normal to that boundary are zero. The boundary specification is the same for both the gas and aqueous
phases. The domain boundary is divided into 4 sections; top, bottom, left side, and right side. Each section
may be entirely impervious. The top boundary may also be partially impervious (i.e. a partial cap may
exist). The left boundary is adjusted for the presence of a well.
5.5 DESCRIPTION OF OUTPUT FILES
Table 5.3 describes all the output files that can potentially be used in a single simulation run. A given
simulation may not generate every listed output file depending upon user specifications. Only those files
that are required on the basis of user specifications are opened. The following sections provide a
description of the output files.
5.5.1 Main Output File - 'Outpre.out'
The main output file, 'Outpre.out', is always generated and is written to device 21. 'Outpre' contains both
the file name and path, and is specified in data block A, Field 1. 'Outpre.out' contains the input parameters
and selected output variables. The user may elect not to print out the entire set of grid information (see Data
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Block D, Field 1) and the initial conditions (see Data Block L, Field 1) in order to reduce output file size.
The selected output parameters are printed at user specified intervals (see Data Block A, Field 8). The
selected output variables are specified in Data Block L, Field 2. Selection of the individual components in a
phase is done with the global component numbers used to specify the component properties in Data Block
E.
5.5.2 Convergence History and Runtime Information Output File - 'Outpre.cnv'
The convergence history and runtime information output file is optional. This output can be directed to the
screen by setting the ipt(28) = 6 (Data Block A, Field 3), to 'outpre.out' by setting ipt(28) = 21, to
'outpre.cnv' by setting ipt(28) = 23, or not generated by setting ipt(28) = 0. Convergence history and
runtime information output consists of iteration information from the various routines, maximum element
Peclet and Courant numbers for both the gas and aqueous phases (set lctcl(4) = .true.; Data Block B, Field
7), time step information, and error messages from the solver.
5.5.3 Error Message Output File - 'Outpre.err'
Error message output consists of messages from the input error message file, (specified in Data block A,
Field 2) and relates primarily to error checking of input values. The error message output file is optional.
This output can be directed to the screen by setting ipt(29) = 6 (Data Block A, Field 3), to 'outpre.out' by
setting ipt(29) = 21, to 'outpre.err' by setting ipt(29) = 22, or not generated by setting ipt(29) = 0.
5.5.4 Mass Balance Output File - 'Outpre.mb'
The mass balance output file is optional and is generated when lprnt(6) = .true. (Data Block A, Field 5).
When generated, mass balance output is always written to the file, 'outpre.mb' (device 25). The mass
balance output is printed at user specified intervals (see Data Block A, Field 5). Mass balance output is
available in two forms, referred to as report form (lprnt(27) = .true.; Data Block A, Field 5), and in multiple
files as time series form (lprnt(27) = .false.; Data Block A, Field 5).
The report form mass balance contains self explanatory headings and contains both phase and
component mass balances. The boundary, reaction, and source fluxes are also reported, along with separate
values for the boundary fluxes at the surface and at the extraction well. Three types of mass balance errors
are also reported (see Section 4.1). A maximum of nine components are allowed when generating report
form mass balance output.
The time series form mass balance also contains self explanatory headings at the beginning of the
generated output file(s). 'Outpre.mb' only contains the phase mass balance information. Only the first type
mass balance error is reported (see Section 4.1) and surface flux is not reported in 'outpre.mb'. An
additional output file is generated for each of the components present. These additional files are named
'outpre.mb#' (device 28+#) where # is the global component number as defined in data block E. A
maximum of ten components are allowed when generating time series form mass balance output. In the
files, 'outpre.mb#', the surface flux is reported in place of the first type mass balance error. All time series
mass balance output files are formatted: ell.5,llell.4.
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5.5.5 Contour Plot Output File - 'Outpre.con*
The contour plot output file is optional and is generated when lprnt(23) = .true. (Data Block A, Field 4).
When generated, contour plot output is written to the file 'outpre.con' (device 26). The contour plot output
is printed at the same intervals specified for the main output file (see Data Block A, Field 8). The selected
contour variables are specified in Data Block L, Field 2 and may be different than the output variables
selected for the main output file, 'outpre.out'. Selection of the individual components in a phase is done
with the global component numbers used to specify the component properties in Data Block E. The contour
plot file contains self explanatory headings at the beginning of each group of contour variables. Each group
of nodal contour variables has the nodal x (or r) location in the first column and the nodal z location in the
second column. For element contour variables the corresponding locations are for the element centroids.
All contour plot output files are formatted: 8el5.8.
5.5.6 Time Series Plot Output File - 'Outpre.plt'
The time series plot output file is optional and is generated when lprnt(l 5) = .true. (Data Block A, Field 6).
When generated, time series plot output is always written to the file, 'outpre.plt' (device 27). The time
series plot output is printed at user specified intervals (see Data Block A, Field 6). The selected time series
plot variables are specified in Data Block L, Field 3 (gas phase) and 4 (aqueous phase). Time series
plotting is only available for components of the gas and aqueous phases. Specification of time series plot
output requires both the global component numbers used to specify the component properties in Data Block
E and a node number. A given component may be specified at several locations in a phase. A maximum of
six components can be specified for the combined gas and aqueous phases. The time series plot file does
not contain headings. All time series plot output files are formatted: 7el 1.8. The first column contains the
current simulation time in seconds, subsequent columns contain the component mole fractions at the
specified locations in order of their appearance in Data Block L, Field 3 and 4.
5.5.7 Restart Output File - 'Outpre.rst'
The restart output file is optional and is generated when lprnt(5) = .true. (Data Block A, Field 7). When
generated, the restart file is always written to the file, 'outpre.rst' (device 28). The restart file is printed at
the same intervals specified for the main output file (see Data Block A, Field 8). At each print time the
restart file is rewound and restart information is printed over restart output from the previous print time.
Thus 'outpre.rst' contains only restart information corresponding to the latest output time. To use a restart
file, rename 'outpre.rst' to the name specified in Data Block M, Field 2.
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Table 5.1: MISER program modules.
Routine Type
Description
atri.f subroutine Evaluates the area and radial centroid of all elements. Performs minor
error checking on grid geometry.
bcflux.f subroutine Computes gas and aqueous phase fluxes at prescribed pressure and source
nodes.
bio.f subroutine Computes the biological reaction terms using Monod kinetics. Solves the
biophase transport equations when a separate biophase is considered.
cbal.f subroutine Computes global and time step mass balance errors for the aqueous and
gas phases, and for all components in all phases.
commntf subroutine Determines comment lines in the input data files and positions the file
pointer to the next input data field.
dimen.inc include file Included in most MISER routines, this program unit is used to define
parameter variables for array dimensions.
disper.f subroutine Computes the phase dependent portion of the tortuosity coefficient and
the dispersion tensor.
error.f subroutine Reads and writes error message from the error message file. Terminates
execution if the error is designated as fatal.
flow.f subroutine Solves the mobile aqueous and gas phase mass balance equations using
the simultaneously solution method for a single time step.
grid.f subroutine Generates a union jack or herring bone grid for a rectangular solution
domain.
har.f subroutine Contains the subroutines comprising the Harwell sparse matrix package
for linear system solutions.
inputl.f subroutine Reads the input and output file names and opens appropriate file units.
Reads input data for: model control options; time step and iteration con-
trol information; grid information; component chemical properties; mass
exchange information; material property block data; sorption parameters;
biological parameters; temperature data; and output control parameters.
Creates pointers and performs basic error checking on input data.
input2.f subroutine Reads the initial and boundary conditions and performs basic error check-
ing of input data. Reads restart information.
miser.f main program Performs primary controls of simulation: initiates the read of all input
data; loops over all time steps; controls cycling between calls to appro-
priate routines for solution of the flow and transport equations; controls
time step size; and controls calls to output routines.
mobil.f subroutine Evaluates capacity coefficients, and aqueous and gas phase mobility terms
in stacked storage.
molewtf subroutine Updates the gas, aqueous, and organic liquid phase molecular weight,
phase molar density, and phase mass density, based on composition, tem-
perature and pressure.
mpex.f subroutine Computes the mole and mass exchange terms for the flow and transport
routines.
napls.f subroutine Updates the immobile organic liquid saturation using the finite element
solution of the organic liquid phase mass balance equation.
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Table 5.1 (continued).
Routine
Description
naplx.f subroutine
prnt.f subroutine
satw.f subroutine
solid.f subroutine
tlhs.f subroutine
trans.f subroutine
vel.f
subroutine
Updates the immobile organic liquid component mole fractions using the
finite element solution of the component molar balance equation for the
organic liquid phase.
Writes current values of selected variables to the main output, contour
plot, or time series plot files.
Computes water and gas saturation at all nodes based on current values
of nodal capillary pressure.
Updates the solid phase mass loadings using the finite element solution
of the component mass balance equation for the solid phase.
Assembles the finite element matrices for the two dimensional component
mole balance equations.
Controls the sequential solution of the component molar balance equa-
tions for all components in all phases. The solution order is: the organic
components, water, oxygen and nutrient. For each component the solu-
tion order is: biophase; gas phase, aqueous phase, organic liquid phase;
and solid phase.
Computes the mobile phase specific discharge. This routine is not called
when constant velocity simulations are being run.
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Table 5.2: Selected parameter variables defined in the include file 'dimen.inc.'
Type Variable Description
integer nnmx Maximum number of nodes.
integer nelmx Maximum number of elements.
integer nmblk Maximum number of material property blocks.
integer nxmax Maximum number of horizontal blocks in a generated grid.
integer nzmax Maximum number of vertical blocks in a generated grid.
integer ncmpb Maximum number of biomass populations. Currently restricted to one.
integer ncmpo Maximum number of organic components.
integer ncmp Maximum number of components; 3(always) + ncmpb + ncmpo + l(if nutrient is
present).
Maximum number of nodal variables in stacked storage. Currently computed as
1.05*nnmx.
Maximum number of unknowns in the linear system. Currently set to 2*nnmx.
Maximum number of nonzero entries in the coefficient matrix.
Maximum number of nonzero entries in the coefficient matrix.
Minimum difference between the specified residual aqueous phase saturation and
the computed aqueous phase saturation. Currently set to 10~16.
real sgtest Minimum value of gas phase saturation for which a transport equation is written.
Currently set to 0.05.
Solver parameter. Currently set to 0.1.
Solver parameter. Currently set to 1.
Minimum mole fraction for convergence testing in the routine naplx.f. Currently
set to 10~3.
real xround Minimum mole fraction for convergence testing. Currently set to 10~16.
real smino Minimum sustainable organic liquid saturation. Currently set to 10~16.
integer nnstk
integer nsolve
integer icnl
integer irnl
real srwmin
real u
integer mtype
real xmino
79
-------
Table 5.3: Description of input and output files.
File name input/output Unit Description
miser.dl
D2*
input
input
11 Contains user supplied input data for the model control options,
grid information, and the physical, chemical,.and biological
parameters.
13 Contains user supplied input data defining the initial and bound-
ary conditions.
14 Data file containing error and warning messages.
28 A restart input file. Contains restart information necessary to
either continue a terminated run or to use results from a previous
simulation as the initial conditions for a new run. This file is a
renamed copy of 'outpre.rst' generated as output
21 Main output file containing: a listing of most input variables; a
description of boundary and initial conditions; simulation results
for specified variables at selected times.
23 Listing of convergence history and runtime performance.
22 Listing of runtime generated error and warning messages.
25 Listing of runtime generated global mass balance calculations.
24 A contour plot data file. Lists values of selected variables at,
specified times together with their nodal coordinates in a column
format.
26 A time series plot data file. Lists values of selected variables for
each time step.
27 A restart output file generated at the end of the simulation. Con-
tains restart information necessary to either continue a termi-
nated run or to use results from a previous simulation as the
initial conditions for a new run.
* input file name is a user defined input variable and can contain path information
t 'restart.file' for the input restart file is a user defined input variable and can contain path information
t prefix 'outpre' for all output file names is a user defined input variable and can contain path information
miser.error input
restart.file^ input
outpre*.out output
outpre.cnv output
outpre.err output
outpre.mb output
outpre.con output
outpre.plt output
outpre.rst output
80
-------
Table 5.4: Input Data in Block A - Input/Output Files and Control Options.
Record Type
Variable Description
Field 1 - Input files:
1 char*20 infile(2)
2 char*20 infile(3)
Path and name of file D2 containing the initial and boundary conditions
(must be in single quotes).
Path and name of error message file (must be in single quotes). Normally the
file is named 'miser.error' and is located in the directory with the executable
code.
Field 2
1
Field3
1
Prefix name of all output files:
char* 16 outpre Path and prefix name for all output files (must be in single quotes); e.g. if
outpre is defined as 'vent', then the main output file is named 'vent.out'.
- Output unit numbers for error and performance information:
Field 4-
1
integer ipt(29)
integer ipt(28)
Contour plot file:
logical lctrl(23)
Field 5 - Mass Balance Output:
1 logical lprnt(6)
logical lprnt(25)
logical lprnt(27)
integer
real
ipt(83)
t(27)
Field 6-
1
Time series output file:
logical lctrl(15)
The unit number of the output file to which error messages should be directed:
0 = do not print error messages; 6 = screen; 21 = main output file; or 22 =
error message file. The file 'outpre.err' is opened when unit number 22 is
specified.
The unit number of the output file to which runtime performance information
should be directed: 0 = do not print performance information; 6 = screen;
21 = main output file; or 23 = convergence history file. The file 'outpre.cnv'
is opened when unit number 23 is specified.
Set the switch to .true, to open the contour plot output data file 'outpre.con'.
Set the switch to .true, if material balance information should be computed
and printed in the output file 'outpre.mb'.
This record begins on a new line and is required only if lprnt(6) is .true.
Set this switch to .true, if the print interval for material balance output is set
by the number of iterations. Otherwise set the switch to .false, if the print
interval is a constant time interval.
This record is required only if lprnt(6) is .true. Set this switch to .true, if
the material balance output is in report form, otherwise the output will be in
multiple files in time series form.
This record begins 6n a new line and is required only if lprnt(6) is .true. Enter
the number of iterations if lprnt(25) = .true., or the time interval if lprnt(25)
= .false, (s).
Switch is set to .true, to open the time series plot output data file 'outpre.plt'.
81
-------
Table 5.4 (continued).
Record "type
Variable Description
logical lprnt(26)
logical lprnt(28)
integer
real
ipt(84)
t(28)
Field 7 - Restart file:
1 logical lctrl(5)
This record begins on a new line and is required only if lctrl(15) is .true. Set
this switch to .true, if the print interval for time series output is set by the
number of iterations. Otherwise set the switch to .false, if the print interval is
a constant time interval.
This record is required only if lctrl(15) is .true. A logical switch indicating
the concentration units in the time series output: set to .true, for mole fraction;
otherwise set to .false, for mass concentration.
This record begins on a new line and is required only if lctrl(15) is .true. Enter
the number of iterations if lprnt(26) = .true., or the time interval if lprnt(26) =
.false, (s).
Switch is set to .true, to open and print restart data to the file 'outpre.rst'.
Field 8 - Uniform print interval to the main output file:
\ logical Iprnt(O) Set this switch to .true, if the print interval for MISER output to the main
output file 'outpre.out' is set by the number of iterations. Otherwise set the
switch to .false, indicating the print interval is a constant time interval.
2 integer ipt(25) This record begins on a new line. Enter the number of iterations if Iprnt(O) =
real t(12) .true., or the time interval if lprnt(25) = .false, (s).
82
-------
Table 5.5: Input Data in Block B - General Model Control Options.
Record Type Variable Description
Field 1 - Coordinate system:
1 integer ipt(27) Variable designating the coordinate system: 0 = cross-sectional (x-z); 1 =
axisymmetric (r-z).
2 real t(21) Horizontal component of the gravity vector (m / s2).
3 real t(22) Vertical component of the gravity vector (m / s2).
Field 2 - Equation solution options:
1
2
3
logical lctrl(l)
Switch is set to .true, if the aqueous and gas phase mass balance equations are
to be solved.
logical lctrl(2) Switch is set to .true, if the component mass balance equations are to be solved.
logical lctrl(24) Switch is set to .true, if the NAPL phase mass balance equations are to be
solved. Set to .false, if NAPL is absent.
4 logical lctrl(25) Switch is set to .true, if the solid phase mass balance equations are to be solved.
Set to .false, if equilibrium sorption or no sorption is considered .
5 logical lctrl(3) Switch is set to .true, if the biotransformation equations are to be solved. Set
to .false, if biotransformations are not considered.
Field 3 - Mass lumping options:
1 logical lctrl(7) Switch is set to .true, for mass matrix lumping in the solution of the phase
mass balance equations.
2 logical lctrl(8) Switch is set to .true, for mass matrix lumping in the solution of the component
mass balance equations.
Field 4 - Flow solution skipping:
1 integer ipt(85) Number of time steps to be skipped between solutions of the phase phase mass
balance equations. For example if the flow equations are to be solved every
other time step, then a skipping factor of 1 is specified.
Field 5 - Not currently used:
Field 6 - Coupling between flow and transport:
1 logical lctrl(14) Switch is set to .true, if mass exchange terms should be included in the solution
of the flow equations.
Field 7 - Element dimensionless numbers:
1 logical lctrl(4) Switch is set to .true, if element dimensionless numbers should be calculated
for the transport solution.
83
-------
Table 5.6: Input Data Block C - Time Step and Iteration Control Information.
Record Type Variable Description
Field I - Simulation time frame: I
1 real t(l) Initial simulation time (s). \
2 real t(2) Final simulation time (s).
Field 2 - Time weighting:
1 real t(10) Time weighting parameter: 0 = explicit; 1 = implicit; 0.5 = Crank-Nicolson.
Field 3 - Number of time steps:
1 integer ipt(30) Maximum number of time steps.
Field 4 - Convergence tolerance:
1 real t(13) Convergence tolerance in the solution of the phase mass balance equations.
2 real t(14) Convergence tolerance in the solution Of the component mass balance equa-
tions for the mobile phases (aqueous and gas).
3 real t(15) Convergence tolerance in the solution of the organic phase saturation
equations.
4 real t(16) Convergence tolerance in the solution of the component mass balance equa-
tions for the immobile phases.
Field 5 - Time step range:
1 real t(3)
real t(4)
real t(5)
2
3
Field 6-
I
Initial time step (s).
Minimum time step (s).
Maximum time step (s).
Iterations for convergence:
integer ipt(31) Maximum number of iterations for convergence of the phase mass balance
equations.
2 integer ipt(32) Maximum number of iterations for convergence of the component balance
equations.
3 integer ipt(33) Maximum number of iterations for convergence of the organic phase saturation
equations.
Field 7 - Iterations for time step amplification:
1 integer ipt(34) Number of iterations in the solution of the phase mass balance equations below
which time step amplification is permissible. Must be less than the maximum
number of iterations - ipt(31).
2 integer ipt(35) Number of iterations in the solution of the component mass balance equations
below which time step amplification is permissible. Must be less than the
maximum number of iterations - ipt(32).
Field 8 - Time step multiplications factors:
1 real t(6) Empirical time step amplification factor. Must be greater than or equal to one.
2 integer t(7) Empirical time step reduction factor. Must be less than or equal to one.
84
-------
Table 5.7: Input Data Block D - Grid Information and Control Options Information.
Record Type Variable
Description
Field 1
\
Field 2
1
Field3-
1
2
Field 4-
1
2
Output grid geometry:
logical Iprnt(l)
Grid specification options:
integer igrid
FieldS-
1
2
3
Field 6 -
1
2
Set switch to .true, to output all grid geometry to the main output file.
Integer variable indicating if a grid should be generated: 0 = input all element
numbers and nodal coordinates; 1 = generate a union jack grid; 2 = generate
herring bone grid.
Number of blocks in the generated grid (required only if igrid > 0):
integer nx Number of blocks in the horizontal direction of the generated grid.
integer ny Number of blocks in the vertical direction of the generated grid.
Horizontal Block spacing in the generated grid (required only if igrid > 0):
logical Idel Set to .true, if the horizontal spacing is uniform.
real xzero Horizontal coordinate of the left boundary. This should be equal to the well
radius in an axial symmetric domain.
real delx Starting on a new line, enter the horizontal spacings (m) from left to right.
Provide a single value if Idel = .true., otherwise provide nx values. If a single
negative value is provided then the nodal spacing is calculated from eq. (4.12).
Vertical Block spacing in generated grid (required only if igrid > 0):
logical Idel Set to .true, if the vertical spacing is uniform.
real zzero Vertical coordinate of the top boundary.
real delz Starting on a new line, enter of the vertical spacings (m) from top to bottom.
Provide a single value if Idel = .true., otherwise provide nz values.
Material property blocks in the generated grid (required only if igrid > 0):
integer ipt(26) Number of horizontally aligned material property blocks in the generated grid.
integer imblk Required if the ipt(26) > 1. Starting on a new line enter nz integer values
corresponding to the material block number of each vertical spacing from top
to bottom.
Field 7 - Grid dimensions (required only if igrid = 0):
1 integer ipt(O) Number of nodes in the grid.
2 integer ipt(l) Number of elements in the grid.
3 integer ipt(26) Number of material property blocks in the grid.
Field 8 - Nodal incidence list (required only if igrid = 0):
1 integer iel element number.
2 integer nodal(3*iel-2) Global node number of node 1.
3 integer nodal(3*iel-l) Global node number of node 2.
4 integer nodal(3*iel) Global node number of node 3.
5 integer matel(iel) Material block number of element iel. Only required if ipt(26) ^ 1.
Field 8 is repeated for all elements, with data for each element beginning on
a new line. The elements do not need to be listed in sequential order.
Field 9 - Nodal coordinates (required only if igrid = 0):
1 integer ind Node number.
2 real xnode(ind) x-coordinate (horizontal) of node ind (m).
3 real znode(ind) z-coordinate (vertical) of node ind (m).
Field 9 is repeated for all nodes, with data for each node beginning on a new
line. The nodes do not need to be listed in sequential order.
85
-------
Table 5.8: Input Data Block E - Component Chemical Properties.
Record Type Variable
Description
Field 1 - Number ofNAPL components:
1
integer ipt(15)
Enter the number of organic liquid, phase components.
Field 2 - NAPL component chemical properties (required only ifipt(15) > 0):
I integer ic Component number - must range between 1 and ipt(15).
2 char* 10 cname(ic) Component name - must be enter in single quotes.
3 real cmw(ic) Component molecular weight (g / mole).
4 real cvp(ic) Component vapor pressure (atm). A negative value indicates this component
in involatile and is excluded from the gas phase composition.
5 real cvvis(ic) Component vapor viscosity (cPoise).
6 real cden(ic) Component liquid density (g /1).
7 real cmdif(2*ic-l) Component gas diffusivity (cm2 / s).
8 real cmdif(2*ic) Component aqueous diffusivity (cm2 / s).
9 real chen(ic) Component Henry's Law constant (atm 1 / g). Not currently used.
10 real casol(ic) Component aqueous solubility (g /1). A negative value indicates this compo-
nent in insoluble and is excluded from the aqueous phase composition.
Field 2 is repeated for all components in the organic liquid phase. Data for
each component must begin on a new line.
Field 3 - Chemical property data for water, oxygen, and nitrogen:
1-10 - - Provide the same 10 data inputs described in field 2 above for water, oxygen,
and nitrogen. The input order and component numbers are fixed: water =
ipt(15)+l; oxygen = ipt(15)+2; and nitrogen = ipt(15)+3.
Set to .true, if a nutrient is to be modeled.
Field 4 - Nutrient inclusion:
1 logical lctrl(9)
Field 5 - Nutrient chemical properties (required only iflctrl(9) = .true.):
1-10 - - Provide the same 10 data inputs described in field 2 for the nutrient component.
The component number for nutrient must equal ipt(15)+4.
86
-------
Table 5.9: Input Data Block F - Mass Transfer Coefficients.
Record Type Variable
Description
Field 1 - Interphase mass exchange
1
2
3
4
5
6
7
9
10
11
12
integer ic
real kex(5*ic-4)
real kex(5*ic-3)
real kex(5*ic-2)
real kex(5*ic-l)
real kex(5*ic)
integer ic
real
real
real
real
real
kmax(5*ic-4)
kmax(5*ic-3)
kmax(5*ic-2)
kmax(5*ic-l)
kmax(5*ic)
coefficients and minimum deviations from equilibrium:
Component number as defined in data block E.
Aqueous/gas mass exchange coefficient (sec~l).
Aqueous/NAPL mass exchange coefficient (sec~l).
Gas/NAPL mass exchange coefficient (sec~l).
Aqueous/biophase mass exchange coefficient (see"1).
Aqueous/solid mass exchange coefficient (sec~l).
Component number as defined in data block E. This record must start on a
new line.
Aqueous/gas minimum deviation from equilibrium.
Aqueous/NAPL minimum deviation from equilibrium.
Gas/NAPL minimum deviation from equilibrium.
Aqueous/biophase minimum deviation from equilibrium.
Aqueous/solid minimum deviation from equilibrium.
Field 1 is repeated for all components. Data for each component must be
separated by at least one comment line. When a component aqueous-solid
mass transfer coefficient is defined to be zero, that component is not present
in the solid phase. A negative value of the aqueous-solid mass exchange
coefficient indicates that the Freundlich Kf = f0c * ^input where f0c is
defined in bfoc and K- is defined in bok.
87
-------
Table 5.10: Input Data Block G - Material Property Block Information.
Record Type Variable
Description
Field
I
2
3
4
5
6
1 - Soil physical properties:
integer
real
real
real
real
real
iblk
bphi(iblk)
bpermh(iblk)
bpermv(iblk)
bsden(iblk)
bfoc(iblk)
Material property block number - must range between
Porosity (-).
Horizontal component of intrinsic permeability (m2).
Vertical component of intrinsic permeability (m2).
Bulk soil density (g / cm3).
Solid phase organic carbon fraction.
1 and ipt(26).
Field 1 is repeated for all material property blocks. Data for each'block must
start on a new line.
Field 2 - Water retention parameters:
1
2
3
4
integer iblk
real bsrw(iblk)
real bvgn(iblk)
bvga(iblk)
real
Field3
1
2
3
• Dispersion parameters:
integer iblk
real bdisl(iblk)
real bdist(iblk)
Material property block number - must range between 1 and ipt(26).
Residual water saturation (-).
'n' parameter of the van Genuchten fitting function for air/water retention data.
'a' parameter of the van Genuchten fitting function for air/water retention data
(Pa-1).
Field 2 is repeated for all material property blocks. Data for each block must
start on a new line.
Material property block number - must range between 1 and ipt(26).
Longitudinal dispersivity (m).
Transverse dispersivity (m).
Field 3 is repeated for all material property blocks. Data for each block must
start on a new line.
Field 4 - Dispersion tensor computation:
1 logical lctrl(21) Set to .true, if the dispersion tensor should be calculated as a function of the
dispersivities and velocity distribution. Enter .false, if a constant dispersion
tensor is to be input.
Field 4- Dispersion tensor (required only iflctrl(21) = .false.):
1
2
3
4
5
6
7
8
9
10
integer
real
real
real
real
integer
real
real
real
real
ic
d(8*ic-7)
d(8*ic-6)
d(8*ic-5)
d(8*ic-4)
ic
d(8*ic-7)
d(8*ic-6)
d(8*ic-5)
d(8*ic-4)
Component number as defined in data block E.
Dxx - dispersion coefficient of component ic in the gas phase (m2/s).
Dxv - dispersion coefficient of component ic in the gas phase (m2/s).
D^x - dispersion coefficient of component ic in the gas phase (m2/s).
Dy - dispersion coefficient of component ic in the gas phase (m2/s).
Component number as defined in data block E. This record must start on a
new line.
Dxx - dispersion coefficient of component ic in the aqueous phase (m2/s).
£>5 - dispersion coefficient of component ic in the aqueous phase (m2/s).
D*x - dispersion coefficient of component ic in the aqueous phase (m2/s).
£>JL - dispersion coefficient of component ic in the aqueous phase (m2/s).
Field 4 is repeated for all components. Data for each component must be
separated by at least one comment line.
-------
Table 5.11: Input Data Block H - Sorption Parameter Data.
Record Type Variable
Description
Field 1 - Sorption Model (required iflctrl(25) = .true.):
1 logical lctrl(19) Set to .true, if a two compartment sorption model is used (can only be used
under conditions of a homogeneous soil domain and a single component or-
ganic liquid). Set to .false, if sorption is modeled with a single compartment
model.
Field 2 - Two compartment sorption parameters (required iflctrl(25) = .true, and lctrl(J9) = .true.):
\ real xbok Multiplier to convert the slow compartment value of kf defined in bok to the
fast compartment value.
2 real xbom Multiplier to convert the slow compartment value of n defined in bom to the
fast compartment value.
3 real xkex Multiplier to convert the slow compartment value of of the exchange coefficient
to the fast compartment value.
4 real xden Mass fraction of solid phase in the fast compartment.
Field3 - Sorption parameters (required if lctrl(25) = .true.):
1 integer iblk Material property block number - must range between 1 and ipt(26).
2 real bok(see text) Freundlich isotherm kf parameter for each organic component in order from
1 to the number of components (enter ipt(15) values). Units are /j,g I g solid,
with aqueous concentration in mg /1. Index number is (iblk-l)*ipt(15)+ic.
3 integer iblk Material property block number - must range between 1 and ipt(26). This
record must start on a new line.
4 real bom(see text) Freundlich isotherm n parameter for each organic component in order from 1
to the number of components (enter ipt(15) values). Index number is (iblk-
l)*ipt(15)+ic.
Field 3 is repeated for all material property blocks. Data for each block must
start on a new line,
Field 4 - Include retardation factors (required iflctrl(25) - .false.):
1 logical Iretrd Set to .true, if retardation factors should be used.
Field 5 - Retardation factors (required iflctrl(25) = .false, and Iretrd = .true.):
1 integer ic Component number - must range between 1 and ipt(15)+3 if no nutrient is
present, or between 1 and ipt(15)+4 if nutrient is present.
2 real krtd(ic) Retardation factor.'
Field 5 is repeated for all components with data for each component beginning
on a line.
89
-------
fatiie 3:12: Input Data Block I - Biological feamfetef b'ata.
Record Type Variable Description
Field 1 - Number of biodegradable substrates: . . i .
1 iHteger ipt"(i?) Specify the nuMber of 'bfdtiegr'aiiaBie substrates. Miist be less than or equal
ttf ttie number of components in Irie drganic liquid (ipi'(i£)).
Field 2 - Biodegradation control switches:
1 logical Ictrl(l7) Set to .true, if a steady state biomass is to be modeled, otherwise set to .false.
if the biomass is time dependent.
2 logical lctrl(16) Set to .true, if biotransformations are modeled as a sink term in the aqueous
transport equations; otherwise set to .false, if a separate rate limited biophase
is modeled.
Field $ - Growth kimtic's options:
integer
Field 4 - Monod parameters:
1
2
3
4
5
6
7
integer
real
real
real
real
real
real
1C
fuse(ic,l)
fuse(ic,2)
umax(ic)
khalf(ic)
xyield(ic)
kinhib(ic)
Variable indicating ike type of growth" kiffetics: 1 p standard Moiildcl kinetics; 2
= Monod kinetics with substrate inhibition; 3 = Moii'od kinetics with lumped
substrate inhibition; 4 = Monod kinetics with saturation Dependency; 5 =
Monod kinetics with saturation dependency and substrate inhibition.
Component number as defined in block E.
Electron acceptor use coefficient (mole 62 / mole substrate).
Nutrient use coefficient (mole nutrient / mole substrate).
Maximum substrate use rate (g substrate / g biomass / sec).
Half saturation constant (g substrate /1).
Yield coefficient (g biomass / g substrate).
Inhibition constant (unitless) expressed as a fraction of the aqueous solubility.
Constant multiplies the sum of all substrate aqueous solubilities for type 3
growth kinetics.
Field 4 is repeated for all degradable substrates, for oxygen, and additionally
for nutrient, if present (i.e. field 4 is repeated ipt(17)+l times if no nutrient is
present, and ipt(17)+2 times if nutrient is present). Data for each component
must start on a new line.
Field 5 - Decay and biomass range coefficients:
1
2
3
4
5
real
real
real
real
real
kd
xbmin
xbmax
xinit
t(H)
Decay coefficient (sec !).
Minimum biomass (g biomass /1 media).
Maximum biomass (g biomass /1 media).
Initial uniform biomass (g biomass /1 media).
Delay period for initiation of bioreactions (sec).
90
-------
Table 5.13: Input Data Block J - Phase Parameter Data.
Record Type Variable Description
Field 1 - Water phase viscosity:
1 real wvis Water phase viscosity (cPoise).
Field 2 - Gas phase slip flow parameters:
1 logical lctrl(20) Set to .true, if gas phase slip flow is simulated with the Klinkenberg model.
2 real b Klinkenberg parameter (atm). Set the value to zero if lctrl(20) = .false.
91
-------
Table 5.14: Input Data Block K - Temperature Parameter Pata.
Record Type Variable Description
Field I - Temperature distribution:
1 logical lctrl(lO) Set to -true, if the steady state temperature distrjbutipn is .uniform, or set to
.false, if the temperature distribution is depth .dependent.
Field2 - Uniform temperature (required only iflctrl(lO) •= .true.):
I real ctemp Specify the uniform temperature (°C).
FieldS - Nommiform temperature distribution (required iflctrl(lO) = false.):
1 real depthnd Depth (m). .
2 real tnode Temperature at the depth = depthnd (°C).
Field 3 is repeated for all vertical .nodes along the boundary starting at the
surface, downward (ny+1 values). Data for each node begins a new line.
Field 4 - Temperature dependent vapor pressure (required iflctrl(10) = false.):
1 real dtemp Temperature dependent vapor pressure (atm). Provide ny+1 values, one for
each node in the vertical direction.
Field 5 - Temperature dependent vapor viscosity (required iflctrl(lO) = false.):
1 real dtemp Temperature dependent vapor viscosity (cPoise). Provide ;ny+l values, one
for each node in the vertical direction.
Field 6 - Temperature dependent Henry's Law constant (required iflctrl(lO) = .false.):
1 real dtemp Temperature dependent Henry's Law constant (atm 1/g). Provide ny+1 values,
one for each node in the vertical direction.
Field 7 - Temperature dependent aqueous solubility (required iflctrl(lO) = false.):
1 real dtemp Temperature dependent aqueous solubility (g /I). Provide :ny+l values, one
for each node in the vertical direction.
Field 8 - Temperature dependent maximum substrate use rate (required iflctrl(lO) - .false.):
\ real dtemp Temperature dependent maximum substrate use rate (g substrate / g biomass
/ sec). Provide ny+1 values, one for each node in the vertical direction.
Fields 4-8 are repeated for all components in the order established in block
E: organic liquid components, water, oxygen, nitrogen, nutrient. Data for
each component property begins on a new line, separated from the previous
information by at least one comment line.
Field 9 - Temperature dependent biomass decay rate (required iflctrl(10) = false.):
1 real dtemp Temperature dependent biomass decay rate (sec""1). Provide ny+1 values, one
for each node in the vertical direction.
92
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Table 5.15: Input Data Block L - Output Control parameters.
Record Type Variable Description
Field 1 - Print initial conditions:
1 logical lprnt(3) Set to .true, if the initial conditions should be printed to the main output file.
Field 2 - Print switches for selected variables:
la
Ib
2a
2b
3a
3b
4a
4b
5a
5b
6a
6b
7a
7b
8b
8c
8d
9a
9b
9c
9d
logical
logical
logical
logical
logical
logical
logical
logical
logical
logical
logical
logical
logical
logical
logical
logical
integer
lprnt(8)
lcon(l)
lprnt(9)
lcon(2)
Iprnt(lO)
lcon(3)
Iprnt(ll)
lcon(4)
lprnt(12)
lcon(5)
lprnt(13)
lcon(6)
lprnt(14)
lcon(7)
lprnt(15)
lcon(8)
ipt(69)
integer icp
logical lprnt(16)
logical lcon(9)
integer ipt(70)
integer icp
Phase concentrations in the main output file are reported in mole fractions
(.true.) or mass concentration (.false.).
Phase concentrations in the contour plot file are reported in mole fractions
(.true.) or mass concentration (.false.).
Print nodal gas phase pressure to the main output file. This record starts on a
new line.
Print nodal gas phase pressure to the contour plot file.
Print nodal aqueous phase pressure to the main output file. This record starts
on a new line.
Print nodal aqueous phase pressure to the contour plot file.
Print nodal gas/aqueous capillary pressure to the main output file. This record
starts on a new line.
Print nodal gas/aqueous capillary pressure to the contour plot file.
Print nodal gas phase density to the main output file. This record starts on a
new line.
Print nodal gas phase density to the contour plot file.
Print nodal aqueous phase density to the main output file. This record starts
on a new line.
Print nodal aqueous phase density to the contour plot file.
Print nodal NAPL phase density to the main output file. This record starts on
a new line.
Print nodal NAPL phase density to the contour plot file.
Print nodal gas phase component concentrations to the main output file. This
record starts on a new line.
Print nodal gas phase component concentrations to the contour plot file.
The number of gas phase components to be outputted. This sub-record is
required only if Iprnt or Icon is .true, in 8a or 8b above. This sub-record starts
on a new line.
Enter ipt(69) component numbers of the corresponding components to be
outputted. This sub-record is required only if Iprnt or Icon is .true, in 8a or 8b
above.
Print nodal aqueous phase component concentrations to the main output file.
This record starts on a new line.
Print nodal aqueous phase component concentrations to the contour plot file.
The number of aqueous phase components to be outputted. This sub-record is
required only if Iprnt or Icon is .true, in 9a or 9b above. This sub-record starts
on a new line.
Enter ipt(70) component numbers of the corresponding components to be
outputted. This sub-record is required only if Iprnt or Icon is .true, in 9a or 9b
above.
93
-------
Table 5.15 (continued).
Record Type Variable Description
lOa
lOb
lOc
lOd
lib
lie
lid
12a
12b
12c
12d
13a
13b
14a
14b
15a
15b
16a
16b
17a
17b
13a
18b
logical Iprht(17)
logical
integer
lcon(10)
ipt(71)
integer icp
lla logical lprnt(18)
logical
integer
logical
integer
logical
logical
logical
logical
logical
logical
logical
logical
logical
logical
lcon(l 1)
ipt(72)
integer icp
logical lprnt(19)
lcon(12)
ipt(73)
integer icp
logical lprnt(29)
lcon(18)
lprnt(20)
lcon(13)
lprnt(21)
lcon(14)
lprnt(22)
lcon(15)
lprnt(23)
lcon(16)
lprnt(24)
logical lcon(17)
Print nodal organic liquid component concentrations to the main output file.
This record starts On a tiew line.
Print nodal organic liquid component concentrations to the contour plot file.
The number of organic liquid components to be outputted. This sub-record
is required only if Iprnt or Icon is .true, in lOa or lOb above. This sub-record
starts on a new line.
Enter ipt(71) component numbers of the corresponding components to be
outputted. This sub-record is required only if Iprnt or Icon is .true, in lOa or
lOb above.
Print nodal solid phase component loadings to the main output file. This
record starts on a new line.
Print nodal solid phase component loadings to the contour plot file.
The number of solid phase component loadings to be outputted. This sub-
record is required only if Iprnt or Icon is .true, in lla or lib above. This
sub-record starts on a new line.
Enter ipt(72) component numbers of the corresponding components to be
outputted. This sub-record is required only if Iprnt or Icon is .true, in 1 la or
lib above.
Print nodal biophase component concentrations to the main output file. .This
record starts on a new line.
Print nodal biophase component concentrations to the contour plot file.
The number of biophase component concentrations to be outputted. This sub-
record is required only if Iprnt or Icon is .true, in 12a or 12b above. This
sub-record starts on a new line.
Enter ipt(73) component numbers of the corresponding components to be
outputted. This sub-record is required only if Iprnt or Icon is .true, in 12a or
12b above.
Print total organic soil concentration to the main output file. This record starts
on a new line.
Print total organic soil concentration to the contour plot file.
Print nodal gas phase saturation to the main output file. This record starts on
a new line.
Print nodal gas phase saturation to the contour plot file.
Print nodal aqueous phase saturation to the main output file. This record starts
on a new line.
Print nodal aqueous phase saturation to the contour plot file.
Print nodal NAPL saturation to the main output file. This record starts on a
new line.
Print nodal NAPL saturation to the contour plot file.
Print gas phase velocity to the main output file. This record starts on a new
line.
Print gas phase velocity to the contour plot file.
Print aqueous phase velocity to the main output file. This record starts on a
new line.
Print aqueous phase velocity to the contour plot file.
94
-------
Table 5.15 (continued).
Record Type Variable Description
Field 3 - Gas Phase time series plot switches:
logical
integer
lplt(D
ipt(81)
3a
3b
integer icp
integer icp
Set to .true, if the time series plot files should be generated for gas phase
components.
If Iplt = .true, then starting a new line, enter the number of gas phase compo-
nents to be reported in the time series plot file.
If Iplt = .true, enter the global component number and the nodal location for
which time series data should be outputted.
If Iplt = .true, enter the nodal location for which time series data should be
outputted.
Field 3a and 3b is repeated ipt(81) times.
Field 4 - Aqueous Phase time series plot switches:
1 logical lplt(2) Set to .true, if the time series plot files should be generated for aqueous phase
components.
2 integer ipt(82) If Iplt = .true, then starting a new line, enter the number of aqueous phase
components to be reported in the time series plot file.
3a integer icp If Iplt = .true, enter the global component number, and the nodal location for
which time series data should be outputted.
3b integer icp If Iplt = .true, enter the nodal location for which time series data should be
outputted.
Field 3a and 3b is repeated ipt(82) times. A maximum of 6 components for
the combined gas and aqueous phases can be defined for time series output.
95
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Table 5.16: Input Data Block M - Restart Identifier.
Record Type Variable Description
Field I - Restart control switches:
1 logical lctrl(26) Specify .true, if initial saturation and component information should be read
from the restart file 'restart.file', where the file path and name is defined in
field 2 of this data block.
2 logical lctrl(32) Specify .true, if the run is a continuation of the previous run and .false, if the
run is a new run using the previous run as initial conditions.
Field 2 - Restart file identifier: (required only if lctrl(26)=.true.
1 char*20 infile(4) Path and name of restart input file (must be in single quotes). This file is a
renamed copy of 'outpre.rst' generated as output. '
96
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Table 5.17: Input Data Block N - Initial Pressure Conditions.
Record Type Variable Description
Field I - Initial pressure distribution:
1 integer ipt(75) Variable indicating how initial conditions are specified: 1 = compute hydro-
static gas and aqueous phase distributions; 2 = input gas and aqueous pressures
for all nodes.
Field 2 - Water table depth (required only ifipt(75) - 1):
1
real wtdpth Water table depth (m).
Field 3 - Initial pressure:
1
2
3
integer
real
real
nd
p(2*rid-l)
p(2*nd)
Node number.
Aqueous phase pressure at node nd (Pa gauge).
Gas phase pressure at node nd (Pa gauge).
Field 3 is repeated for all nodes with data for each node beginning on a new
line. The nodes do not need to be in sequential order. A uniform pressure
distribution can be specified by specifying a single line of data containing a
negative node number and the uniform aqueous and gas pressures.
97
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Table 5.18: Input Data Block O - Velocity Computation.
Record lype Variable
Description
Field I - Velocity computation method:
1 logical lctrl(18) Setto.true.ifnodalvelocitiesshouldbeecffiputedbysolutionoffimteelement
equations. Set to .false, if velocities should be computed as element averages,
or if a steady state velocity field is assumed (i.e. flow equations are not solved
- lctrl(l) = .false.).
Field 2 - Steady state velocity distribution (required only iflctrl(l) = .false.):
1 logical Icssv Set to .true, if the steady state velocity distribution should be calculated from
the pressure field by the method defined in field 1. Set to .false, to input
velocity values at all nodes.
FieldS - Input velocity distribution (required only if Icssv = .false.):
1 logical lev Set to .true, if the user defined steady state velocity distribution has uniform
components.
Field 4- Uniform velocity components (required only if lev = .true.):
1 real qgx Horizontal component of the uniform steady state gas phase Darcy velocity
(m/s).
2 real qgz Vertical component of the uniform steady state gas phase Darcy velocity (m /
s).
3 real qax Horizontal component of the uniform steady state aqueous phase Darcy ve-
locity (m / s).
4 real qaz Vertical component of the uniform steady state aqueous phase Darcy velocity
(m/s).
FieldS - Nonuniform velocity components (required only if lev = .false.):
1 integer i Node or element number.
2 real q(i) Horizontal component,of the steady state gas phase Darcy velocity (m / s) at
node or element i.
3 real q(ipt( 1 )+i) Vertical component of the steady state gas phase Darcy velocity (m / s) at node
or element i.
4 real q(2*ipt(l)+i) Horizontal component of the steady state aqueous phase Darcy velocity (m /
s) at node or element i.
5 real q(3*ipt(l)+i) Vertical component of the steady state aqueous phase Darcy velocity (m / s)
at node or element i.
Field 5 is repeated for all nodes if lctrl(18) = .true., or for all elements if
lctrl(18) = .false. Data for each node or element must start on a new line.
98
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Table 5.19: Input Data Block P - Organic Liquid Saturation and Composition.
Record Type Variable
Description
Field 1 - Elements containing organic liquid saturation:
1 integer inoel Number of elements containing nonzero organic liquid saturation. A number
less than zero indicates that the organic liquid saturation is uniform and con-
tained in all elements. A value of zero must be entered if the organic liquid
mass balance equations are not solved (lctrl(24)=.false.).
Field 2 - Uniform organic liquid saturation and composition (required only if inoel < 0):
1 real soel(l) Uniform organic liquid saturation for all elements.
2 real omfel(ic) Enter the organic liquid mole fraction of each organic component. There must
be ipt(15) mole fractions specified and they must sum to 1. Mole fractions
are entered in sequential order as defined in block E, field 2 (i.e. component
number 1 to ipt(15)).
Field 3 - Nonuniform organic liquid saturation and composition (required only if inoel > 0):
1 integer iel Element number.
2 real soel(iel) Organic liquid saturation in element iel.
3 real omfel(ic,iel) Enter the organic liquid mole fraction of each organic component in element
iel. There must be ipt(15) mole fractions specified and they must sum to 1.
Mole fractions are entered in sequential order as defined in block E, field 2
(i.e. component number 1 to ipt(15)).
Field 3 is repeated for all elements with nonzero organic liquid saturation
(inoel elements). Data for each element must start on a new line.
99
-------
Table 5.20: Input Data Block Q - Oxygen and Nutrient Initial Conditions.
Record type Variable
Description
Field 1 - Uniform gas phase conditions (required if oxygen is present in the gas phase):
1 logical lunfx Set to .true, if the initial oxygen and nutrient (if present) partial pressure
in the gas phase is uniform. Otherwise set to .false, for nonuniform initial
conditions. Skip this input if oxygen is absent from the gas phase (i.e. the
oxygen partial pressure (cvp(ipt(15)+2)) is assigned a negative value).
Field 2 - Uniform oxygen and nutrient conditions in the gas phase (lunfx = .true.):
1 real xog Initial uniform oxygen partial pressure (i.e. mole fraction) in the gas phase.
2 real xng Initial uniform nutrient partial pressure (i.e. mole fraction) in the, gas phase.
Not required if nutrient is absent (i.e. lctrl(9) = .false.).
Field 3 - Nonuniform oxygen and nutrient conditions in the gas phase (lunfx = .false.):
1 integer hd Node number.
2 real xmf(nd+go) Initial oxygen partial pressure (i.e. mole fraction) in the gas phase at node nd
(go is an internally defined pointer).
Initial nutrient partial pressure (i.e. mole fraction) in the gas phase at node nd
(gn is an internally denned pointer). Not required if nutrient is absent (i.e.
lctrl(9) = .false.).
Field 3 is repeated for all nodes. Data for each node must start on a new line.
Field 4 - Uniform aqueous phase conditions (required if 02 is present in the aqueous phase):
1 logical lunfx Set to .true, if the initial oxygen and nutrient (if present) concentrations in
the aqueous phase are uniform. Otherwise set to .false, for nonuniforrn initial
conditions. Skip this input if oxygen is absent from the aqueous phase (i.e.
the oxygen solubility (casol(ipt(15)+2)) is assigned a negative value). Note
that this variable is read twice in this data block.
Field 5 - Uniform oxygen and nutrient conditions in the aqueous phase (lunfx = .true.):
1 real xog Initial uniform oxygen concentration (g /1) in the aqueous phase.
2 real xng Initial uniform nutrient concentration (g/1) in the aqueous phase. Not required
if nutrient is absent (i.e. Ictrl(9) = .false.).
Field 6 - Nonuniform oxygen and nutrient conditions in the aqueous phase (lunfx = .false.):
real xmf(nd+gn)
1
2
integer
real
nd
xmf(nd+ao)
real xmf(nd+an)
Node number.
Initial oxygen concentration (g/1) in the aqueous phase at node nd (ao is an
internally defined pointer).
Initial nutrient concentration (g/1) in the aqueous phase at node nd (ao is an
internally denned pointer). Not required if nutrient is absent (i.e. lctrl(9) =
.false.).
Field 6 is repeated for all nodes. Data for each node must start on a new line.
100
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Table 5.21: Input Data Block R - Boundary Conditions.
Record Type Variable Description
Field 1 - Constant gas pressure nodes equivalent to the initial pressure:
1 integer itypel Specify the number of nodes with a constant gas pressure equal to the initial
gas pressure.
2 integer ibc Beginning on a new line specify the node number of all nodes with a constant
gas pressure equal to the initial gas pressure. There must be a total of itypel
values.
Field 2 - Constant gas pressure nodes different from the initial pressure:
1 integer ipt(18) Specify the number of nodes with a constant gas pressure that is different
from the initial gas pressure.
Node number of a constant gas pressure node different from the initial gas
pressure at that node (required if ipt(18) > 0).
Constant gas pressure at node ibc (Pa gauge).
Records 2 and 3 are repeated for all nodes, with data for each node starting
on a new line. There must be a total of ipt(18) lines.
• Constant aqueous pressure nodes equivalent to the initial pressure:
integer itypel Specify the number of nodes with a constant aqueous pressure equal to the
initial aqueous pressure.
2 integer ibc Beginning on a new line specify the node number of all nodes with a constant
aqueous pressure equal to the initial aqueous pressure. There must be a total
of itypel values.
Field 4 - Constant aqueous pressure nodes different from the initial pressure:
1
2
3
Fields
1
integer ipt(18)
integer ibc
real p(2*ibc)
2
3
integer ipt( 1 9)
integer ibc
real
p(2*ibc-l)
Specify the number of nodes with a constant aqueous pressure that is different
from the initial aqueous pressure.
Node number of a constant aqueous pressure node different from the initial
gas pressure at that node (required if ipt(19) > 0).
Constant aqueous pressure at node ibc (Pa gauge).
Records 2 and 3 are repeated for all nodes, with data for each node starting
on a new line. There must be a total of ipt(18) lines.
Field 5 - Gas phase component boundary conditions:
1
integer ipt(20)
2
3
integer
integer
4 & 5 real
ibc
ibcxmf
bcxmf
dfxmf
Specify the number of nodes for which gas phase component boundary con-
ditions are specified.
Node number (required if ipt(20) > 0).
An integer variable indicating the boundary condition type (1, 2, or 3) for
all gas phase components at the node ibc: 1 = constant mole fraction; 2 =
constant diffusive flux; 3 = mixed type (contact with a known fluid).
For each component in the gas phase provide two values: 1) the partial
pressure (i.e. mole fraction) of the component in the contacting fluid at node
ibc, and 2) the molecular diffusivity divided by a characteristic length, DmfL
(m/s). Each pair of values must be listed in sequential order corresponding to
the component numbers. Only components that are present in the gas phase
are listed; component boundary conditions are not read for components which
are excluded from the gas phase (i.e. negative vapor pressure).
101
-------
Table 5.21 (continued).
Record Type Variable Description
Records 2-5 are repeated for all nodes for which gas phasp component bound-
ary conditions are provided (ipt,(20) nodes). Data for each node must start on
a new line,
Field 6 - Aqueous phase component boundary conditions:
1
2
3
integer ipt(21)
Specify the number of nodes for which aqueous phase component boundary
conditions are specified. \
integer ibc Node number (required if ipt(21) > 0).
integer ibcxmf An integer variable indicating the boundary condition type (1, 2, or'3) for all
aqueous phasp components at the node ibc: 1 = constant mole fraction; 2 =
constant diffusive flux; 3 = mixed type (contact with a known fluid).
4&S real bpxmf For each component in the aqupous phasp provide two values: 1) the con-
dfxmf centration of thp component concentration in the contacting fluid at node ibc
(g/1), and 2) the molecular diffusivity divided by a characteristic length, Dm/L
(m/s). Each pair of values must be listed in sequential order corresponding
to the component numbers. Only components that are present in the aqueous
phase are listed; component boundary conditions are not read for components
which are excluded from the aqueous phase (i.e. negative solubility).
Records 2-5 are repeated for all nodes for which aqueous phase component
boundary conditions are provided (ipt(21) nodes). Data for each node must
start on a new line.
Field 7 - Gas phase boundary fluxes:
1 integer ipt(22) Specify the number of nodes for which a constant gas phase flux is to specified.
2
3
integer ibc
real source
Node number (required if ipt(22) > 0).
The constant gas phase flux referenced to atmospheric pressure and the steady
temperature at the node (m3/s).
Records 2-3 are repeated for all nodes for which gas phase fluxes are provided
(ipt(22) nodes). Data for each node must start on a new line.
FieldS - Aqueous phase boundary fluxes:
1 integer ipt(23) Specify the number of nodes for which a constant aqueous phase flux is to
specified.
2
3
integer
real
ibc Node number (required if ipt(23) > 0).
source The constant aqueous phase flux at the node (m3 / s).
Records 2-3 are repeated for all nodes for which aqueous phase fluxes are
provided (ipt(23) nodes). Data for each node must start on a new line.
102
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Table 5.22: Input Data Block S - Extraction/Injection Well Conditions.
Record Type Variable Description
Field I - Include extraction/injection well:
1 logical lctrl(12) Specify .true, if a extraction/injection well should be simulated in an axisym-
metric domain.
Field 2 - Extraction/injection rate:
1 real qwell Enter the volumetric extraction (negative) or injection (positive) rate (scfm).
Field 3 - Well coordinates:
1 real rwell Enter the well radius (m). This must equal the nodal coordinate along the left
vertical boundary.
2 integer ii Minimum node number along the well screen.
3 integer jj Maximum node number along the well screen.
103
-------
Table 5.23: Input Data Block T - Velocity Boundary Conditions.
Record Type Variable Description
Field 1 - Specify bottom boundary (required only iflctrl(18) = .true.):
1 logical lctrl(28) Specify .true, if the bottom boundary is impervious.
Field 2 - Specify right boundary (required only iflctrl(lS) = .true.):
1 logical lctrl(29) Specify .true, if the right boundary is impervious.
FieldS - Specify left boundary (required only iflctrl(18) = .true.):
1 logical lctrl(SO) Specify .true, if the left boundary is impervious (note: this boundary is ad-
justed for the presence of a well).
Field4 - Specify top boundary (requiredonly iflctrl(18) = .true.):
1 logical lctrl(31) Specify .true, if the top boundary is impervious.
FieldS - Specify the cap length (required only iflctrl(Sl) = .true.):
1 real caplen Length of the impervious segment along the top boundary starting at the left
edge (m).
104
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Section 6
DEMONSTRATION OF MISER
Three example simulations are presented to illustrate usage of the MISER model. The first two
examples present simulations of hypothetical SVE and BV scenarios in domains wherein the water table is
at a large depth and is therefore excluded from the simulation. The third example problem describes the
simulation of bioventing under more realistic field conditions. In this simulation the contaminants are
positioned close to the water table such that the capillary fringe and water table are included in the
simulation. Simulation results illustrate the influence of contaminant migration and partitioning into the
capillary fringe region on the simulated bioventing performance.
Hypothetical SVE and BV scenarios are simulated for a layered soil domain shown in Fig. 6.1. Input
files for the SVE simulation are included in Appendix G. The soil is a medium uniform sand, intersected
with a layer of slightly less permeable fine sand. The soil water is at residual levels throughout the domain.
All soil properties .are listed in Table 6.1.
The organic liquid is pure toluene which is assumed to be present as an immobile residual. The initial
toluene mass is 239 kg with saturations ranging up to 3.5%. This initial distribution was generated with a
two dimensional multiphase flow simulator, M-VALOR [Abriola etal, 1992]. Initial toluene
concentrations in the aqueous and gas phases are assumed to be at equilibrium with the organic liquid when
present, and zero elsewhere. The constituent and transport properties used in the simulations may be found
in the input file listing given in Appendix G.
Numerical simulations of SVE and BV remediation were obtained on a radially symmetric r-z
rectangular solution domain (41.67 m by 4.5 m). No flow boundary conditions were specified along the top
boundary over the radius of the impermeable cap, along the left boundary above and below the well screen,
Q
10m
3m
medium sand
fine sand
medium sand
1 m
1 m
Figure 6.1: Problem depiction used in example simulations. Contours show the initial organic liquid distri-
bution. The contour interval is 0.005 with levels increasing inward.
105
-------
Parameter
4>
kx (in2)
kz (in2)
Srw
h
a (I/Pa)
medium saiid
0.35
ixio-11
sxio-12
0.12
7.0
0.002
fine sand
0.33
6xlQ-12
4xl5-12
0.16
5.0
0.0008
Table 6.1: Soil properties used in example SVE and BV simulations.
Phase Pair
organic-gas
aqueous-gas
aqueous-organic
aqueous-solid
Mass Transfer
Coefficient (I/sec)
5.0 x wr4
5.0 x io-5
5.0 x 10~4
5.0 x 10~5
Minimum Element Deviation
frbffi Equilibrium
D.I
0.1
0.1
0.1
Table 6.2: Mass transfer coefficients used to simulate an SVE system.
and along the bottom boundary. Atmospheric pressure conditions were specified along the right boundary
and the portion of the ground surface open to the atmosphere. Both aqueous and gas phases are assumed to
be in hydrostatic equilibrium initially. Other problem dependent conditions are described below.
6.1 SOIL VAPOR EXTRACTION
Remediation of the contaminated soil by SVE was simulated by the numerical application of a constant
extraction rate of 100 cubic feet per minute (scfm). Biodegradation 'is not included in this simulation. The
solution domain is developed with a generated "herring bone" grid using uniform vertical spacings of 0.25
m and horizontal spacing ranging from 1 cm near the well to 5 m at the right boundary. The solution
domain is divided into 1116 elements and 608 nodes.
Mass transfer coefficients were selected to represent relatively fast organic liquid volatilization and
slower rates for desorption and aqueous/gas partitioning. These later processes are considered primary
factors controlling long term tailing processes frequently observed in SVE systems. Table 6.2 summarizes
the values of mass transfer coefficients used in this simulation.
Fig. 6.2 shows a progression of predicted organic liquid saturation profiles. The greatest rate of organic
liquid is in the surface and bottom layers where the initial organic liquid saturations are smallest and gas
phase velocities are comparatively large. The organic liquid persists in the middle layer due to the larger
initial organic liquid mass present and due to effects from flow bypassing of the lower permeability zone.
The pattern of organic liquid removal is generally radially inward since the greatest mass transfer occurs at
the outward edge of the organic liquid zone.
106
-------
1 -
r 2.
3_
4.
.
*
time = 1 day
time = 3 days
time = 5 days
01234012340
radius (m) radius (m)
1234
radius (m)
Figure 6.2: Predicted organic liquid saturation distribution in SVE simulations with intermediate mass
transfer rates. The contour interval is 0.005 with levels increasing inward.
0
time = 20 days
time = 100 days
1-
2_
3-
4-
50
16Q\\
100\
5.0
0123401234
radius (m) radius (m)
Figure 6.3: Toluene sorbed (ppm) at 20 and 100 days.
Fig. 6.2 shows that organic liquid is removed relatively quickly from the domain, in about 7 days.
However, toluene is retained on the solid phase and in the pore water throughout the simulation, due to low
solid-aqueous and aqueous-gas mass transfer rates. Comparison of the sorbed toluene mass at 20 and 100
days (Fig. 6.3) indicates that very little sorbed mass is removed during this period. Moreover, toluene mass
distributions plotted in Fig. 6.4 indicate that in this simulation the overall SVE efficiency is controlled by
the aqueous-solid desorption rate after the period of organic liquid removal.
6.2 BIOVENTING
Remediation of the contaminated soil by B V was simulated by the numerical application of a constant
injection rate of 1 cubic feet per minute (scfm) to supply oxygen and enhance biotransformation. Air
107
-------
-NAPL
- welt fltix
• sofbed
10
—I—
20
—l—
30
—l—
40
50
times (day)
Figure 6.4: Toluene removal versus time.
injection produces outward radial movement of oxygen (electron acceptor), as well as for toluene
(substrate) due to volatilization from the organic liquid. Sorption is not included in this simulation. The
solution domain is developed with a generated "herring bone" grid using uniform vertical spacings of 0.25
m and horizontal spacing ranging from 1 cm near the well to 2 m at the right boundary. The solution
domain is divided into 1404 elements and 660 nodes.
Because gas phase velocities are smaller in the BV system, the fluid-fluid mass transfer coefficients
used in this simulation were reduced one order of magnitude from those listed in Table 6.2. The resulting
progression of predicted organic liquid saturation profiles is shown in Fig. 6.5. Since the gas flow is radially
outward, organic liquid removal occurs from left to right in BV (injection) in Contrast with the right to left
progression observed in the SVE (extraction) results. Also note that the organic liquid persists substantially
longer in the BV system than in the SVE system due to diminished flow rate. Similar to the SVE results,
organic liquid persists in the lower portion of the lower permeability layer, where bypassing effects are
most pronounced.
Biotransfonnation processes in the BV scenario were simulated using the assumption of equilibrium
partitioning between the aqueous and biophases (i.e. bioreaction was modeled as a sink). The effect of
substrate inhibition was examined by setting the inhibitory threshold to 25% of the toluene aqueous
solubility. The presence of a limiting nutrient was not considered. Other biodegradation parameters
employed in this simulation are listed in Table 6.3.
Fig. 6.6 shows the predicted growth of biomass over the course of BV simulation. Due to substrate
inhibition, biomass growth is concentrated away from the NAPL contaminated core, developing a so-called
'biofence.' Once the 'biofence' has developed, the toluene is removed from the gas phase over a relatively
short distance, and there is little or no growth to the right of the 'biofence' due to an absence of substrate.
Biomass growth is also observed to fill in regions close to the well after organic liquid has been removed
and aqueous concentrations fall below the inhibitory threshold. The maximum oxygen depletion was on the
order of 10%.
108
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time = 20 days
time = 60 days
time = 100 days
1-
*
2-
•
3-
4-
(
0.5—--,
^^— l.(K \
\ \
--^•"^M
^=^JJ
~^^
3123^
•
•
_
.
-
I (
_----"' o.s
~~s^~i-n
^)
) 1 2 3 ^
•
•
.
-
1 (
^\
-------
.constant flux ^- impermeable cap
10m 20m
-constant pressure
30 m 37.6 m
-J -4-0 no/
m
5x10"11 m2
0.7x10"11 m2
-6m
8m
-10m
12m
-14.2m
no flow
Figure 6.7: Simulation domain used in the field scale bioventing demonstration simulation.
and density driven flow and then partition into the capillary fringe region. MISER is applied to a single
well, axisymmetric domain with three horizontally stratified soil layers as shown in Figure 6.7. Soil
properties are listed in Table 6.4 and are roughly based on those of the Borden aquifer. An immobile
residual organic liquid distribution is present above the water table as shown in Figure 6.7. For the purposes
of illustration this organic liquid distribution was developed by simulating the migration from a organic
liquid spill event using an immiscible flow simulator, M-VALOR [Abriola et at., 1992]. The initial organic
liquid distribution shown in Figure 6.7 is composed of a binary mixture of benzene and xylene. All
chemical properties are listed in Table 6.5.
To develop realistic initial conditions for the simulation of BV remediation, the MISER code was first
used to simulate the partitioning and migration of the organic liquid components over a 54 day
redistribution period during which time no stresses are applied at the well. To simulate this process the
domain was discretized into 2337 nodes and 4480 elements, with vertical discretization between nodes
ranging between 0.1 and 0.5 m, and horizontal discretization ranging between 0.05 - 2.0 m. Other transport
parameters used in the simulation are listed in Table 6.6 and boundary conditions are shown in Figure 6.7.
The resulting contaminant and biomass distributions are shown in Figure 6.8. These distributions illustrate
the outward migration of contaminants from the core organic liquid distribution. The migration pathway is
primarily volatilization of organic liquid constituents into the soil gas wherein they can readily migrate by
diffusion and density driven flow. As the organic constituents in the gas phase migrate radially outward
they simultaneously partition into the soil water and subsequently sorb to the soil particles. The increase in
organic substrate in the soil water results in buildup of the biomass and corresponding depletion of oxygen
as shown in the bottom two plots in Figure 6.8. There is no biomass growth within the NAPL contaminated
110
-------
p
k (m2)
c1*
^rw
n*
-------
Mass transfer coefficients diffusion problem
gas-M£L (I/day)
gas-aqueous (I/day)
NAPL-aqueous (i/day)
solid-aqueous (I/day)
Monod parameters
maximum substrate utilization (1/d)
half saturation constant (mg/1)
decay coefficient (1/d)
minimum biomass (mg/1)
maximum biomass (mgVl)
so
1
20
io
high set
1
0.5
0.1
0.001
20
BV simulation
50
1
20
1
low set
0.1
0.5
0.01
0.001
20
Table 6.6: Mass exchange and biokinetie parameters used in the Reid scale bioventihg demonstration simu-
lation.
156 days is observed to be densest along the outside fringe of the organic liquid zone and near the well
screen where organic liquid has been completely removed. High oxygen depletion is observed in the
corresponding regions of high biomass growth. The predicted biomass concentrations increase
substantially between 156 and 256 days, maintaining high concentrations until the end of the simulation at
356 days. This is explained by the increased availability of oxygen as shown in Figure 6.12 resulting from
the decreased oxygen demand due to the reduction of substrate concentrations as shown in Figure 6.10.
Notice that oxygen remains depleted in the capillary fringe region due to the poor accessibility to the air
stream. Consequently there is limited biomass growth in this region resulting in the persistence of the
organic substrate.
112
-------
NAPLsaturation -\Q m T°tal organic concentration (ppm)
0.04 0.01
/0.02
4 m
-8m
biomass concentration (mg/l) aqueous oxygen concentration (mg/l)
Figure 6.8: Initial conditions used for the field scale bioventing demonstration simulation.
113
-------
Icfrri
10m
156 days
256 days
-4m
-8m
356 days
NAPL saturation
Figure 6.9: Predicted organic liquid distributions at specified times for the field scale bioventing demonstration
simulation.
114
-------
1 cfm 16 days
10m
156 days
-4 m =
8 m
256 days
356 days
substrate concentration (mg/l)
Figure 6.10: Predicted benzene substrate distributions at specified times for the field scale bioventing demon-
stration simulation.
115
-------
icfm 16 days
20'm
-4 m
8m
256 days
356 days
biomass concentration (mg/l)
Figure 6.11: Predicted biomass distributions at specified times for the field scale bioventing demonstration
simulation.
116
-------
20m
156 days
256 days
O
-4 m -
-8m
356 days
O
oxygen concentration (mg/l)
Figure 6.12: Predicted oxygen distributions at specified times for the field scale bioventing demonstration
simulation.
117
-------
Appendix A
ELEMENT MATRICES FOR THE SIMULTANEOUS
SOLUTION OF THE PHASE MASS BALANCE EQUATIONS
Integration of (3.17) gives to the element matrix equation,
3(P}e . rn-
[A]e
dt
(A.1)
where [P}e is the vector of alternating aqueous and gas pressures at the three nodes of the element,
ipie _ f pk+l pk+l pk+l pk+l pk+l pk+V
where k is an iteration counter.
The consistent form of the mass matrix is developed from eqs. (3.17a) and (3.17b). It may be expressed
as,
where,
e=l
Aa£ = Aga =
Ne
f
JSl
f\ aa "~
- E^ /0
e=l Ja' [
Evaluating the integrals, the element mass matrix [A~\e in consistent form is,
e _ 4>eAere
~ 12
2dai —1da,
-d
a,
2da2 —1
da2 ~
2d
gl
2d
g2
where,
daj = -(
51
d,, =
Si
-C
—d
a-,,
2dg3
(A.3)
(A.4)
118
-------
where Ae is the area of element e.
It is often advocated to diagonalize the mass matrix [A] by the procedure of "mass lumping" in order to
reduce oscillatory behavior and improve computational stability \Celia etal, 1990; Abriola and Rath/elder,
1993]. Therefore an option is included in MISER for lumping of the mass matrix. The lumped mass matrix
is developed by,
,L_S \ ALaa A,
^-5lJ[ALga A-
e=\ Jae
Ne f
= AJ, = £>./
e=\ »'"<
AL =
PJ
where Sij is the Kronecker delta. Evaluating the integrals, the lumped mass matrix is,
(J)eAere
12
4dai
0
0
-44,
0
0
-4dAl
0
0
4dgl
0
0
0
4da2
0
0
-4da2
0
0
-442
0
0
4dg2
0
0
0
4da3
0
0
-44,
o •
0
-4da3
0
0
44, -
The stiffness matrix developed from eqs. (3.17a) and (3.17b) may be represented by,
Baa Ba!,~\
where,
dz dz
Bag = Bga = 0
dz
(A.5)
(A.6)
(A.7)
119
-------
Evaluating the integrals in (A.7) yields,
ESP-
where,
l2Ae
o
»
o
o
o ft
a
022
oj2
a
a
0 b
Q fea23
0 ba
b 0
- J?I9
^22 &
£»«, 0
0
a
(A.8)
Vctij
+
A'a,- y=l
7=1
and y3i and y,- are defined in (3.5). Notice that uaij = uaj[.
The RHS matrix incorporating density gradient terms may be developed as,
where,
F° -
- I "' \
"['•I
(A.9)
Evaluating these integrals yields,
"T-S
&
&
fo
8x
gx
(A. 10)
120
-------
wherein,
+ p2 +
<,. + E <,
3s
+ E ^
The RHS matrix incorporating compositional effects on density and interphase mass exchange is
represented by:
I w I
*<= 7 (A-ll)
where,
Ne
Pa*; 3?
N<
jNi \ dQ.e
Here it has been assumed that {E} can be evaluated with compositional information from the previous time
step. For the known composition, the terms dp*/dxgc are evaluated from the appropriate differentiation of
Amagat's Law (2.50) or the Ideal Gas Law (2.49). The temporal change in mole fraction, dxac/dt, and
interphase exchange terms, E*pc_, are also lagged by a single time step. Evaluating the integrals above,
yields,
(E}' =
12
eg\
L g^ J
(A.12)
and,
g,.
at
3Mg.
dt
121
-------
TheRHS vector [Q}e represents the phase sources and sinks,
Qi = f 2* 1
Kfl I /~\ I
where Qai is the prescribed extraction or injection rate of phase a at node i [L3/T] at the aquifer
temperature and pressure. Qa is negative for extraction. This vector is used to incorporate fluxes at
simulated injection or extraction wells.
(A. 13)
122
-------
Appendix B
ELEMENT MATRICES FOR THE SOLUTION OF DARCY'S
LAW EQUATION
The element matrix equation for the solution of the Darcy velocities is derived from (3.23) and (3.24).
For purposes of conciseness only the expansion of the aqueous phase equation (3.23) will be shown here,
[A]e {qax}e = {F}e (B.la)
\.A}e {qa,Y = {Fa}e (B.lb)
where {xax}e and {xax}e are the vectors of x and z direction Darcy velocities at the three nodes of the
element e,
{
-------
and,
E ftyir -
+ fav + fan
The varia}3}e$ /fy an.d y; .are :tii
direction?, respectively.
Finally the gravity term, {Fa,}eg, is expressed as,
60
f ?
f
(B.8a)
(B.8b)
(B-9)
Pa3
Pa?,
124
-------
Appendix C
ELEMENT MATRICES FOR THE SEQUENTIAL
SOLUTION OF THE COMPONENT MOLE BALANCE
EQUATIONS
Integration of (3.36) gives the element matrix equation,
[A]e
dt
where {xac }e is the vector of component mole fractions at the three nodes of the element e (1,2, 3),
txac I — [Xai > Xa2 > Xa3 }ac
The mass matrix is developed from eq. (3.37). It may be expressed as,
(C.1)
(C.2)
(C.3)
where in local coordinates the indices i and j can equal 1, 2, or 3. Evaluating the integrals, the element
mass matrix [A]e is,
#11 #12 #13
#21 #22 #23 (C.4)
#31 #32 #33
ie eracAere
where the individual elements of [A]e are defined as follows,
#11 = SSaiA*! + Sa2pa2 + Sa
a\i = #21 — SctiPai + Sa2Pa2 + 0.5
#13 = #31 = SctiPai +0.55a2/0a2 + Sa
#22 = Saipai + 3Sa2pa2 + Sa3pa3
#23 = #32 = Q.5Saipai + S^paz + S
#33 = SctiPai + Sct2pa2 + 3Sa3pa3
An option is included in MISER for mass lumping of [A]e giving,
(C.5a)
(C.5b)
(C.5c)
(C.5d)
(C.5e)
(C.5f)
30Af
#11 +#12+#13 0 0
0 #21 + #22 + #23 0
0 0 «3i + 032 + #33
(C.6)
125
-------
The stiffness matrix developed from eqs. (3.36) may be expressed as,
(C.7)
(c.s)
Bfj =
Evaluating the integrals, the element stiffness matrix [B]e is,
[Bf = [B1]* + [B2]£ +
(C.ll)
where the terms [B1]6, [B2]e, and [B3] are defined as follows. First the advective portion of the stiffness
matrix can be expressed as,
24
b\2
with the individual terms defined as,
Pi
a*, + 2Pd2^ctX2 +
fa +
0H
Zo>,2 + 2pB3^J) ft -\
Oa3qaX3 f ft ~
Next the dispersive portion of the stiffness matrix is,
+
"*3 1 Yl
Y2
Y3
Yi
+
' I 1/5
«JT3 J
J71
'«3^3 ) Y2
3a3^3 } K3
y22 U23
^32 ^33
(C.12)
(C.13a)
(C.13b)
(C.13c)
(C.I 3d)
(C.13e)
(C.13f)
(C.13g)
(C.13H)
(C.131)
(C.I 4)
126
-------
where the individual terms are defined as,
, A
- A „ A
= A , A
XI A
Y2 , A
72
73
, A + , w + n /3 + zz
, A +
-------
The terms Fac are defined in Table 3.2. Upon assembly of the global RHS vector, the boundary integral
terms sum to zero except at the domain boundaries (see Section_3.11.2). Evaluating the remaining portion
of the integral which contains the exchange and reaction term, Facj, yields,
(F}B =
12
(C.I 8)
The development above applies to the mobile phases a = g, a. A similar development starting with
(3.39) for the organic liquid and (3.41) for the biophase leads to the same terms presented above except that
(C.12) and (C.14) are both omitted.
Since significant differences exist for the solid phase development, only the mass matrix and RHS will
be shown below. Integrating (3.40), and assuming that the solid phase bulk density is constant yields for the
mass matrix,
2 1 1
n'" AT~
[A]e =
12A*
2
1
and for the RHS,
{F}e =
AereMc
12
(C.19)
(C.20)
128
-------
Appendix D
ELEMENT MATRICES FOR THE SOLUTION OF THE
ORGANIC PHASE MASS BALANCE EQUATION
The governing matrix, equation for the solution of the organic phase mass balance is derived from
equation (3.47). Integration of (3.47) gives the element matrix equation,
[AY
where {S0}6 is the vector of NAPL saturations at the three nodes of the element,
[S0}e = {S0l, S02, S03}ac
The mass matrix is developed from eq. (3.47). It may be expressed as,
(D.I)
(D.2)
(D.3)
where in local coordinates the indices i and j can equal 1, 2, or 3. Evaluating the integrals, the element
mass matrix [A]e is,
#23
_ *M«r-
[A] ~~30AF
where the individual elements of [A]e are defined as follows,
«H = 3/°0! + Po2 + Po3
012 = 021 = P*0l + Po2 + 0.5p*3
•j: , f\ p* ^j
013 = 031 = Po, + 0.5p0,
2
023 = 0.32 = 0.5p* + p*2 + p
t 2 3
[A] is then "mass lumped" to facilitate solution of the stacked NAPL saturation giving,
0eAere
30A?
+an + ai3 0 0
0 ^21 + #22 + <^23 0
0 0 031+ 032 + «33
(D.4)
(D.5a)
(D.5b)
(D.5c)
(D.5d)
(D.5e)
(D.5f)
(D.6)
129
-------
The RHS vector developed from integration of (3.47) is,
f f * , r, &
Fac = I 4 \E2jNj-$0.j-z
JO.' \ J d
where E* is defined in Table 3.1. Evaluating (D-7) gives,
eAere
12
+
+ £0*3 -
- 5*
This allows a direct solution for {S0}*+1 after assembly of the global matrices as,
S*+1 = Ft/An
where AH ^ 0 and i is iterated over the total number of stacked variables.
(D.7)
(D.8)
(D.9)
130
-------
Appendix E
Description of Major Variables
Integer Scalars
ia Number of nonzero entries in sparse
matrix.
nnhor Maximum number of nodes in the
horizontal direction in a generated grid.
nnver Maximum number of nodes in the
vertical direction in a generated grid.
Real Scalars
b Klinkenberg parameter; Table 5.13:
Field 2.
caplen Radius of impermeable cap on the
ground surface.
kd Decay coefficient; Table 5.12: Field 5.
qwell Extraction/injection rate; Table 5.22:
Field 2.
rwell Well radius; Table 5.22: Field 3.
tmassO Initial total mass in domain.
tmassl Current time step total mass in domain.
trefqg Reference temperature.
wtdpth Depth to water table.
wvis Water viscosity; Table 5.13: Field 1.
xbmax Maximum biomass; Table 5.12: Field
5.
xbmin Minimum biomass; Table 5.12: Field
5.
xbok Two compartment Kf multiplier; Table
5.11: Fields.
xbom Two compartment m multiplier; Table
5.11: Field3.
xden Two compartment density multiplier;
Table5.11: Fields.
xinit Initial biomass; Table 5.12: Field 5.
xkex Two compartment exchange coefficient
multiplier; Table 5.11: Field 3.
zwell
Length of well screen.
Character Scalars
outpre
Integer Arrays
Output file prefix; Table 5.4: Field 2.
ibc(nnmx) Nodal boundary condition locations;
Table 5.21: Field 1 (gas pressures), 2
(gas pressures), 3 (aqueous pressures),
4 (aqueous pressures), 5 (gas phase
components), 6 (aqueous phase
components), 7 (gas phase boundary
fluxes), and 8 (aqueous phase boundary
fluxes).
ibcxmf(nmbc) Nodal component boundary condition
types; Table 5.21: Field 5 (gas phase
components) and 6 (aqueous phase
components).
idepth(nnmx) Nodal depth reference.
icn(icnl) Sparse matrix column indices.
icp(0:50) Vector of control integers for
component identification.
ikeep(icnl,5) Solver work space.
ipt(0:90) Vector of control integers.
ipt(O) Number of elements; Table 5.7: Field
7.
ipt(l) Number of nodes; Table 5.7: Field 7.
ipt(2) Number of stacked variables.
ipt(3) Number of components in the gas
phase.
ipt(4) Number of components in the aqueous
phase.
ipt(5) Number of components in the NAPL
phase.
131
-------
ipt(6) Number of components in the solid
phase.
ipt(7) Number of components in the bio
phase (includes biomass).
ipt(8) Start of gas phase section in xmf
ordering.
ipt(9) Start of aqueous phase section ire xmf
ordering.
ipt( 10) Start of NAPL phase section in xmf
ordering.
ipt( 11) Start of solid phase section in xmf
ordering.
ipt( 12) Start of bio- phase section in xmf
ordering.
ipt( 1'3) Number of organic components in the
gas phase.
ipt(14) Number of organic components in the
aqueous phase.
ipt( 15) Number of organic components in the
NAPL phase; Table 5.8: Field 1.
ipt( 16) Number of organic components in the
solid phase.
ipt( 17) Number of organic components in the
bio phase; Table 5.12: Field 1.
ipt( 18) Number of nodes with constant gas
pressure; Table 5.21: Field2.
ipt( 19) Number of nodes with constant
aqueous pressure; Table 5.21: Field4.
ipt(20) Number of nodes with gas phase
component boundary conditions; Table
5.21: Fields.
ipt(21) Number of nodes with aqueous phase
component boundary conditions; Table
5.21: Field 6.
ipt(22) Number of nodes with constant gas
volumetric flux; Table 5.21: Field 7.
ipt(23) Number of nodes with constant
aqueous volumetric flux; Table 5.21:
FieldS.
ipt(24) Number of nodes along the well screen.
ipl(25) Print results every ipt(25) time steps if
Iprnt(O) is true; Table 5.4: Field 8.
ipt(26) Number of material property blocks;
Table 5.7: Field 6.
ipt(27) Integer variable denoting the type of
domain (ipt(27) = 0 - xz domain;
ipt(27) = 1 - rz domain); Table 5.5:
Field 1.
ipt(28) Device designator for performance
output; Table 5.4: Field 3.
ipt(29) Device designator for error messages;
Table 5.4: Field 3.
ipt(30) Maximum number of time steps; Table
5.6: Fields.
ipt(31) Maximum phase balance iterations,
also used as the criterion for decreasing
dt in phase balance; Table 5.6: Field 6.
ipt(32) Maximum component balance
iterations, also used as the criterion for
decreasing dt in component balance
routines; Table 5.6: Field 6.
ipt'(33) Maximum' NAPL saturation iterations;
Table 5.6': Field 6.
ipt(34) Maximum number of iterations in
phase balance for increasing dt; Table
5.6: Field?.
ipt(35) Maximum number of iterations in
component balance routines for
increasing dt; Table 5.6: Field 7.
ipt(36) Flag from flow.f for time step
modification.
ipt(37) Flag from tran.f for time step
modification.
i'pt(38) Flag from' napls.f for time step
modification.
ipt(39) Integer flag determining the biokinetics
type (1 - standard monod kinetics; 2 -
monod kinetics with substrate
inhibition; 3 - monod kinetics with
lumped substrate inhibition; 4 - monod
kinetics with saturation dependency; 5
- monod kinetics with saturation
dependency and substrate inhibition);
Table 5.12: Field3.
ipt(40) Constant - ipt( 1) * 2.
ipt(41) Constant-ipt(l)* 3.
ipt(42) Constant - ipt(l) * 4.
ipt(43) Constant - ipt(l) * 5.
ipt(44) Constant - ipt( 1) * 6.
ipt(45) Constant - ipt(l) * 7.
ipt(46) Constant-ipt(l>* 8.
ipt(47) Constant - ipt(l) * 9.
ipt(48) Constant - ipt(l) * 10.
ipt(49) Constant - ipt(2) * 2.
ipt(50) Constant - ipt(2) * 3.
132
-------
ipt(51) Constant - ipt(2) * 4.
ipt(52) Constant - ipt(2) * 5.
ipt(53) Constant - ipt(2) * 6.
ipt(54) Constant - ipt(2) * 7.
ipt(55) Constant - ipt(2) * 8.
ipt(56) Constant - ipt(2) * 9.
ipt(57) Constant - ipt(2) * 10.
ipt(58) Constant - ipt(3) + ipt(4).
ipt(59) Constant - ipt(3) + ipt(4) + ipt(5).
ipt(60) Constant - ipt(3) + ipt(4) + ipt(5) +
ipt(6).
ipt(61) Constant - ipt(3) + ipt(4) + ipt(5) +
ipt(6) + ipt(7).
ipt(62) Constant - ipt(18) + ipt(19) + ipt(20) +
ipt(21).
ipt(63) Constant - ipt(62) + ipt(22).
ipt(64) Constant - ipt(63) + ipt(23).
ipt(65) Number of components present.
ipt(66) Constant - ipt(65) * ipt(l).
ipt(67) Constant - ipt(0) * 2.
ipt(68) Constant - ipt(O) * 3.
ipt(69) Number of gas phase components in
output; Table 5.15: Field 2.
ipt(70) Number of aqueous phase components
in output; Table 5.15: Field 2.
ipt(71) Number of NAPL components in
output; Table 5.15: Field 2.
ipt(72) Number of solid phase components in
output; Table 5.15: Field 2.
ipt(73) , Number of bio phase components in
output; Table 5.15: Field 2.
ipt(74) Constant - ipt(69) + ipt(70) + ipt(71) +
ipt(72) + ipt(73).
ipt(75) Initial condition type; Table 5.17: Field
1.
ipt(76) Restart input value of current time step
number.
ipt(77) Not Used.
ipt(78) Not Used.
ipt(79) Not Used.
ipt(80) Current number of time steps.
ipt(81) Number of time series plot gas phase
components; Table 5.15: Field 3.
ipt(82) Number of time series plot aqueous
phase components; Table 5.15: Field 4.
ipt(83)
ipt(84)
ipt(85)
ipt(86)
ipt(87)
ipt(88)
ipt(89)
irn(icnl)
iw(icnl,8)
matel(nelmx)
matpt(nn6)
nbdB(nxmax)
nbdL(nzmax)
nbdR(nzmax)
nbdT(nxmax)
nbw(0:2)
nelpt(nelS)
nodel(ne!3)
nodept(nnmx)
Real Arrays
a(icnl)
aby!2(nelmx)
aby30(nelmx)
amb(icnl)
area(nelmx)
bcf(nn2)
Print mass balance every ipt(83) time
steps if lprnt(25) is true; Table 5.4:
Field 5.
Print time series every ipt(84) time
steps if lprnt(26) is true; Table 5.4:
Field 6.
Compute flow field every ipt(85) time
steps; Table 5.5: Field 4.
Number of nodes in the vertical
direction.
Number of nodes in the horizontal
direction.
Pointer for temperature dependencies.
Constant - 5 * ipt(88).
Sparse matrix row indices.
Solver work space.
Element material blocks; Table 5.7:
Fields.
Nodal material blocks.
Node numbers along the bottom
boundary of a generated rectangular
domain.
Node numbers along the left boundary
of a generated rectangular domain.
Node numbers along the right
boundary of a generated rectangular
domain.
Node numbers along the top boundary
of a generated rectangular domain.
Sparse matrix band widths.
Element stacking references.
Element connectivity vector; Table 5.7:
Fields.
Nodal stacking references.
Global FEM matrix.
Element; rbar * area 712.
Element; rbar * area/ 30.
Global FEM matrix for phase mass
balance.
Element areas.
Nodal phase boundary fluxes.
133
-------
bcxmf(nmbc)
bdisl(nmblk)
bdist(nmblk)
beta(nelS)
bfoc(nmblk)
bok(nbcmp)
bom(nbcmp)
bpermh(nmblk)
bpermv(nmblk)
bphi(nmblk)
bsden(nmblk)
bvga(nmblk)
bvgm(nmblk)
bvgn(nmblk)
bsrw(nmblk)
cc(nnstk)
casol(ncmp)
cden(ncmp)
ccx(nmf)
chcn(ncmp)
cmassO(ncmp5)
cmassl(ncmp5)
Nodal component boundary condition
in contacting fluid; Table 5.21: Field 5
(gas phase components) and 6
(aqueous phase components).
Block longitudinal dispersivities; Table
5.10: Fields.
Block transverse dispersivities; Table
5.10: Fields.
Nodal basis function ^-derivatives.
Block organic carbon contents; Table
5.10: Field 1.
Block component Freundlich Kf
parameters; Table 5.11: Field 2.
Block component Freundlich m
parameters; Table 5.11: Field 2.
Block horizontal intrinsic
permeability; Table 5.10: Field 1.
Block vertical intrinsic permeability;
Table 5.10: Field 1.
Block porosity; Table 5.10: Field 1.
Block bulk soil densities; Table 5.10:
Field 1.
Block van Genuchten a parameters;
Table 5.10: Field 2.
Block van Genuchten 1 — £.
Block van Genuchten n parameters;
Table 5.10: Field 2.
Block residual aqueous phase
saturations; Table 5.10: Field 2.
Nodal capacity coefficients.
Component aqueous solubility; Table
5.8: Field 2 (organic components), 3
(water, oxygen, and nitrogen), and 4
(nutrient).
Component densities; Table 5.8: Field
2 (organic components), 3 (water,
oxygen, and nitrogen), and 4 (nutrient).
Nodal gas, aqueous, NAPL, solid, and
bio phase mole component left hand
side exchange terms.
Component Henry's Law constants;
Table 5.8: Field 2 (organic
components), 3 (water, oxygen, and
nitrogen), and 4 (nutrient).
Component initial storages.
Component current time step storages
cmdiff(ncmp2) Component gas and aqueous phase
molecular diffusivities; Table 5.8:
Field 2 (organic components), 3 (water,
oxygen, and nitrogen), and 4 (nutrient).
cmf(ncmpp5) Phase and component cumulative total
boundary fluxes.
cmw(ncmp) Component molecular weights; Table
5.8: Field 2 (organic components), 3
(water, oxygen, and nitrogen), and 4
(nutrient).
cphex(ncmppS) Phase and component cumulative
exchange fluxes.
crsink(ncmpp5) Phase and component cumulative
reaction sinks.
csflux(ncmpp5) Cumulative surface flux.
csink(ncmpp5) Phase and component cumulative
sinks.
cvp(ncmp) Component vapor pressures; Table 5.8:
Fie Id 2 (organic components), 3 (water,
oxygen, and nitrogen), and 4 (nutrient).
cvvis(ncmp) Component vapor viscosity; Table 5.8:
Field 2 (organic components), 3 (water,
oxygen, and nitrogen), and 4 (nutrient).
cwsink(ncmppS) Phase and component cumulative
well sinks.
d(nmd) Element dispersivities; Table 5.10:
Fields.
dden(nn6) Nodal gas, aqueous, and NAPL phase
mole and mass density derivatives.
den(nn6) Nodal gas, aqueous, and NAPL phase
current time step mole and mass
densities.
dent(nn6) Nodal gas, aqueous, and NAPL phase
previous time step mole and mass
densities.
denO(nnmx) Initial gas phase mass density.
dfxmf(nmbc) Nodal component boundary diffusive
flux; Table 5.21: Field 5 (gas phase
components) and 6 (aqueous phase
components).
dtemp(nzmax6) Depth temperature corrections; Table
5.14: Field 4 (component vapor
pressures), 5 (component vapor
viscosity), 6 (component Henry's Law
constants), 7 (component aqueous
solubility), 8 (component maximum
substrate utilization rates), and 9
(biomass decay coefficients).
first(ncmp) Boundary fluxes at nodes with constant
concentration conditions.
134
-------
flux(ncmppS) Phase and component boundary fluxes.
fmb(icnl) Global FEM right hand side vector for
phase mass balance.
fuse(ncmp2) Oxygen and nutrient use factors; Table
5.12: Field 4.
gama(nelS) Nodal basis function z-derivatives.
gamma(ncsqd) Nodal component coefficients for
vapor viscosity expression.
kex(ncmp5) Component aqueous/gas,
aqueous/NAPL, gas/NAPL,
aqueous/biophase, and aqueous/solid
exchange coefficients; Table 5.9: Field
1.
khalf(ncmp) Component half saturation constants;
Table 5.12: Field 4.
kinhib(ncmp) Inhibition constants; Table 5.12: Field
4.
kmax(ncmp5) Component aqueous/gas,
aqueous/NAPL, gas/NAPL,
aqueous/biophase, and aqueous/solid
minimum deviations from
equilibriums; Table 5.9: Field 1.
krtd(ncmp) Component retardation factors; Table
5.11: Fields.
p(nn3) Nodal gas phase, aqueous phase, and
capillary current time step pressures;
Table 5.17: Field 3.
pex(nnlO) Nodal gas, aqueous, NAPL, solid, and
bio phase mole and mass phase
exchange terms.
pmob(nnstk4) Nodal aqueous and gas phase x and z
mobilities.
pmw(nnS) Nodal gas, aqueous, and NAPL current
time step phase molecular weights.
pmwt(nnS) Nodal gas, aqueous, and NAPL
previous time step phase molecular
weights.
pmwO(nnmx) Initial gas phase molecular weights.
por(nelmx) Element porosity.
pt(nn3) Nodal gas phase, aqueous phase, and
capillary previous time step pressures.
q(ne!4) Gas phase and aqueous phase specific
fluxes; Table 5.18 Field 4 (uniform) or
5 (nonuniform).
rbar(nelmx) Element radial coordinates.
rhs(nsolve) Global FEM right hand side vector.
rhsex(nmf) Nodal gas, aqueous, NAPL, solid, and
bio phase mole component right hand
side exchange terms.
rxn(nmf) Nodal aqueous and bio phase
component reaction terms.
rxnp(nn2) Nodal aqueous and bio phase reaction
terms.
sat(nnstkS) Nodal gas phase.aqueous phase, and
NAPL current time step saturations.
satk(nnstk2) Nodal gas phase and aqueous phase
previous iteration saturations.
satt(nnstkS) Nodal gas phase,aqueous phase, and
NAPL previous time step saturations.
sflux(ncmpp5) Phase and component boundary fluxes
at ground surface.
source(nn2) Nodal phase boundary fluxes; Table
5.21 Field 7 (gas phase) and 8 (aqueous
phase).
srw(nelmx) Nodal aqueous phase residual
saturations.
str 1 (ncmppS) Current time step phase and
component storages.
strO(ncmpp5) Initial phase and component storages.
t(50) Vector of real variables.
t(l) Initial time of simulation; Table 5.6:
Field 1.
t(2) Maximum or final time of simulation;
Table 5.6: Field 1.
t(3) Initial time step size; Table 5.6: Field
5.
t(4) Minimum time step size; Table 5.6:
Fields.
t(5) Maximum time step size; Table 5.6:
Fields.
t(6) Time step multiplier for increases;
Table5.6: Fields.
t(7) Time step multiplier for decreases;
Table5.6: Fields.
t(8) Current time step size.
t(9) Current simulation time.
t(10) Time weighting factor; Table 5.6: Field
2.
t(l 1) Delay period for initiation of
bioreaction; Table 5.12: Field 5.
t( 12) Print results at t( 12) intervals if Iprnt(O)
is false; Table 5.4: Field 8.
t( 13) Convergence criterion for pressures;
Table 5.6: Field 4.
135
-------
t(14)
t(15)
t(16)
t(I7)
t(18)
t(19)
t(20)
t(21)
t(22)
t(23)
t(24)
t(25)
t(26)
t(27)
1(28)
tcmp(nnmx)
tort(nclmx)
umax(ncmp)
vis(nnmx)
w(icnl)
xmf(nmf)
xmft(nmf)
xnode(nnmx)
xyield(ncmp)
znode(nnmx)
Logical Arrays
Convergence criterion for mole
fractions; Table 5.6: Field 4.
Convergence criterion for NAPL
saturations; Table 5.6: Field 4.
Convergence criterion for immobile
phases; Table 5.6: Field 4.
Not used.
Not used.
Not used.
Not used.
Horizontal component of gravity
vector; Table 5.5: Field 1.
Vertical component of gravity vector;
Table 5.5: Field 1.
Maximum gas phase cell Peclet
number.
Maximum aqueous phase cell Peclet
number.
Maximum gas phase cell Courant
number.
Maximum aqueous phase cell Courant
number.
Print mass balance at t(27) intervals if
lprnt(25) is false; Table 5.4: Field 5.
Print time series at t(28) intervals if
lprnt(26) is false; Table 5.4: Field 6.
Nodal temperatures.
Element tortuosity factors.
Maximum substrate use rate; Table
5.12: Field 4.
Nodal gas phase viscosity.
Solver work space.
Nodal gas, aqueous, NAPL, solid, and
bio phase current time step mole
fractions.
Nodal gas, aqueous, NAPL, solid, and
bio phase previous time step mole
fractions.
Nodal ^-coordinates; Table 5.7: Field
9.
Biomass yield coefficient; Table 5.12:
Field 4.
Nodal z-coordinates; Table 5.7: Field
9.
lcon(50) Vector of logical switches to print
specified variables to the contour plot
file at specified print intervals.
lcon(l) Contour in molar form; Table 5.15:
Field 2.
lcon(2) Contour gas phase pressures; Table
5.15: Field 2.
lcon(3) Contour aqueous phase pressures;
Table 5.15: Field 2.
lcon(4) Contour gas/aqueous phase pressures;
Table 5.15: Field 2.
lcon(5) Contour gas phase mass and molar
density; Table 5.15: Field 2.
lcon(6) Contour aqueous phase mass and
molar density; Table 5.15: Field 2.
lcon(7) Contour NAPL phase mass and molar
density; Table 5.15: Field 2.
lcon(8) Contour gas phase mole fractions;
Table 5.15: Field 2.
lcon(9) Contour aqueous phase mole fractions;
Table 5.15: Field 2.
lcon( 10) Contour NAPL phase mole fractions;
Table 5.15: Field 2.
lcon( 11) Contour solid phase mole fractions;
Table 5.15: Field 2.
lcon( 12) Contour bio-phase mole fractions;
Table 5.15: Field 2.
lcon( 13) Contour gas phase saturation; Table
5.15: Field 2.
lcon(14) Contour aqueous phase saturation;
Table 5.15: Field 2.
lcon(15) Contour NAPL phase saturation; Table
5.15: Field 2.
lcon(16) Contour gas phase Darcy velocities;
Table 5.15: Field 2.
lcon(17) Contour aqueous phase Darcy
velocities; Table 5.15: Field 2.
lcon(18) Contour total organic soil
concentration; Table 5.15: Field 2.
Ictrl(50) Vector of logical control switches.
lctrl(l) Solve transient phase balance; Table
5.5: Field 2.
lctrl(2) Solve transient component balance;
Table 5.5: Field 2.
lctrl(3) Include bioreactions; Table 5.5: Field
2.
136
-------
lctrl(4) Compute/print element dimensionless
numbers; Table 5.5: Field 7.
lctrl(5) Generate a restart file; Table 5.4: Field
7.
lctrl(6) Not used.
lctrl(7) Mass lump flow equation; Table 5.5:
Field 3.
lctrl(8) Mass lump transport equation; Table
5.5: Field3.
lctrl(9) Switch defining if nutrient is to be
modeled; Table 5.8: Field 4.
lctrl(lO) Generate uniform temperature
distribution; Table 5.14: Field 1.
lctrl(ll) Not used.
lctrl(12) True if an extraction is to be simulated;
Table 5.22: Field 1.
lctrl(13) Make gas phase viscosity composition
dependent.
lctrl(14) Couple flow and transport through
exchange; Table 5.5: Field 6.
lctrl(15) Print time series output; Table 5.4:
Field 6.
lctrl(16) Include bioreaction in aqueous
transport; Table 5.12: Field 2.
lctrl(17) Model biomass a steady state; Table
5.12: Field 2.
lctrl(18) Use nodal Darcy velocities for
transport; Table 5.18: Field 1.
lctrl(19) Use two compartment sorption model;
: Table 5.11: Field 1.
lctrl(20)' Include Klinkenberg effect; Table 5.13:
Field 2.
lctrl(21) Calculate hydrodynamic dispersion;
Table 5.10: Field 4.
lctrl(22) Calculate density derivative terms.
lctrl(23) Print contour plot data; Table 5.4:
Field 4.
lctrl(24) NAPL is present in the domain; Table
5.5: Field 2.
lctrl(25) Consider sorption; Table 5.5: Field 2.
lctrl(26) Run is a restart; Table 5.16: Field 1.
lplt(20) Vector of logical switches to print
specified variables to the time series
file.
lplt(l) Generate time series output for the gas
phase; Table 5.15: Fields.
lplt(2) Generate time series output for the
aqueous phase; Table 5.15: Field4.
lprnt(0:30) Vector of logical switches to print
specified variables to the output file at
specified print intervals.
Iprnt(O) T=print at specified time steps, f=print
by time increment; Table 5.4: Field 8.
Iprnt(l) Print grid information; Table 5.7: Field
1.
lprnt(2) Not used.
lprnt(3) Print initial conditions; Table 5.15:
Field 1.
lprnt(4) Not used.
lprnt(5) Not used.
lprnt(6) Compute and print mass balance
information; Table 5.4: Field 5.
lprnt(7) Not used.
lprnt(8) Print in molar form; Table 5.15: Field
2.
lprnt(9) Print nodal gas phase pressure; Table
5.15: Field 2.
Iprnt(lO) Print nodal aqueous phase pressure;
Table 5.15: Field 2.
Iprnt(ll) Print nodal gas/aqueous capillary
pressure; Table 5.15: Field 2.
lprnt(12) Print nodal gas phase mole and mass
density; Table 5.15: Field 2.
lprnt(13) Print nodal aqueous phase mole and
mass density; Table 5.15: Field 2.
lprnt(14) Print nodal NAPL mole and mass
density; Table 5.15: Field 2.
lprnt( 15) Print gas phase mole fractions; Table
5.15: Field2.
lprnt( 16) Print aqueous phase mole fractions;
Table 5.15: Field2.
lprnt(17) Print NAPL phase mole fractions;
Table 5.15: Field 2.
lprnt(l8) Print solid phase mole fractions; Table
5.15: Field 2.
lprnt(19) Print bio-phase mole fractions; Table
' 5.15: Field 2.
lprnt(20) Print nodal gas phase saturation; Table
5.15: Field 2.
lprnt(21) Print nodal aqueous phase saturation;
Table 5.15: Field 2.
lprnt(22) Print nodal NAPL phase saturation;
Table 5.15: Field 2.
137
-------
lprnt(23) Print gas phase Darcy velocities; Table
5.15: Field 2.
lprnt(24) Print aqueous phase Darcy velocities;
liable 5.15: Meld 2.
lprnt(25) T=print mass balance at specified time
steps, f=print by time increment; Table
5.4: FieldS.
lprnt(26) T=print time series at specified time
steps, f=print by time increment; Table
5.4: Field 6.
lprnt(27) T=print material balance in report
form, f=print material balance in time
series form with multiple output files;
Table5.4: FieldS.
lprnt(28) T=print time series file in mole
fractions, f=print time series file in
concentrations; Table 5.4: Field 6.
lprnt(29) T=print total organic soil
concentration; Table 5.4: Field 6.
Character Arrays
cname(ncmp) Component labels; Table 5.8: Field 2
(organic components), 3 (water,
oxygen, and nitrogen), and 4 (nutrient).
infile(4) Input file labels; Table 5.4: Field 1.
outfile(8+ncmp) Output file labels.
138
-------
Appendix F
EXAMPLE MAKE FILE
Below is a sample make file for compiling MISER on an IBM6000 or Sun Spare workstation platform.
In this example the source and object files are located in subdirectories called 'src' and 'obj', respectively.
The executable file is named 'miser' and is generated in the directory containing the makefile.
# makemiser - to compile and link MISER code on Sun Spare workstations.
# ' '
# Define aliases for compilation and linking.
xl= f77 -OS -o
xc = m -O5 -c -o
#
# Define paths to source and object files.
ps = ./src/
po = ./obj/
#
# Define an include file alias.
includes = $(ps)dimen.inc
#
# Define an object files alias.
objects = $(po)atri's.o $(po)bcflux's.o $(po)bio's.o \
$(po)cbal's.o $(po)commnfs.o $(po)disper's.o \
$(po)error's.o $(po)fiow's.o $(po)grid's.o \
$(po)har's.o $(po)inputl's.o$(po)input2's.o \
$(po)miser's.o $(po)mobirs.o $(po)molewfs.o \
$(po)mpex's.o ${po)napls's.o $(po)naplx's.o \
$(po)prnfs.o $(po)satw's.o $(po)solid's.o \
$(po)tlhs's.o $(po)trans's.o $(po)vel's.o\
#
# Link object files into an executable named 'miser'.
miser: $(objects) $(includes)
$(xl) $@ $(objects)
#
# Define object file dependencies.
$(po)atri's.o: $(ps)atri.f $(includes)
$(xc)$@ $(ps)atri.f
$(po)bcflux's.o: $(ps)bcflux.f $(includes)
$(xc)$@ $(ps)bcflux.f
$(po)bio's.o: $(ps)bio.f S(includes)
$(xc)$@ $(ps)bio.f
$(po)cbal's.o: $(ps)cbal.f$(includes)
$(xc)$@ $(ps)cbal.f
$(po)commnt's.o: $(ps)commnt.f$(includes)
$(xc)$@ $(ps)commnt.f
$(po)disper's.o: $(ps)disper.f $(includes)
$(xc)$@ $(ps)disper.f
$(po)error's.o: $(ps)error.f $(includes)
$(xc)$@ $(ps)error.f
$(po)flow's.o: $(ps)flow.f $(includes)
$(xc)$@ $(ps)flow.f
$(po)grid's.o: $(ps)grid.f S(includes)
$(xc)$@ $(ps)grid.f
$(po)har's.o: $(ps)har.f
$(xc)$@ $(ps)har.f
$(po)inputrs.o: $(ps)inputl.f$(includes)
$(xc) $@ $(ps)inputl!f
$
-------
Appendix G
EXAMPLE MT4 FILES
Below are sample input files for the three example problems described in Section 6: example 1 is the
SVE problem; example 2 is the first BV problem; and example 3 is the field scale BV problem. Note that
data for example problems 2 and 3 ate included as comment lines using the # in column 1.
The first input file should be named 'iriiset.dr and located in the directory with the executable code.
# This is the data file for input 1 for example 1 (SVE)
* Data for examples 2 (BV) and 3 (field scale BV) are included.
# Data fields can be separated by comment lines beginning with the '#'
H All data are input in free format.
H
((1======= BLOCK A: INPUT/OUTPUT FILES AND OP-
H
# Field 1 - Input files.
# Specify the name of D2 and the error message file.
» The file name must be in single quotes.
#
H far example 1 , the datafile for input2 is located in the subdirectory
Ndau
'data/d2,cxampler 'miser.error'
H for example 2, the datafile for input2 is located in the subdirectory
ti 'dat3/d2.cxamplc2' 'miser.enor'
* for example 3, tire datafile for input2 is located in the subdirectory
Hdata
(f 'data/d2,example3' 'miser.error'
»
# Reid 2 - Prefix name for all output files.
» e.g. 'outprc.out', 'outprc.err', etc.
tt The prefix name must also be entered in single quotes.
*
H for example 1 , output is written to the tmp directory
"Amp/examplel1
It for example 2, output is written to the tmp directory
» Vtmp/cxample2'
# for example 3, output is written to the tmp directory
H '/tmp/exampleS'
H
# Field 3 - Output unit numbers for error and performance information.
H Device numbers for:
* (1) printing error and warning messages, and
If (2) printing performance information.
H 0 * do not print information;
6 « screen:
21 = main output file (prefix. out);
22 = error message file (prefix.err) (only for error messages);
23 « convergence history file (prefix.cnv) (only for performance
output),
I* for examples 1,2 and 3, print information to the screen
6 6
tf
H Field 4 - Contour plot file.
H Logical switch to open and print contour plot data to the file
# "outprc.con' (lclrl(23) = (or f).
H
It for examples 1,2 and 3
t
H
# Field 5 - Mass balance Output file.
# Enter either 1 or 3 lines of data.
# line 1: A logical switch to open and print mass balance results to
# the file 'outpre.mb' (lprnt(6) = t or f).
# line 2: Only needed if lprnt(6) above is true, otherwise disregard.
Enter a logical variable lprnt(25) indicating if the print
interval is set by the number of time steps (true) or by a
# constant time interval (false). Enter a logical variable
# lprnt(27) indicating if the material balance is in report
# form (t) orin multiple files in time series form (f).
# line 3: Only needed if lprnt(6) above is true, otherwise disregard.
# Enter either the number of time steps ipt(83) or the uniform
# print interval in seconds t(27).
#
# for examples 1, 2 and 3, print the mass balance every 10 days
t
f f
8.64d5
#
# Field 6 - Time series output file.
# Enter either 1 or 3 three lines of data.
# line 1: A logical switch to open and print time series results to
# the file 'outpre.plt' (lctrl(15) = t or f).
# line 2: Only heeded if lctrl(15) above is true, otherwise disregard.
# Enter a logical variable lprnt(26) indicating if the print
# intervalis set by the number of time steps (true) or by a
# constant time interval (false). Enter a second logical
# switch lprnt(26) indicating the concentration units for
# output (t=mole fraction, f=concentration).
# line 3: Only needed if lctrl(15) above is true, otherwise disregard.
# Enter either the number of time steps ipt(84) or the uniform
# print interval in seconds t(28).
#
# for examples 1,2 and 3
f
# Field 7 -Restart file.
# Open and print restart data to the file 'outpre.rst'
#(Ictrl(5) = torf).
#
# for examples 1,2 and 3
t
#
# Field 8 - Uniform print interval to the main output file.
# Enter two lines:
# (1) a logical variable indicating if the print interval is set
# by the number of time steps (true) or by a constant time
# interval (false);
# (2) either the number of time steps ipt(25) or the uniform print
# interval in seconds t(12).
#
# for examples 1, 2 and 3, print the main output file every 20 days
f
I.7280d6
140
-------
======= TITLE CARDS ===========
#
$
#
# Define an unspecified number of title cards, including zero, if none
# are desired. Title or comment cards are indicated with an '&' symbol
# in column one. These can be placed anywhere in the main output file,
# provided they are positioned in the input files between data fields.
#
&
&Sample data file for input 1: examples 1, 2, and 3.
#
#====== BLOCK B: GENERAL MODEL CONTROL OPTIONS ==
#
# Field 1 - Coordinate system.
# Specify: (1) an integer switch: 0=cross-sectional (x-z);
# 1 = axial-symmetric (r-z);
# (2) horizontal component of the gravitational constant
# (m/s"2); .
# (3) vertical component of the gravitational constant
# (m/s"2);
#
# for examples 1,2 and 3
1 O.dO 9.81dO
#
# Field 2 - Equation solution options.
# Define 3 logical variables (t or f) indicating which balance equations
# are to be solved:
# (1) solve the phase balance eqs;
# (2) solve the component transport eqs;
# (3) solve napl equations
# (4) solve solid phase equations
# (5) solve biophase equations
# The flow equations can be solved without solving transport equations;
# the transport eqs can be solved with an input steady state flow
# distribution, option 2 must be true for options 3,4, or 5 to be true;
# for example 1
t t t t f
# for example 2
#t t t f t
# for example 3
#t t t t t
#
# Field 3 - Mass lumping options.
# Define two logical variables indicating if lumping of the mass matrix
# is to be performed in the solution of the flow eqs and in the
# solution of the transport equations.
# for examples 1,2 and 3
tt
#
# Field 4 - Flow solution skipping option.
# Read an integer parameter denoting the number of time steps to be
# skipped between.solving for the flow equations.
#
# for examples 1,2 and 3
0
#
# Field 5 - not used
# Field 6 - Coupling between flow and transport.
# Enter a logical variable indicating if mass exchange terms
# should be included in the solution of the flow equations.
# for examples 1, 2 and 3
t
#
# Field 7 - Element dimensionless numbers.
# Enter a logical variable indicating if element dimensionless
# numbers are to be calculated for the transport solution
#
# for examples 1,2 and 3
t
#
#=== BLOCK C: TIME STEP AND ITERATION CONTROL =
#
# Field 1 - Simulation time frame.
#The initial (t(l)) and final (t(2)) simulation time in seconds.
#
# for examples 1, 2 and 3, run simulation for 100 days
O.dO 8.640d6
#
# Field 2 - Time weighting.
# Specify the time weighting parameter (t(10)): 0=explicit; l=implicit;
# 0.5 = Crank-Nicolson.
#
# for examples 1, 2 and 3
l.dO
#
# Field 3 - Maximum number of time steps (ipt((30)).
#
# for examples 1,2 and 3
100000000
#
# Field 4 - Convergence tolerance.
# Convergence tolerance in the solution of:
# the phase balance eqs t(13); the component transport eqs 1(14);
# the bioreaction eqs. t(15); the immobile phase eqs. t(16).
#
# for examples 1,2 and 3
l.d-5 l.d-8 l.d-8 l.d-8
#
# Field 5 - Time step range.
# Initial time step size (t(3)) in seconds; the minimum time step size
# t{4)); and the maximum time step size (t(5)).
#
# for examples 1,2 and 3
l.dO l.d-4 3.6d3
#
# Field 6 - Maximum iterations for convergence.
# Maximum number of iterations for convergence in the solution of:
# the phase balance eqs ipt(31); the component transport eqs
#ipt(32); the bioreaction eqs. ipt(33) (ipt(33) currently not used).
#
# for examples 1,2 and 3
15 30 30
#
# Field 7 - Maximum iterations for time step amplification.
# Maximum number of iterations for time step amplification in the
# solution of: the phase balance solution ipt(34), and in the
# solution of the transport eqs. ipt(35).
# The minimum must be less than the maximum number of iterations.
#
# for examples 1,2 and 3
7 7
#
# Field 8 - Time step multiplication factors.
# Empirical time step amplification t(6) and reduction t(7) factors.
# The time step is increased by a factor t(6) if the number of
# iterations for convergence is less than the minimum; conversely the
# step is reduced by the factor t(7) if the number of iterations for
# convergence is greater than the maximum.
#
# for examples 1, 2 and 3
1.05dO 0.75dO
#
#== BLOCK D: GRID PARAMETERS AND OPTIONS =====
#
# Field 1 - Output grid geometry.
# Enter a logical switch indicating if all grid information should be
# printed to the main output file?
#
# for examples 1,2 and 3
f
#
# Field 2 - Grid specification options.
# Generate the grid for a rectangular homogeneous domain?
# Enter an integer value: 0 = don't generate the grid, input all
# element numbers and nodal coordinates.
# 1 = generate union jack grid.
# 2 = generate herring bone grid.
#
# for examples 1,2 and 3
2
141
-------
* Held 3 - Number of blocks.
ft If a grid is 10 be generated (igrid>0), then enter the number of
ft blocks in the horizontal (nx) and vertical (nz) directions,
ft respectively, Skip if no grid is generated (igrid=0).
ft
ft for example I
31 13
ft for example 2
ft 39 IS
ft for example 1
II40 56
ft
ft Held 4 - Horizontal Block spacing in generated grid.
ftIf a grid is to be generated (igrid>0), then enter:
ft first line • a logical variable indicating if the spacing is uniform,
ft and the horizontal coordinate of the left boundary;
ft succeeding lines - horizontal spacing (one value if uniform, or nx
(f values if nonuniform). Units are assumed to be
ft melers.
ft Skip if no grid is generated (igrid=0).
ft
ft for example 1
f 0,2SdO
0.01d00.02d00.03dO
0 (MdO 0 05dO 0,06dO O.OVdO O.OSdO 0.09dO 0.1 dO 0.12dO 0.15dO 0.20dO
0,25dQ 0.3(10 0.4d00.5dOO,6d00.75d00.95dO 1.2dO 1.5dO 1.85dO
2,25(10 2,75dO 3,35dO 4.dO 4.75dO S.dO S.dO S.dO
ft for example 2
ft f 0.250), then enter:
ft first line - a logical variable indicating if the spacing is uniform,
ft and the horizontal coordinate of the left boundary;
ft succeeding lines - horizontal spacing (one value if uniform, or nx
ft values if nonuniform). Units are assumed to be
ft meters.
ft Skip if no grid is generated (igrid=0).
ft
ft for example 1 and 2
I O.dO
0.25JO
ft for example 3
#f O.dO
ft 0.25(10 0.25dO 0,25dO 0.25dO
ft 0.25dO 0,25dO 0.25dO 0.25dO
ft 0.25dO 0.25dO 0.25dO 0.25dO
ft 0.25dO 0.25dO 0.25(10 0.25dO
ft 0.25(10 0.25dO 0.25dO 0.25dO
ft 0,25(10 0.25(10 0.25dO 0.25dO
ft 0.25dO 0.25dO 0.25dO 0.25dO
* 0.20dO 0.20dO 0.10(10 O.lOdO O.lOdO O.lOdO O.IOdO O.lOdO
ft 0,10(10 O.lOdOO.lOdO O.ISdO O.lSdO 0.20dO 0.20dO
ft 0.25UO 0.25dO 0.25dO 0.25dO
ft 0-30dO 0.40JO O.SOdO 0.5CWO O.SOdO
ft 0.50(10 O.SOdO O.SOdO 0.50dO
H
ft field 6 - Horizontally aligned material property blocks.
ft If a grid is to be generated (igrid>0), then enter an integer number
ft of horizontal material property blocks (ipt(26)).
ft If the number of blocks is greater than 1, then beginning on the
ft following line, enter the material block number for each vertical
spacing. There must be nz integer values in order from top to bottom.
# Skip if no grid is generated (igrid=0).
#
# for example 1 and 2
2
1 1 1222211 I 1 1 1 I 1 1 1
# for example 3
#3
#11111111
#22222222
#2222
#33333333
#33333333
#33333333
#33333333
#3333
#
# Field 7 - Grid dimensions.
# If a grid is to be input (igrid=0), then enter:
* the number of elements (ipt(0)); the number of nodes (ipt(l))! and the
t number of material property blocks (ipt(26)).
# Skip if the grid is generated (lgrid>0).
#
# Field 8 - Nodal incidence list.
# If a grid is to be input (igrid=0), then enter the nodal incidence
# list and the material property block number for each element.
# The element node incidence list consists of the arbitrary global
# element number followed by that element's three global node numbers.
# Each element has its own line. The element node numbers
# start at an arbitrary node. If the z coordinate is positive
# downwards proceed in the clockwise direction, otherwise proceed
# in the counterclockwise direction. If there is only one material
# property block for the entire domain, the material property input
# assignment for each element is omitted. The minimum material
# property block is a two element quadrilateral.
#
# Field 9 - Nodal coordinates
# If a grid is to be input (igrid=0), then enter the nodal coordinates.
# For each node enter 1 line of data giving: the node number; horizontal
# coordinate; and the vertical coordinate. Units are assumed to be
# meters. Skip if the grid is generated (igrid>0).
#==== BLOCK E: COMPONENT INFORMATION ======
#
# Field 1 - Number of NAPL components.
# Specify the number of components in the NAPL (ipt( 15))
#
# for example I and 2
1
# for example 3
#2
#
# Field 2 - NAPL component chemical properties.
# For each NAPL component enter in order:
# (1) component number
# (2) component name (character variable in single quotes)
# (3) component molecular weight (g/mole)
# (4) component vapor pressure (atm)
# (5) component vapor viscosity (cPoise)
# (6) component liquid density (g/1)
# (7) component gas diffusivity (cm"2/s)
# (8) component aqueous diffusivity (cm"2/s)
# (9) component henry's constant (atm 1/g)
# (10) component aqueous solubility (g/1)
# Data for each component must start on a new line.
# Note: a component can be excluded from the gas phase or the aqueous
# phase by entering a negative value for the vapor pressure or aqueous
# solubility, respectively. Organic components should be entered in
# order of volatility starting with the most volatile.
# Skip this item if no NAPL components are specified (ipt(I5)=0).
#
# for example 1 and 2
1 ' toluene ' 92.1340dO 2.940d-2 7.0d-3 867.0dO
8.5d-2 9.540d-6 5.70d-2 .5150dO
# for example 3
#1 'benzene ' 78.10dO 0.102dO 7.5d-3 879.0dO
#8.8d-2 9.0d-6 5.70d-2 1.78dO
#2 'xylene ' 106.2dO 0.0092dO 7.0d-3 880. IdO
142
-------
#6.2d-2 7.2d-6 5,70d-2 .I75dO
#
# Field 3 - Chemical property data for water, oxygen, and nitrogen.
# Enter the 10 parameter values listed above. The ordering is assumed
# to be: water, oxygen, and nitrogen.
# The component number is always: water = ipt(l 5)+l; oxygen = ipt(15)+2;
# nitrogen = ipt(15)H-3
# Any of these components can be eliminated by specifying negative
# values for both the vapor pressure and water solubility.
# Note, if water is eliminated then there is no aqueous phase pressure
# and the flow equations cannot be solved.
# If nitrogen is eliminated, then there is no gas phase, (i.e. the vapor
# pressure must be negative for all components). The nitrogen
# solubility is a dummy input; it is not used in computations.
# for example 1
2 ' water ' IS.OdO -2.310d-2 9.750d-3 998.0dO
.2450dO O.OdO O.OdO l.OdO
3 ' oxygen ' 32.0dO -0.20dO 0.0192dO 998.0dO
8.5d-2 2.I53d-5 O.OdO -.009dO
4 ' nitrogen ' 28.02dO l.OdO 0.0172dO 998.0dO
O.OdO O.OdO O.OdO -l.OdO
# for example 2
#2 'water ' IS.OdO -2.310d-2 9.750d-3 998.0dO
#.2450dO O.OdO O.OdO l.OdO
# 3 ' oxygen ' 32.0dO 0.20dO 0.0192dO 998.0dO
#8.5d-2 2.153d-5 O.OdO .009dO
#4 ' nitrogen ' 28.02dO l.OdO 0.0172dO 998.0dO
# O.OdO O.OdO O.OdO -l.OdO
# for example 3
#3 'water ' IS.OdO -0.0231dO 9.50d-3 998.2dO
#.2450dO O.OdO O.OdO l.OdO
#4 'oxygen ' 32.0dO 0.20dO 0.02dO 998.0dO
#8.5d-2 2.153d-5 O.OdO .009dO
#5 ' nitrogen ' 28.02dO l.OdO 0.0174dO 998.0dO
# O.OdO O.OdO O.OdO -l.OdO
#
# Field 4 - Nutrient inclusion. .
# Enter a logical variable indicating whether a nutrient component is
# to be modeled.
#
# for examples 1, 2 and 3
f
#
# Field 5 - Nutrient Chemical Properties.
# If a nutrient is modeled, then specify the 10 chemical
# property parameters listed above.
# The component number of nutrient is always = ipt(15)+4.
# Skip this item if no nutrient is modeled.
#
#=== BLOCK F: MASS EXCHANGE INFORMATION =====
#
# Field 1 - Interphase mass exchange coefficients.
# Enter: (1) component number which is identical to the order entered
# above; nitrogen = ipt(15)+3; nutrient=ipt(15)+4)
# (2) aqueous/gas exchange coefficient (I/sec)
# (3) aqueous/NAPL exchange coefficient (I/sec)
# (4)gas/NAPL(l/sec)
# (5) aqueous/biophase (1 /sec)
# (6) aqueous/solid (I/sec)
# Note: a zero value for aqueous/biophase mass exchange coefficient
# indicates that the component does not partition between that phase
#pair.
# On a second line enter minimum deviations from equilibrium for each
# exchange coefficient entered on the previous line. DO NOT ENTER A
# VALUE LESS THAN 0.05DO.
# Enter: (1) component number which is identical to the order entered
#
#
#
#
#
#
#
# for example 1
# toluene
1 5.0d-55.0d-45.0d-40.dO 5.d-5
1 O.ldO O.ldO O.ldO O.ldOO.ldO
# water
above; nitrogen = ipt(l 5)+3; nutrient=ipt(l 5)+4)
(2) aqueous/gas minimum deviations from equilibrium
(3) aqueous/NAPL minimum deviations from equilibrium
(4) gas/NAPL minimum deviations from equilibrium
(5) aqueous/biophase minimum deviations from equilibrium
(6) aqueous/solid minimum deviations from equilibrium
2 O.dO O.dO O.dO O.dO O.dO
2 O.ldO O.ldO O.ldO O.ldOO.ldO
# oxygen
3 O.dO O.dO O.dO O.dO O.dO
3 O.ldO O.ldO O.ldO O.ldOO.ldO
# nitrogen
4 O.dO O.dO O.dO O.dO O.dO
4 O.ldO O.ldO O.ldO O.ldOO.ldO
# for example 2
# toluene
# 1 5.0d-6 5.0d-5 5.0d-5 O.dO O.dO
#1 O.ldO O.ldO O.ldO O.ldOO.ldO
# water
#2 O.dO O.dO O.dO O.dO O.dO
#2 O.ldO O.ldO O.ldO O.ldOO.ldO
# oxygen
# 3 5.0d-6 5.0d-5 5.0d-5 O.dO O.dO
#3 O.ldO O.ldO O.ldO O.ldOO.ldO
# nitrogen
#4 O.dO O.dO O.dO O.dO O.dO
#4 O.ldO O.ldO O.ldO O.ldOO.ldO
^fpr example 3
# benzene
#1 1.157d-52.315d-45.787d-40.dO 1.157d-5
#1 0.075dO 0.075dO 0.075dO 0.075dO 0.075dO
# o-xy!ene
#2 1.157d-52.315d-45.787d-40.dO 1.157d-5
#2 0.075dO 0.075dO 0.075dO 0.075dO 0.075dO
# water \
#3 O.dO I O.dO O.dO O.dO O.dO
#3 0.075dO 0.075dO 0.075dO 0.075dO 0.075dO
# oxygen
#4 1.157d-52.315d-45.787d-40.dO 1.157d-5
#4 0.075dO 0.075dO 0.075dO 0.075dO 0.075dO
# nitrogen
#5 O.dO O.dO O.dO O.dO O.dO
#5 0.075dO 0.075dO 0.075dO 0.075dO 0.075dO
#
#=== BLOCK G: MATERIAL PROPERTY BLOCK DATA =
#
# Field 1 - Soil physical properties:
# For each material property block specify:
# (1) material block number;
# (2) porosity;
# (3) horizontal permeability (m"2);
# (4) vertical permeability (m"2).
# (5) bulk soil density (gm/cm"3)
# (6) organic carbon content
# Data for all blocks must be defined.
# Data for each block begins on a new line
#
# for example 1 and 2
1 0.33dO l.d-11 O.Sd-11 1.7dO O.OOldO
2 0.35dO 0.6d-ll 0.4d-ll 1.7dO O.OOldO
# for example 3
#1 0.33dO l.Od-Il l.Od-11 1.7dO O.OOldO
#2 0.33dO 5.0d-ll 5.0d-ll 1.7dO O.OOldO
#3 0.33dO 0.7d-ll 0.7d-ll 1.7dO O.OOldO
#
# Field 2 - Water retention parameters:
# For each material property block specify:
# (1) material block number;
# (2) residual water saturation;
# (3) van Genuchten n for air/water retention data;
# (4) van Genuchten alpha for air/water retention data (I/Pa).
# Data for all blocks must be defined.
# Data for each block begins on a new line
#
# for example 1 and 2
1 0.12dO 7.0dO .002dO
2 0.16dO S.OdO .OOOSdO
# for example 3
#1 0.073dO 3.97dO 4.34d-4
#2 0.073dO 3.97dO 7.47d-4
#3 0.073dO 3.97dO 2.79d-4
#
# Field 3 - Dispersion parameters:
# For each material property block specify:
143
-------
H (I) material block number;
ft (2) longitudinal dispersivity (m);
ft (3) transverse dispersivity (m);
ft
ft for example 1 and 2
t l.OdO 0.01dO
I I OdO 0.01 dO
ft for example 3
M 1 0.5JO 0.01 dO
it 2 OS-JO 0.01 dO
»3 0.5JO O.OloO
«
# Field 4 - Dispersion tensor computation.
fl Enter a logical variable (lclrl(21)) indicating that the
ft hydrodynamic dispersion tensor should be calculated. Enter false if
ft a known and. constant dispersion tensor is to be input.
ft for examples 1,2 and 3
I
ft
It Field 5 • Dispersion tensor.
It If kttl(2l) above is false then enter the hydrodynamic dispersion
It tensor for each component present with two lines, the first line is
* for the gas phase and the second line is for the aqueous phase. The
If first entry on each line is Ihe component number.
H
ffnmz BLOCK H: SORPTION PARAMETERS =====
(t ReJd 1 - Sorption model (required if lclrl(25)=true):
ft Enter a logical variable (lctrl(19)) indicating if sorption is
It modeled as a one (false) or two (true) compartment process.
It Note; lire two compartment model is currently limited to conditions of
If a homogeneous soil domain and a single component NAPL.
It Tor examples land 3
t
(t Field 2 - Single compartment Freundlich sorption parameters
H (required if I«rK25)=true):
It For each material property block enier two groups of data:
H (1) Ihe material block number, followed by the k parameter values
H for each organic component in order
ft from I to the number of components (micrograms/gram solid,
ft with aqueous concentration in mg/1)
ft (2) the material block number, followed by the n=l/m parameter
ft (dimensionlcss) values ordered in the same way.
II
H for example 1
I 7,72dO
1 0.544dO
2 7,72dO
2 0,S44dO
H for example 3
#1 l,I6dO 0..16JO
ft I 0.862dO 1.07dO
II2 IJ6dO 0,36dO
H2 0862JO 1.07dO
ft 3 U6dO 0.36dO
It 3 O.S62dO 1.07dO
ft
H Field 3 - Two compartment sorption data:
K Tlic two compartment model has a slow and a fast compariment.
H Both compartments are modeled with Ihe Freundlich equation.
It Four parameters must be input:
If (I) multiplier to convert slow compartment kf parameter to the fast
If compartment value;
H (2) mtilliptler lo convert slow compartment n=l /m parameter to the
H compartment value;
ft (3) multiplier to convert slow compartment mass transfer
If coefficient to the fast compartment value;
K (4) mass fraction of solid phase in the fast compariment.
H Skip this item if Ihe single compartment model is used
»(lctrl(19)=false)
It
It Field 4 - Include retardation factor (required if Ictrl(25)=false).
M Enter a logical variable indicating if retardation factors are used.
H for example 2
#f
#
# Field 5 - Retardation factors (required if lctrl(25)=false and
# lretrd=true)
# For each component give the component number and the retardation
# factor. Retardation factors must be entered for all components,
# however 1,0 implies no sorption.
^
#=== BLOCK I: BIOLOGICAL PARAMETERS ====
#
# Field I - Number of biodegradable substrates.
# Specify the number of biodegradable substrates, ipt(17). The biophase
# always contains oxygen and nutrient if present.
#
# for example 2
#1
# for example 3
#2
#
# Field-2 - Biodegradation control switches.
# Specify 2 logical variables indicating:
# (1) if a steady state biomass is to used (value=true), or if a
# transient, biomass is to be modeled (value=false).
# (2) if biodegradation equations are modeled as a sink term
# in.the aqueous transport equations (value=true),
# otherwise their modeled as. rate-limed1 exchange to a
# separate biophase (value=false).
#
# for examples 2 and 3
#f t
#
# FieUfS - Growth kinetics option.
# Specify an integer value indicating the type of growth
# kinetics: (ONLY OPTIONS 1 AND 2 AVAILABLE NOW)
# 1 = standard Monod kinetics
# 2 = Monod kinetics with substrate inhibition
# 3 = Monod kinetics with lumped substrate inhibition
# 4 = Monod kinetics with saturation dependency
# and substrate inhibition
# 5 = Monod kinetics with saturation dependency and
# substrate inhibition
#
# for examples 2 and 3
#2
#
# Field 4 - Monod parameters:
# For each component in the biophase provide the following information:
# (1) component number as defined in block E.
# (2) electron acceptor use coefficient (gm-O2/gm-substrate)
# (3) nutrient use coefficient (gm-nutrient/gm-substrate)
# (4) maximum substrate use rate (gm-substrate/gm-biomass/sec)
# (5) half saturation constant (gm-component/1)
# (6) yield coefficient (gm-biomass/gm-substrate)
# (7) inhibition constant (dimensionless) expressed as a fraction of
# the aqueous solubility. For substrate and nutrient this
# turns off metabolism when the concentration is above this
# threshold concentration and for electron acceptor this
# turns off metabolism when the concentration is below this
# threshold concentration. In both cases hyperbolic functions
# are used.
#
# for example 2
# toluene
#1 2.19dO 1.5dO 1.157d-6 !7.4d-3 0.5dO 0.25dO
# oxygen
#3 2.I9dO I.SdO 1.157d-6 O.Id-3 O.SdO 0.2dO
# for example 3 (high set)
# benzene
#1 2.19dO O.dO 1.157d-5 0.5d-3 O.SdO 0.5dO
# o-xylene
#2 2.I9dO
# oxygen
#4 2.19dO
# .
# Field 5 - Decay and biomass range coefficients.
# Specify:
# ( 1 ) the decay coefficient (sec)
# (2) the minimum biomass (g/1)
O.dO l.!57d-5 0.5d-3 O.SdO O.SdO
O.dO 1.157d-5 0.5d-3 O.SdO 0.5dO
144
-------
l.d-6 2.d-2 l.d-6 8.64d4
# (3) the maximum biomass (g/1)
# (4) the initial uniform biomass (g/1)
# (5) delay period for initiation of bioreaction (sec)
#
# for example 2
#1.157407d-7 l.d-3 100.0d-31.62d-38.64d4
# for example 3
#1.157407d-6
#
#===== BLOCK J: PHASE PARAMETERS =====
#
# Field 1 - Water phase viscosity.
# Specify the water phase viscosity (cPoise)
#
# for examples 1 and 2
1.124dO
# for example 3
# 1.002dO
#
# Field 2 - Gas phase slip flow parameters.
# Specify:
# (1) a logical variable indicating if the Klinkenberg
# effect is to be modeled (value=true);
# (2) the Klinkenberg parameter (arm). Set the parameter to zero
# if the previous line is false.
# for examples 1,2 and 3
f O.dO
#
#====== BLOCK K: TEMPERATURE PARAMETERS =====
#
# Field 1 - Temperature distribution.
# Specify a logical variable indicating if temperature
# distribution is uniform (true).
#
# for examples 1, 2 and 3
t
#
# Field 2 - Uniform temperature distribution.
# If the temperature distribution is uniform, enter a single uniform
# value (degree C); otherwise enter a temperature value for each node
# along the vertical edge of the domain.
#
# for examples 1,2 and 3
20.dO
#
# Field 3 - Nonuniform temperature distribution.
# A vertical nonuniform temperature distribution can be defined only in
# association with a generated rectangular grid.
# Temperature values are needed for each vertical node along the
# boundary starting at the surface, downward (ny+1 values).
# For each node enter 1 line of data giving the:
# 1) vertical depth of node (for error checking)
# 2) temperature .at the node (degree C)
#
# Field 4 - Temperature dependent chemical properties.
# Temperature dependent chemical properties are needed for each
# component for the following 6 properties:
# (1) component vapor pressure
# (2) component vapor viscosity
# (3) component Henry's law constant
# (4) component aqueous solubility
# (5) component maximum specific utilization rate
H (6) biomass decay rate
# For each of these properties give the temperature dependent value at
# each of the ny+1 nodes along the vertical boundary.
# Provide the information for all 6 properties for a given component and
# then repeat for the next component.
# Use the original component ordering as in the component information
# section. After all the component values give the kd values.
#
# Vapor pressure of component 1 at ny+1 nodes
#
# Vapor viscosity of component 1 at ny+1 nodes
#
# Henry's law constant of component 1 at ny+1 nodes
#
# aqueous solubility of component 1 at ny+1 nodes
#
# maximum specific utilization rate of component 1 at ny+I nodes
$
# Repeat above for all NAPL components, then water, oxygen, nitrogen and
# nutrient if present.
# After all components have been entered, provide ny+1 nodal values for
# the Kd coefficient.
#
#=== BLOCK L: OUTPUT CONTROL PARAMETERS =====
#
# Field 1 - Print initial conditions.
# Enter a logical variable (LPRNT(3)) indicating if initial conditions
# should be printed for selected variables.
#
# for examples 1, 2 and 3
t
#
# Field 2 - Print switches.
# Read print switches for specified variables, the first switch for
# each variable is for the printed output, the second switch for
# each variable is for the contouring output: Use component numbers
# based established in block E above:
# This input is currently set for minimal output. The user should
# specify output of interest.
t f print/contour output in molar form
t f print/contour nodal gas phase pressure
t f print/contour nodal aqueous phase pressure
f f print/contour nodal gas/aqueous capillary pressure
f f print/contour nodal gas phase density
ff print/contour nodal aqueous phase density
f f print/contour nodal NAPL phase density
t f print/contour nodal gas phase components
1 1
11 print/contour nodal aqueous phase components
1 1
f f print/contour nodal NAPL phase components
f f print/contour nodal solid phase loadings
f f print/contour nodal bio-phase components
t f print/contour element avg total organic soil mass fraction
t f print/contour nodal gas phase saturation
t f print/contour nodal aqueous phase saturation
t f print/contour nodal NAPL phase saturation
t f print/contour gas phase Darcy velocities
f f print/contour aqueous phase Darcy velocities
#
# Field 3 - Gas phase time series plot switches.
# Iine(l) - enter a logical variable indicating if time series plot
output files should be generated for gas phase
line(2) - If .true, enter the number of gas phase components;
followed by the global component number and the
associated node number for the location from which to
output.
A maximum of 6 components can be defined for the combined gas and
aqueous phase below.
f time series plot nodal gas phase components
#
# Field 4 - Aqueous phase time series plot switches.
# Iine(l) - enter a logical variable indicating if time series plot
# output files should be generated for gas phase
# line(2) - If .true, enter the number of gas phase components;
# followed by the global component number and the
# associated node number for the location from which to
# output.
# Amaximumof6 components can be defined for the combined gas and
# aqueous phase below.
f time series plot nodal aqueous phase components
In this example the second input file is named 'd2.examplel' and is located in a subdirectory called
'data.'
145
-------
» This is the dan file for input2 for example 1 (SVE)
# Data for examples 2 (BV) and 3 (field scale BY) are included.
(t Data field can be separated by comment lines beginning with the '#'
H All 0, then for each element containing NAPL provide the
# following information:
# (1) element number
# (2) The uniform nodal NAPL saturation;
# (3) NAPL mole fraction of each organic component.
# There must be ipt(15) mole fractions specified.
# Mole fractions are entered in sequential order (i.e. component
# numbers 1 to ipt(15). The mole fractions must sum to 1.
# for examples 1 and 2 - this is a partial file.
1.531656E-02.1000E+01
2.562525E-02.1000E+01
572.566822E-09 .1000E+01
573 .566507E-09 .1000E+01
# for example 3 - this is a partial file.
# 1 0.326712E-01 0.5000E+00 0.5000E+00
#20.285502E-010.5000E+00 0.5000E+00
# ...
#2168 0.703352E-15 0.5000E+00 0.5000E+00
# 2169 0.696703E-15 0.5000E+00 O.SOOOE^OO
#
#== BLOCK Q: OXYGEN AND NUTRIENT INITIAL CONDI-
TIONS =====
#
# Field 1 - Gas phase initial conditions.
# Read a logical variable (lunfx) indicating if the gas phase initial
# conditions for oxygen and/or nutrient are uniform.
# Skip this input if oxygen is absent from the gas phase (i.e. the
# oxygen vapor is assigned a negative value)
#
# for examples 2 and 3
#t
#
# Field 2 - Uniform gas phase conditions.
# Enter the uniform gas phase initial conditions for oxygen and
# nutrient.
# Initial conditions are read as partial pressures (i.e. mole
# fractions). Nutrient can only be present if oxygen is present.
# (I) the uniform oxygen partial pressure in the gas phase
# (2) the uniform nutrient partial pressure in the gas phase. This
# item is omitted if nutrient is absent.
146
-------
#
# for examples 2 and 3
#0.20dO
#
# Field 3 - Nonuniform gas phase initial conditions for oxygen and
# nutrient.
# If lunfx=F, then for each node enter:
# (1) node number;
# (2) the uniform oxygen partial pressure in the gas phase
# (3) the uniform nutrient partial pressure in the gas phase
# Nodes need not be in order.
#
# Field 4 - Aqueous phase initial conditions.
# Read a logical variable indicating if the aqueous phase initial
# conditions are uniform.
# Skip this input if oxygen is absent from the aqueous phase (i.e. the
# oxygen aqueous solubility is assigned a negative value)
#
# for examples 2 and 3
#t
#
# Field 5 - Uniform aqueous phase conditions.
# Read the aqueous phase initial conditions for oxygen and nutrient.
# Inital conditions are read as concentrations (g/L). Nutrient
# can only be present if oxygen is present.
# If lunfx=T, then enter:
# (1) the uniform oxygen concentration (g/L) in the aqueous phase
# (2) the uniform nutrient concentration (g/L) in the aqueous phase
#
# for examples 2 and 3
#0.0090dO
#
# Nonuniform aqueous phase initial conditions for oxygen and nutrient.
# If lunfx=F, then for each node enter:
# (1) node number;
# (2) the uniform oxygen concentration (g/L) in the aqueous phase
# (3) the uniform nutrient concentration (g/L) in the aqueous phase
# Nodes need not be in order.
#
#=== BLOCK R: BOUNDARY CONDITIONS =====
#
# field 1 - Constant gas pressure nodes equivalent to the initial
# pressure.
# (1) Enter the number of nodes with a constant gas pressure equal
# to the initial gas pressure.
# (2) If nonzero, then starting on a new line, specify the node
# number of all such nodes.
#
# for example 1
26
457 476 495 514 533 552 571 590 591 592 593 594 595 596 597 598
599 600 601 602 603 604 605'606 607 608
# for example 2
#34
#742
# 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760
# 457 476 495 514 533 552 571 590 609 628 647 666 685 704 723
# for example 3
#76
# 22 23 24 25 26 27 28 29 30
# 31 32 33 34 35 36 37 38 39 40
# 41 82 123 164 205 246 287 328 369 410
# 451 492 533 574 615 656 697 738 779 820
# 861 902 943 984 1025 1066 1107 1148 1189 1230
#1271 1312 1353 1394 1435 1476 1517 1558 1599 1640
#1681 1722 1763 1804 1845 1886 1927 1968 2009 2050
#2091 2132 2173 2214 2255 2296 2337
#
# Field 2 - Constant gas pressure nodes different from the initial
# pressure.
# (1) Enter the number of nodes with a constant gas pressure that is
# different from the initial gas pressure.
# (2) If nonzero, then for each such node provide one line of data
# giving the node number and constant gas pressure (Pa gauge).
#
# for examples 1, 2 and 3
0
#
# Field 3 - Constant aqueous pressure nodes equivalent to the initial
# pressure.
# (1) Enter the number of nodes with a constant aqueous pressure
# equal to the initial gas pressure.
# (2) If nonzero, then starting on a new line, specify the node
# number of all such nodes.
#
# for example 1
26
457 476 495 514 533 552 571 590 591 592 593 594 595 596 597 598
599 600 601 602 603.604 605 606 607 608
# for example 2
#34
#742
# 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760
# 457 476 495 514 533 552 571 590 609 628 647 666 685 704 723
# for example 3
#76
# 22 23 24 25 26 27 28 29 30
# 31 32 33 34 35 36 37 38 39 40
# 41 82 123 164 205 246 287 328 369 410
# 451 492 533 574 615 656 697 738 779 820
# 861 902 943 984 1025 1066 1107 1148 1189 1230
#1271 1312 1353 1394 1435 1476 1517 1558 1599 1640
#1681 1722 1763 1804 1845 1886 1927 1968 2009 2050
#2091 2132 2173 2214 2255 2296 2337
#
# Field 4 - Constant aqueous pressure nodes different from the initial
# pressure.
# (1) Enter the number of nodes with a constant aqueous pressure
# that is different from the initial gas pressure.
# (2) If nonzero, then for each such node provide one line of data
# giving the node number and constant aqueous pressure (Pa gauge)
#
# for examples 1,2 and 3
0
#
# Field 5 - Gas phase component boundary conditions.
# (1) Enter the number of nodes for which gas phase component
# boundary conditions are specified.
# (2) For each such node, starting on a new line
# enter the following information:
# (2a) the node number
# (2b) an integer variable indicating the boundary condition
# type for all gas phase components at the node.
# 1 = constant mole fraction
# 2 = specified diffusive flux
# 3 = mixed type (contact with a known fluid).
# (2c) the boundary condition values for each component in the
# gas phase. The values are listed in sequential order
# corresponding to the component numbers. Only components
# that are present in the gas phase are listed. Component
# boundary conditions are not provided for components which
# are excluded from the gas phase (i.e. negative vapor
# pressure). Two values are needed for each boundary node
# component. These values are used as needed to specify the
# boundary condition.
# 1 = specified gas phase concentration (partial pressure)
# in contacting fluid. The partial pressures must sum
# to one (used for first type boundary).
# 2 = user supplied value of Dm/length.
#
# for example 1
35
420.dOO.d01.dOO.dO
520.dOO.d01.dOO.dO
620.dOO.d01.dOO.dO
720.dOO.d01.dOO.dO
820.dOO.d01.dOO.dO
920,dOO.dO l.dOO.dO
1020.dOO.d01.dOO.dO
11 20.dOO.d01.dOO.dO
1220.dOO.d01.dOO.dO
45730.dOO.d01.dOO.dO
47630.dOO.d01.dOO.dO
49530.dOO.d01.dOO.dO
51430.dOO.d01.dOO.dO
53330.dOO.d01.dOO.dO
147
-------
5S230.dOO.d01.dOO.dO
57130.dOO,d01.dOO.dO
5903O.d0O.dO l.dOO.dO
S9130.dOO.d01.dOO.dO
59230dOO.cK)l,dOO.dO
S9330.dOO.dOI.dOO.dO
S9430,dOO,d01.dOO,dO
59530.dOO,d01.dOO.dO
S9630dOO,d01.dOO,dO
59730.dOO.d01.dOO.dO
59330dOO.d01.dOO.dO
S9930dOO.d01.dOO.dO
60030.dOO.d01.dOO.dO
60130.dQO.d01.dOO.dO
6023 0,dOO.dO l.dOO.dO
60330dOO.d01.
-------
59730.dOO.d01.dOO.dO
59830.dOO.d01.dOO.dO
59930.dOO.d01.dOO.dO
60030.dOO.d01.dOO.dO
601 30.dOO.d01.dOO.dO
60230.dOO.d01.dOO.dO
60330.dOO.d01.dOO.dO
60430.dOO.d01.dOO.dO
60530.dOO.d01.dOO.dO
60630.dOO.d01.dOO.dO
60730.dOO.d01.dOO.dO
60830.dOO.d01.dOO.dO
# for example 2
#47
#43 O.dO O.dO 1 .dO O.dO 0.009dO O.dO
#53 O.dO O.dO 1 .dO O.dO 0.009dO O.dO
#63 O.dO O.dO l.dO O.dO 0.009dO O.dO
#73 O.dO O.dO 1 .dO O.dO 0.009dO O.dO
#83 O.dO O.dO l.dO O.dO 0.009dO O.dO
#93 O.d0 O.dO 1 .dO O.dO 0.009dO O.dO
#103 O.dO O.dO 1 ,dO O.dO 0.009dO O.dO
#113 O.dO O.dO l.dO O.dO 0.009dO O.dO
#123 O.dO O.dO l.dO O.dO 0.009dO O.dO
#133 O.dO O.dO l.dO O.dO 0.009dO O.dO
# 14 3 O.dO O.dO l.dO O.dO 0.009dO O.dO
#153 O.dO O.dO l.dO O.dO 0.009dO O.dO
#163 O.dO O.d0 l.dO O.dO 0.009dOO.dO
# 742 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 743 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 744 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 745 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 746 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 747 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 748 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 749 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 750 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 751 2 O.dO O.dO O.dO O.dO O.d0 O.dO
# 752 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 753 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 754 2 O.d0 O.dO O.dO O.dO O.dO O.dO
# 755 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 756 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 757 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 758 2 O.d0 O.dO O.dO O.dO O.dO O.dO
# 759 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 760 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 457 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 476 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 495 2 O.dO O.dO O.dO O.dO O.dO O.dO
#5142 O.dO O.dO O.dO O.dO O.dO O.dO
# 533 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 552 2 O.dO O.dO O.dO O.d0 O.dO O.dO
# 571 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 590 2 O.dO O.dO 0,dO O.dO O.dO O.dO
# 609 2 O.d0 O.d0 O.dO O.dO O.dO O.dO
# 628 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 647 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 666 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 685 2 O.dO O.dO O.dO O.dO O.dO O.dO
# 704 2 O.d0 O.dO O.dO O.dO O.dO O.dO
# 723 2 O.dO O.dO O.dO O.dO O.dO O.dO
# for example 3
#33
#22 2 O.dO O.dO O.dO O.dO 1.dO O.Od00.009dO O.dO
# 23 2 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
#24 2 O.dO O.dO O.dO O.dO 1.dO O.OdO 0.009dO O.dO
#25 2 O.dO O.dO O.dO O.dO I.d00.0d00.009d0 O.dO
#26 2 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
#27 2 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
# 28 2 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
#29 2 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
#30 2 O.dO O.dO O.dO O.dO 1.dO O.OdO 0.009dO O.dO
#312 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
#32 2 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
#33 2 O.dO O.dO O.dO O.dO 1.dO O.OdO 0.009dO O.dO
# 34 2 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
#35 2 O.dO O.dO O.dO O.dO 1.dO O.OdO 0.009dO O.dO
#36 2 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
#37 2 O.dO O.dO O.dO O.dO 1.dO O.OdO 0.009dO O.dO
# 38 2 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
#39 2 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
#40 2 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
#412 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
# 493 3 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
# 534 3 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
# 575 3 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
#6163 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
# 657 3 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
# 698 3 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
# 739 3 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
# 780 3 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
# 821 3 O.dO O.dO O.dO O.dO l.dO O.OdO 0.009dO O.dO
# 862 3 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
# 903 3 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
# 944 3 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
#9853 O.dO O.dO O.dO O.dO 1 .dO O.OdO 0.009dO O.dO
#
# Field 7 - Gas phase boundary flux.
# Enter two lines of data:
(1) Enter the number of nodes with a constant gas phase volumetric
flux.
(2) If nonzero, then for each such node provide one line of data
giving the node number and gas phase flux referenced to
atmospheric pressure and the steady temperature at the
injected node (m~3/s).
# for examples 1,2 and 3
0
#
# Field 8 - Aqueous phase boundary flux.
# Enter two lines of data:
(1) Enter the number of nodes with a constant aqueous phase
volumetric flux.
(2) If nonzero, then for each such node provide one line of data
giving the node number and aqueous phase flux (m~3/s).
# for examples 1,2 and 3
0
#
*== BLOCK S: EXTRACTION / INJECTION WELL =====
#
# Field 1 - Include an extraction / injection well.
# Enter a logical variable (LCTRL(12)) indicating if an
# extraction/injection well is to be simulated.
#
# for examples 1,2 and 3
t
# for example 3, generation of initial condition
#f
# Field 2 - Extraction / injection rate.
# Enter the total volumetric extraction/injection rate (scfin). A
# negative value indicates extraction, and a positive value indicates
# injection.
# Required only if LCTRL(12)=F
#
# for example 1
-lOO.dO
# for examples 2 and 3
#1.0dO
# for example 3, generation of initial condition
# O.OdO
#
# Field 3 - Well coordinates.
# Specify:
# (1) the well radius (m);
# (2) two integers identifying the minimum and maximum node
# numbers along the vertical well screen.
# Note all nodes along the well screen must have a horizontal
# coordinate equal to the well radius
# Not required if LCTRL(12)=F
#
# for example 1
0.25dO 4 12
# for example 2
#0.25dO 416
# for example 3
149
-------
* O.OSdQ 493 985
H^^, BLOCK R: VfeLOClTY BOUNDARY CONDITIONS
# Field 1 - Bottom boundary of domain.
ft Enter 8 logical variable (LCTRU28)) if the bottom boundary is
* impervious.
If for examples 1,2 and 3
t
« Reid 2 - R.H.S. boundary of domain.
K Enter a logical variable (LCTRL(29)) if the R.H.S. boundary is
H impervious.
It
H for examples 1,2 and 3
f
H Field 3 - L.H.S. boundary of domain.
* Enter a logical variable (LCTRL(30)) if the L.H.S. boundary is
# impervious. Nolc thai this boundary will be adjusted in the
# presence of a well
SforbXarhples l,2ah(S3
t
#
# Field 4 - fop b'oiinMy of domain.
rf Enter a logical variable (LCtKL(3 1 )) if the lop Boundary is
# irhpefvibus.
Mictrit315 is true read the length bf trie cap, CAJPlfak the cap is
# assumed Id extend frtirh the wbll td the inpUl value.
# Not required if LCtRL(3 1 )=F
#
# for examples 1 and 2
lO.OdO
#fdr example 3
#9.585dO
END OF DAf A2
150
-------
Appendix H
SOURCE CODE LISTING
Following is a source code listing of MISER. The main program is given first followed by all other
routines in alphabetical order. The Harwell sparse matrix package is excluded.
Main Routine - miser.f
c-
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c-
c
c-
c
MISER.f - Numerical model of two-dimensional multiphase,
multicomponent flow and transport. Designed
for soil vapor extraction (SVE) and bioventing
(BV) simulations. Nonequilibrium interphase
mass exchange and kinetic bioreaction terms are
included. Version 1.0-nonadaptive.
Computational domain: xz, rz
Project directed by: L.M. Abriola
Written by: J.R. Lang and K.M. Rathfelder
Version 1.0, January, 1997
Required Control Flags:
ipt(0) - number of elements
ipt(l) - number of nodes
ipt(2) - number of stacked variables
ipt(25) - print results every ipt(25) time steps if lprnt(0)
is true
ipt(30) - maximum number of timesteps
Control Flags computed internally in routine:
lctrl(14) - logical variable controlling coupling of flow and
transport solutions
lctrl(14) = .true. - exchange couples flow and
transport solutions
lctrl(14) = .false. - flow and transport
solutions not coupled
program MISER
— Include parameter and type declarations, common block definitions,
— and dimension statements.
include 'dimen.inc'
character* 20 infile(4),outpre,outfile(8-Hicmp)
Declare and define common block variables.
common/cb2/ p(nn3)
common /cb2b/ pt(nn3)
common/cb3/ sat(nnstkS)
common /cb3b/ satt(nnstk3)
common /cb8/ vis(nnmx),pmw(nn3)
common /cb9/ xmf(nmf)
common /cb9b/ xmft(nmf)
common /cblO/ den(nn6)
common /cblOb/ dden(nn6),pmwt(nn3),dent(nn6)
common /cbll/ pex(nnslO),rxnp(nn2)
common /cb62/ rxn(nmf),cex(nmfs)
common /cb62b/ rhsex(nmfs)
common /cb90/ infile.outpre.outfile
dimension pkeep(nnstk2)
C
C— Open input devices. The input and output devices are summarized
C— as follows: input; 11, file='infile(l)' - input for INPUT1 .f,
C— read from console input
C— 13, file='infile(2)' - input for INPUT2.f,
C— read from ifile( 1) by INPUT 1 .f
C— 14, file='infile(3)' - input for ERRMESSAGE.f,
C— read from infile(l) by INPUTl.f
C— 28, file='infile(4)' - input for restarts,
C— read from infile(2) by INPUT2.f
C— output: 21, fi!e='outpre.out' - echo of input,'outpre'
C— read from infile(l) by INPUTl.f
C— 22, file='outpre.err' - error messages,
C— 'outpre' read from infile(l) by INPUTl.f
C— 23, file='outpre.cnv' - convergence data when
C— ipt(28) .gt. 0,
C— 'outpre' read from infile(l) by INPUTl.f
C— 24, file='outpre.con' - plotting data
C— 'outpre' read from infile(l) by INPUTl.f
C— 25, file='outpre.mb' - mass balance data,
C— 'outpre' read from infile(l) by INPUTl.f
C— 26, file='outpre.plt' - time series plot,
C— 'outpre' read from infile(l) by INPUT1 .f
C— 27, file='outpre.rst' - restart data,
C— 'outpre' read from infile( 1) by INPUT 1 .f
C—
open(ll,file='miser.dl',status='unknown')
infile(l)='miser.dr
501 format (a)
C
C— Read the input from main input file.
C
call INPUT 1
C
C— Initialize vectors as needed.
C
Ikeep = .false.
doli=l,10*ipt(2)
1 pex(i) = zerO
do 2 i = l,(ipt(3)+ipt(4)+ipt(5)+ipt(6)-!-ipt(7)-l)*ipt(2)
cex(i) = zerO
2 rhsex(i) = zerO
do3i=l,ipt(l)*3
dent(i+3*ipt(l)) = zerO
151
-------
3 ddcn(i)
pmwt(i) = pmw{i)
4 rxn(i) = z«0
if (,not,|prni(0),and.(int(|<3yt(t2)) .gt. 0)) then
lprn = .lrue,
else
Iprn = .false,
end if
if(lprnt(6),and..not.lprnt(25).and.(im(t(3)/!(27)).gt.O))
+ llwn
Ipcbul = .true,
else
Ipcbal = .false.
end if
C
C— Finish input with INPUT2.f.
C
call INPUTS
C
C— Use ATJU.f to compute clement areas.
C
call ATRI
C
C — Initialize the simulation time, lime step, and time step number
C — if this run is not a restart.
C
if(,not,lctrl(26))thcn
1(9) s z«rO ! initialize the simulation time
l(S) = t(3) 1 initialize the time step
islart = 1
else
C — Initialize variables.
C
lsWp = . false.
iukip = 0
Iskip = zerO
do33i = ljpt(49)
33 pkccp(i)=zerO
ipt(36)=0
ipt(37)=0
ipt(38)=0
if(,noUclrltipt(6)+ipt(7))
7 xmft(i) = xmf(i)
C
C— Solve the phase mass balance equations. This is not
C— needed when a steady-state flow/saturation field has been input.
C — When the component mass balance equations are also solved,
C — update the Darcy velocities.
if(mod(itsjdp,ipt(85)tl).eq.D)then
if(ipt(85).ne,0) then
tkeep = t{8)
wl=t|;8)/!skip
do44i = l,ipt(49)
44 pex(ipt(52')ti) - vy 1 *pex(ipt(52)fi) f w2*pkeep(i)
end, It '
end if
100 t(9) = t(9J +1,(8) ! increment the cijrrent gjmulation time
if(mod(i'tskip,ipt(85)+l).eq.b) then
if(lctrl(14).and.its.eq.l) then
lctrl(14) = .false.
Ikeep = .true.
end if
if(lctrl(l))then
if (lctrl(2).and.its.gt.l) cal) MQLEWT
call FLOW (its.iter)
if(ipt(36).lt.Q.and.ipt(85).gt.Q)then,
ipt(36) = P '
46 t(S) = t(S)/2.0dO
if(t(8).l!.t(4)) then
write(ipt(28),SOO) t(4)
stop
end if
inter = 2*inter
do47i = 1, inter
if(i.gt.l) call CBAL(its,.true.
+ ,.false.,.false.,i.eq.l)
47 if(ipt(36).ge.O) call FLOW(its,iter)
if(ipt(36).lt.O) goto 46
end if
if(ipt(36).ge.O) then
callCBAL(its,.true.,.false.,.false.,inter.eq.l)
inter = 1
end if
if(lkeep) then
lctrl(14) = .true.
Ikeep = .false.
end if
if (lctrl(2).and.ipt(36).gt.O) then
call BCFLUX
call VEL
end if
end if
if(ipt(85).ne.O) t(8) = tkeep
else
write (ipt(29),*) 'Skipping Flow Computation'
tskip = tskip + 1(8)
wl = t(8)/tskip
w2 = rone-wl
do66i = l,ipt(49)
66 if(.not.lskip) pkeep(i) = wl *pex(ipt(52)+i) + w2*pkeep(i)
if(lskip) Iskip = .false.
end if
C
C — Save the values of the density vectors after pressure effects
C — have been included for calculation of the compositional density
C — derivatives. Save the phase molecular weights before compositional
C — effects are included.
C
if(mod(itskip,ipt(85)+l).eq.0)then
do!2i=l,ipt(l)
12 pmwt(i) = pmw(i)
do!3i=l,6*ipt(l)
13 dent(i) = den(i)
end if
C
C — tjse TRANS.f to solve the component mass balance equations. This
C — • is not needed when only the multiphase flow field is being
C — calculated.
C
if (lctrl(2).and.(ipt(36).ge.O))
+ call TRANS (its.ibconv)
C
152
-------
C— Check for time step reduction in solution of flow or transport
C— eqs. Adjust time step size and re-solve current time step.
C
if «ipt(36).It.O).or.(ipt(37).lt.O).or.(ipt(38).lt.O)) then
if (t(8).!e.t(4)) then ! If dt = dtmin, don't reduce dt.
write (ipt(28),500) t(4) ! Print error and terminate.
stop
endif
t(9) = t(9)-t(8) ! Return simulation time to old value.
tskip = tskip-t(S)! Reset cumulative time step
t(8) = t(8)*t(7) ! Decrease time step.
itskip = itskip -1 ! Reset flow skipping counter
Iskip = .true.
if (t(8).lt.t(4)) t(8)=t(4) ! If dt< dtmin, setdt=dtmin.
if (lctrl(J)) then ! Reset pressure and saturation values.
if(mod(itskip,ipt(85)+l).eq.0)then
do!5i = l,3*ipt(l)
15 p(i) = pt(i)
endif
do!6i = l,3*ipt(2)
16 sat(i) = satt(i)
call SATW
endif
if(Iprn) Iprn = .false. ! don't print after next iteration.
goto 100 ! Re-solve flow and transport with new time step.
endif
C
C— Reset skipping variables.
C
if(mod(itskip,ipt(85)+l).eq.0)then
tskip = zerO
do77i = l,ipt(49)
77 pkeep(i) = zerO
endif
C
C— Check for time step increase.
C
itsum = ipt(36)+ipt(37)+ipt(38)
101 if(itsum.ge.3) then
t(8) = t(8) * t(6) ! increase time step
if (t(8).gt.t(5)) t(8)=t(5) ! constrain time step to dtmax
endif
C
C— Always print at end of simulation.
C
if(t(9).ge.t(2))then
C
C— Determine execution time of simulation.
C
c call TSYSftend)
c write(*,*) tend-timeO
call prnt(its)
stop
endif
C
C— Perform mass balance calculation if desired.
C
if(lprnt(6)) then
if(lprnt(25)) then
if(mod(its,ipt(83)) .eq. 0) Ipcbal = .true.
call CBAL(its,.not.lctrl(l)
+ ,lctrl(2),lpcbal,.not.lctrl(l))
Ipcbal = .false.
else if(.not.lprnt(25)) then
call CBAL(its,.not.lctrl(l)
+ ,lctrl(2),lpcbal,.not.Ictrl(l))
if(lpcbal) then
t(8) = t(3) ! reset time step to previous value
Ipcbal = .false.
end if
if(int((t(9)+t(8))/t(27)).gt.int(t(9)/t(27))) then
Ipcbal = .true.
t(3) = t(8)
t(8) = t(8)-(t(9) + t(8)
+ - int((t(9)+t(8))/t(27))*t(27))
endif
if (t(9)+t(8) .gt. t(2)) then IDoes time exceed tmax?
t(8) = t(2) -1(9) iReduce time step so time=tmax.
Ipcbal = .true.
endif
endif
endif
C
C— Output results at intermediate times.
C ;
if (lpmt(0)) then ! output results after 'ipt(25)' time steps
if(mod(its,ipt(25)).eq. 0) then
call prnt (its)
endif
else ! output results after a time increment of 't(ll)'
if (Iprn) then
call prnt (its)
t(8) = t(3) ! reset time step to previous value
Iprn = .false.
end if ! check if print occurs at next time step
if (int((t(9)+t(8))/t(12)) .gt. int(t(9Vt(12))) then
if(lpcbal) then
if(t(9)+t(8)-int((t(9)+t(8))/t(12))*t(12).gt.zerO)
+ Ipcbal = .false.
else
t(3) = t(8)
end if
Iprn = .true.
t(8)=t(8Ht(9) +1(8) - int((t(9)+t(8))/t(12))*t(12))
endif
if (t(9)+t(8) .gt. t(2)) then ! Does time exceed tmax?
t(8) = t(2) -1(9) ! Reduce time step so time=tmax.
Iprn — .true.
endif
endif
C
C— Loop to next time step.
C
10 continue
C
C— Print the results and determine the execution time if the maximum
C— number of time steps is reached.
C
c callTSYS(tend)
c write(*,*) tend-timeO
call prnt(its)
stop
C
C— Formats:
500 format (/' Solution failed to converge'/
+ ' at the minimum time step size =',e!2.4)
502 format (/ 'Maximum iterations of ',i4,' between solution of'/
+ ' flow and transport equations was exceeded')
end
Subroutine - atri.f
153
-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c-
ATRI.f - Subroutine which computes the area of each element.
These areas arc used in the element matrices for both
the (low and transport equations. Nodes are numbered
counterclockwise in an element starting with an
arbitrary node when z is positive downwards. This
routine stops program execution if one or more of the
clement areas is less than zero. In this case, all
the element areas are printed out, as well as more
detailed information about the problem elements.
Required Control Flags:
ipl(27) - integer variable indicating type of domain
ipt(27) = 0 - xz domain
ipt(27) = 1 - rz domain
letrl(2) - logical variable controlling presence of transport
solution
Ictrl{2) s .true. - compute transport solution
lclrl(2) = .false. - skip transport solution
subroutine ATRI
include 'dimcn.inc'
C
C— Declare and define common block variables.
C
common /cbl/ matcl(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ matpt(nn6)
common Aiblc/ xnode(nnmx),znode{nnmx),rbar(nelmx),area(nelmx)
common /cblc/abyl2(nelmx),aby30(nelmx)
C
C— Loop over the elements.
C
dolOOi-l.ipt(O)
C
C— Compute areas by taking the standard area coordinate determinant,
C— but subtract row 1 from rows 2 and 3 before taking the determinant
C— (i.e. area=det[L]/2).
C
i3=i*3
n3=nodel(i3)
n2=nodel(i3-l)
nl=nodel(i3-2)
xl=xnode(nl)
x2=xnode(n2)
x3=xnpde(n3)
zl=znode(nl)
z2=zn.pde(n2)
z3=znode(n3)
area(i)=((x2-xl)*(z3-zl)-(x3-xl)*(z2-zl))/2.0dO
if (area(i).Ie.zerf» Call ErrMessage (46,0,ipt(29))
100 continue
c
c— Compute the radial centroid of each element fpr axisymetric
c— coordinates. This is set to pne if the xz coordinates are used.
C
if(ipt(27).eq.0)then
do!51i = l,ipt(0)
151 rbar(i) = rpne
else
dol52j=Upt(0)
j3 = 3*(i-l)
152 rbar(i) = pfhird * (xnode(nodel(i3fl)) +
+ xnpde(nodel(i3+2)) + xnpde(npdel(i3+3)))
endif
C
C— Compute terms needed in cpmponent balance solution.
C
if(lctrl(2)) then
do!50i = l,ipt(0)
aby!2(i) = rbar(i)*area(i)/12.0dO
150 aby30(i) = rbar(i)*area(i)/30.0dO
endif
c
return
end
Subroutine - bcflux.f
c
c
c
c
c
c
c
c
c
c
c-
BCFLUX.f - Subroutine which computes the boundary fluxes using
lite flow solution.
Required Control Flags:
ktrl(12) - logical variable denoting presence of a well
lctrl(12) - .true. - well present
ktrl{12) = .false. - well not present
subroutine BCFLUX
include 'dimcn.inc'
common/cb2/ p(nn3)
common /cbfic/ lemp(nnmx)
common /cb30/ ibc(nnmx)
common /cb31/ sourcc(nn2)
common /cb32/ bcf(nn2)
common /cb42/ amb(icnl),fmb(nsolve)
C
C— Initial variables,
C
doIOOi=l,ipt<40)
100 bcf(i) = zcrO
C
C—Compute gas phase boundary fluxes at all specified first type
C— boundary nodes.
C
if(ipt(18).gt. 0)then
do300jj = l,ip
irowd2 = ib
irow = 2 * irowd2
300 bcf(irowd2) = fmb(irow)
endif
C
C— Compute aqueous phase boundary fluxes at all specified first type
C— boundary nodes.
C
if(ipt(19).gt. 0)then
do320jj = l,ip
irowd2 = ib
irpw = 2*irowd2 -1
irpwd2 = irowd2 + ipt( 1)
320 bcf(irowd2) = fmb(irow)
endif
C
C— Cpmpute gas phase bpundary fluxes at all nodes with cpnstant flux.
C
if (ipt(22) .gt. 0) then
ii = ipt(62)
do340i = l,ipt(22)
igl =ibc(ii+i)
340 bcf(igl) = spurce(i) * patm * temp(igl)
+ /((patm + p(igl))*tstd)
endif
C
154
-------
C— Compute aqueous phase boundary fluxes at all nodes with constant
C— flux.
C
if(ipt(23).gt. 0)then
ii = ii + ipt(22)
do350i = l,ipt(23)
ial = ipt(l) + ibc(ii+i)
iii = ipt(22) + i
350 bcf(ial) = source(iii)
endif
C
C— Compute gas phase boundary fluxes at all well nodes.
C
if(lctrl(12))then
ii = ipt(64)
jstrt = ipt(22) + ipt(23)
do360i = l,ipt(24)
igl = ib
bcf(ig 1) = source(jstrt+i) * patm * temp(igl)
+ /((patm + p(igl))*tstd)
C
C— Compute aqueous phase boundary fluxes at all well nodes when
C— operating in extraction mode.
C
if (qwell.lt. zerO)then
ial = ipt(l) + ibc(ii+i)
jstrt2 = jstrt + ipt(24) + i
bcf(ial) = source(jstrt2)
endif
360 continue
endif
return
end
Subroutine - bio.f
C
C
C BlO.f - Subroutine which computes the biological reaction
C terms using Monod kinetics. Also update the biophase
C mole fractions using the finite element method by
C computing a mole balance if a biophase is considered.
C The equations are solved sequentially at each node
C until convergence. Only bioreactive components are
C included in the biophase.
C
C Arguments: iconv - integer flag for global convergence
C ibconv - integer flag for bioreaction convergence
C
C Required Control Flags:
C
C t(15)-convergence criterion for bioreactions
C ipt(39) - integer flag determining the kinetics type
C 1 - standard monod kinetics
C 2 - monod kinetics with substrate inhibition
C 3 - monod kinetics with lumped substrate
C . inhibition
C 4 - monod kinetics with saturation dependency
C 5 - monod kinetics with saturation dependency
C and substrate inhibition
C lctrl(8) - logical variable controling type of FEM
C solution for transport
C lctrl(8)= .true. - use mass lumping
C Ictrl(8) = .false. - full FEM solution
C lctrl(9) - logical variable denoting presence of nutrient
C lctrl(9) = .true. - nutrient considered
C lctrl(9) = .false. - nutrient not considered
C lctrl(l 6) - logical variable denoting method of including
C biological reaction
C lctrl(16) = .true. - include bioreaction in
C aqueous transport
C lctrl(16) = .false. - solve FEM solution for
C rate limited biophase
C lctrl(17) - logical variable indication steady state biomass
C lctrl(17) = .true. - steady state biomass
C lctrl(17) = .false. - transient biomass
C
C
subroutine BIO(iconv,ibconv)
include 'dimen.inc*
character* 10 cname(ncmp)
C
C— Declare and define common block variables.
C
common /cbl/ matel(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ marpt(nn6)
common /cble/ abyl2(nelmx),aby30(nelmx)
common/cb3/ sat(nnstkS)
common /cb6b/ por(nelmx),srw(nnstk)
common /cb6d/ dtemp(nzmax6),idepth(nnmx)
common /cb7b/ cmw(ncmp),cvp(ncmp),cden(ncmp),
+ chen(ncmp),casol(ncmp),cmdif(ncmp2)
common /cb8/ vis(nnmx),pmw(nn3)
common /cb9/ xmf(nmf)
common/cb9b/ xmft(nmf)
common /cblO/ den(nn6)
common /cbl I/ pex(nns 10),rxnp(nn2)
common 7cb40/ a(icnl),rhs(nsolve),w(icnl)
common /cb41/ irn(icnl),icn(icnl),iw(icnl,8),ikeep(icnl,5)
common /cb41b/ nbw(0:2),ia
common /cb60/ khalf(ncmp),fuse(ncmp2),umax(ncmp),xyield(ncmp),
+ kinhib(ncmp)
common IcbSlI rxn(nmf),cex(nmfs)
common /cb62b/ rhsex(nmfs)
common /cb63/ kex(ncmp5),kmax(ncmp5)
common /cb64/ bok(nbcmp),bom(nbcmp),krtd(ncmp)
common /cb91/ cname
C
C— Dimension local arrays.
C
dimension sum(3),xmonod(ncmp),xinhib(ncmp)
+ ,xtmin(ncmp)
C
C— Data the minimum detectable limit.
C
datadIimit/l.Od-9/
C
C—• Set pointers: iptbc points to the start of the biophase section
C— in icp; ib points to the start of biophase phase storage; ibs
C— points to the start of biophase stacked storage.
C
iptbc = ipt(60)
iptl=ipt(l)
ipt2 = ipt(2)
ig = ipt(3)
C
C— Set the biophase concentrations equal to the corresponding
C— aqueous phase concentrations when no mass transfer rate
C— is considered for aqueous/biophase interactions.
C
if(lctrl(16))then
isum = 0
do2ia=l,ipt(4)
if(icp(ig+ia).eq.icp(iptbc+isum+l))then
na = ipt(9) + iptl * (ia-1)
nb = ipt(12) + iptl * isum
isum = isum + 1
do 3 i = 1, iptl
3 xmf(nb+i) = xmf(na+i)
end if
155
-------
2 continue
end if
C— Iterate over the nodes to compute the reaction terms..
C
do!00i= I.iptl
C
• Calculate the lumped organic substrate concentration and lumped
• solubility for inhibition.
C-
C-
C
if(ipl(39).cq,3) then
subsum = zcrO
solsum = zcrO
do!01icb=l,ipt(17)
tc = icp(iptbc+icb)
if(ipt(39),eq.3)then
ifflclrl(lO)) then
solsum = casol(ic) + solsum
else
ilmp m (ic-l)*ipt(89)+3*ipt(88Hidepth(i)
solsum = casol(ic) -f dtemp(itmp) + solsum
end if
end if
nbc = ipt(12)-Kicb-l)*iptl + i
101 subsum - subsum -f xmf(nbc)
end if
if(ktrl(10)) then
Wl = W
else
itmp « iptC65)»ipt(89)+5*ipt(88}+idepth(i)
kd« = kd +• dtemp(itmp)
end if
rxnp(i) = zcrO
rxnp(i+iptl)szerO
C
C— Update the Monod expressions. xmonod(l) to xmonod(ipt(17)) are
C— for the substrates, xmonodCipt(17>H) is for the electron
C— - acceptor, and xmonod(ipt(17)+2) is for the nutrient when present.
C
dol05icb = l.ipt(7)-l
C
C
C
C
C
C
C
C
C
C
C
ic = icp(iptbc+icb)
xmonod(icb) = xmf(nbc) / ( xmf(nbc)
4- kh»lf
-------
ibo = ipt(7)-2
ibn = ipt(7) - 1
term = xmonod(ibo) * xmonod(ibn)
else
ibo = ipt(7) - I
term = xmonod(ibo)
end if
C
C— Update the biophase oxygen and nutrient (if present) mole
C— fractions.
C
isum = 0
do 120 icb = ipt(17)+l, ipt(7)-l
ic = icp(iptbc+icb)
isum = isum + 1
nacrx = icb*ipt( 1) + i
nac = ipt(9) + nacrx
nbc = ipt(12) + (icb-l)*iptl + i
xmfold = xmf(nbc)
dxmf = xmf(nbcx) * sum(isum) * term/cmw(ic)
C
C— Limit bioreaction during initial startup period.
C
if (t(9).It.t(ll)) dxmf = (t(9)/t(l l))*dxmf
C
C— Update the bio-reaction term.
C
if(xmf(nbc).ne.zerO) then
rxn(nac) = -dxmf/xmf(nbc)
rxn(nbc) = -dxmf/xmf(nbc)
else
rxn(nac) = zerO
rxn(nbc) = zerO
end if
rxnp(i) = rxnp(i) - dxmf
rxnp(i+iptl) = rxnp(i+iptl) - dxmf
120 continue
C
C— Update the biophase substrate mole fractions.
C
isum = 0
do!25ia = l,ipt(14)
if(icp(ig+ia).eq.icp(iptbc+isum+l))then
nac = ipt(9) + ipt(l) * (ia-1) + i
nbc = ipt(12) + ipt(l) * isum + i
isum = isum + 1
ic = icp(iptbc+isum)
if(lctrl{10)) then
umaxt = umax(ic)
else
itmp = (ic-l)*ipt(89)+4*ipt(88)+idepth(i)
umaxt = (umax(ic) + dtemp(itmp))
end if
xmfold = xmf(nbc)
dxmf=umaxt*xmf(nbcx)*xmonod(isum)*term / cmw(ic)
C
C— Limit bioreaction during initial startup period.
C
if (t(9).lt.t(l 1)) dxmf = (t(9)/t(l l))*dxmf
C
C— Update the bio-reaction term.
C
if(xmf(nbc).ne.zerO) then
rxn(nac) = -dxmf/xmf(nbc)
rxn(nbc) = -dxmf/xmf(nbc)
else
rxn(nac) = zerO
rxn(nbc) = zerO
end if
rxnp(i) = rxnp(i) - dxmf
rxnp(i-Hiptl) = rxnp(i+iptl) - dxmf
end if
125 continue
100 continue
c
c— Check the size of the bioreaction term.
c
isumg = 0
isuma = 0
isumb = 0
nbcx = ipt(12) + iptl * (ipt(7)-l)
do!50ic = l,ipt(65)
if(ic.eq.icp(isumg+I)) isumg = isumg + 1
if(ic.eq.icp(ig+isuma+l)) isuma = isuma + 1
if(ic.eq.icp(iptbc+isumb+l)) isumb = isumb + 1
if(ic.eq.icp(isumg).and.ic.eq.icp(ig+isuma)
+ .and.ic.eq.icp(iptbc+isumb)) then
ngc = ipt(8) + iptl * (isumg-1)
nac = ipt(9) + iptl * (isuma-1)
nbc = ipt(12) + iptl * (isumb-1)
do I55iel = l,ipt(0)
ieB = iel*3
iell=ie!3-2
iel2 = ie!3-l
il=nodel(iell)
i 1 s = nodept(i 1 )+ne!pt(ieI 1)
i2 = nodel(ie!2)
i2s = nodept(i2)+nelpt(iel2)
i3 = nodel(ie!3)
i3s = nodept(i3)+nelpt(ie!2)
ifGctrl(lO)) then
cvpt = cvp(ic)
casolt = casol(ic)
else
itemp = (ic-l)*ipt(89)
itemp2 = itemp + ipt(88)*2
itmpl = itemp+idepth(il)
itmp2 = itemp+idepth(i2)
itmpS = itemp+idepth(i3)
itmp21 = itemp2+idepth(il)
itmp22 = itemp2+idepth(i2)
itmp23 = itemp2+idepth(i3)
cvpt = cvp(ic) + third*(dtemp(itmpl)
+ + dtemp(itmp2) + dtemp(itmp3))
casolt = casol(ic) + third*(dtemp(itmp21)
+ + dtemp(itmp22) + dtemp(itmp23))
end if
ngcl = ngc + il
nacl = nac + il
nbcl = nbc -f il
ngc2 = ngc + i2
nac2 = nac + i2
nbc2 = nbc + i2
ngc3 = ngc + i3
nac3 = nac + i3
nbc3 = nbc + i3
denl =den(il+iptl)
den2 = den(i2+iptl)
den3 = den(i3+iptl)
keq = patm * casolt / cvpt
if(lctrl(16))then
if(ic.le.ipt(16)) then
is = (ipt(3)+ipt(4)+ipt(5)+ic-l)*iptl
ism = (matel(iel)-l)*ipt(15)+ic
if(xmf(is+il).le.zerO) then
efracl =zerO
else
efracl = ((xmf(is+il) / bok(ism)) ** bom(ism) )
+ / ( cmw(ic) * den(iptl+il) * 1.0d3 )
end if
if(xmf(is+i2).le.zerO) then
efrac2 = zerO
else
efrac2 = ((xmf(is+i2) / bok(ism)) ** bom(ism))
+ / (cmw(ic) * den(iptl+i2) * 1.0d3 )
end if
if(xmf(is+i3).le.zerO) then
efracS = zerO
else
efracS = ((xmf(is+i3) / bok(ism)) ** bom(ism))
+ / (cmwflc) * den(iptl+i3) * 1 .Od3 )
end if
extols = t(8) * por(iel) * kex(5*(ic-l)+5) *
+ (denl *(efracl-xmf(nacl)) +
+ den2 * (errac2-xmf(nac2)) +
+ den3 * (efrac3-xmf(nac3)))
157
-------
156
157
else
extols = zert)
end if
xtot = por(icl) * (
denl * sa({its+ipt2) * xmf(nacl) +
dcn2 * sa|(i2stip|2) * xmf(nac2) +
dcn3 * sal(i3s+ipt2) * xrnf(nae3) )
cxttH = 1(8) * por(iel) * kex(5*(ic-l>H) *
( den 1 * (keq*xmf(ngo 1 >xmf(nac 1 )) +
dcn2 * (keq*xmf(ngc2)-xmf(nac2)) +
dcn3 * (keq*xmf(ngc3)-xmf(nac3)) ) + exjots
rxtot = 1(8) * (rxn(nael)*xmf(nacl) +
rxn{nae2)*xmf(nac2) + rxn(nac3)*xmf(nac3))
else
sbl = xbmax /pmw(iptl-ril)
sb2 = xbmax / pmw(iptl+i2)
sb3 ~ xbmax / pmw(iptl+i3)
xtot * xbmax * (
xmf(nbcl ) / pmw(ipcl +i 1 ) +
xmf(nbc2)/pmw(iptl-fi2) +
xmf(nbc3) / pmw(ipt 1 +i3) )
cxicrt » 1(8) * por(iel) » kex(5*(ic-l)+4) *
( denl * (xmf(nacl)-xmf(nbcl)) t
den2 « (xmf(nac2)-xmf(nbc2)) +
den3 * (xmf(nac3)-xmf(nbc3)) )
rxtol s t(8) * (rxn(nbcl)*xmf(nbcl) +
rxn(nbe2)*xmf(nbc2) + ntn(nbc3)*xmf(nbc3))
end if
if(-rxtot,gt.xtot+extot) then
rxnp(il) = rxnp(il)-rxn(nacl)*xmf(nbcl)
rxnp(i2) = rxnp(i2) - rxn(nac2) * xmf(nbo2)
rxnp(i3) = rxnp(i3) - rxn(nac3) * xmf(nbc3)
ntnp(il+ipH) = txnp(il+iptl)
- rxn(nbel) * xmf(nbcl)
rxnp(i2+iptl) * rxnp(i2+iptl)
- rxn(nbc2) * xntf(nbc2)
rxnp(i3+iptl) ~ rxnp(i3+iptl)
- rxn(nbc3) * xmf(nbc3)
rxn(nacl) = zciO
rxn(nac2) = zcrt)
txn(nac3) = zciO
ifl(isumb.gt,ipt(17))then
rxn(nica+il) = zetO
rxn(nica+i2) = zeiO
rxn(nica+i3) = zeiO
continue
dol57il = 1,ipl(7)
nlcb = (ii-l)*iptl
rxn(nicb+il) = zerO
rxn{nicb+i2) = zetO
rxn(nicb+i3) = zerO
continue
end if
end if
continue
155
end if
ISO continue
C
C — Return when no mass transfer rate limitation is considered for
C— aqucous/biophase interactions.
C
if(letrl{16)) then
RETURN
end if
C
C— Now sequentially solve for the biophase mole fractions.
C
do200kbio=I,ipt(7)-l
iptc = iplbc + icbio
icpt = (iptc-I)*iptl
iepts = (ip|c-l)*ipt2
ic = icp(iptc)
C
O — Zero tire finite clemem matrices.
C
do210i = l,iptl
rhs(i) = zerO
nrqw = (i-l)*
21 Q
C
a(rirg\v+j) = zerO
— Cprnpiite the local flnjte element matrices.
C-^ Set the pointers tp the local nod.es 1J, 12, an.d. !3. The
C^ postscript s is for stacked local node?, p is for phase, and
C^— p is for component. Compute cpnstants.
C
ie!3 = i*3
iell = ie!3-2
ieI2 = ie!3-l
il=nodel(iell)
ils = nodept(il)+nelpt(iell)
ilc = icpt + il
ilps = icpts+ ils
i2 = nodel(iel2)
i2s = nodppt(i2)+nelpt(ie!2)
i2c = iept +- i2
j2cs = icpts + i2?
i3 = nodel(iel3)
i3s = nodept(i3)+nelpt(iel3)
i3s = 13
i3c = icpt +• i3
i3cs = icpts + i3s
C
C— Compute the biomass "saturation". This is based on the
C— maximum allowable biomass and uses water properties.
C
sb = xbmax / por(i)
sbl = sb/den(ipt(41)+il)
sb2 = sb / den(ipt(41)+i2)
sb3 = sb / den(ipt(41)+i3)
term = aby30(i)/t(8)
C
C— Compute the mass matrix in lumped form.
C
aU = term*(sbl*3.0dOi + sb2 +sb3 )
al2 = term*( sbl + sb2 •)• sb3/2.0dO )
a!3 = term*( sbl + sb2/2.0dO + sb3 )
a21 = a!2
a22 = term*(sbl + sb2*3.0dO + sb3 )
a23 = term*( sbl/2.0dO + sb2 + sb3 )
a31 = a!3
a33 = term*( sbl +sb2 -hsb3*3.0dO)
if(lctrl(8)) then
all =all+al2 + al3
a!2 = zerO
a!3 = zerO
a22 = a21 + a22 + a23
a21 = zerO
a23 = zerO
a31 =zerO
a32 = zerO
end if
C
C— Now compute the exchange matrix. First consider the terms
C— multiplied by the biophase mole fraction. These terms are the
C— phase mole exchange and the phase mole reaction.
C
pexl =-rxn(ilc)
pex2 = -rxn(i2c)
pex3 = -rxn(i3c)
bl 1 = aby30(i) * (pexl*3.0dO + pex2 + pex3 )
b!2 = aby30(i) * (pexl + pex2 + pex3/2.0dO)
b 13 = aby30(i) * (pex 1 + pex2/2.0dO + pex3 )
b21=b!2
b22 = aby30(i) * (pexl + pex2*3.0dO + pex3 )
b23 = aby30(i)*(pexl/2.0dO-l-pex2 +pex3 )
b31=b!3
158
-------
b32 = b23
b33 = aby30(i) * (pexl
pex2 + pex3*3.0dO)
C— Now compute the right hand side terms. These terms are the
C— component mole exchange and the component mole reaction.
C
rhsl =por(i)*rhsex(ilcs)
rhs2 = por(i)*rhsex(i2cs)
rhs3 = por(i)*rhsex(i3cs)
fl=aby!2(i)*(2.0dO*rhsl+ rhs2+ rhs3)
f2 = aby!2(i)*( rhsl+2.0dO*rhs2+ rhs3)
f3 = aby!2(i) * ( rhsl + rhs2 + 2.0dO*rhs3)
C
C— Assemble global matrix and right hand side vector in banded form
C
irowl =(il-l)*nbw(l)
irow2 = (i2-l)*nbw(l)
irow3 = (i3-l)*nbw(l)
icolll = 1 + nbw(0)
icol!2 = icoll 1 + (i2 - il)
icol!3 = ic
ico!22 = ic
ico!21 = ico!22 + (il - i2)
ico!23 = ico!22 + (i3 - i2)
ico!33 = icolll
icol31=ico!33 + (il-i3)
abll=alH-t(10)*bll
abl2 = al2 + t(10)*bl2
abl3=a!3 + t(10)*bl3
ab21 = a21 + t(10)*b21
ab22 = a22 + t(10)*b22
ab23 = a23 + t(10)*b23
ab31 =a31+t(10)*b31
ab32 = a32 + t(10)*b32
ab33 = a33 + t(10)*b33
a(irowl + icolll) = a(irowl + icoll 1) + abl 1
a(irowl 4- icol!2) = a(irowl + icol!2) + ab!2
a(irowl + icollS) = a(irowl + icol!3) + ab!3
a(irow2 + ico!21) = a(irow2 + ico!21) + ab21
a(irow2 + ico!22) = a(irow2 + ico!22) + ab22
a(irow2 + ico!23) = a(irow2 + ico!23) + ab23
a(irow3 + ico!31) = a(irow3 + ico!31) + ab31
a(irow3 + ico!32) = a(irow3 + ico!32) + ab32
a(irow3 + ico!33) = a(irow3 + ico!33) + ab33
rhs(il) = rhs(il) + fl - bll * xmft(ilc)
- b!2 * xmft(12c) - b!3 * xmft(i3c)
rhs(12) = rhs(i2) + f2 - b21 * xmft(ilc)
- b22 * xmft(i2c) - b23 * xmft(i3c)
rhs(i3) = rhs(i3) + i3 - b31 * xmft(ilc)
+ - b32 * xmft(i2c) - b33 * xmft(i3c)
220 continue
C
C— Collapse full matrix into sparse form used by Harwell. Also
C— scale array by dividing rows through by the diagonal value
C
ia = 0
do230irow= l,ipt(l)
nrow.= (irow-l)*nbw(l)
aii = rone / a(nrow+l+nbw(0))
rhs(irow) = rhs(irow) * aii
do230icol = l,nbw(l)
if (a(nrow+ico!) .ne. zerO) then
ia = ia + 1
a(ia) = a(nrow+icol) * aii
irn(ia) = irow
icn(ia) = icol+irow-nbw(0)-l
endif
230 continue
C
C— Solve the linear system using Harwell routines.
C
callma28ad(ipt(l),ia,a,icnl,irn,irnl,icn,u,ikeep,iw,w,iflag)
if (iflag.lt. 0)then
write (ipt(28),*) Mflag return from harwell is '.iflag
write (ipt(28),*) 'bio component is: ', cname(ic)
endif
call ma28cd (ipt(l),a,icnl,icn,ikeep,rhs,w,mtype)
C
C— Update the solution and determine the max norm of the updated
C— solution.
C
dxmf =zerO
xmfrnax = xround
do 240 i = l+iptc,iptl+iptc
xmfold=xmf(i)
xmf(i) = xmft(i) + rhs(i-iptc)
xmfmax = dmax 1 (xmfmax,dabs(xmf(i)))
240 dxmf = dmaxl(dxmf,dabs(xmf(i)-xmfold))
if(dxmf/xmfmax.gt.t(15)) ibconv = ibconv + 1
200 continue
C
C— Biological equation set is converged if each component equation
C— has converged (i.e. ibconv = 0).
if(ibconv.gt.O) iconv = iconv + 1
return
end
Subroutine - cbal.f
C-
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
CBAL.f - Subroutine which computes the mole balance check for the
aqueous and gas phase components and phases.
Arguments: its - integer time step
Ibalp - compute the phase mass balance when true
Ibalc - compute the component mass balance when true
Ipcbal - print the mass balance information when true
Ifirst - indicates the first call during a time step
Required Control Flags:
lctrl(l) - logical variable controlling presence of flow
solution
lctrl(l) = .true. - compute flow solution
lctrl(l) = .false. - skip flow solution
Ictrl(2) - logical variable controlling presence of transport
solution
lctrl(2) = .true. - compute transport solution
lctrl(2) = .false. - skip transport solution
lctrl(12) - logical variable denoting presence of a well
lctrl(12) = .true. - well present
lctrl(12) = .false. - well not present
lctrl( 16) - logical variable denoting method of including
biological reaction
lctrl(16) = .true. - include bioreaction in
aqueous transport
lctrl(16) = .false. - solve FEM solution for
rate limited biophase
C
C
C
C
C
C
C
C
C
c
c
c
C WARNING: THIS ROUTINE IS DIMENSIONED FOR 9 COMPO-
NENTS WHEN USING
C REPORT STYLE OUTPUT
C
subroutine CBAL (its,lbalp,lbalc,lpcbal,lfirst)
include 'dimen.inc'
character*10 cname(ncmp)
159
-------
common /cbt/ matel{nelmx),nodcl(nel3),nodept(nnmx),nelpt(neI3)>
+ nu!pl(nn6)
common kbld xnode(nnmx)^node(nnmx),rbar(nelmx),area(nelmx)
common /cb2/ p(nn3)
common /cb3/ sat{nnstk3)
common /eb6b/ por(nelmx),srw(nnstk)
common /cb6c/ lcmp(nnmx)
common /cb7b/ cmw(ncmp),cvp(ncmp),cden(ncmp),
+> ehcn(ncmp)p«ol(ncnip),cmdif(ncmp2)
common /cb8/ vis(nnmx),pmw(nn3)
common /cb9/ xmf(nmf)
common /cbl(V dcn(nn6)
common /cbl l/pex(nnslO),rxnp(nn2)
common /cb30/ ibe(nnmx)
common /cb32/ bef(mi2)
common /cb31/ sourcc(nn2)
common /cb42/ amb{ienl),fmb(nsolve}
common /cb62/ rxn{nmf),ccx(nmfs)
common /cbfrV bok(nbcmp),bom(nbcmp),lcrtd{ncmp)
common /cbfrlb/ bsdcn(nmblk)
common /cb84/ ibcxmf(nmbe),bcxmf(nmbc),dfxmf(nmbc)
common /cb85/ flux(ncmpp5),sflux(ncmpp5),first(ncmp)
common /cbS67 Strl(ncmpp5),str0(ncmpp5),cmf(ncmpp5),csink(ncmpp5)
+ ,cwsink(ncmpp5),csflux(ncmpp5),cmassl(ncmp5),cmassO(ncmp5)
+ ,cphex(ncmpp5),crsink(ncmpp5),tmassl .ImassO
common /cb9 1 / cname
dimension 5tr(nempp5)jesid(ncmppS),sink(ncmpp5),wsink(ncmpp5)
+ ,cmass(ncmp5),phex(ncmpp5),perrl(ncmppS),perr2(ncmpp5)
+ ,rsir.k(ncmpp5)
C
C— Describe variables: strl(l-S) arc the total mass storage of each
C — phase al H-l , strl (6..) are the total mass storage of each
C — component at H-l; str(...) are the total mass storages at t;
C — strO(,..) are the initial mass storages; residual(...) are the
C— changes in phase and component mass not accounted for by sinks,
C — sources, phase exchange, etc.; cmf(...) are the cumulative total
C — mass fluxes for the phases and components; sink(...) are the
C — tout mass sinks for the phases and components; csink(...) are
C — llie cumulative total mass sinks for the the phases and components;
C — wslnk(,,,) are the total mass sinks at the well for the phases
C— and components; cwsink(...) are the cumulative total mass sinks
C— at the well for the phases and components; sflux(...) are the
C— total mass fluxes at the surface for the phases and components;
C— ciflux(.,,) are the cumulative total mass fluxes at the surface
C — fot lire phases and components; cmass !(...) are the mass storages
C— of each component in each phase at H-l ; cmass(...) are the mass
C — storages of each component in each phase at t; cmassO(...) are
C — the initial mass storages of each component in each phase;
C — rsink(.,.) arc the total mass reation sinks for the phases
C— and components; crsinkf....) are the cumulative total mass reaction
C — sinks for the phases and components
C
istop = ipt(65)
ipUx3sip((41)
C— Initialize mass storage vectors.
C
if(llinl) then
ifuis nc.O) muss = imassl
tnussl sa zcrO
lphcx=zcrO
bmnss = zerO
C
C — Save previous mass storage.
C
doIOi=l,istop+5
if(ktrl(l)) then
flux(i) = zerO
sflux(i) = zcrO
end if
sink(i) m zcrO
rsink(i) = zcrO
wsink(i) = zcrO
resid(i) * zerO
phcx(i) = zerO
if(its.nc.O) str(i) = strl(i)
10 strl(i) = zerO
.do 11 i= l,istop*5
if(its.ne,0) cmass(i) = cmassl(i)
11 cmass l(i) = zerO
end if
Z — First compute the mass storage of the phases.
do 100 jel = l,ipt(0)
n3 = Gel-J)*3
il = nodel(n3+l) ! element node numbers
i2 = node1(n3+2)
i3 = nodel(n3+3)
igl = il ! nodel gas phase storage locations
ig2 = i2
ig3 = i3
ial = ipt(l)+igl ! nodel aqueous phase storage locations
ia2 = ipt(l)+ig2
ia3 = ipt(l)+ig3
inl = ipt(l)tial ! nodel napl phase storage locations
in2 = ipt(l)+ia2
in3 = ipt(l)+ia3
ndstkl = nodept(il) + nelpt(n3+l) ! node position in stack
ndstk2 = npdept(i2) + nelpt(n3+2)
ndstkS = nodept(i3) + nelpt(n3+3)
igls = ndstkl ! gas phase stacked node numbers
ig2s = ndstk2
ig3s = ndstkS
ials = ipt(2)+igls ! aqueous phase stacked node numbers
ia2s = ipt(2)+ig2s
ia3s = ipt(2)+ig3s
inls = ipt(2)+ials ! napl phase stacked node numbers
in2s = ipt(2)+ia2s
in3s = ipt(2)+ia3s
isls = ipt(2)+inls ! solid phase stacked node numbers
is2s = ipt(2)+in2s
is3s = ipt(2)+in3s
ibis = ipt(2)+isls ! bio phase stacked node numbers
ib2s = ipt(2)+is2s
ib3s = ipt(2)+is3s
xbio = rbar(jel) * area(jel) * third
x = xbio * por(jel)
C
C — First the gas phase mass storage and exchange terms.
C
if(lbalp) then
strl(l) = strl(l) + x * (
+ den(iptlx3+igl) * sat(igls) +
+ den(iptlx3+ig2) * sat(ig2s) +
+ den(iptlx3+ig3) * sat(ig3s) )
phex(l) = phex(l) + x * t(8) * ( pex(ipt2x5+igls)
+ + pex(ipt2x5+ig2s) + pex(ipt2x5+ig3s) )
C
C — Now the aqueous phase mass storage and exchange terms.
C
strl(2) = strl(2) + x*(
+ den(iptlx3+ial) * sat(ials) +
+ den(iptlx3+ia2) * sat(ia2s) +
+ den(iptlx3+ia3)*sat(ia3s))
phex(2) = phex(2) + x * t(8) * ( pex(ipt2x5+ials)
+ + pex(ipt2x5+ia2s) + pex(ipt2x5+ia3s) )
Now the gas phase component mass storages.
end if
if(lbalc) then
do 15 i = l,ipt(3)
ic = icp(i)
igasc = (i-l)*ipt(l)
eel = x * cmw(ic) * (
den(igl) * sat(igls) * xmf(igasc+il) +
den(ig2) * sat(ig2s) * xmf(igasc+i2) +
den(ig3) * sat(ig3s) * xmf(igasc+i3) )
cmass l(ic) = cmass l(ic) + eel
str 1 (5+ic) = strl (5+ic) + eel
continue
Now the aqueous phase component mass storages.
160
-------
20
C
c—
C
c—
c
25
C
c—
c
c
c-
c
30
C
C—
do20i = l,ipt(4)
ipiptS = i + ipt(3)
ic = icp(ipipt3)
iaqc = (ipipt3-l)*ipt(l)
eel = krtd(ic) * x * cmw(ic) * (
den(ial) * sat(ials) * xmf(iaqc+il) +
den(ia2) * sat(ia2s) * xmf(iaqc+i2) +
den(ia3) * sat(iaSs) * xmf(iaqc+i3))
cmass 1 (istop+ic) = cmass 1 (istop+ic) + eel
strl(5-t-ic) = strl(5+ic) + eel
continue
Now the napl phase mass storage and exchange terms.
if(ipt(5).gt.O) then
srrl(3) = strl(3) + x*(
den(iptlx3+inl) * sat(inls) +
den(iptlx3+in2) * sat(in2s) +
den(iptlx3+in3) * sat(in3s))
phex(3) = phex(3) + x * t(8) * (pex(ipt2x5+inls)
+ pex(ipt2x5+in2s) + pex(ipt2x5+in3s))
Now the napl phase component mass storages. This form assumes
that all the organic components are present in the napl phase.
do25i = l,ipt(5)
ipiptS = i + ipt(58)
ic = icp(ipiptS)
inc = (ipipt5-l)*ipt(l)
eel = x * cmw(ic) * (
den(inl) * sat(inls) * xmf(inc+il) -1-
den(in2) * sat(in2s) * xmf(inc+i2) +
den(in3) * sat(in3s) * xmf(inc+i3))
cmass l(2*istop+ic) = cmass l(2*istop+ic) + eel
strl(5+ic) = strl(5+ic) + eel
continue
end if
Now the solid phase mass balance and exchange terms.
if(ipt(6).gt.O) then
phex(4) = phex(4) + xbio * t(8) * ( pex(ipt2x5+isls)
•J- pex(ipt2x5+is2s) + pex(ipt2x5+is3s))
Now the solid phase component mass balances.
do30i = l,ipt(6)
ipiptS = i + ipt(59)
ic = icp(ipiptS)
isc = (ipipt5-l)*ipt(l)
if(xbok.gt.zerO) then
if(i.eq.l)then
solden = (rone-xden)*bsden(matel(i))
else if(i.eq.2) then
isum = ipt(3)+ipt(4)+ipt(5)
ic = icp(isum+i-l)
solden = xden*bsden(matel(i))
end if
eel = solden *
( xmf(isc+i 1) + xmf(isc+i2) + xmf(isc+i3))
* xbio
else
eel = bsden(matel(jel)) *
(xmf(isc+il) + xmf(ise+i2) + xmf(isc+i3))
* xbio
end if
cmassl(3*istop+ic) = cmassl(3*istop+ic) + eel
strl(5+ic) = strl(5+ic) + eel
strl(4) = strl(4) + cel
continue
end if
Now the biophase mass balance and reaction terms.
This assumes a constant biophase volume.
if(ipt(7).gt.O) then
do35i = l,ipt(7)-l
ipipt6 = i + ipt(60)
ic = icp(ipipt6)
ibioc = (ipipt6-l)*ipt(l)
C
C— First consider a separate biophase.
C
if(.not.lctrl(16))then
strl(5) =strl(5) + xbio * xbmax * 3.0dO
phex(5) = phex(5) + xbio * t(8) * (pex(ipt2x5+ibls)
+ + pex(ipt2x5+ib2s) + pex(ipt2x5+ib3s))
eel = xbio * cmw(ic) * (
+ xbmax/pmw(ial)*xmf(ibioc+il) +
+ xbmax/pmw(ia2) * xmf(ibioc+i2) +
+ xbmax/pmw(ia3) * xmf(ibioc+i3))
C
C— Now the bio reaction mass sinks.
C
sel = xbio * cmw(ic) * (rxn(ibioc+il)
+ * xmf(ibioc+i 1) + rxn(ibioc+i2)
+ * xmf(ibioc+i2) + rxn(ibioc+i3)
+ * xmf(ibioc+i3)) * t(8)
C
C
C— Now sum the bio reaction mass sinks into the mass balance.
C
cmass l(4*istop+ic) = cmass l(4*istop+ic) + eel
rsink(5) = rsink(5) + sel
rsink(5+ic) = rsink(5-i-ic) + sel
strl(5) = strl(5) + cel
strl(5+ic) = strl(5+ic) + eel
C
C— Otherwise sum the bioreaction sinks when a separate biophase
C— is not considered. Use biophase reaction terms since they are
C— the same as the aqueous phase reaction terms.
C
elseif(lctrl(16))then
sel = xbio * cmw(ic) * (rxn(ibioc+il)
+ * xmf(ibioc+i 1) + rxn(ibioc+i2)
+ * xmf(ibioc+i2) + rxn(ibioc+i3)
+ * xmf(ibioc+i3)) * t(8)
C
C—• Now sum the bio reaction mass sinks into the mass balance. When
C— a separate biophase is not considered the reaction terms are
C— used for the aqueous phase mass balance.
C
rsink(2) = rsink(2) + sel
rsink(5+ic) = rsink(5+ic) + sel
end if
35 continue
C
C— Now sum the biomass. Do not include the biomass in the phase mass.
C
ibioc = ipt(12) + (ipt(7)-l) * ipt(l)
eel = xbio * ( xmf(ibioc+i 1) + xmf(ibioc-t-i2) +
+ xmf(ibioc+i3))
bmass = bmass -t- eel
end if
end if
100 continue
C
C— Now initialize variables and return if this is the first call.
C
if(its.eq. 0)then
do200i = l,5+istop
cphex(i) = zerO
csink(i) = zerO
cwsink(i) = zerO
crsink(i) = zerO
csflux(i) = zerO
cmf(i) = zerO
200 strO(i)=strl(i)
do210i = l,5*istop
210 cmassO(i) = cmassl(i)
tmassO = zerO
tcsink = zerO
tcwsink = zerO
tcrsink = zerO
tcflux = zerO
tcphex = zerO
161
-------
220
do220isl,5
liiussl =tmassO
if(lprnt{27))thcn
write (25,501) ils,((9)
wrilc{25,502) 'Phase mass (kg)
,(sttO(i),!=l,S),lmiissO
do230ii = l,istop
230
240
•f
write<25,503) cname{ii)
,(ctnassO(!ii*istop+ii),m=0,4),strO(i)
if(tctrl(3)) write(25,S03) cname(ii)
1zctO,zcrO,zetO,zcrO,bmass,zerO
else
wriic(25,504)
wriIc(25,500)zetO,(sli
-------
c-
c-
c
+
355
Compute aqueous phase component boundary flux at constant flux
nodes. Note: the surface flux is included in the boundary flux.
if(lbalc) then
do355i = I,ipt(4)
ipipt3 = i + ipt(3)
ic = icp(ipipt3)
icxmf = ipt(9) -f (i-l)*ipt(l) + ibc(jj+ii)
if(ibcxmf(nbc).eq.3) then
fkeep = den(nbc) * bcf(nbc) * bcxmf(icxmf)
* cmw(ic) * t(8)
flux(ic+5) = flux(ic+5) + fkeep
else if(ibcxmf(nbc).eq.2) then
fkeep = den(nbc) * bcf(nbc) * xmf(icxmf)
* cmw(ic) * t(8)
flux(ic+5) = flux(ic+5) + fkeep
else if(ibcxmf(nbc).eq.l) then
fkeep = flrst(icxmf)
if(lbalc) flux(ic+5) = flux(ic+5) + fkeep
end if
if(znode(nbc-ipt(l)).eq.zerO)
sflux(ic+-5) = sflux(ic+5) + fkeep
continue
endif
if(lbalp) then
nbcd = ipt(41)+nbc
ipt22 = ipt(22)
sink(2) = sink(2) + den(nbcd)
* source(ipt22+jj) * t(8)
end if
continue
endif
Now compute the gas phase flux at the well.
if(lctrl(12))then
ii = ipt(64)
jstrt=ipt(22) + ipt(23)
do360jj = l,ipt(24)
nbc = ibc(ii+jj)
nbcd = ipt(41) + nbc
deng = den(nbcd)
C
C— Now compute the gas phase component flux at the well.
C
pmwbc = zerO
do365i = l,ipt(3)
ic = icp(i)
icxmf = (i-l)*ipt(l)+ibc(ii+jj)
if(ibcxmf(nbc).eq.3) then
xmfbc = bcxmf(icxmf)
pmwbc = pmwbc + bcxmf(icxmf) * cmw(ic)
fkeep = den(nbc) * bcf(nbc) * xmfbc
+ * cmw(ic) * t(8)
else if(ibcxmf(nbc).eq,2) then
fkeep = den(nbc) * bcf(nbc) * xmf(icxmf)
+ * cmw(ic) * t(8)
flux(ic+5) = flux(ic+5) + fkeep
else if(ibcxmf(nbc).eq.l) then
fkeep = first(icxmf)
if(lbalc) flux(ic+5) = flux(ic+5) + fkeep
else
xmfbc = xmf(icxmf)
end if
if(lbalc) wsink(5+ic) = wsink(5+ic) + fkeep
continue
if(ibcxmf(nbc).eq.3) deng = den(nbc) * pmwbc
if(lbalp) wsink(l) = wsink(l) + deng * t(8) *
source(jstrt+jj) * patm * temp(nbc)
/ ({patm + p(nbc)) * tstd)
350
C
C—
C
365
Now compute the aqueous phase flux at the well when extracting.
if (qwell.lt. zerO)then
nbcw = ip
C
C—
C
Now compute the aqueous phase component flux at the well.
ifflbalc) then
do370i = l,ipt(4)
ipipt3 = i + ipt(3)
ic = icp(ipipt3)
icxmf = ipt(9) + (i-1 )*ipt( 1) + nbc
fkeep = den(nbcw) * bcf
-------
400
•105
wile (25,502) 'Sources (kg)',
(sink(i),i=l,5),tsink
write (25,502) 'Well sources (kg)',
(Wink(i),i=l,5),lvvsink
write (25,502) 'Reactions (kg)',
(«ink(i),i=l,5),lrslnH
write (25,502) 'Phase transfer (kg)*,
(pbex(i),i=l,5),tpoex
do 400 1=1,5
resid(i) = strl(i) - str(i) - flux(i)
-\vsinfc(i)-ph«(i)
write (25,502) 'Residual (kg)'
,(resid(i),i=l,S),tmassl T tmass
- tflux - twsink - tphex
do 405 1=1,5
iftstrO(i),gt,zerO) then
pcrrl(i) » 1.0d2*dabs(resid(i))/strO(i)
else
•106
407
end if
continue
if(tm.issO gt.zerfl) then
write (25,502) 'Time step errorl(%)',
(pcrrl(i),i=;l,5), 1.0d2*dabs(tmassl - trnass
- tflux - twsink - tphex)/tmassQ
else
write (25,502) 'Time step errorl(%)',
(pcrrl(i),i=l,5), zerO
end if
do 406 i- 1,5
term = dmaxl(dabs(wsink(i))+dabs(flux(i))+dabs(phex(i)),
dabs(strl(i)-slr(i)))
if(tcrm.ne,zerO) then
perrl(i) « 1.0d2*dabs(resid(i))/term
else
perrl(i) = zcrO
end if
continue
lcrm=!dmaxl(dabs(twsink)+dabs(tflux>Hlabs(tphex),
dabs(tmassl-tmass))
if(tcrm.ne,zcrO) then
tpcrrl = 1.0d2*dabs(lmassl - tmass - tflux - twsink
- tphcxyierm
cite
tpcrrl = zerO
end if
write (25302) 'Time step error2(%)',
do 407 i- 14
if(slrl(i)-slr(i),ne.zeK)) then
pcrrl(i) = 1.0d2*(rone-(dabs(wsink(i)+flux(i)
+phex(i» / (dabs(strl (i)-str(i)))))
else
pcrrl(i) = zerO
end if
continue
iftlnussl-lmass.ne.zcrO) then
tpcrrl = 1.0d2*(rone-(dabs(twsink+tfiux+tphex)
/ (dabs(tmassl -tmass))))
else
Ipctrl =zerO
end if
write (25,502) 'Time step cnor3(%)',
(pcrrl(i),i=l, 5), tpcrrl
write (25,509)
write (25,502) 'Delta storage (kg)',
(strl(i)-strO(i),i=l,5),tmassl-tmassO
write (25,502) 'Boundary flux (kg)',
(cmf(i),i=l,5),tcflux
write (25^02) 'Sources (kg)',
(csink(i),i=l,5),tcsink
write (25,502) 'Well sources (kg)',
(cwsink(i),i=lj),tcwsink
write (25,502) 'Reactions (kg)',
(crsink(i),i=l,5),tcrsink
write (25,502) 'Phase transfer (kg)',
(cphcx(i),i=l,5),tcphex
do410i=l,5
410 resid(i) = strl(i).- strO(i) - cmf(i)
+ - cwsink(i)- crsink(i) - cphex(i)
write (25,502), 'Residual (kg)'
+ ,(resid(ij,i=rl,5),tmassl - tmassO.
+ - tcwsink - (cflux
4o 425 ( = 1,5.
if(strO(i).gt.zerO) then
perr2(i) = 1.0.d2*dab5(resid(i))/strp(i)
else
perr2(i) - zerO
end if
425 continue
if(tmass0.ne.zerO) then
write (25,502) 'Cumulative errl (%)',
+ (perr2(i),i=l,5),dabs(tmassl -tmassO
+ - tcwsink - tcflux - tcphex)* 1 .Od2/tmassO
else
write (25,502) 'Cumulative errl (%)',
+ (perr2(i),i=l,5),zerO
end if
do 426 i = 1,5
term = dnjaxKdabs(pwsink(i)),H-daibs(cnu:(i))
+ +dabs.(cphLex(i)))d8bs(s.tcl(i)-SjrO,(i»)
if(term.ne1.zetO)i
+ then
perr2(i) = 1.0d2*dabs(resid(i))/term
else
perr2(i) = zerO
end if
426 continue
term = dmaxl(dabs(tcwsink)+dabs(tcflux)+dabs(tcphex),
+ dabs(tmassl - tmassO))
if(term.ne.zerO) then
tperrZ = 1.0d2*dabs(tmassl - tmassO - tcwsink - tcflux
+ - tcphex)/term
else
tperr2 = zerO
end if
write (25,502) 'Cumulative err2 (%)',
+ (perr2(i),i=l,5), tperr2
do 427 i = 1,5
if(strl(i)-strO(i).ne.zerO) then
perr2(i) = 1.0d2*(rone-(dabs(cwsink(i)+cmf(i)
+ +cphex(i)) / (dabs(strl (i)-strO(i)))))
else
perr2(i) =zerO
end if
427 continue
if(tmassl - tmassO.ne.zerO) then
tperr2 = 1.0d2*(rone-(dabs(tcwsink+tcflux+tcphex)
+ / (dabs(tmassl - tmassO))))
else
tperr2 = zerO
end if
write (25,502) 'Cumulative err3 (%)',
+ (perr2(i),i=l,5), tperr2
if(Ictrl(3)) write(25,502) 'Biomass (kg)',
+ zerO,zerO,zerO,zerO,bmass,zerO
— Write the component material balance report.
if(lctrl(2)) then
write (25,506) its,t(9),(cname(i),i=l,istop)
write (25,502) 'Gas Phase (kg)',
+ (cmassl(i),l=l,istop)
write (25,502) 'Aqueous Phase (kg)',
+ (cmassl(istop+i),i=l,istop)
write (25,502) ' NAPL (kg)' ,
+ (cmass 1 (2*istop+i),i= 1 ,istop)
write (25,502) 'Solid Phase (kg)',
+ (cmass l(3*istop+i),i=l,istop)
write (25,502) 'Biophase (kg)',
+ (cmassl(4*istop+i),i=l,istop)
write (25,502) 'Total (kg)',
+ (strl(5+i),i=l,istop)
write (25,508)
write (25,502) 'Delta storage (kg)',
+ (strl(i+5)-str(i+5),i=l,istop)
164
-------
write (25,502) 'Boundary flux (kg)',
+ (flux(i+5),i=l,istop)
write (25,502) 'Surface flux (kg)',
+ (sfiux(i+5),i=l,istop)
write (25,502) 'Sources (kg)',
+ (sink(i+5),i=l,istop)
write (25,502) 'Well sources (kg)',
+ (wsink(i+5),i=l,istop)
write (25,502) 'Reactions (kg)',
+ (rsink(i+5),i=l,istop)
do 430 i = 6,istop+5
430 resid(i) = strl (i) - str(i)
+• - wsink(i) - rsink(i) - fiuxffl
write (25,502) 'Residual (kg)'
+ ,(resid(i+5),i=l,istop)
do 435 i = 6,istop+5
if(strO(i).gt.zerO) then
perrl© = 1.0d2*dabs(resid(i))/strO(i)
else
perrl(i) = zerO
end if
435 continue
write (25,502) 'Time step errorl(%)',
+ (perrl(i+5),i=l,istop)
do 436 i = 6,istop+5
term = dmaxl(dabs(rsink(i))+dabs(wsink(i))
+ +dabs(flux(i)),dabs(strl(i)-str(i)))
if(term.ne.zerO) then
perrl(i) = 1.0d2*dabs(resid(i))/term
else
perrlffi = zerO
end if
436 continue
write (25,502) 'Time step error2(%)',
+ (perrl(i+5),i=l,istop)
do 437 i = 6,istop+5
if(strl(i)-str(i).ne.zerO) then
perrl(i) = 1.0d2*(rone-(dabs(rsink(i)+wsink(i)
+ +flux(i)) / (dabs(strl(i)-str(i)))))
else
perrl(i) = zerO
end if
437 continue
write (25,502) 'Time step error3(%)',
+ (perrl(i+5),i=l,istop)
write (25,509)
write (25,502)'Delta storage (kg)',
+ (strl(i-t-5)-strO(i+5),i=l,istop)
write (25,502) 'Boundary flux (kg)',
+ (cmf(i+5),i=l,istop)
write (25,502) 'Surface flux (kg)',
+ (csflux(i+5),i=l,istop)
write (25,502) 'Sources (kg)',
+ (csink(i+5),i=l,istop)
write (25,502) 'Well sources (kg)',
+ (cwsink(i+5),i=l,istop)
write (25,502) 'Reactions (kg)',
+ (crsink(i+5),i=l,istop)
do 440 i = 6,istop+5
440 resid(i) = strl(i) - strO(i) -
+ cwsink(i) - crsink(i) - cmf(i)
write (25,502) 'Residual (kg)'
+ ,(resid(H-5),i=l,istop)
do 445 i = 6,istop+5
if(strO(i).gt.zerO) then
perr2(i) = 1.0d2*dabs(resid(i))/strO(i)
else
perr2(i) = zerO
end if
445 continue
write (25,502) 'Cumulative errl (%)',
-I- (perr2(i+5),i=l,istop)
do 446 i = 6,istop+5
term = dmaxl(dabs(crsink(i))-Hlabs(cwsink(i))
+ +dabs(cmf(i)),dabs(strl(i)-strO(i)))
if(term.ne.zerO) then
perr2(i)= 1.0d2*dabs(resid(i))
+ /term
else
perr2(i) = zerO
end if
446 continue
write (25,502) 'Cumulative err2 (%)',
+ (perr2(i-t-5),i=l,istop)
do 447 i = 6|istop+5
if(crsink(i)+cwsink(i)+cmf(i).ne.zerO)then
perr2(i) = 1.0d2*(rone-(dabs(crsink(i)+cwsink(i)
+ +cmf(i))/(dabs(strl (i)-strO(i)))))
else
perr2(i) = zerO
end if
447 continue
write (25,502)'Cumulative err3 (%)',
+ (perr2(i+5),i=l,istop)
end if
else
C
C— Write the time series style phase material balance.
C
if(tmass0.ne.zerO) then
tperrl = dabs(tmassl - tmass - tsink
+ - twsink-tflux)*1.0d2/tmassO
else
tperrl = zerO
end if
Write(25,500)t(9y3600.0d0/24.0d0,(strl(i),i=l,5)
+. ,tmassl,tcflux,tcsink,tcwsink,tcrsink,tperrl
C
C— Write the time series style component material balance.
C
if(lctrl(2)) then
do455i=l,ipt(15)
455 write(28+i,500) t(9)/3600.0dO/24.0dO
+ ,(cmassl(ii*istop+i),ii=0,4),strl(i+5),cmf(i+5)
+ ,csink(i+5),cwsink(i+5),crsink(i+5),csflux(i+5)
end if
end if
end if
do450i = l,ipt(65)
450 first(i) = zerO
return
C
C— formats
500 format(ell.5,llell.4)
501 format(/'** TIME STEP =',i6,5x,'SIMULATION TIME (s) =',e!5.5/
+ 'INITIAL REPORT',8x,'Gas',8x,'Aqueous',4x,'NAPL',7x,'Solid'
+ ,6x,'Biophase',3x,'Total')
c502 format(
c +",al9,9ell.4)
502 format(
+ ' ',a,9ell.4)
503 format (
+ ' ',alO ,'(kg) ',9ell.4)
504 format ('Phase totals (kg); errors (%)',/
+' time (day) ','Gas',8x,'Aqueous',4x,'NAPL',7x,'SoIid',6x
+ ,'Biophase',3x,'Totar,6x,'Flux',7x,'Source',5x,'WeH',7x,
+ 'Reaction',3x,'Step err')
505 format (alO.'totals (kg); errors (%)',/
+ ' time (day) ','Gas',8x,'Aqueous',4x,'NAPL',7x,'Solid',6x
+ ,'Biophase',3x,'Totar,6x,'Flux',7x,'Source',5x,'WeH',7x,
+ 'Reaction',3x,'Surface')
506 format(/'** TIME STEP =',i6,5x,'SIMULATION TIME (s) =',e!5.5/
+ 'COMPONENT REPORT ,6x,9all)
507 format(/'** TIME STEP =',i6,5x,'SIMULATION TIME (s) =',el5.5/
+ 'PHASE REPORT',10x,'Gas',8x,'Aqueous',4x,'NAPL',7x,'Solid'
+ ,6x,'Biophase',3x,'Total')
508 format('Time step balance')
509 formatOCumulative balance')
c
end
165
-------
Subroutine - commnt.f
c~
c
c
c
c
c
c
c
c
c-
COMMNT.f - Subroutine which reads comment lines from 'infrom'
and ignores lines starting with '#' and prints to
'outto* lines starting with '&'.
Argument list - infrom: integer; number of input device
ioutto: integer; number of output device
subroutine COMMNT(infrom,ioutto)
integer infrom.ioutto
cliaraetcr*80 echo
1 read (infrom,501) echo
if(ecbo(:l).eq.'#')then
goto 1
elsei£(echo,(:l) .eq. '&') then
writeftoutto.SOI) .echo(2:)
goto 1
end if
backspace infrom
501 format (a)
return
end
Include File - dimen.inc
c
c
c
c-
DIMEN.inc - Declares array dimensions of common block variables.
implicit rcal*8 (a-h,k,o-x,z), logical (1), integer (i-j,m-n)
+• , charactcr*20 (y)
c
c— Define array dimensions:
c nnmx = maximum number of nodes
c nclnix = maximum number of elements
c nmblk = maximum number of material property blocks
c nxmax = maximum number of horizontal blocks in the generated grid
c nzmax = maximum number of vertical blocks in the generated grid
c nnslk = maximum number nodal variables in stacked storage
c ncmpo = maximum number of organic components to be simulated
C ncmpb = 1 if bioJegradation is to be considered
c ncmp = maximum number of total components to be simulated
c = 3(always) + ncmpb + ncmpo + 1 (if nutrient is considered)
c nonp2 = 2 x maximum number of total components to be simulated
c nempS = 5 x maximum number of total components to be simulated
c nsolvc a maximum number of unknowns in the linear system
c = nn2
c ienl - number of nonzero entries in the coefficent matrix
c irnl = number of nonzero entries in the coefficent matrix
c maxdima = maximum number of elements in matrix A in Ax=b
c nmd = maximum number of dispersion coefficients
e nmbc = maximum number of component boundary conditions
c !nnstk = nnmx+nnmx/3,
parameter (nnmx = 2350, nelmx = 4500, nxmax = 100, nzmax = 100,
•f nmblk = 3, ncmpb =1, ncmpo = 2, ncmp = ncmpo+ncmpb+3,
+ nc!3 m 3*nclnix,nel4 = 4*nelmx,
+ nn2 = 2*nnmx, nn3 = 3*nnmx, nn4 = 4*nnmx, nn6 = 6*nnmx,
+ nnstk = nnmx*1.05,nnslO= 10*nnstk,
JT nnstk2 = 2*nnstk, nnstkS = 3*nnstk,
+ nnstk4 = 4*nnstk, nnstkS = 8*nnstk,
+ ncmp2 = 2*ncmp,ncmp5 = 5*ncmp, nbcmp = ncmp*nmblk,
+ ncmppS = ncmp+5, ncsqd = ncmp*ncrnp*nnmx,
+ nzmax6 = 6^nzmax,nmd = 6*nelmx,nmbc = 2*ncmp*nnmx,
+ nmf = nnmx*(ncmp+2*(ncmp- 1+ncmpo)),
+ nmfs = nnstk*(ncmp+2*(ncmp-l+ncmpo)))
parameter (nsolve = nn2, icnl = 900000, irnl = 900000)
parameter (patm=101327.0dO,pi=3.14159265360dO,third=1.0dO/3.dO,
+ pthird=2.0dO*pi*third,tstd = 293.150dO
+ ,tabs = 273.150dO,zerO=O.OdO,rone=1.0dO)
C
C— R in (m"3 Pa) / (mole degree K)
parameter (r = 0.082060dO * 101327.0dO / lOOO.OdO)
parameter (srwmin = 1.0d-16,sgtest = O.OSOdO)
parameter (u=0.10dO, mtype=l)
C
C— Parameter values to modify code
C
parameter (xmmo=1.0d-3,xround=1.0d-I6,smino=1.0d-16)
C
C— Include logical control variables
common /cbl/ lctrl(50),lprnt(0:30),lcon(50),lplt(20)
C
C— Include integer control variables
common /cbi/ipt(0:90),icp(0:50)
C
C— Include real*8 scalars
common /cbs/ t(50),b,xkex,xden,xbom,xbok,wvis,kd,xinit,xbmin
+ ,xbmax,qwell,rwell,zwell,trefqg,wtdpth,caplen
Subroutine - disper.f
c-
c
c
c
c
c
c
c
c
c
e
DISPER.f - Subroutine which computes the phase dependent
portion of the dispersion tensor and the tortuosity.
Arguments: iphasc - integer scalar denoting the phase
gas phase: iphase = 1
aqueous phase: iphase = 2
Required Control Flags:
C lctrl(l 8) - logical variable denoting type of q calculation
C Ictrl(l 8) = .true. - nodel FEM q
C lctrl(l 8) = .false. - element average q
C
C •
subroutine DISPER(iphase)
include 'dimen.inc'
C
C— Declare and define common block variables.
C
common /cbl/ matel(oelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
166
-------
+ matpt(nn6)
common /cb2c/ q(ne!4)
common/cb3/ sat(nnstkS)
common /cb6b/ por(nelmx),srw(nnstk)
common /cb70/ d(nmd),tort(nelmx),bdist(nmblk),bdisl(nmblk)
ipt2s = (iphase-l)*ipt(2)
iptl = ipt(l)
iptO = ipt(0)
C
C— Compute the tortuosity after Millington and Quirk (1961).
C— Averaged saturations are used since the dispersion tensor is an
C— element wise constant.
C
do 100i=l,ipt(0)
ie!3 = i*3
iell=ie!3-2
ie!2 = ieI3-l
il=nodel(iell)
i 1 s = nodept(i I )+nelpt(iel 1)
ilps = ils + ipt2s
i2 = nodel(ie!2)
i2s = nodept(i2)+nelpt(ie!2)
i2ps = i2s 4- ipt2s
i3 = nodel(ieB)
i3s = nodept(i3)+nelpt(iel3)
i3ps = i3s + ipt2s
satavg = third * (sat(ilps)+sat(i2ps)+sat(i3ps))
poravg=por(i)
C
C— Millington and Quirk (1959).
C
c tort(i) = ((poravg*satavg)**(third * lO.OdO)) / poravg**2
C
C— Millington and Quirk (1961) for variably saturated media.
C
tort(i) = ((poravg*satavg)**(third * 7.0dO)) /poravg**2
C
C— Calculate averaged q.
C
if(lctrl(18))then
iptq = (iphase-l)*iptl*2
qx = dabs(third * (q(iptq+il)+q(iptq+i2)+q(iptq+i3)))
qz = dabs(third * (q(iptq+iptl+il)+q(iptq-t-iptl+i2)
+q(iptq+iptl+i3)))
else
iptq = i+(iphase-l)*ipt(67)
qx = dabs(q(iptq))
qz = dabs(q(iptq+iptO))
end if
qxz = dsqrt(qx**2 +• qz**2)
Convert q to velocity.
if(satavg.ge.sgtest) then
vxz = qxz/(poravg*satavg)
else
vxz = zerO
end if
id = (iphase-l)*ipt(68)
C— Calculate dispersion.
C
if(dabs(qxz).gt.l.0d-15) then
idp3xi = id+3*i
imat = matel(i)
d(idp3xi-2) = bdist(imat)*vxz
+ + bdisl(imat)*(qx*qx)/(qxz*poravg*satavg)
d(idp3xi-l) = bdisl(imat)*dabs(qx*qz)/(qxz*poravg*satavg)
d(idp3xi) = bdist(imat)*vxz
+ H- bdisl(imat)*(qz*qz)/(qxz*poravg*satavg)
else
idpSxi = id+3*i
d(idp3xi-2) = zerO
d(idp3xi-l) = zerO
d(idp3xi) = zerO
end if
100 continue
return
end
Subroutine - error.f
c
c
C ERRMESSAGE.f - Finds and prints error and warning messages
C from the error file.
C Warning if itype = 1; fatal error if itype = 0
C
C
subroutine ErrMessage (MessNum.itype.ierr)
implicit real*8 (a-h,k,o-z), logical (1), integer (i-j,m-n)
character Iine*80
c
c— Find the specified error or warning in the error file.
rewind (14)
1 read (14,800) line
800 format (a)
If(line(:l).eq.'#')then
GoTol
Else
backspace 14
read (14,*) number.nlines
Endif
c—• Print the error or warning to the screen and the error file if
c— opened.
If (number .eq. MessNum) then
write (terr,*)
If (itype .eq. l)then
write (ierr,*) '***** WARNING *****'
Else if (itype .eq. 0) then
write (ierr,*) '***** FATAL ERROR *****'
Endif
Doi = l.nlines
read (14,800) line
write (ierr,*) line(2:80)
EndDo
Else
GoTo 1
Endif
c
c— If a fatal error then teminate execution.
If (itype .eq. 0) stop
return
end
Subroutine - flow.f
167
-------
c-
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c-
FLOW.f - Subroutine which solves Ihe phase balance equations.
Solution of the mobile aqueous and gaseous phases is
done simultaneously.
Required Control Rags;
t( 13) - convergence criterion for pressures
ipl(27) - integer variable indicating type of domain
ipl(27) >* 0 - xz domain
ipt(27) = 1 - rz domain
iplOl) - maximum phase balance iterations, also used as the
criterion for decreasing dt in phase balance
ipt(34) - maximum number of iteriations in phase balance for
increasing dt
IctrU?) - logical variable controlling type of FEM
solution for flow
lctrl<7)= .inic. - use mass lumping
lctrt(7) = .false. - full FEM solution
lctrl(12) - logical variable denoting presence of a well
Ictrl(12) = -true. - well present
Ictrl(12) = .false. - well not present
lclrl(|3) - logical variable denoting compositional dependence
of the gas phase viscosity
lctrl(13) = .true. - gas phase viscosity is
dependent on composition
lctrl(13) = .false. - gas phase viscosity is not
dependent on composition
lctrl(14) - logical variable controlling coupling of flow and
transport solutions
lelrl(14) - .true, - exchange couples flow and
transport solutions
lctrl{14) = .false. - flow and transport
solutions not coupled
Control Flags computed internally in routine:
!pt<36) - flag specifying time step modification
subroutine FLOW (its,iO
include 'dimen.inc'
common /cbl/ malcl(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ m.iipt(nn6)
common /cblc/ xnode(nnmx),znode(nnmx),rbar(nelmx),area(nelmx)
common /cbloV gama(nel3),beta(ncl3)
common/cb2/ p(nn3)
common /cb2W pt(nn3)
common/cb3/ sat(nnstk3)
common /ch-l/ sa!k(nnslk2).cc(nnstk)
common /cbSa/ bphi(nmblk),bpermh(nmblk),bpermv(nmblk)
common /cb6V pmob(nnstk4)
common /cbfib/ por(nelmx),srw(nnstk)
common /cbfic/ temp(nnmx)
common /cb6d/ dtemp(nzmax6),idepth(nnmx)
common /cb7/ cvvis(ncmp),gamma(ncsqd)
common /cbS/ vis(nnmx),pmw(nn3)
common/cb9/ xmf(nmf)
common /cblO/ den(nn6)
common /cblOW dden(nn6),pmwt(nn3),dent(nn6)
common /cbl I/ pex(nnslO),rxnp(nn2)
common /cb30/ ibc(nnmx)
common /cb31/ source(nn2)
common /cb40/ a(icnl),rhs(nsolve),w(icnl)
common /cb41/ irn(icnl),icn(icnl),iw(icnl,8),ikeep(icnl,5)
common /cb41b/ nbw(0:2),ia
common /cb42/ amb(icnl),fmb(nsolve)
- Local arrays.
dimension ael(36),bel(36),fel(6),nd(3),dn(3),c(l 1)
dalaisparge/0/
- Initialize current iterations saturations.
Doi*l,2'ipt(2)
satk(i) = sat(i)
EiulDo
Update gas phase viscosity.
If (Ictrljl 3)) then ! compute a mixture viscosity
Do node = l,ipt(l)
yis(node) = zerO
Doj = l,ipt(3)
ii = icp(i)
if(lctrl()0)) then
cvvist = cvyis(ii)
else
cwist = cvvis(ii)
t + dtemp(ipt(88)+(ii-l)*ipt(89)+idepth(node))
end if
i3 = (i-1) * ipt(3) + (node-l)*ipt(3)*ipt(3)
sum = O.OdO
Doj = l,ipt(3)
sum = sum + xmf((jj-l)*ipt(I)+node) * gamma
-------
if (isparge .eq. 0) then
source(ipt2+i) = source(ipt2+i) + zel * pmob(ndstkl) *
+ qwell * sum ! gas discharge at top node
source(ipt2+i+l) = source(ipt2+i+l) + zel *
+ pmob(ndstkl) * qwell * sum ! lower node gas discharge
else if (isparge .eq. 1) then
source(ipt2+i) = source(ipt2+i) +
+ zel*qwell/zwell/2.0dO
source(ipt2+i+l) = source(ipt2+i+l) +
+ zel*qwell/zwell/2.0dO
endif
if (qwell.It. O.OdO) then
source(ipt2+ipt(24)+i) = source(ipt2+ipt(24)+i) +
+ zel * pmob(2*ipt(2)+ndstkl) * qwell * sum
source(ipt2+ipt(24)+i+l) = source(ipt2+ipt(24)+i+l) +
+ zel * pmob(2*ipt(2)+ndstk2) * qwell * sum
endif
63 continue
end if
c
c— Zero the local 'a' and 'rhs' vectors.
Doi = l,2*ipt(l)*nbw(2)
a(i) = zerO
EndDo
Doi = l,2*ipt(l)
rhs(i) = zerO
EndDo
c
c— Loop over the number of elements.
do 101 jel = l,ipt(0)
i3 = (jel-l)*3
mblk = matelQel)
ndl = nodel(i3+l) ! element node numbers
nd2 = nodel(i3+2)
nd3 = nodel(i3+3)
nd(l) = nodel(i3+l) ! element node numbers
nd(2) = nodel(i3+2)
nd(3) = nodel(i3+3)
ndstkl = nodept(ndl) + nelpt(i3+l)! node position in stack
ndstk2 = nodept(nd2) + nelpt(i3+2)
ndstkS = nodept(nd3) + nelpt(i3+3)
c(9) = rbar(jel) / (12.0dO * area(jel)) ! element constants
c(10) = rbar(jel) * area(jel) * porQel) / (t(8) * 12.0dO)
c(ll) = rbar(jel)/24.0dO
c
c— Compute the element mass matrix; either lumped or consistent.
if(lctrl(7))then
Do i = 1,36
ael(i) = zerO
EndDo
c(l) = -4.dO * c(10) * cc(ndstkl)
c(3) = 4.dO * c(10) * sat(ndstkl)
ael(l) = c(l)
ael(4) = -c(l)
ael(7) = -c(l)
ael(10) = c(3) * (l.OdO / (r*temp(ndl)*den(ndl))) + c(l)
c(l) = -4.dO * c(10) * cc(ndstk2)
c(3) = 4.dO * c(10) * sat(ndstk2)
ael(14) = c(l)
ael(17) = -c(l)
ael(20) = -c(l)
ael(23) = c(3) * (l.OdO / (r*temp(nd2)*den(nd2))) + c(l)
c(l) = -4.dO * c(10) * cc(ndstk3)
c(3) = 4.dO * c(10) * sat(ndstk3)
ael(27) = c(l)
ael(30) = -c(l)
ael(33) = -c(l)
ael(36) = c(3) * (l.OdO / (r*temp(nd3)*den(nd3))) + c(l)
else
c(l) = -c(10) * cc(ndstkl)
c(3) = c(10) * sat(ndstkl)
ael(l) = 2.0dO*c(l)
ael(2) = c(l)
ael(3) = c(l)
ael(4) = -2.0dO*c(l)
ael(5) = -c(l)
ael(6) = -c(l)
ael(7) = -2.0d0*c(l)
ael(8) = -c(l)
ael(9) = -c(l)
ael(l 1) = c(3) * (l.OdO/ (r*temp(ndl)*den(ndl))) + c(l)
ael(12) = ael(ll)
ael(10) = 2.0dO*ael(ll)
c(l) = -c(10) * cc(ndstk2)
c(3) = c(10)*sat(ndstk2)
ael(I3) = c(l)
ael(14) = 2.0dO*c(l)
ael(15) = c(l)
ael(16) = -c(l)
ae!(17) = -2.0dO*c(l)
ael(18) = -c(l)
ael(19) = -c(l)
ael(20) = -2.0dO*c(l)
ael(21) = -c(l)
ael(22) = c(3) * (l.OdO/ (r*temp(nd2)*den(nd2))) + c(l)
ael(23) = 2.0dO*ael(22)
ael(24) = ael(22)
c(l) = -c(10)*cc(ndstk3)
c(3) = c(10)*sat(ndstk3)
ael(25) = c(l)
ael(26) = c(l)
ael(27) = 2.dO*c(l)
ael(28) = -c(l)
ael(29) = -c(l)
ael(30) = -2.dO*c(l)
ael(31) = -c(l)
ael(32) = -c(l)
ael(33) = -2.dO * c(l)
ael(34) = c(3) * (l.dO / (r*temp(nd3)*den(nd3))) + c(l)
ael(35) = ael(34)
ael(36) = 2.d0*ael(34)
endif
c
c— Compute the element stiffness matrix for the aqueous equation.
imbxl = 2*ipt(2)+ndstfcl
imbx2 = 2*ipt(2)+ndstk2
imbx3 = 2*ipt(2)+ndstk3
imbzl = 3*ipt(2)+ndstkl
imbz2 = 3*ipt(2)+ndstk2
imbzS = 3*ipt(2)+ndstk3
c(3) = pmob(imbzl) + pmob(imbz2) + pmob(imbz3)
c(4) = bpermh(mblk) * c(3) ! c(4)=sum of x mobilities
dn(l) = den(4*ipt(l)+ndl)
dn(2) = den(4*ipt(l)+nd2)
dn(3) = den(4*ipt(l)+nd3)
c(5) = pmob(imbzl)/dn(l) -t- pmob(imbz2)/dn(2) +
+ pmob(imbz3)/dn(3)
c(6) = bpermh(mblk) * c(5) ! c(6)=x mobil/density
c(7) = beta(i3+l)*dn(l) + beta(i3+2)*dn(2) +
+ beta(i3+3)*dn(3) ! c(7)=sum of density * beta
c(8) = gama(i3+l)*dn(l) + gama(i3+2)*dn(2) +
+ gama(i3+3)*dn(3) ! c(8)=sum of density* gamma
c(l) = c(9) * (c(4)*beta(i3+l) - 0.250dO *
+ (c(6)+pmob(imbxl)/dn(l)) * c(7))
c(2) = c(9) * (c(3)*gama(i3+l) - 0.250dO *
+ (c(5)+pmob(imbzl)/dn(l)) * c(8))
bel( 1) = beta(i3+1 )*c( 1) + gama(i3+1 )*c(2)
bel(13) = beta(i3+2)*c(l) + gama(i3+2)*c(2)
bel(25) = beta(i3+3)*c(l) + gama(i3-H3)*c(2)
c(l) = c(9) * (c(4)*beta(i3+2) - 0.250dO *
+ (c(6)+pmob(imbx2)/dn(2)) * c(7))
c(2) = c(9) * (c(3)*gama(i3+2) - 0.250dO *
+ (c(5)+pmob(imbz2)/dn(2)) * c(8))
bel(2) = beta(i3+l)*c(l) + gama(i3+l)*c(2)
bel(14) = beta(i3+2)*c(l) + gama(i3+2)*c(2)
bel(26) = beta(i3+3)*c(l) + gama(i3+3)*c(2)
c(i) = c(9) * (c(4)*beta(i3+3) - 0.250dO *
+ ' (c(6Hpmob(imbx3)/dn(3)) * c(7»
c(2) = c(9) * (c(3)*gama(i3+3) - 0.250dO *
+ (c(5)+pmob(imbz3)/dn(3)) * c(8))
bel(3) = beta(i3+l)*c(l) + gama(i3-H)*c(2)
bel(15) = beta(i3+2)*c(l) + gama(i3+2)*c(2)
bel(27) = beta(i3+3)*c(l) + gama(i3+3)*c(2)
c
c— Compute the element rhs vector for the aqueous equation.
c(2) = 4.dO * (dn(l)*pmob(imbzl) + dn(2)*pmob(imbz2) +
169
-------
+ dn(3)*pmob(imbz3)) ! haz
c( 1 ) * bpcrmh(mblk) * c(2) ! hax
fcl(l) " (t(2I) * (bela(i3-H)Ml) -
+ (c(4)+pmobpmob(imbz3)/dn(3)) * c(8))
bel(12) = beta(i3s-l)*c{l) + gama(i3+l)*c(2)
bel(24) = beta(i3t2)*c(l) + gama(i3+2)*c(2)
bel(36.) = beta(i3+3)*c(l) + gama(i3+3)*c(2)
c— Compute the elementihs vectorfor the gas equation.
c"(2) = 4.dO * (dn(l)*pmbb(imbzl) + dn(2)*pmob(imbz2) +
+ dn(3)*pmob(imbz3)) ! hg±
c(l) = bpermh(mblk) * c(2) ! 'hgx
fel(4) = (t(21) * (beta(i3-H)*c(l) -
+ (c(4)+pmob(imbxl))*c(7)) +
+ t(22) * (gama(i3+1 )*c(2) -
+ (c(3)+pmob(imbzl))*c(8)))*c(ll)
fel(5) = (t(21) * (beta(i3+2)*c(l) -
+ :(c(4)*pmob(imbx2))*c(7)) *
+ t(22) * (gama(i3+2)*c(2) -
+ (c(3)+pmob(imbz2))*c<8))) * c(l 1)
fel(6)=
-------
ii = jj+ipt(22)
If (ipt(23) .gt. 0) then ! nodes with constant aqueous flux
Doi = l,ipt(23)
irowg = 2*(ibc(ii+i)-l) + 1
rhs(irowg) = rhs(irowg) + source(ipt(22)+i)
EndDo
Endlf
If(ipt(22).gt. 0)then
Do i = I ,ipt(22) ! nodes with constant gas flux
irowg = 2*ibc(jj-M)
rhs(irowg) = rhs(irowg) + source(i) * patm *
+ temp(ibc(ij+i)) / ((patm + p(ibc(jj+i))) * tstd)
EndDo
Endlf
c
c — Adjust rhs vector for flow at nodes along the well screen.
If(lctrl(12))then
iptbc = ipt(18)+ipt(19)+ipt(20)+ipt(2I)+ipt(22)+ipt(23)
ii = ipt(22)+ipt(23)
jj = ii+ipt(24)
Doi = l,ipt(24)
irowg = 2*(ibc(iptbc+i)-l) + 1
if (qwell.It.O.OdO) rhs(irowg) = rhs(irowg)+source(jj+i)
irowg = irowg + 1
rhs(irowg) = rhs(irowg) + source(ii+i) * patm *
+• temp(ibc(iptbc+i)) / ((patm+
+ p(ibc(iptbc+i))) * tstd)
EndDo
Endlf
c
c — Save matrices for mass balance computation.
If (lprnt(6).or.lctrl(2)) then
Doi = l,2*ipt(l)*nbw(2)
amb(i) = a(i)
EndDo
Doi = I,2*ipt(l)
fmb(i) = rhs(i)
Enddo
Endlf
c
c — Adjust rows of global matrix for constant pressure conditions
If (ipt(l 8).gt.O) then ! Constant gas pressure nodes
Doi = l,ipt(18)
ii = (2*ibc(i)-l)*nbw(2)
Do j = ii+ 1 ,ii+nbw(2)
a(j) = zerO
EndDo
a(ii+nbw(l)+l) = l.OdO
rhs(2*ibc(i)) = zerO
EndDo
Endlf
If (ipt(l 9).gt.O) then ! Constant aqueous pressure nodes
Do i = l,ipt(19)
ii = 2*(ibc(ipt(18)+i)-l)*nbw(2)
a(j) = zerO
EndDo
a(ii+nbw(l)+l) = 1.0dO
rhs(2*ibc(ipt(18)+i)-l) = zerO
EndDo
Endlf
c
c— Collapse banded storage of linear system into sparse matrix form
c — used by Harwell. At the same time scale array by dividing rows
c — • through by value on the main diagonal,
ia = 0
nx = 0
do 29 irow = l,2*ipt(l)
aii = 1 .OdO / a(irow*nbw(2)-nbw( 1 ))
rhs(irow) = rhs(irow) * aii
do 30 j = l,nbw(2)
nx = nx + 1
if (a(nx) .ne. O.OdO) then
ia = ia + 1
a(ia) = a(nx) * aii
irn(ia) = irow
icn(ia) = nx - (irow-l)*nbw(2) + irow - nbw(l) - 1
endif
30
29
continue
continue
c— Solve linear system using Harwell.
call ma28ad (2*ipt(l),ia,a,icnl,irn,irnl,icn,u,
+ ikeep,iw,w,iflag)
if (iflag.lt. 0)
+ write (ipt(28),*) 'flow iflag return from harwell is '.iflag
call ma28cd (2*ipt(l),a,icnl,icn,ikeep,rhs,w,mtype)
c
c— Transfer solutions to the pressure vectors. Calculate the capillary
c— pressure and the maximum relative differences.
pa = zerO
dpa = zerO
pg = zerO
dpg = zerO
Doi = l,ipt(l) ,
pkpl =pt(ipt(l)+i) + rhs(2*i-l)
pa = dmaxl (pa, abs(pkpl))
dpa = dmaxl (dpa, abs(pkpl-p(ipt(l)+i)))
p(ipt(l)+i) = pkpl
pkpl = pt(i) + rhs(2*i)! gas P at k+1 iteration
pg = dmaxl (pg, abs(pkpl))
dpg = dmaxl (dpg, abs(pkpl-p(i)))
p(i) = pkpl
p(2*ipt(l)+i) = P(i)-p(ipt(l)+i)
EndDo
c
c— Update saturation and save previous iterate values.
call SATW
Doi = l,2*ipt(2)
satk(i) = sat(i)
EndDo
c
c— Update gas phase mass and molar density as a function of pressure.
n3 = ipt(41)
Doi = l,ipt(l)
den(i) = (patm+pffi) / (r*temp(i))
den(n3+i) = pmw(i) * den(i)
EndDo
c
c— Check convergence.
if (dpa/pa .le. t(13) .and. dpg/pg .le. t(13)) then
if (ipt(28).gt.O) write (ipt(28),200)
+ its,it,lctrl(14),t(9),t(9)/86400.dO,t(8)
If (it .le. ipt(34)) then ! update time step adj. flag
ipt(36) = 1
. . Else
ipt(36)=0 •
Endlf
c
c— Compute fluxes for mass balance
if(lprnt(6).or.lctrl(2))then
do 800 irow = 2,ipt(40),2
if (irow .le. nbw(l)) then
jstrt = nbw(l) + 2 - irow
jend = nbw(2)
else if (irow .ge. ipt(40)-nbw(l)) then
jstrt = 1
jend = nbw(2) - nbw(l) + 2*ipt(l) - irow
else
jstrt = 1
jend = nbw(2)
endif
sum = O.dO
do805j=jstrtjend
805 sum = sunn-amb(nbw(2)*(irow-l)+j)
+ *rhs(irow-nbw(l)-l+j)
800 fmb(irow) = (sum-fmb(irow))
do 820 irow = l,ipt(40)-l,2
if (irow .le. nbw(l)) then
jstrt = nbw(l) + 2 - irow
jend = nbw(2)
else if (irow .ge. ipt(40)-nbw(l)) then
jstrt = 1
jend = nbw(2) - nbw(l) + ipt(40) - irow
else
jstrt = 1
171
-------
jcnd = nbw(2)
cndif
sum = 0.dO
do825j=jstrtjcnd
S2S sum = sum + amb(nbw(2)*(irow-l)+j)
+ * ths(irow-nbw(l)-l+j)
820 fmb(irow) = (sum - fmb(irow))
endif
return
cmlif
c
c—Convergence not achieved. Iterate unless ipt(31) has been reached.
100 continue
c
c— Max iterations exceeded; increment flag for time step reduction.
it = it-1
ipt(36) = -l
If(ipt(28).gt.0)then
write(ipt(28),*)'»> Time step reduction in flow it>=',ipt(31)
write (ipt(28),500) its,t(9),t(8),it
Endif
c
c— Formats.
200 format ('Flow sol converged at step =',i6,
+ ' iterations =',13,' Ictrl(14) =',13/
+ ' Time (s,d) =',2el2.4,
+ ' time step (s) = ',e!0.4)
500 format ('flow sol: t step=',i4,' tlme=',el0.4,' dt=',e!0.4,
+' its =',i4)
return
end
Subroutine - grid.f
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GRID.U - Subroutine which generates a union jack based
subdivision of a rectangular grid.
On input this subroutine reads the number of rectangular
spaces in the x-direction (nx) and the z-direction (nz).
The spacing can be uniform or nonuniform in each
direction.
Input logical variables (Ix) and (Iz), if true,
indicate if the spacing is uniform in the x and z
directions respectively.
If Ix or Iz ore true, then a corresponding uniform
spacing is input (udelx or udelz).
If Ix or Iz arc false, then nx anf nz values of the
spacing is input.
On output, Grid.f gives the number of nodes itp(l), the
number of elements ipt(O), the nodel coordinates xnode
and znode, and the clement incidence list nodel.
subroutine gridu
include 'dimcn.ine'
common /cbl/ matel(nclmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ matpi(nn6)
common /cblc/ xnode(nnmx),znodc(nnmx),rbar(nelinx),araa(nelmx)
common /cb95/ nbdL(nzmax),nbdR(nzmax),nbdT(nxmax),nbdB(nxmax),
+ nnhor.nnvcr
C
C— Dimension local arrays.
C
dimension delx(nxmax),delz(nzmax),imblk(nzmax)
c
C— read the number of rectangular spaces in the x and z directions
call commntt 11,21)
read(ll,*)nx,nz
ipt(86) * nz +1
ipt(87) = nx + I
if (nx.lc.O .or. nx.gt.nxmax) call En-Message (15,0,ipt(29))
if (nz,le.O .or, nz.gt.nzmax) call ErrMessage (16,0,ipt(29))
c
c—read horizontal spacing;
call commnt(l 1,21)
read (11,*) ldcl,xzcro ! is horizontal spacing uniform
if(Idcl)thcn
read (11,*) delx(l) ! uniform spacing in x-direction
do!0i-2,nx
10 Jelx(i) = delx(l)
else
rcad(ll,*)delx(l)
if (iklxt 1) ,ll, O.OdO) then 'make unifrom grid linear in In r.
rmult = (-delxUXxzero) ** (1.0dO/dble(nx))
rad = xzero
Do i « I ,nx
radpl = rad * rmult
delx(i) = radpl -rad
rad=radpl
EndDo
else
backspace 11
read (11,*) (delx(i),i=l,nx) ! nonuniform x spacing
endif
endif
Doi = l,nx
If (delx(i) .Ie. O.OdO) Call ErrMessage (17,0,ipt(29))
EndDo
c
c— read vertical spacing
call commnt(l 1,21)
read (11,*) Idel.zzero ! is vertical spacing uniform
if(ldel)then
read (11,*) delz(l) ! uniform spacing in z-direction
do 11 j — 2,nz
11 delz(j) = delz(l) .
else
read (11,*) (delz(j)j=l,nz) ! nonuniform z spacing
endif
Doj = l,nz
If (delz(j) -le. O.OdO) Call ErrMessage (18,0,ipt(29))
EndDo
c
c— Calculate the number of elements and nodes.
ipt(0) = 4 * nx * nz ! number of elements
ipt(l) = 2*nx*nz + nx + nz + 1 ! number of nodes
if (ipt(0) .gt. nelmx) Call ErrMessage (19,0,ipt(29))
if (ipt(l) .gt. nnmx) Call ErrMessage (20,Q,ipt(29))
nnhor = nx + 1
nnver = nz + 1
c
c— Read the number of horizontally aligned material property blocks,
c— followed by the material block number for all vertical spacings.
call commnt( 11,21)
read(ll,*)ipt(26)
If(ipt(26).lt. l)Then
Call ErrMessage (24,0,ipt(29))
Elself(ipt(26).eq. IJThen
Doi = l,nz
imblk(i) = 1
EndDo
Else
Read (11,*) (imblk(i),i=l ,nz)
Do i = 1 ,nz
if (imblk(i).lt.l .or. imblk(i).gt.ipt(26))
+ Call ErrMessage (24,0,ipt(29))
EndDo
Endif
172
-------
c— Assign nodel coordinates.Number nodes along the shortest dimension.
if (nx .le. nz) then ! number nodes horizontally
nd= 1
z = zzero
x = xzero
xnode(nd) = x
znode(nd) = z
do20i = l,nx
nd = nd + 1
x = x + delx(i)
xnode(nd) = x
20 znode(nd) = z
do 21 j = l,nz
nd = nd + 1
z = z + delz(j)*0.50d0
x = xzero + delx(l) * O.SOdO
xnode(nd) = x
znode(nd) = z
if(nx.gt. l)then
do22i = l,nx-l
nd = nd + 1
x = x + (delx(i)+delx(i+l)) * O.SOdO
xnode(nd) = x
22 znode(nd) = z
endif
nd = nd + 1
x = xzero
z = z + delz(j)*0.50dO
xnode(nd) = x
znode(nd) = z
do 21 i = l,nx
nd = nd + 1
x = x + delxffi
xnode(nd) = x
21 znode(nd) = z
else ! number nodes vertically
nd = l
z = zzero
x = xzero
xnode(nd) = x
znode(nd) = z
do30j = l,nz
nd = nd + 1
z = z + delz(j)
xnode(nd) = x
30 znode(nd) = z
do31i = l,nx
nd = nd + 1
x = x + delx(i) * O.SOdO
z = zzero + delz(l) * O.SOdO
xnode(nd) = x
znode(nd) = z
if(nz.gt. l)then
do32j = l,nz-l
nd = nd + 1
z = z + (delz(j)+delz(j+l)) * O.SOdO
xnode(nd) = x
32 znode(nd) = z
endif
nd = nd + 1
x = x + delx(i) * O.SOdO
z = zzero
xnode(nd) = x
znode(nd) = z
do 31 j = l,nz
nd = nd + 1
z = z + delz(j)
xnode(nd) = x
31 znode(nd) = z
c— define the incidence lists
jel = 0
i3=-3
if (nx .le. nz) then ! number elements horizontally
do40j = l,nz
do 40 i = l,nx
ndul = (j-l)*(2*nx+l) + i
ndur = ndul + 1
ndmd = ndur + nx
ndll = ndmd + nx
ndlr = ndll+l
If (i.eq.l) then iidentify boundary nodes(left and right)
nbdL(j) = ndul
if (j.eq.nz) nbdL(j+l) = ndll
Else if (i.eq.nx) then
nbdR(j) = ndur
if (j.eq.nz) nbdR(j+l) = ndlr
Endif
If (j.eq.l) then 'identify boundary nodes(top and bottom)
nbdT(i) = ndul
if (i.eq.nx) nbdT(i+l) = ndur
Else if (j.eq.nz) then
nbdB(i) = ndll
if (i.eq.nx) nbdB(i+l) =ndlr
Endif
jel=jel + l
i3 = i3 + 3
nodel(i3+l) = ndul
nodel(i3+2) = ndur
nodel(i3+3) = ndmd
matel(jel) = imblk(j)
jel = jel + 1
i3 = i3 + 3
nodel(i3+l) = ndur
nodel(i3+2) = ndlr
nodel(i3+3) = ndmd
matelQel) = imblk(j)
jel = jel + 1
i3 = i3 + 3
nodel(i3+l) = ndmd
nodel(i3+2) = ndlr
nodel(i3+3) = ndll
matel(jel) = imblkQ)
jel = jel + 1
nodel(i3+l) = ndul
nodel(i3+2) = ndmd
nodel(i3+3) = ndll
matel(jel) = imblk(j)
40 continue
else ! number elements vertically
do50i = l,nx
do50j = I,nz
ndll = ndul + 1
ndmd = ndll -f nz
ndur = ndmd + nz
ndlr = ndur + 1
If (i.eq. 1) then Hdentify boundary nodes(Ieft and right)
nbdL© = ndul
if (j.eq.nz) nbdL(j+l) = ndll
Else if (i.eq.nx) then
nbdR(j) = ndur
if (j.eq.nz) nbdR(j+l) = ndlr
Endif
If (j.eq.l) then (identify boundary nodes(top and bottom)
nbdT(i) = ndul
if (i.eq.nx) nbdT(i+l) = ndur
Else if (j .eq.nz) then
nbdB(i) = ndll
if (i.eq.nx) nbdB(i+l) = ndlr
Endif
jel = jel + 1
i3=i3 + 3
nodel(i 3+1) = ndul
nodel(i3+2) = ndur
nodeI(i3+3) = ndmd
mate! (jel) =imblk(j)
jel = jel + 1
nodel(i3+l) = ndur
nodel(i3+2) = ndlr
nodel(i3+3) = ndmd
matelQel) = imblkQ)
jel = jel + 1
173
-------
nodcI(i3-H)
rtQdcl(i3+2)=ndlr
nodd(i3+3) =
malel(jcl) = i
SO continue
endif
return
end
C —
C GRID.HB - Subroutine which generates a non-symetric triangular
C grid system based subdivision of a rectangular grid
C (Similar to the grid used by howard).
C On input this subroutine reads the number of rectangular
C spaces in the x-direction (nx) and (he z-direction (nz).
C The spacing can be uniform or ponuniform in each
C direction.
C Input logical variables (Ix) and (Iz), if true,
C indicate if the spacing is uniform in the x and z
C directions respectively.
C If Ix or Iz are true, then a corresponding uniform
C spacing is input (udelx or udelz).
C If Ix or Iz are false, then nx anf nz values of the
C spacing is input,
C On output, Grid.f gives the number of nodes itp( 1), the
C number of elements ipt(0), the nodel coordinates xnode
C and znodc, and the element incidence list nodel.
C
C
subroutine gridhb
include 'dimcn.ine'
common /cbl/ matcl(nclmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+• malpt(nn6)
common /cblc/ xnode(nnmx),znode(nnmx),rbar(nelmx),area(nelmx)
common /d>95/ nbdL(nzmax),nbdR(nzmax),nbdT(nxmax),nbdB(nxmax),
+ nnhor,nnver
C
C— Dimension local arrays.
C
dimension delx(nxmax),delz(nzmax),imblk(nzmax)
c
c— read the number of rectangular spaces in the x and z directions
call commnt (11,21)
read (11,*) nx.nz
ipt(86) = nz + I
ipt(87) = nx + 1
if (nx.lc.O .or. nx.gt.nxmax) call ErrMessage (15,0,ipt(29))
if (nz,lc.O .or. nz.gt.nzmax) call ErrMessage (16,0,ipt(29))
c
c— read horizontal spacing:
call commntU 1,21)
read (11,*) Idcl.xzcro ! is horizontal spacing uniform
if(ldel)lhcn
read (11,*) dclx(l) 1 uniform spacing in x-direction
do 10i = 2,nx
10 dclx(i)-delxd)
else
read(ll.*)delx(I)
if (dclxt 1) .11. O.OdO) then Imake uniform grid linear in In r.
rmult«(-dclx(l)/xzcro) ** (1.0dO/dble(nx))
rail = xzero
Doi = l,nx
ntdpt = rad * rmult
dclx(i) = radpl-rad
rad = radpl
EndDo
else
backspace 11
read (11,*) (delx(i),i=l,nx)! nonuniform x spacing
endif
endif
Doi= l,nx
If ,(dejx(i) .le. O.OdO) Call ErrMessage .(17,0,ipt(29))
.EndDo
- read vertical spacing
.cal)commntOH,2J)
read ;(•»,*) JdeUzerp
! js vertical spacing uniform
read ()!,*) dejzp) ! uniform spacing in z-direction
doll j-l,nz
else
read .(11,*) £delzi(j)j=l,nz)! nonuniform z spacing in
endif
Doj = l,nz
If (delzO) .le. O.OdO) Call ErrMessage (18,0,ipt(29))
EndDo
c— Calculate the number of elements and nodes.
ipt(0) = 2 * nx * nz ! number of elements
ipt(I) a (nx+1) * (nz+1) ! number of nodes
if (ipt(O) .gt. nelmx) Call ErrMessage (19,0,ipt(29))
if (iptO) .gt. nnmx) Call ErrMessage (20,0,ipt(29))
nnhor = nx +1
nnver = nz -f-1
c— Read the number of horizontally aligned material property blocks,
c— followed by the material block number for all vertical spacings.
call commnt (11,21)
read(ll,*)ipt(26)
If(ipt(26).lt. l)Then
Call ErrMessage (24,0,ipt(29))
Else If (ipt(26).eq.l) Then
Do i = l,nz
imblk© = 1
EndDo
Else
Read(ll,*)(imblk(i),i=l,nz)
Do i = 1 ,nz
if (imblk(i).lt.I .or. imblk(i).gt.ipt(26))
+ Call ErrMessage (24,0,ipt(29))
EndDo
Endif
c
c— Assign nodel coordinates. Number nodes along the shortest
c— dimension.
if (nx .le. nz) then ! number nodes horizontally
nd = l
z = zzero
x = xzero
xnode(nd) = x
znode(nd)= z
dp20i = l,nx
nd = nd + 1
x = x +• delx(i)
xnode(nd) = x
20 znode(nd) = z
do 21 j = 1 ,nz
nd = nd + 1
x = xzero
z = z + delz(j)
xnode(nd) = x
znode(nd) = z
do21i = l,nx
nd = nd + 1
x = x + delx(i)
xnode(nd)= x
21 znode(nd) = z
else ! number nodes vertically
nd = l
z = zzero
x = xzero
xnode(nd)= x
znode(nd) = z
do30j = l,nz
nd = nd + 1
z = z + delz(j)
xnode(nd) = x
30 znode(nd) = z
174
-------
31
do 31 i = I,nx
nd = nd + I
x = x + delx(i)
z = zzero
xnode(nd) = x
znode(nd) = z
do 31 j = l,nz
nd = nd + 1
z = z + delz(j)
xnode(nd)=x
znode(nd) = z
endif
c — define the incidence lists
jel = 0
13 = -3
if (nx .le. nz) then ! number elements horizontally
do40j = l,nz
if (2*(j/2) .eq.j) then
idir=l
else
idir = -I
endif
do40i= l,nx
ndul = Q-l)*(nx+l) + i
ndur = ndul + 1
ndll = ndul + nx + 1
ndlr = ndll + 1
If (i.eq.l) then lidentify boundary nodesfleft and right)
nbdL(j) = ndul
if (j.eq.nz) nbdL(j+l) = ndll
Else if (i.eq.nx) then
nbdR(j) = ndur
if (j.eq.nz) nbdR(j+l) = ndlr
Endif
If (j.eq.l) then lidentify boundary nodes(top and bottom)
nbdTffl = ndul
if (i.eq.nx) nbdT(i+l) = ndur
Else if (j.eq.nz) then
nbdB(i) = ndll
if (i.eq.nx) nbdB(i+l) = ndlr
Endif
if (idir.lt. 0)then
jel = jel + 1
13 = i3 + 3
nodel(i3+l) = ndul
nodel(i3+2) = ndlr
nodel(i3+3) = ndll
matel(jel) = imblk®
jel=jel-H
i3=i3 + 3
nodel(i3+l) = ndul
nodel(i3+2) = ndur
nodel(i3+3) = ndlr
matel(jel) = imblk(j)
idir = -idir
else if (idir.gt. 0) then
nodel(i3+l) = ndul
nodel(i3+2) = ndur
nodel(i3+3) = ndll
matel(jel) = imblk(j)
jel = jel + 1
i3 = 13 + 3
nodel(i3+l) = ndur
nodel(i3+2) = ndlr
nodel(i3+3) = ndll
• matelflel) = imblk(j)
idir = -idir
endif
40 continue
else ! number elements vertically
do50i = l,nx
if (2*(i/2) .eq.i) then
idir = 1
else
idir = -l
endif
do50j = l,nz
ndll = ndul + 1
ndur = ndul + nz + 1
ndlr = ndur + 1
If (i.eq.l) then lidentify boundary nodes(left and right)
nbdL(j) = ndul
if Q.eq.nz) nbdL(j+l) = ndll
Else if (i.eq.nx) then
nbdR(j) = ndur
if (j.eq.nz) nbdR(j+l) = ndlr
Endif
If (j.eq. 1) then lidentify boundary nodes(top and bottom)
nbdT(i) = ndul
if (i.eq.nx) nbdT(i+l) = ndur
Else if (j.eq.nz) then
nbdBffl = ndll
if (i.eq.nx) nbdB(i+l) = ndlr
Endif
if (idir. It. 0) then
jel = jel + 1
nodel(i3+l) = ndul
nodel(i3+2) = ndur
nodel(i3+3) = ndlr
matel(jel) = imblk(j)
jel = jel + 1
i3=i3 + 3
nodel(i3+l) = ndul
nodel(i3+2) = ndlr
nodel(i3+3) = ndll
matel(jel) = imblk(j)
idir = -idir
else if (idir .gt. 0) then
jel = jel + 1
nodel(i3+l) = ndul
nodel(i3+2) = ndur
nodel(i3+3) = ndll
matel(jel) = imblk(j)
jel = jel +1
50
nodel(i3+l) = ndur
nodel(i3+2) = ndlr
nodel(i3+3) = ndll
matel^el) = imblk(j)
idir = -idir
endif
continue
endif
return
end
Subroutine - inputl.f
175
-------
c-
c
c
c
c
c
c
c
c
c
c
c
c
c
c-
INPUTKf • main input routine. Reads model control information,
fluid and soil parameters, and grid information.
Control Flags conputed internally in routine:
Ictrl(l3) - logical variable denoting compositional dependence
of the gas phase viscosity
lclrl(l 3) = .true. - gas phase viscosity is
dependent on composition
ktrl{13) = .false. - gas phase viscosity is not
dependent on composition
subroutine 1NPUT1
include 'dimen,ine'
charaeter*20infile(4),outpre,outfile(8+ncmp)
character* 1C cnamc(ncmp)
ch»rw:lct*3 cmb(10)
common /ebU matel(nclm)(),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ matpt(nn6)
common /cblc/ xnode(nnmx),znode(nnmx),rbar(nelmx),area(nelmx)
common /cbld/ gama(ne13),beta(neI3)
common /cbSa/ bphKnmblk),brjenrfi(nmblk),bpermv(nmblk)
common KbSbt bvgn(nmblk),bvga(nmblk),bvgm(nmblk),bsrw(nmblk)
common /cb5c/bfoc(nmblk)
common /cbfic/ temp(nnmx)
common /cbfioV dtemp(nzmax6),idepth(nnmx)
common /cb7/ cwis(ncmp),gamma(ncsqd)
common /cbTW cmw(ncmp),cvp(ncmp),cden(ncmp),
+ chcn(ncmp),casol(ncmp),cmdif(ncmp2)
common /cb8/ vis(nnmx),pmw(nn3)
common /cb41b/ nbw(0:2),ia
common /cboW khalf(ncmp),fuse(ncmp2),umax(ncmp),xyield(ncmp),
+ kinhib(ncmp)
common /cb63/ kex(ncmp5),krnax(ncmp5)
common /cb64/ bok(nbemp),bom(nbcmp),krtd(ncmp)
common /cb64b/ bsden(nmblk)
common /cb70/ d(nmd),tort(nelmx),bdist(nmblk),bdisl(nmblk)
common /cb90/ infilc.outpre.outfilc
common /cb9I/ cname
common /cb95/ nbdL(nzmax),nbdR(nzmax),nbdT(nxmax),nbdB(nxmax),
+> nnhor.nnvcr
C
C-
c
Dimension local arrays.
dimension mp(4),zdeplh(nzmax)
C-- r- i READ INPUT/OUTPUT FILES AND OPTIONS =====
c
c— Read the name of input file 2 (ICs and BCs) and open as unit 13;
c— define the error and warning message input data file as unit 14.
call commm{! 1,21)
r«id(ll,»)infile<2).infile(3)
opcn(13,file=infi!c(2),status='unknown')
opcn(14,filc=infile(3),status='unknown')
e
c— Read the prefix name of all output files; determine output file
c— names: and open the main output file.
call commntO 1,21)
rcad(Il,*)outpre
ti = indcx(oulpre,' *)•!
oulfilc( I) = outpre(l ;iiy/'.out' ! main output file
oulfile(2) = outpre(l ;iiy/'.err' ! error messages
ou(filc(3)« outpre(l :!iV/'.cnv' ! performance output
outfilc(4) = outpre(l:ii)//'.con' ! contourdata
ouifilc(S) = outpreO :iiV/'.mb' ! mass balance checks
oulfi1e(6) soulpre{l:iiV/'.pU> ! time series plot data
outfitc(7) = outpre(l:iiy/'.rst' ! restart file
open (21 ,filc=outfile(l ),status='unknown')
C
C— Read the device specifications for error messages and
C— performance output.
C— 0 is no output; 6 is the screen;
C— 21 Is the .out file; 22 is the ,err file (only for error messages)
C— , 23 is the ,cnv file (only for performance output).
call commnUl 1,21)
read(ll,*)ipt(29),ipt(28)
- Open outfile(2) if ipt(29) = 22. Error message/runtime information.
if(ipt(29).eq.22)then
open (22,flie=outfile(2),status=>unknown')
else if (ipt(29) .eq. 6) then
outfile(2) = 'To Screen
else if (ipt(29) .eq. 0) then
outfile(2) = ' None Opened '
else if (ipt(29) .eq. 21) then
outfile(2) = outfile(l)
else
call ErrMessage (62,0,6)
endif
— Open outfile(3) if ipt(28) = 23. Performance and iteration output.
if(ipt(28).eq. 23) then
open(23,file=outfile(3),status='unkno\vn')
elseif(ipt(28).eq. 6) then
outfile(3) = To Screen '
else if (ip<(28) .eq. 0) then
outfHe(3) = ' None Opened '
else if (ipt(2S) .eq. 21) then
outfile(3) = putfile(l)
else
call ErrMessage (61,0,ipt(29))
endif
— Read a logical parameter indicating if contour plot data should be
c— printed to the file 'outpre.con'. Open the file, if yes.
call commnt(l 1,21)
read(ll,*)lctrl(23)
if(lctrl(23))then
open(24,file=outfile(4),status='unknown')
else
outfile(4) = 'None Opened '
endif
c— Read A logical parameter indicating if mass balance checks
c— should be computed and printed to the file 'outpre.mb'. Open the
c—file, if yes.
call commnt(l 1,21)
read(ll,*)lprnt(6)
if(lprnt(6))then
open(25,file=outfile(5),status='unknown')
else
outfile(5) = 'No Mass Balance '
endif
c
c— Read the uniform material balance print interval, either
c— by the number of time steps or a specified time increment. Also
c— read a logical variable controlling the type of material balance
c— output (report style if true).
if(lprnt(6)) then
read(ll,*) lprnt(25),lprnt(27)
if(lprnt(25)) then
read(U,*)ipt(83)
else
read(ll,*)t(27)
end if
endif
c
c— Read a logical parameter indicating if time series plot data
c— should be printed to the file 'outpre.plt'. Open the file, if yes.
call commntO 1,21)
read(ll,*)lctrl(15)
if(lctrl(15))then
open(26,file=outfile(6),status='unknown')
else
outfile(6) = 'None Opened '
endif
c
c— Read the uniform time series print interval, either by
c— the number of time steps or a specified time increment. Also read
c— a logical variable controlling the form in which the component
c— information is outputted (t=mole fraction, f=concentration).
if(lctrl(15))then
read(ll,*) lprnt(26),lprnt(28)
176
-------
if(lprnt(26)) then
read(ll,*)ipt(84)
else
read(ll,*)t(28)
end if
end if
c
c— Read a logical parameter indicating if restart data
c— should be printed to the file 'outpre.rst'. Open the file.
call commnt(l 1,21)
read(ll,*)Ictrl(5)
if(lctrl(5))then
open(27,file=outfile(7),status='unknown')
else
outfile(7) = 'No Restart Available'
endif
c
c— Write to the main output file: banner, title cards, I/O file names.
write (21,500)
call commnt (11,21)
backspace 11 - <
write (21,501) (infile(i),i=l,3),(outfile(i),i=l,7)
c
c— Read and write the uniform print interval, either by the number of
c— time steps or a specified time increment.
call commnt(l 1,21)
read(ll,*)lprnt(0)
if(Iprnt(0))then
read(ll,*)ipt(25)
write (21,529) ipt(25)
else
read(ll,*)t(12)
write (21,530) t(12)
endif
c
c— Write the uniform material balance print interval and the type of
c— material balance.
if(lprnt(6)) then
if(lprnt(27)) then
write(21,553)
else
write(21,554)
endif
if(lprnt(25)) then
write(21,549) ipt(83)
else
write(21,550) t(27)
endif
endif
c
c— Write the uniform time series print interval and the form in which
c— the component information is outputed (t=mole fraction,
c— f=concentration).
if(lctrl(15)) then
if(lprnt(28)) then
write(21,557)
else
write(21,558)
endif
if(lprnt(26)) then
write(21,551)ipt(84)
else
write(21,552)t(28)
endif
endif
===== BLOCK B - GENERAL MODEL CONTROL OPTIONS =
if(ipt(29).ne.O) write (ipt(29),*)
•J- 'Reading Model Control information'
c— Read the coordinate system: 0=xz; l=rz.
c— Read the horizontal and vertical gravity components.
c— Error check: ipt(27) (0-1)
call commnt(l 1,21)
read (11,*) ipt(27),t(21),t(22)
if (ipt(27).lt.O .or. ipt(27).gt.l) call ErrMessage (l,0,ipt(29))
c— Read a logical variables defining which balance equations are
c— solved:
c— lctrl(l)=> solve flow equations
c— lctrl(2) => solve transport equations
c— Ictrl(24) => solve napl equations
c— lctrl(25) => solve solid phase equations
c— lctrl(3) => solve biophase equations
call commnt(ll,21)
read (11,*) lctrl(l),Ictrl(2),lctrl(24),lctrl(25),lctrl(3)
if(Ictrl(2)) then
lctrl(22) = .true.
else
lctrl(22) = .false.
endif
c
c— Error Check: lctrl(24),lctrl(25),lctrl(3)=true only if lctrl(2)
c— = true.
if (lctrl(24) .and. .not. Ictrl(2)) Call ErrMessage (76,0,ipt(29))
if (lctrl(25) .and. .not. Ictrl(2)) Call ErrMessage (75,0,ipt(29))
if (lctrl(3) .and. .not. lctr!(2)) Call ErrMessage (42,0,ipt(29))
c
c— Read mass lumping options in the solution of the flow eqs
c— (lctrl(7)) and the transport eqs (lctrl(8)).
callcommnt(ll,21)
read(ll,*)lctrl(7),lctrl(8) '
c
c— Read an integer parameter denoting the number of time steps to be
c— skipped between solving for the flow equations.
call commnt(l 1,21)
read(ll,*)ipt(85)
c
c— Read in coupling term between flow and transport. lctrl(14)
c—• indicates if mass exchange terms are to be included in the
c—solution of the flow eqs. :
call commnt(l 1,21)
read(ll,*)lctrl(14)
if (lctrl(l) .and. .not. lctrl(2)) lctr!(14)=.false.
c
c— Lelnum indicates if element dirnensionless numbers are to be
c— calculated for the transport solution and written to ipt(28).
call commnt(l 1,21)
read(ll,*)Icrrl(4)
c
c— Write the general model control information.
write (21,502) ipt(27),t(21),t(22),lctrl(l),ipt(85),lctrl(2)
+ ,lctrl(24),lctr!(25),lctrl(3),lctrl(7),lctrl(8)
+ ,lctrl(14),lctrl(4)
c
c== TIME STEP/ITERATION CONTROL OPTIONS =====
c
if(ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Time Step/Iteration Control information'
c
c— Read the initial and final simulation time (sec).
c— Error check: t(2)>t(l); t(l) and t(2) .ge. 0.
call commnt(l 1,21)
read(ll,*)t(l),t(2)
if (t(l).lt.zerO) call En-Message (2,0,ipt(29))
if (t(l).ge.t(2)) call ErrMessage (3,0,ipt(29))
c
c— Read the time weighting factor.
c— Error check: O.ge.weight.le. 1
call commnt(l 1,21)
read(ll,*)t(10)
if(t(10).lt.zer0.or.t(10).gt.rone)
+ call ErrMessage (13,0,ipt(29))
c
c— Read the maximum number of iterations.
c— Error check:ipt(30) .gt. 0.
call commntO 1,21)
read(ll,*)ipt(30)
if (ipt(30).le.O) call ErrMessage (4,0,ipt(29))
c
c— Read the convergence tolerance for the flow, transport, NAPL
c— saturation and immobile transport eqs.
c— Error check: tol>0.
call commnt(l 1,21)
read (11,*) t(13),t(14),t(15),t(16)
177
-------
if (t(13).lt.zcrO .or. l(14),It.zerO .or. t(15).lt.zerf>
+ ,or, t( 16).lt.zcrO) call ErrMessage (9,0,ipt(29))
c
c— Read the inilial, minimum and maximum time step size (s).
e— Error check: dtmin0; dtmin.le.dtinitial.le.dtmax
call commnt(l 1,21)
read(ll,*)t(3),t<4).t(5)
if(K4)Je.zcrt» call ErtMessage (5,0,ipt(29))
if (IW8I.K5)) ca« ErrMessage (6,0,ipt(29»
if (t(3).lu(4) .or, t(3),gt,t(5» call ErrMessage (7,0,ipt(29))
e
c— Read (lie maximum number of iterations for the flow, transport, NAPL
c— saturation, and immobile eqs.
call commntU 1,21)
read (11,») ipt(31),ipt(32),ipt(33)
c
c— Read tire minimum number of iterations for the flow, and transport
c—cqs. Error check: itmin«dtmax.
call commnt(l 1,21)
rcad(ll.')ipt(34),ipt(35)
if (ipt(34),gt.ipt(31) .or. ipt(35).gt.ipt(32) .or.
+ ipt(35).gt.lpt(33)) call ErrMessage (8,0,ipt(29))
c
c— Read the empirical time step amplification and reduction factors.
c—Error check: t(6).gc,lU(7).Ie.l.
call commnt(l 1,21)
rcad(ll,*)t(6),t(7)
if (l(6).U,rone) call ErrMessage (10,0,ipt(29))
if (t(7),gt,rone) call ErrMessage (1 l,0,ipt(29))
c
c— Write the time step control information.
write (21403) t(l),t(2),t(10),ipt(30),t(13),t{14),t(15),t(16),
+ t(3),t(4),t(5),ipt(3 l),ipt(32),ipt(33),
+ ipt(34)jpt(35),t(6),t(7)
c
c— Initialize the time step.
1(8) = 1(3)
c
CM^.i»u^^ GRID PARAMETERS AND OPTIONS =m
e
if(ipl(29),ne.O) write (ipt(29),»)
+ 'Reading Grid Parameters and Options'
C
o— Read a logical variable indicating if grid info should be printed
c— to lite main output file.
call commnt(l 1,21)
read(ll,*)Iprnt(l)
c
c— Generate the grid?
c 0 = don't generate the grid;
c 1 - generate a union jack grid;
c 2 = generate a herring bone grid.
c— Error check: igrid (0-2)
c— Error check: number of nodes and elements.
Call commnK 11,21)
Read (II,*) igrid
If (igrid.It.O .or. igrid,gt.2) call ErrMessage (14,0,ipt(29))
irtigrid.cq. l)Thcn
if(ipt(29).nc.O) Write (ipt(29),*)
+ 'Generating a uniform union jack grid'
Call gridu
Else If (igrid .cq. 2) Then
if(ipt(29),nc.O) Write (ipt(29).*)
+ 'Generating a uniform herring bone grid'
Call gridhb
Endlf
c
c— Input the grid,
If (igrid .eq.O) Then
c
e— Read the number of elements, number of nodes, and the number of
c— material property blocks.
c— Error check: number of nodes, elements, material property blocks.
Call commntU 1,21)
Read (tl,*)ipt(0),ipt(l),ipt(26)
write (6,*) ipl(0),ipt(l),ipt(26)
if (ipt(O) .gt. nelmx) Call ErrMessage (19,0,ipt(29))
if(ipt(l) ,gt. nnmx) Call ErrMessage (20,0,ipt(29))
if (ipt(26) .gt. nmblk) Call ErrMessage (21,0,ipt(29))
C— Read the nodal incidence list and material property block
C— for each element. The element node incidence list consists of
C— the arbitrary global element number followed by that element's
C— three global node numbers. Each element has its own line. The
C— element node numbers start at an arbitrary node. If the z
C— coordinate is positive downwards proceed in the clockwise
C— direction, otherwise proceed in the counterclockwise direction.
C— If there is only one material property block for the entire
- domain, the material property input assignment for each element
- may be omrnited; The minimum material property block is a two
element quadralateral.
Error check: node and material block numbers are within the
c— defined range.
call commnt(l 1,21)
if(ipt(26).eq.l)then
do!00i = l,ipt(0)
read(ll,*)ii,nodel(ii*3-2),nodel(ii*3-l),nodel(ii*3)
100 matel(ii) = 1
else
dol!0i = l,ipt(0)
110 read(ll,*)ii,nodel(ii*3-2),nodel(ii*3-l>,nodel(ii*3)
+ ,matel(ii)
endif
Dol20i=l,ipt(0)
i3 = 3*i
If (matel(i).lU .or. matel(i).gt.ipt(26))
+ Call ErrMessage (24,0,ipt(29))
If (nodel(i3-2).lt.l .or. nodel(i3-2).gt.ipt(l) .or.
+ nodel(i3-l).lt.l .or. nodel(i3-l).gUpt(L) .or.
+ nodel(i3).lt.l .or. nodel(i3).gt.ipt(l))
+ Call ErrMessage (25,0,ipt(29))
120 continue
c
c— Read the nodal coordinates.
call commnt( 11,21)
do!30i=l,ipt(l)
130 read(ll,*)j,xnodeO),znode(j)
Endlf
C
C— Compute the pointers for the nodal storage vectors. Multiple
C— entries are needed for each node whose contiguous elements have
C— different material properties. Pressure is always continuous,
C— while as an example saturation is not when adjacent elements
C— have different saturation/pressure relationships. The number
C— of entries at a given node is equal to the number of different
C— contiguous material property sets. This routine is configured to
C— allow a maximum of four different material property sets to be
C— contiguous at a given node.
C
if (ipt(29).ne.O) write (ipt(29),*)
+ 'Computing pointers for stacked storage'
dol40i=l,ipt(l)+l
nodept(i)=i
140 continue
do!50i=l,4*ipt(l)
matpt(i)=0
150 continue
do!60i=l,3*ipt(0)
nelpt(i)=0
160 continue
C
C— First, determine the number of different material property
C— sets that are contiguous at each node. Search the entire
C— node incidence list node by node, storing the material property
C— identifiers in the local array mp.
C
do!70i=l,ipt(l)
C
C— Initialize local counters to zero before each element search.
C
i4max=0
do!75j=l,4
mp(j)=0
175 continue
do 180 ii=l,ipt(0)
do 18013=2,0,-1
178
-------
C— If the node incidence list for element ii contains node i, check
C— if matel(ii) is contained in one of the four entries of mp for
C— node i.
C
if(nodel(3*ii-i3).eq,i) then
do!85i4=l,4
C
C— If matel(ii) is already an entry in mp, create the corresponding
C— entry in nelpt and go to the next element.
C
if(matel(ii).eq.mp(i4)) then
nelpt(3*ii-i3)=i4-I
go to 180
C
C— Store a new value of matel(ii) in the first zero entry of mp.
C— Keep track of the number of nonzero entries in mp for node i in
C— in isum. Create the corresponding entry in nelpt and continue on
C— to the next element.
C
else if(mp(i4).eq.O) then
mp(i4)=matel(ii)
nelpt(3*ii-i3)=i4-l
if(i4.gt.i4max+l) !4max=i4-l
goto 180
end if
C
C— If all entries of mp for node i are nonzero and matel(ii) is
C— not contained in mp, too many contiguous material properties
C— have been defined. Write an error message and stop.
C
if(i4.eq.4) then
write(ipt(29),*)' ATTENTION: EXCESS MATERIAL',
+ ' PROPERTY at Node Number',!
Call ErrMessage (22,0,ipt(29))
end if
185 continue
end if
180 continue
C
C— Use i4max and mp to construct nodept and matpt. The value of
C— nodept for node H-l is the value of nodept for node i plus the
C— number of stacked entries for node i (i4max). Matpt is the nonzero
C— values of mp in order, nodept has dimension itp(l)-)-l to allow
C— for determination of the number of stacked variables at the last
C— global node.
nodept(i+l) = nodept(i)+i4max+l
do 170i5=0,i4max
matpt(nodept(i)-»-i5)=mp(i5+l)
170 continue
C
C— Define the dimension of stacked nodal storage.
c— Error check: number of nodal variables in stacked storage.
ipt(2) = nodept(ipt(l)+!)-!
if (ipt(2) .gt. nnstk) Call ErrMessage (23,0,ipt(29))
c
c— Determine the full bandwidth of the global matrix; one each for
c— the transport solution and the flow solution.
nbw(0) = 0
do!90i=l,ipt(0)
i3 = (i-l)*3
190 nbw(0) = max(nbw(0), iabs(nodel(i3+2)-nodel(i3+l)),
+ iabs(nodel(i3+3)-nodel(i3+2)),
+ iabs(nodel(i3+3)-node!(i3+l)))
nbw(l) = 2*nbw(0) + l
nbw(2) = 2*nbw(l)-H
c
c—Compute elemental areas
call ATRI
c
c— Compute beta and gamma coefficients for computation of integration
c— Also compute radial centroid of each element for axysymetric
c— coordinates. This is set to one if the xz coordinates are used.
do 200 i = l,ipt(0)
i3 = 3*(H)
beta(i3+l) = znode(nodel(i3+2)) - znode(nodel(i3+3))
beta(i3+2) = znode(nodel(i3+3)) - znode(nodel(i3+l))
beta(i3+3) = znode(nodel(i3+l)) - znode(nodel(i3+2))
gama(i3+l) = xnode(nodeI(i3+3)) - xnode(nodel(i3+2))
gama(i3+2) = xnode(nodel(i3+l)) - xnode(nodel(i3+3))
gama(i3+3) = xnode(nodel(i3+2)) - xnode(nodel(i3+l))
200 continue
c
c— Output basic grid information.
write (21,504) igrid,nelmx,ipt(0),nnmx,ipt(l),nmblk,ipt(26),nnstk,
+ ipt(2),nbw(l),nbw(2)
c
c— Output the boundary nodes for the case when the grid is generated.
If(igrid.ne.0)then
write (21,559)
write (21,560) 'Left boundary',(nbdL(i),i=l,nnver)
write (21,560) 'Right boundary',(nbdR(i),i=l,nnver)
write (21,560) 'Top boundary',(nbdT(i),i=l,nnhor)
write (21,560)'Bottomboundary',(nbdB(i),i=l,nnhor)
Endlf
c
c— Output nodel coordinates, and incidence list.
If(lprnt(l))Then
If(ipt(27).eq.O)Then
Write (21,505)
Else
Write (21,506)
Endlf
Do210i=l,ipt(l)
210 Write (21,507) i,xnode(i),znode(i)
Write (21,508)
Do220i = l,ipt(0)
i3 = 3*i
220 Write (21,509) i,nodel(i3-2),nodel(i3-l),nodel(i3),
+ matel(i),area(i)
Endlf
c
c— Generate grid based pointers.
ipt(40) = ipt(l)*2
ipt(4I) = ipt(l)*3
ipt(42) = ipt(l) * 4
ipt(43) = ipt(l)*5
ipt(44) = ipt(l) * 6
ipt(45) = ipt(l)*7
ipt(46) = ipt(l)*8
ipt(47) = ipt(l) * 9
ipt(48) = ipt(l) * 10
ipt(49) = ipt<2)*2
ipt(50) = ipt(2)*3
ipt(51) = ipt(2)*4
ipt(52) = ipt(2)*5
ipt(53) = ipt(2)*6
ipt(54) = ipt(2)*7
ipt(55) = ipt(2)*8
ipt(56) = ipt(2)*9
ipt(57) = ipt(2)*10
ipt(67) = ipt(0) * 2
ipt(68) = ipt(0) * 3
c
c====== COMPONENT CHEMICAL PROPERTIES =====
c
if(ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Component Chemical Properties'
c
c— Read the number of organic components.
c— Error check: ipt(l 5) must be nonnegan've.
c— Error check: If NAPL (lctrl(24)=t),sorption (lctrl(25)=t)> or
c— biodegradation (lctrl(3)=t) is considered ipt(15)>0,
call commnt (11,21)
read(ll,*)ipt(15)
if (ipt(15) .It. 0) Call ErrMessage (26,0,ipt(29))
if (ipt(15) .gt. ncmp) Call ErrMessage (43,0,ipt(29))
if (ipt(15) .eq. 0 .and. Ictrl(24)) Call ErrMessage (80,0,ipt(29))
if (ipt( 15) .eq. 0 .and. lctrl(25)) Call ErrMessage (87,0,ipt(29))
if (ipt(15) .eq. 0 .and. lctrl(3)) Call ErrMessage (88,0,ipt(29))
c
c— Read the organic component chemical properties.
c— Input units assumed: molecular weight (g/mole)
vapor pressure = arm
vapor viscosity = centipoise
liquid density = g/1
179
-------
c— vapor diffusivity = cm"2/s
c— liquid diffusivity = cm"2/s
c— henry's constant = arm I/g
c— aqueous solubility = g/l
c— Error checfc values must be nonegative except vapor pressure
c— and solubility.
call commnUt 1,21)
If(ipl05).gt.O)Thcn
Oo230i«l,ipKtS)
read (11,*) ic,cnameOc),cmvv(ic),cvp(ic),cvvis(ic)
+ ,cdcn(ic),cmdif(2*ic-l),cmdif(2*ic),chen(ic)
+ .casoKic)
if (Ic ,nc. i) Call ErrMessage (44,0,ipt(29))
if (cmw(ic),l(.zerO) Call ErrMessage (89,0,ipt(29))
If (cwis(ic).lt.zerO) Call ErrMessage (90,0,ipt(29))
if (cdcn(ic),lt.zerO) Call ErrMessage (91,0,ipt(29))
if (cmdif(2*ic-l).It.zctO) Call ErrMessage (92,0,ipt(29))
if (cmdif(2*ic),lt.zerO) Call ErrMessage (92,0,ipt(29))
if (chen(ic).lt.zerO) Call ErrMessage (93,0,ipt(29»
230 continue
c
c— If lprnl(27) is false, open an additional material balance output
c— file for each component.
dam cmb(l ),cmba),cmb(3),cmb(4),cmb(5),cmb(6),cmb(7),cmb(8)
+ ,mb<9),cmb(10)/'r,>2Y3Y4V5V6V7V8Y9','10>/
ifCncmp,gt,10) Cal! ErrMessage (I26,0,ipt(29))
call commntd 1,21)
if(lptm(6),»nd,.not.lpmt<27)) then
li = !ndex(oulprc,' ')-l
do22Si = l.ipt<15)
iii=index(cmb(i),")-l
otMfikKSti) = outpre(l :iiy/'.mb'//cmbCO(l :iii)
225 open (28+i,file=outfile(8+i),status='unknown')
writc<21,55S)
write(21,556)(cnarne(i),28+i,outfile(8+i),i=l,ipt(15))
end if
Endlf
c
c— Read chemical property data for water, oxygen, and nitrogen
c— Error cheek; values must be nonegative except vapor pressure
0— and solubility.
if (iplUSHS .gt. ncmp)Call ErrMessage (43,0,ipt(29))
call comnwl(l 1,21)
Do 240 i - ipt(15H-l,ip«15>+3
read(ll,*)ic,cnarnc(i),cmw(i),cvp(i),cvvisfO,cden(i),
4. cmdif(2»i-l),cmdif(2*i),chen(i),casol(i)
if (ic ,ne. i) Call ErrMessage (44,0,ipt(29))
if (cmw(ie).It.zerO) Call ErrMessage (89,0,ipt(29))
if (cvvis(ic).lt,zerO) Call ErrMessage (90,0,ipt(29))
if (cden(ic),It.zerO) Call ErrMessage (91,0,ipt(29))
if (cmdif(2*ic-l).H.zerO) Call ErrMessage (92,0,ipt(29))
if(cmdif(2*ic).U.zerO) Call ErrMessage (92,0,ipt(29»
if (chcn(ic),lt,zerO) Call ErrMessage (93,0,ipt(29))
240 continue
c
e— Error clieck: oxygen must be present in the aqueous phase when
c— biodcgradaiion is considered.
if(ktrl(3),and,casol(ipt(15>K2).It.0.dO)
+ Call ErrMessage (79,0,ipt(29))
c
c— Nutrient information:
c— Read a logical variable indicating if a nutrient
c— is 10 be modeled.
call commnt(l 1,21)
rttad(ll,*)lctrl(9)
c
e— Error check; Ictrl(3) = true for nutrient to be considered.
if (ktrl(9).and..noUctri(3)) Call ErrMessage (77,0,ipt(29))
C
c— If nutrient is modeled, then read the nutrient chemical properties.
c— Error check: values must be nonegative except vapor pressure.
istop = ipt(15) + 3
If(lctrl<9))Thcn
islop = istop + 1
if (istop .gt. ncmp) Call ErrMessage (43,0,ipt(29))
call commnt(l 1,21)
read (11,*) ic,cnamc(istop),cmw(istop),cvp(istop),
H- cwis(istop),cden(istop),cmdif(2*istop-l).
+ cmdif(2*istop),chen(istop),casol(istop)
if (ic .ne. istop) Call ErrMessage (44,0,ipt(29))
if (ic .ne. i) Call ErrMessage (44,0,ipt(29))
if (cmW(ic).lt.zerO) Call ErrMessage (89,0,ipt(29))
if (cvvis(ic).lt.zerO) Call ErrMessage (90,0,ipt(29))
if (cden(ic).lt.zerO) Call ErrMessage (91,0,ipt(29))
if (cmdif(2*ic-l).lt.zerO) Call EirMessage (92,0,ipt(29))
if (cmdif(2*ic).lt.zer0) Call ErrMessage (92,0,ipt(29))
if (chen(ic).It.zerO) Call ErrMessage (93,0,ipt(29))
- Error check: casol(nutrient) must be positive if Ictrl(9) = true.
if (casol(istop).lt.zerO) Call ErrMessage (78,0,ipt(29))
Endlf
ipt(65) = istop
ipt(66) = istop *ipt(l)
- Write component data.
Write (21,510) ipt(15)
Do 250 i = l,istop
Write (21,511) cname(i),i,cmw(i),cvp(i),cvvis(i),
+ cden(i),cmdif(2*i-1 ),cmdif(2*i),chen(i),casol(i)
250 continue
c— Adjust units.
;— Convert aqueous solubilities to mole ratios.
;— Convert all others to SI units.
cmwaq = cmw(ipt(15)+l)
do260i=l,istop
if(cvp(i).gt.rone) then
cvp(i) = chen(i) * casol(i)
else
cvp(i) = cvp(i) * patm ! vapor pressure = Pa
end if
casol(i) = casol(i)*cmwaq/(cmw(i)*cden(ipt(15)+l))
cmw(i) = cmw(i) * l.Od-3 ! molecular weight = kg/mole
cvvis(i) = cvvis© * 1 .Od-3 ! viscosity = Pa s
cmdif(2*:-l) = cmdif(2*i-l) * l.Od-4 ! diffusivity = m"2/s
cmdif(2*i) = cmdif(2*i) * l.Od-4
260 chen(i) = chen(i) * patm ! henry's constant = Pa m"3/kg
c
c==== MASS EXCHANGE INFORMATION =====
c
if(ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Mass Transfer Information'
C
C— Read the mass exchange coefficients for the various components
C— betweeen contiguous phases. If the mass exchange coefficient
C— for a given component and phase pair is zero, that component
C— does not partition between that phase pair. Exchange coefficients
C— are ordered aqueous/gas, aqueous/NAPL, gas/NAPL, aqueous/biophase,
C— and aqueous/solid.
C— Error Check: Component number must be between 1 and istop.
C
write (21,512)
do270i=l,istop
call commnt(l 1,21)
read (11,*) ic,kex(5*(ic-l)+l),kex(5*(ic-l)+2)
+ ,kex(5*(ic-l)+3),kex(5*(ic-l)+4),kex(5*(ic-l)+5)
read (11,*) ic,kmax(5*(ic-l)+l),kmax(5*(ic-l)+2)
+ ,kmax(5*(ic-l)+3),kmax(5*(ic-l)+4),kmax(5*(ic-l)+5)
if (ic.lt.l .or. ic.gt.istop) Call ErrMessage (45,0,ipt(29))
270 write (21,513) cname(ic),kex(5*(ic-l)+l),kex(5*(ic-l)+2)
+ ,kex(5*(ic-l)+3),kex(5*(ic-l)+4),kex(5*(ic-l)+5)
write (21,582)
do 275 i=l,istop
write (21,513) cname(i),kmax(5*(i-l)+l),kmax(5*(i-l)+2)
+ ,kmax(5*(i-l)+3),kmax(5*(i-l)+4),kmax(5*(i-l)+5)
do275ii = l,5
275 if(kmax(5*(i-1 )+ii).lt.0.050d0.or.kmax(5*(i-1 )-)-ii).gt.rone)
+ Call ErrMessage (134,0,ipt(29))
C
C— Create the pointer for phase compositions. First consider
C— the gas phase. Components are not included if their vapor
C— pressures are negative. ipt(3) is the number of components in
C— the gas phase and ipt(l 3) is the number of organic components in
C— the gas phase.
ipt(3)=0
ipt(13)=0
180
-------
do280i=l,istop
if(cvp(i).ge.zerO) then
ipt(3)=ipt(3)+l
icp(ipt(3))=i
end if
if(i.eq.ipt(15)) ipt(13)=ipt(3)
280 continue
c
c— Error check: if present gas phase must contain nitrogen.
if (ipt(3).gt.O .and. cvp(ipt(15)+3).lt.zerO)
+ Call En-Message (69,0,ipt(29))
C
C— Next consider the aqueous phase. Components are not included if
C— their aqueous solubilies are negative. ipt(4) is the number of
C— components in the aqueous phase and ipt(14) is the number of
C— organic components in the aqueous phase.
ipt(4)=0
ipt(14)=0
do290i=l,istop
if(casol(i).ge.zer0) then
ipt(4)=ipt(4)+l
icp(ipt(3)+ipt(4))=i
end if
if(i.eq.ipt(15))ipt(14)=ipt(4)
290 continue
c
c— Error check: if present aqueous phase must contain water,
if (ipt(4).gt.O .and. casol(ipt(15)+l).lt.zerO)
+ Call En-Message (70,0,ipt(29))
C
C— Next consider the organic phase if lctrl(24) = true. AH organic
C— components are included in the NAPL when present.
ipt(5) = 0
if(lctrl(24)) then
ipt(5)=ipt(15)
do300i=l,ipt(5)
icp(ipt(3)+ipt(4)+i)=i
300 continue
Endlf
C
C—• Next consider the solid phase. Sorpa'on is considered for all
C— organic component in the aqueous phase with nonzero aqueous/solid
C— exchange coefficients. ipt(6) is the number of components in the
C— solid phase. ipt(16) is the number of organic components in the
C— solid phase.
ipt(6)=0
ipt{16)=0
If(lctrl(25))Then
do310i=l,ipt(15)
if(kex(5*(i-l)+5).ne.zerO) then
ipt(6)=ipt(6)+l
icp(ipt(3)+ipt(4)+ipt(5)+i)=i
end if
if(i.eq.ipt(15)) ipt(16)=ipt(6)
310 continue
Endlf
C
C— Define pointers:
C— ipt(8) - start of gas phase component section -1
C— ipt(9) - start of aqueous phase component section -1
C— ipt(10) - start of organic phase component section -1
C— ipt(l 1) - start of solid phase component section -1
C— ipt( 12) - start of bio-phase component section - 1
ipt(8) =0
ipt(9) =ipt(8) + ipt(3)*ipt(l)
ipt(10) = ipt(9)-4-ipt(4)*ipt(l)
ipt(l 1) = ipt(lO) + ipt(5)*ipt(l)
ipt(12) = ipt(ll) + ipt(6)*ipt(l)
ipt(58) = ipt(3)-t-ipt(4)
ipt(59) = ipt(3) + ipt(4) + ipt(5)
ipt(60) = ipt(3) + ipt(4) + jpt(5) -t-ipt(6)
c
c==== MATERIAL PROPERTY BLOCK DATA =====
c
if(ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Material Property Block Data'
c
c— Read soil physical properties:
c— porosity (-); horizontal and vertical permeability (m**2);
c— bulk density (gm/1);
c—• organic carbon fractional content(-)
c— Error Check: block number=(0,ipt(26)); porosity=(0,l);
c— permeability>0; density>0; foc=(0,l);
call commnt (11,21)
Do340i = l,ipt(26)
Read (11,*) ii,bphi(ii),bpermh(ii),bpermv(ii),bsden(ii),
+ bfoc(ii)
If (ii.lt. I .or. ii.gt.ipt(26)) Call ErrMessage (27,0,ipt(29))
If (bphi(ii).lt.zerO .or. bphi(ii).gt.rone)
+ Call ErrMessage (28,0,ipt(29))
If (bpermh(ii).lt.zerO .or. bpermv(ii).lt.zerO)
+ Call ErrMessage (29,0,ipt(29))
If (bsden(ii).lt.zerO) Call ErrMessage (30,0,ipt(29))
If (bfoc(ii).lt.zerO .or. bfoc(ii).gt.rone)
+ Call ErrMessage (31,0,ipt(29))
340 continue
c
c— Read the water retention parameters:
c— residual water saturation(-); van Genuchten n value;
c— van Genuchten alpha value
c— Define the van Genuchten m value.
c—Error Check: block number=(0,ipt(26)); residual saturation=(0,l);
c— n value>0; alpha value>0.
call commnt (11,21)
Do350i = l,ipt(26)
Read (11,*) ii,bsrw(ii),bvgn(ii),bvga(ii)
If (ii.lt. 1 .or. ii.gt.ipt(26)) Call ErrMessage (27,0,ipt(29))
If (bsrw(ii).lt.zerO .or. bsrw(ii).gtrone)
+ Call ErrMessage (33,0,ipt(29))
If (bvgn(ii).lt.zerO) Call ErrMessage (34,0,ipt(29))
If (bvga(ii).lt.zerO) Call ErrMessage (35,0,ipt(29))
bvgm(ii) = rone - rone / bvgn(ii)
350 continue
c
c— Read the dispersion parameters:
c— longitudinal and transverse dispersivity (m).
c— Error Check: all parameters > 0.
call commnt (11,21)
Do 360 i = l,ipt(26)
Read (11,*) ii,bdisl(ii),bdist(ii)
If (ii.lt.l .or. ii.gt.ipt(26)) Call ErrMessage (27,0,ipt(29))
If (bdisl(ii).lt.zerO .or. bdist(ii).lt.zerO)
H- Call ErrMessage (36,0,ipt(29))
360 continue
c
c— Write the material, properties for each block.
write (21,514)
Do370i = l,ipt(26)
Write (21,515) i,bphi(i),bpermh(i),bpermv(i),bsden(i),bfoc(i),
+ bsrw(i),bvgn(i),bvga(i),
+ bdisl(i),bdist(i)
370 continue
c
===== DISPERSION TENSOR
- If lctrl(21) is true the hydrodynamic dispersion tensor is
- computed internally for all components. If lctrl(21) is false
c— read hydrodynamic dispersion tensor information directly. The
- hydrodynamic dispersion tensor is read for compound ic first
- for the gas phase and then for the aqueous phase on separate
- lines. Hydrodynamic dispersion tensors must be entered for all
c— components present when lctrl(21) is false. Units (m**2/sec).
if(ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Dispersion Parameters'
call commnt(l 1,21)
read(ll,*)lctrl(21)
write (21,580) lctrl(21)
call commnt(l 1,21)
if(.not.lctrl(21)) then
write (21,581)
do 380 i = 1, istop
call commnt(l 1,21)
read (11,*) ic, d(8*ic-7),d(8*ic-6),d(8*ic-5),d(8*ic-4)
read (11,*) ic, d(8*ic-3),d(8*ic-2),d(8*ic-l),d(8*ic)
write (21,585) cname(ic),'gas ',d(8*ic-7),d(8*ic-6)
181
-------
+ ,d 0; slow/fast fraction = (0,1)
If(ktr](19))Then
call commnl(l 1,21)
read (11,*) xbok, xbom, xkex, xden
if (xbok .It, zcrO) Call ErrMessage (39,0,ipt(29))
if (xbom ,lt. zerO) Call ErrMessage (40,0,ipt(29))
if (xdcn.lt.rxrO .or. xden.gt.rone)
+ Call ErrMessage (41,0,ipt(29))
ipt(60)-H
icp(ipt(3Hipt(4)+ipt(5)+ipt(6)) =
+ icp(ipl(3)+ipt(4)+ipt(5)+l)
Endlf
c
c — Read sorption parameters data:
c — Read for each material property block enter:
e — (1 ) the kf parameter values for each organic component in
c— order from 1 to the number of components:
c — units (micro gm)/(gm solid) with aqueous concentration
e— inmg/1;
c— • (2) the n parameter values order in the same way.
o — Error Check: Kf and n=l/m>0
call commntd 1,21)
do400UO,ipt(26)-l
read (1 1.*) ii,(bok((ii-l)*ipt(15)+j)o=l,ipt(15))
read (1 1,*) ii,(bom«ii-l)*iPt(15)+j)j=l,ipt(15))
400 continue
0,ipt(26)-l
do40Jj = J,ipt(15)
if (bok.(i*ipt(15)+j) ,U..zerO)
Call prrMessage (39,0,ipt(29))
401 if (bom(i*HM(I5)+j) .It. .zerO)
-H Call ErrMessage (40,0,ipt(29))
.— Write rate-limited .sorption parameters:
write (21,51.6) ! write sorpti.on.data
Pp410j = 0,ipt(26)-l
write (2J,517) j+J
write (21,5,18) ,{cnameg),bpk(i*ipt.(15)+j),cname(j),
bo.m.(i*jp.t(15)+j)j=J,ipt()5))
410 continue
If (lctrl( 19)) Then ! write two compartment data
write (21,519) xbok, xbom, xden, xkex
Endlf
Conversions:
C— Convert .units for sorption parameters. This assumes the input
;— values for JCf or Koc .are rnjcrograms/grarn (with aqueous
;— concentration in mg/I) .and bom is 1/m (unitless).
:— The converted Kf or Koc is in grams organic / gram solid.
do420i=ftipt(26)-l
do420j = l,ipt(15)
jf(bok(i*ipt(15)+j).ge.zerO) then
bok.(i*ipt(!5)+j) = bok(i*ipt(15)+j) * l.Od-6
bom(i*ipt(15)+j) = rone / bom(i*ipt(15)+j)
else if(bok(i*ipt(15)+j).!t.zerO) then
bok(i*ipt(15)+j) = -bok(i*ipt(15)+j)*1.0d-6*bfoc(i+l)
bom(i*ipt(15)+j) = rone
end jf
420 .contipue
C
C— Convert xbom to be consistent with bom.
if(lctrl(19)) xbom = rone/xbom
C
C— Initial the retardation factors to one when a separate solid
C— phase is considered.
do404i= l.istop
404 krtd(i) = rone
c
c— Read equilibrium sorption parameters (retardation factors).
Else
lctrl(19) = .false.
C
C— Read retardation factors if desired. Retardation factors
C— can only be used when nonequilibrium sorption is not
C— being considered. Retardation factors are input as
C— component number as input above and then the retardation
C— factor. Retardation pan be considered for oxygen or nutrient.
C
callcommnt(n,21)
read(ll,*)lretrd
call commnt( 11,21)
if(.not.lretrd) then
write(21,590)
do4p5i = l,istop
405 krtd(i) = rone
else
write(21,588)
do406i = l.istop
read(ll,*)ic,krtd(ic)
write(21,574) cname(ic),krtd(ic)
if(krtd(ic).lt.rone)
+ Call ErrMessage (128,l,ipt(29))
406 continue
end if
Endlf
c
c===== BIOLOGICAL PARAMETERS =====
c
c—This block read only if biotranformation eqs are solved.
If(lctrl(3))Then
if (ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Biological Parameters'
c
c— Read an integer indicating the number of organic components in
c— the biophase. The biophase always contains oxygen and nutrient
182
-------
c—if present.
c— Error Check: Ictrl(3) must be true if ipt(17)>0.
call commnt(l 1,21)
read(ll,*)ipt(17)
if (.not.lctrl(3) .and. ipt(17).gt.O)
+ Call ErrMessage (81,0,ipt(29))
if (ipt(17) .gt. ipt(15)) Call ErrMessage (130,l,ipt(29))
C
C— Biological parameters.
C— ipt(7) is the number of components in the bio-phase. The bio-phase
C— always includes oxygen and nutrient if present.
if(ipt(17).gt.O) then
if(lctrl(9))then
ipt(7) = ipt(17) + 2
icp(ipt(3)+ipt(4)+ipt(5)+ipt(6)+ipt(17)+2) = ipt(15) + 4
else
ipt(7) = ipt(17)-H
end if
icp(ipt(3)«pt(4)+ipt(5)+ipt(6)+ipt(17)-H) = ipt(15) -1- 2
c
c— Add the biomass as a component to the biophase.
c— Initial cname with"biomass".
ipt(7) = ipt(7)+l
icp(ipt(3)-t-ipt(4)+ipt(5)+ipt(6)+ipt(7)) = istop+1
cname(istop+l) = ' biomass '
else if(ipt(17).eq.O) then
ipt(7) = ipt(17)
end if
c
c— Generate pointer.
ipt(61) = ipt(3) + ipt(4) + ipt(5) + ipt(6) + ipt(7)
c
c— Read 2 logical biodegradation'control switches:
c— lctrl(17) indicates if a steady state biomass is to used;
c— Ictrl( 16) indicates biodegradation equations are modeled as a
c— sink term in the aqueous transport equations; otherwise their
c— modeled as rate-limited exchange to a separate biophase.
call commnt(l 1,21)
read (11,*) lctrl(17),lctri(16)
c
c— Determine the type of kinetics.
c— 1 - standard monod kinetics
c— 2 - monod kinetics with substrate inhibition
c— 3 - monod kinetics with lumped substrate inhibition
c— 4 - monod kinetics with saturation dependency
c— 5 - monod kinetics with saturation dependency and
c— substrate inhibition
if(lctrl(3)) then
call commntC 11,21)
read(ll,*)ipt(39)
c
c— Error Check: Current version restriction.
if (ipt(39).gt.2) call ErrMessage (68,l,ipt(29))
c
c— Read Monod parameters for each component of the biophase:
c— (1) component number
c— (2) electron acceptor use coefficient gm O2/gm substrate)
c— (3) nutrient use coefficient (gm n/gm substrate)
c— (4) maximum substrate use rate (gm substrate/gm biomass*sec)
c— (5) half saturation constant (gm substrate/1)
c— (6) yield coefficient (gm biomass/gm substrate)
c— (7) inhibition constant (unitless) expressed as a fraction of
c— the aqueous solubility. For substrate and nutrient this
c— turns off metabolism when the concentration is above this
c— threshold concentration and for electron acceptor this
c— turns off metabolism when the concentration is below this
c— threshold concentration. In both cases hyperbolic
c— functions are used.
c— Error Check: Component number must be defined; parameters values
c—• must be nonnegative.
ibpt = ipt(3)+ipt(4)+ipt(5)+ipt(6)
do430i=l,ipt(7)-l
call commnt(l 1,21)
read(ll,*)ic,fuse(ic),
+ fuse(ic+istop),umax(ic),
+ khalf(ic),xyield(ic),
+ kinhib(ic)
icp(ibpt+i) = ic
if (icp(ibpt-t-i).lt.O .or. icp(ibpt+i).gt.istop)
+ Call ErrMessage (45,0,ipt(29))
if(fuse(ic).lt.zerO)
+ Call ErrMessage (94,0,ipt(29))
if (fuse(ic+istop).lt.zerO)
+ Call ErrMessage (95,0,ipt(29))
if(umax(ic).It.zerO)
+ Call ErrMessage (96,0,ipt(29))
if(khalf(ic).lt.zerO)
+ Call ErrMessage (97,0,ipt(29))
if(xyield(ic).lt.zerO)
+ Call ErrMessage (98,0,ipt(29))
if(kinhib(ic).lt.zerO)
+ Call ErrMessage (99,0,ipt(29))
430 continue
c
c— Read five more bio parameters:
c— (1) decay coefficient (I/sec)
c— (2) minimum biomass (gm/1 media)
c— (3) maximum biomass (gm/1 media)
o— (4) initial uniform biomass (gm/1 media)
c— (5) delay period for initiation of bioreactions (sec)
c— Error Check: parameters must be nonnegative, initial biomass must
C— be between minimum and maximum biomass.
call commnt(l 1,21)
read (11,*) kd,xbmin,xbmax,xinit,t(ll)
if (kd.lt.zerO) Call ErrMessage (99,0,ipt(29))
do 441 i = 1, ipt(17)
441 if (9.990dO*kd.gt.umax(i)) Call ErrMessage (37,l,ipt(29))
if (xbmin.lt.zerO) Call ErrMessage (100,0,ipt(29))
if (xbmax.lt.zerO) Call ErrMessage (101,0,ipt(29))
if (xinit.lt.zerO) Call ErrMessage (102,0,ipt(29))
if (t(l l).lt.zerO) Call ErrMessage (103,0,ipt(29))
if (xinit.ltxbmin .or. xinit.gt.xbmax)
+ Call ErrMessage (104,0,ipt(29))
c
c— Write biological parameters.
write (21,520) ipt(17),lctrl(17),Ictrl(16),ipt(39),xinit
+ ,xbmin,xbmax,kd,t(ll)
Do440i = l,ipt(7)-l
write (21,521) cname(icp(ibpt+i)),fuse(icp(ibpt+i)),
+• fuse(icp(ibpt+i)+istop),umax(icp(ibpt+i)),
-I- khalf(icp(ibpt4-i)),xyield(icp(ibpt+i)),
+ kinhib(icp(ibpt+i))
440 continue
Endlf
c
c—• Bio eqs are not solved. Set control switches.
Else
ipt(17) = 0
ipt(7) = 0
lctrl(16) = .false.
ipt(61) = ipt(60)
-------
wrire<21, 523) 'Solid1, !pt(6)
wrfte<21,524)
write<21.523> 'MierobM',5pt<7)
K(ipl<7).st.O) «fte<41,S24)
,i=l ,ipt(6))
Convert Viscosity frOrn ePoise to Pa-s
wvis = rone / (wvis * 1 ttcl-3)
aaaaaaj. TEMPERATURE PARAMETERS
ifCi|X(29),iw.O) write Opt(29),*)
+ 'Reading Temperature Parameters'
c
c— Read a logical variable indicating if the temp dist is uniform.
callcommnt(l!,2I)
icad(n,*)tarl(10)
write (21,525) 1*1(10)
C
C— Read and Write the Uniform tcrnperarure distribution in
C ccmrigraJc.
c»Hcornmnt(ll,21)
tf(kttt(10)) theft
tead(U,*)ctemp
write (21,526) etcmp
do450i=4,ipt, — five paranie'ters feeW for 'every cofriponeft. rl
endif
ip't(89) = 5*ipt(88)
ii = 0
c
c — Loop '6Ver fee number of component's.
d6477ic = l,istop
write(21,570) cname(ic)
c
c — Read component vapor pressure.
call commnt(l 1,21)
read(ll,*) (dtemp(i+ii),i=l,ipt(86))
do 471 1 = ip'f(86),l,-l ! read nodal vapor pressure
if(igrid.eq.2) then
dtemp(Wi) = dtemp(i+ii)*'patm - cvp(ic)
else if (igrid.eq.l) 'then
•dternp(2*i-l+ii) = •dtenip(i+ii)*pa'tih - 'cvp(ic)
endif
471 continue
if(igrid.'eq.2) then
ii=ipt(86)4li
else if (igrid.eq. 1 ) then
ii = 2*ip't(8'6)-l+ii
endif
c
c — Read component vapor viscosity.
call commnt(l 1,21)
read(l 1,*) (dtemp(i+ii),i=l,ipt(86))
do472i = ipt(86),l,-l
if(igrid.eq.2) then
dtemp(i+ii) = dtemp(i+ii)*1.0d-3 - cvvis(ic)
else if (igrid.eq.l) then
dtemp(2*i-l+ii) = dtemp(i+ii)*1.0d-3 - cvvis(ic)
if(i.gt.l) dtemp(2*i-2+ii) = l.Od-3*
+ (dtemp(i+ii)+dtemp(i-H-ii))/2.0dO - cvvis(ic)
endif
472 continue
if(igrid.eq.2) then
ii=ipt(86)+ii
else if (igrid.eq.l) then
ii = 2*ipt(86)-l+ii
endif
c
c — Read component Henry's law coefficients.
callcommnt(ll,21)
read(l 1,*) (dtemp(i+ii),i=l,ipt(86))
do473i = ipt(86),l,-l
if(igrid.eq.2) then
dtemp(i+ii) = patm*dtemp(i+ii) - chen(ic)
else if (igrid.eq.l) then
184
-------
dtemp(2*i-l+ii) = patm*dtemp(i+ii) - chen(ic)
if(i.gt.l) dtemp(2*i-2+ii) = patm*
+ (dtemp(i+ii)+dtemp(i-l+ii))/2.0dO - chen(ic)
end if
473 continue
if(igrid.eq.2) then
ii=ipt(86)+ii
else if (igrid.eq.l) then
ii = 2*ipt(86)-l+ii
endif
c
c— Read component aqueous solubilities.
call commnt( 11,21)
read( 11 ,*) (dtemp(i+ii),i=l ,ipt(86))
cmwaq = cmw(ipt(15)+l)/(cmw(ic)*cden(ipt(15)+l))
do474i = ipt(86),l,-l
if(igrid.eq.2) then
dtemp(i+ii) = cmwaq*dtemp(i+ii) - casol(ic)
else if (igrid.eq.l) then
dtemp(2*i-l+ii) = cmwaq*dtemp(i+ii) - casol(ic)
if(i.gt.l) dtemp(2*i-2+ii) = cmwaq*
+ (dtemp(i+ii)+dtemp(i-l+ii))/2.0dO- casol(ic)
endif
474 continue
if(igrid.eq.2) then
ii=ipt(86)+ii
else if (igrid.eq.l) then
ii = 2*ipt(86)-l+ii
endif
c
c— Read component maximum substrate utilization rate.
call commnt(l 1,21)
read(ll,*)(dtemp(i+ii),i=l,ipt(86))
do 475 i = ipt(86),l,-l
if(igrid.eq.2) then
dtemp(i+ii) = dtemp(i+ii) - umax(ic)
else if (igrid.eq.l) then
dtemp(2*i-l+ii) = dtemp(i+ii) - umax(ic)
if(i.gt.l) dternp(2*i-2+ii)
+ = (dtemp(i+ii)+dtemp(i-1 +ii))/2.0dO - umax(ic)
endif
475 continue
if(igrid.eq.2) then
ii=ipt(86)+ii
else if (igrid.eq. 1) then
ii = 2*ipt(86)-l+ii
endif
do477ip=l,ipt(86)
write(21,571) zdepth(ip)
+ ,(dtemp(ip+ipp*ipt(88)+(ic-l)*ipt(89)),ipp=0,4)
477 continue
c
c— Read biomass decay rate.
call commntU 1,21)
write(21,572)
read(l 1,*) (dtemp(i+ii),i=l,ipt(86))
do 476 i = ipt(86), 1,-1
if(igrid.eq.2) then
dtemp(i+ii) = dtemp(i+ii) - kd
else if (igrid.eq.l) then
dtemp(2*i-l-t-ii) = dtemp(i+ii) - kd
if(i.gt.l) dtemp(2*i-2+ii)
+ =(dtemp(i+ii)+dtemp(i-l+ii))/2.0dO-kd
endif
476 continue
write(21,573) (zdepth(ip),dtemp(ip+istop*ipt(89)),ip=l ,ipt(86))
endif
c
c— Compute the gamma factor for computing mixture vapor viscosities.
c— Initialize gas phase viscosity if it is a constant.
lctrl(13) = .false.
if (ipt(3) .gt. l)then
lctrl(13) = .true.
do320node = l,ipt(l)
do320i=l,ipt(3)
ii = icp(i)
if(lctrl(10)) then
.cvvist = cvvis(ii)
else
cvvist = cvvis(ii)
+ + dtemp(ipt(88)+(ii-l)*ipt(89)+idepth(node))
endif
i3 = (i-1) * ipt(3) + (node-l)*ipt(3)*ipt(3)
do 320 j = l,ipt(3)
jj = icp(j)
if(lctrl(10)) then
cvvist2 = cvvis(jj)
else
cvvist2 = cvvis(jj)
+ + dtemp(ipt(88)+(jj-l)*ipt(89)+idepth(node))
endif
gamma(i3+j) = ((rone + dsqrt(cvvist/cvvist2) *
+ (cmw(ij)/cmw(ii))**0.250dO) ** 2) /
+ dsqrt(8.0dO * (rone + (cmw(jj)/cmw(ii))))
320, continue
else ! vapor viscosity is a constant
do330i = l,ipt(l)
if(lctrl(10)) then
cvvist = cvvis(icp(l))
else
cvvist = cvvis(icp(l))
+ + dtemp((icp(l)-l)*ipt(88)+idepth(i))
endif
vis(i) = rone / cvvist
330 continue
endif
c
c
= OUTPUT CONTROL PARAMETERS =====
if(ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Output Control Parameters'
c
c— Read a logical variable indicating if initial conditions
c— should be printed.
call commnt(l 1,21)
read(ll,*)Iprnt(3)
c
c— Initial print counters.
ipt(69) = 0
ipt(70) = 0
ipt(71) = 0
ipt(72) = 0
ipt(73) = 0
c
c—• Read and write print switches for specific variables:
call commntO 1,21)
iend = ipt(3) + ipt(4) + ipt(5) + ipt(6) + ipt(7)
do 4801 = 1,7
480 read(l 1 ,*) lprnt(i+7),lcon(i)
read(ll,*) lprnt(15),lcon(8)
if(lprnt(15).or.lcon(8))
+ read(ll,*) ipt(69),(icp(iend+i),i=l,ipt(69))
read(l 1,*) lprnt(16),lcon(9)
if(lprnt(16).or.lcon(9))
+ read(l 1,*) ipt(70),(icp(iend+ipt(69)+i),i=l,ipt(70))
read(l 1,*) lprnt(17),lcon(10)
if(lprnt(17).or.lcon(10))
+ read(l 1,*) ipt(71),(icp(iend-t-ipt(69)+ipt(70)+i),i=l,ipt(71))
read(l 1 ,*) Iprnt(l 8),lcon(l 1)
if(Iprnt(18).or.lcon(ll))read(ll,*)ipt(72)
+ ,(icp(iend+ipt(69)+ipt(70)+ipt(71 )+i),i=l ,ipt(72))
read(l 1,*) lpmt(19),lcon(12)
if(Iprnt(19).or.lcon(12)) read(ll,*) ipt(73)
+ ,(icp(iend+ipt(69)+ipt(70)+ipt(71)+ipt(72)+i),i=l,ipt(73))
read(l 1,*) lprnt(29),lcon(18) ! element TPH cocnentration
do 485 i = 13, 17
485 read(l 1 ,*) lprnt(i+7),lcon(i)
c
c— Setup pointers.
ipt(81) = 0
ipt(82) = 0
iend2 = ipt(69) + ipt(70) + ipt(71) + ipt(72) + ipt(73)
ipt(74) = iend2
call commnt(l 1,21)
read(ll,*)lplt(l)
,*) ipt(81),(icp(iend+2*iend2+i),i=l,2*ipt(81))
185
-------
call commnKi 1,21)
rcad(!I,*)lplt(2)
if then
do495i = l,2*ipt(82),2
c- Error check: node numbers for time series input must be within
c- domain.
if(icp(iend+2*iehd2+2*ipt(8 1 )+i+l ).It.O
.or.icp(iend+2*iend2+2*ipt(81)+i-t-l).gt.ipt(l))
call ErrMessage (125,l,ipt(29»
495 write(21,547) cname(icp(iend4-2*iend2+2*ipt(81)+i))
+ ,icp(fend4-2*iend2+2*ipt(81)4-i+l)
end if
iadd=l
iadd2 = 1
if(ipt(69).gt.O) then
ii = 0
do 600 i = l,ipt(3)
if((icp(i).eq.icp(iend+iadd)).and.(ii.le.ipt(69)))then
ii = ii + 1
icp(iend+iend2+iadd) = (i-l)*ipt(l)
iadd = iadd + 1
end if
600 continue
end if
if(ipt(81).gt.O) then
ii = 0
do60ii=l,ipt(3)
if((icp(i).eq.icp(iend+2*iend2+iadd2))
+ .and.(ii.le.ipt(81)))thert
ii = ii + 1
icp(iend+2*iend2+iadd2+ 1 )
+ = (i- 1 )*ipt(l )+icp(iend+2*iend2+iadd2+ 1 )
iadd2 = iadd2 + 2
end if
601 continue
end if
if(ipt(70).gt.O) then
ii = 0
do 605 i = l+ipt(3),ipt(3)+ipt(4)
if((icp(i).eq.icp(iend+iadd)).and.
+ (ii-ipt(3).le.ipt(70))) then
ii = ii -t- 1
icp(iend+iend2+iadd) = (i-l)*ipt(l)
iadd = iadd + 1
end if
605 continue
end if
if(ipt(82).gt.O) then
ii = 0
do 606 i = l+ipt(3),ipt(3)+ipt(4)
if((icp(i).eq.icp(iend+2*iend2+iadd2))
+ .and.(ii-ipt(3).le.ipt(82))) then
ii = ii + 1
icpfiend+2*iend2+iadd2+l )
+ = (i-l)*ipt(l)+icp(iend+2*iend2+iadd2+l)
iadd2 = iadd2 + 2
end if
606 continue
end if
if(ipt(71).gt.0)then
ii = 0
do 610 i = l+ipt(3)+ipt(4),ipt(3)+ipt(4)+ipt(5)
if((icp(i).eq.icp(iend+iadd)).and.
+ (ii-ipt(3)-ipt(4).le.ipt(7 1 ))) then
icp(iend+iend2+iadd) = (i-
iadd = iadd + 1
end if
610 continue
end if
if(ipt(72).gt.O) then
ii = 0
do 615 i = l+ipt(3)+ipt(4)+ipt(5),ipt(3)+ipt(4)+ipt(5)+ipt(6)
if((icp(i).eq.icp(iend+iadd)).and.
+ (ii-ipt(3)-ipt(4)-ipt(5).le.ipt(72))) then
ii = ii + l
icp(iend+iend2+iadd) = (i-l)*ipt(l)
iadd = iadd + 1
end if
615 continue
186
-------
end if
if(ipt(73).gt.O) then
ii=0
do 620 i = l+ipt(3)+ipt(4)+ipt(5)+ipt(6),
+ ipt(3)+ipt(4)+ipt(5)+ipt(6)+ipt(7)
if((icp(i).eq.icp(iend+iadd)).and.
+ (ii-ipt(3)-ipt(4)-ipt(5)-ipt(6).le.ipt(73))) then
ii = ii -I-1
icp(iend+iend2+iadd) = (i-l)*ipt(l)
iadd = iadd + 1
end if
620 continue
end if
c
c— Error check: contour file must be opened if any Icon is true.
do 625 i= 1,17
625 if (lcon(i).and..not.lctrl(23)) call ErrMessage (106,0,ipt(29))
c
c— Error check: time series file must be opened if any Iplt is true.
do 630 i = 1,2
630 if (lplt(i).and..not.lctrl(15)) call ErrMessage (123,0,ipt(29))
return
c
c— formats
500 format (76('*')/76('*')/
+' MISER7
+' Michigan Soil vapor Extraction Remediation model'
+• ' Project directed by: L.M. Abriola'
+ ' Written by: J.R. Lang and K.M. Rathfelder'
+' Beta Version 1.0; May 1,1996'
+ 76('*')/76('*'))
501 format ('INPUT AND OUTPUT FILES ',53('=')/
+ ' Main input file; control and field data: (unit Il) = ',a20/
+ ' Input file #2; ICs and BCs: (unit 13) =',a20/
+' Error and warning message input data: (unit 14) = ',a20/
+ ' Main output file: (unit 21) =',a20/
+ ' Error messages: (unit 22) = ',a20/
+ ' Performance Output: (unit 23) = ',a20/
+ ' Contour plot data: (unit 24) = ',a20/
+ ' Material balance information: (unit 25) = ',a20/
+ ' Time series plot data: (unit 26) = ',a20/
+ ' Restart data: (unit27) = ',a20)
502 format (/'GENERAL MODEL CONTROL OPTIONS ',46('=')/
+' Domain configuration (0=xz,l=rz): ipt(27) = ',i5/
-t-' Gravitational constant (m/s"2)-horizontal:t(21) =',e!2.4/
+•' Gravitational constant (m/s"2)-vertical: t(22) = ',e!2.4/
+ ' Solve transient phase balance: lctrl(l) =',15/
+ ' Skip ipt(85) time steps for phase blnce: ipt(85) = ',i5/
+' Solve transient component balance: lctrl(2) = ',15/
+' Solve NAPL equations: lctrl(24) = ',15/
+ ' Solve solid phase equations: lctrl(25) = ',15/
+ ' Solve biophase equations: lctrl(3) = ',15/
+ ' Lump the phase balance mass matrix: lctrl(7) = ',I5/
+ ' Lump the component balance mass matrix: lctrl(8) = ',I5/
+ ' Include phase mass exchange in flow eqs: lctrl(14) =',15/
-1-' Calculate element dimensionless numbers: lctrl(4) =',I5)
503 format ( /'TIME STEP/ITERATION CONTROL OPTIONS ',40('=')/
+ ' Initial simulation time (sec): t(l) =',e!2.4/
+ ' Final simulation time (sec): t(2) =',e!2.4/
+ ' Time weighting factor: t(10) =',e!2.4/
+ ' Maximum number of time steps: ipt(30) =',112 /
+ ' Convergence tolerance for pressure: t(13) =',e!2.4/
H-' Convergence tolerance for concentration: t(14) =',e!2.4/
+ ' Convergence tolerance for NAPL saturation:t(l5) =',e!2.4/
+•' Convergence tolerance for immobile phases:t(16) = ',e!2.4/
•)•' Initial time step: t(3) =',e!2.4/
+ ' Minimum time step: t(4) =',e!2.4/
+ ' Maximum time step: t(5) =',e!2.4/
+ ' Maximum phase balance iterations: ipt(31) =',i5 /
+ ' Maximum component balance iterations: ipt(32) =',i5 /
+ ' Maximum NAPL saturation iterations: ipt(33) =',i5 /
+ ' Minimum phase balance iterations: ipt(34) =',i5 /
+ ' Minimum component balance iterations: ipt(35) =',i5 / -
+ ' Time step multiplier for amplification: t(6) =',e!2.47
+ ' Time step multiplier for reduction: t(7) =',e!2.4)
504 format(/'GRID INFORMATION ',59('=')7
+ ' Generate grid: igrid =',i5 /
+ ' 0 = don"t generate the grid; 7
+ ' 1 = generate a union jack grid;'/
+' 2 = generate a herring bone grid.'/
+ ' Maximum dimension for number of elements: nelmx =',i5 /
+ ' Actual number of elements: ipt(0) =',i5 /
+ ' Maximum dimension for number of nodes: nnmx =',i5 /
+ ' Actual number of nodes: ipt(l) =',i5 /
+ ' Maximum dimension for the number of'/
+' material property blocks: nmblk = ',i5 /
+ ' Number of material property blocks: ipt(26) =',i5 /
H-' Maximum dimension for the number of 7
+ ' nodal variables in stacked storg: nnstk = ',i5 /
+ ' Actual number of stacked nodal variables: ipt(2) =',i5 /
+ ' Full bandwidth of transport matrix: nbw(l) =',i5 /
+ ' Full bandwidth of flow matrix: nbw(2) =',i5 )
505 format(
+ ' Nodal Coordinates in the cross-sectional (xz) domain:'/
+' Node Number X-Location Z-Location' )
506 format(
+ ' Nodal Coordinates in the radial-vertical (rz) domain:'/
+ ' Node Number R-Location Z-Location' )
507 format(6x,i5,9x,el4.5,6x,el4.5)
508 format(
•f' Element Information:'/
+ ' Element Number Nodal Incidence List ',
+'Material Block Area(m"2)')
509 format(6x,i5,12x,3i5,8x,i5,6x,el4.4)
510 format(/'COMPONENT CHEMICAL PROPERTY DATA ',43('=')/
+ ' Number of organic components: ipt(15) =',i5 )
511 format(
+' Component chemical property data for: ',a/
+' Component number: = ',i5/
+ ' Molecular weight (g/mole): =',e!2.4/
+ ' Vapor pressure (arm): =',e!2.4/
+ ' Vapor viscosity (cPoise): =',e!2.4/
+' Liquid density (g/1): = ',e!2.4/
+' Gas diffusivity (cm"2/s): = ',e!2.4/
+' Aqueous diffusivity (cm"2/s): = ',e!2.4/
+ ' Henry's Law constant (atml/g): =',e!2.4/
+' Aqueous solubility (g/1): = ',e!2.4)
512 format(/'MASS EXCHANGE COEFFICIENTS ',49('=')/2x,
+ ' Component Aqueous/gas Aqueous/NAPL Gas/NAPL'
+ ,' Bio/Aqueous Solid/Aqueous')
513 format(2x,alO,5e!2.4)
582 format(/'MINIMUM DEVIATION FROM EQUILIBRIUM ',41('=')/2x,
+' Component Aqueous/gas Aqueous/NAPL Gas/NAPL'
+ ,' Bio/Aqueous Solid/Aqueous')
514 format(/'MATERIAL BLOCK PROPERTY DATA ',47('='))
515 format(
+ ' Material Block Number: ',i5/
+' Porosity: = ',e!2.4/
+' Horizontal permeability (m"2): = ',e!2.4/
+•' Vertical permeability (m"2): = ',e!2.4/
+ ' Bulk soil density (gm/cm"3): = ',e!2.4/
+' Organic carbon content: = ',e!2.4/
+ ' Residual water saturation: =',e!2.4/
+ ' van Genuchten n for air/water retention data: =',e!2.4/
+ ' van Genuchten alpha value (I/Pa): =',e!2.4/
+' longitudinal dispersivity (m): = ',e!2.4/
+ * transverse dispersivity (m): =',e!2.4)
580 format(/'HYDRODYNAMIC DISPERSION TENSOR INFORMA-
TION ',33('=')/
+ ' Compute hydrodynamic dispersion tensor: lctrl(21) =',15)
581 format(
+' Input values of hydrodynamic dispersion:'/
+ ' component phase',7x,'dir,9x,'dl2',9x,'d21',9x,'d22')
585 format(al2,all,4el2.4)
589 format(/'SORPTION PARAMETERS ',56('='))
516 format(
+' Isotherm parameters')
517 format(
+ ' Material Block Number ',15)
518 format(
+ ' Kf (micrograms/gram-solid) for: ',aIO,' =',e!2.4/
187
-------
+ ' m parameter (unitlcss) for: ',alO,' =',e!2.4)
519 format(
+ * Two Compartment Model is in use'/
+ ' §Iow to fast compartment Kf multiplier: =',e!2.4/
•»•* Slow to fast compartment m multiplier: = ',el2.4/
•»•' Fast compartment fraction of solid phase: = ',e!2.4/
+ * Slow to fast compartment exchange multiplier: = ',e!2.4)
588 format{ . , •,.
+' Retardation is considered for the following components')
590 formatC
+' Socption is not considered for this simulation')
574 format(
+ ' Retardation factor for:',a!0 ,' =',e!2.4)
520 formalC/'BIOLOGlCAL PARAMETERS ',54('=')/
+ ' Number of degradable organic components: ipt(17) =',i5/
+ ' Steady state biomass is assumed: Ictrl(17) =',157
+ * Biophasc mass transfer is at equilibrium: lctrl(16) = ',I5/
+ ' Degradation kinetics: ipt(39) =',i5/
+' 1 = standard Monod kinetics'/
+ ' 2 = Monod kinetics with substrate inhibition'/
•*•' 3 * Monod kinetics with lumped substrate inhibition'/
+ • 4s Monod kinetics with saturation dependency'/
+•' 5s monod kinetics with saturation dependency and'/
+' substrate inhibition'/
+ ' Initial uniform biomass (g/1): xinit =',e!2.4/
•f' Minimum biomass (g/1): xbmin =',e!2.4/
+ ' Maximum biomass (g/1): xbmax =',e!2.4/
+ ' Decay coefficient (I/sec): kd =',e!2.4/
+ ' Delay period for bioreaction (sec): 1(11) =',e!2.4)
521 formaK
•(•' Component biological parameter data for: ',ai
+ ' Oxygen Use coefficient (gmO2/gm substrate): =',e!2.4/
+ ' Nutrient Use coefficient (gm n/gm substrate): =',el2.4/
+ ' Maximum substrate use rate (gm/(gm cell sec)): =',e!2.4/
+' Half saturation constant (gm substrate/1): = ',e!2.4/
•t-' Yield coefficient (gm cell/gm substrate): =',e!2.4/
•t-* Inhibition multiplier: =',e!2.4)
522 focmatf/PHASE PARAMETERS AND COMPOSITION ',43('=')/
+ ' Water phase viscosity (cPoise): wvis =',e!2.4/
+ ' Include Klinkenberg effect: lctrl(20) =',15/
+' Klinkenberg parameter (compute if b=<0)): b = ',e!2.4)
523 format(2x,a,' Phase has ',12,' components listed below:')
524 rormat(6x,7»10) „ , ,
525 formaK/'TEMPERATURE DISTRIBUTION ',51('=')/
+•' Constant temperature distribution: lctrl(lO) =',15)
526 formatC
+ ' Uniform temperature (degreeC): ctemp =',e!2.4)
527 format(
+' Temperature distribution (node number; temperature)')
528 format(4(i5,':',ell.5,lx))
570 formatC/' Temperature dependent parameters for: ',alO/
+' dcpth',7x,'cvp',10x,'cvvis',8x,'chen',9x,'casor,8x,'umax')
571 format(6(cl2.5,lx))
572 fonnat(/
+' Temperature dependent decay coefficient (depth; kd)')
573 farmat(3(cl2.5,':',eI2,5,lx))
529 format (/'PRINTING INTERVAL VARIABLES ',48('=')/
4- "The print interval h set by time steps: ipt(25) =',i5)
530 formal (/-PRINTING INTERVAL VARIABLES ',48('=')/
+ 'Tlie print interval is set by time units: t(12) =',e!2.4)
531 format ('PRINTING CONTROL VARIABLES ',49('=')/
+' Generate output for the selected items' /
+•' Output in molar form: lprnt(8) =',15 /
+ ' Gas phase pressure: lprnt(9) =',15 /
+' Aqueous phase pressure: Iprnt(lO) = ',15 /
+ ' Gas/aqueous capillary pressure: lprnt(l 1) =',15 /
+ ' Gas phase density: lprnt(12) = ',15 /
+ ' Aqueous phase density: lprnt(13) =',15 /
+ ' NAPL density: lprnt(14) =',15 )
532 format (
+ ' Gas phase components: lprnt(15) = ',I5 )
533 formaU
,+ ' Aq'ueoiis phase components: Iprnt(16) =',15 )
534 format {.,-..
-(•', NAPL components': lphit(17) =',15 )
535 format ( . .. .. ,.
', Solid phase loadings: lprnt(18) =',15 )
536 forrnaU . _. . t: .,,,., _,._ r
+ ' Bio-phase components: lpjcnt(19)' = ',15,/
+ '. Total organic soif concentration lprnt(29") =',15 )
537 format ( , .. „ ,
+ ' Gas phase saturation: , IprnfpO) =',15 /,
+ ' Aqueous phase saturation: „ lprnt(2l) = ',15 /
+•' ti&PL saturation: lprnt(22)'=',15 /
+' Gas phase D'aircy velocity: Iprnt(23) = ',15 /
+ ' Aqueous phase Darcy velocity: lprnt(24) =',15 )
538 format (' Generate contour files for the selected items' /
+ ' Contour in molar form: lcon(l) =',15/
+ ' Gas phase pressure: lcon(2) =',15/
+ ' Aqueous phase pressure: Icori(3), =', 15/
+' 0as/acjueous capillary pressure: jcpri(4) =', 15 /
-i-' tSs phase density:, lcon(5 j. =', 15 /
+ ' ^quebus^hase clerisiiy: , lcon(6) =', 15 /
+ ' NAPL density: lcbn(7) =',15)
539 format (. ,,,,,..,
+ ' . Gas phase compbiierits: lcori(8) =',15)
540 format (
+ ' Aqueous phase components: lcon(9) =',15)
541 format (
+ ' NAPL components: lcon(10) =',15)
542 format (
+' Solid phase loadings: lcon( 11) =', 15)
543 format (
+ ' Bio-phase components: lcon(12) =', 15 /
+ ' Total organic soil concentration lcon(18) =',15 )
544 format (
+ ' Gas phase saturation: lcon(13) =',15/
+ ' Aqueous phase saturation: lcon(14) =', 15 /
+ ' NAPL saturation: . lcon(15) =', 15 /
+ ' Gas phase Darcy velocity: lcon(lfi) =', 15 /
+ ' Aqueous phase Darcy velocity: Icon(17) =',15)
545 format (5x,7alty ...,..,,,, i.
546 forrnat(' tieiierate time series files for the s.elected items ' /
+ ', ..Gas phase components: lplt(l) = MS )
547 fbnria't(
+ ' ',alO,'at node number',! 10 )
548 formatC
+' Aqueous phase components: lplt(2) = ', 15)
549 formate
+ 'Mass balance print interval in time steps: ipt(83) =',i5)
550 format (
+' Mass balance print interval is time units: t(27) = ',e!2.4)
551 formate
-1-' time series print interval in time steps: ipte84) =',i5)
552 formate . .
+ ' Time series print interval in time units: te28) = ',e!2.4)
553 format (
+ ' Material balance output in report form')
554 format(
+ ' Material balance output in time series form')
555 format e/'OUTPUT FILES FOR COMPONENT MASS BALANCE',37('='»
556 formate
+ ' ',alO,' (unit',i2,') = ',a20)
557 format(
+ ' Time series output in mole fractions')
558 format(
+' Time series output in concentrations')
559 formate
+ ' Boundary nodes of the generated grid:')
560 format(5x,a/50eiOx,10i6/))
end
188
-------
Subroutine - input2.f
c-
c
c
c
c
c
c
c-
INPUT2.f - Subroutine which reads the initial and boundary
conditions from device 13 and writes to device 21.
This routine is written so that data2 can serve as
a restart file generated by an option in datal.
C
C-
c
c
c-
c
subroutine INPUT2
include 'dimenjnc'
character*20innle(4),outpre,outfile(8-l-ncmp)
character* 10 cname(ncmp) :
common /cbl/ matel(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3), .;
+ matpt(nn6)
common /cblc/ xnode(nnmx),znode(nnmx),rbar(nelmx),area(nelmx)
common /cb2/ p(nn3)
common /cb2c/ q(ne!4)
common /cb2d/ pmwO(nnmx),denO(nnmx)
common /cb3/ sat(nnstk3)
common /cbSa/ bphi(nmblk),bpermh(nmblk),bpermv(nmblk)
common /cbSb/ bvgn(nmblk),bvga(nmblk),bvgm(nmblk),bsrw(nmblk)
common /cb6b/ por(nelmx),srw(nnstk)
common /cb6c/ temp(nnmx)
common /cb6d/ dtemp(nzmax6),idepth(nnmx)
common /cb7b/ cmw(ncmp),cvp(ncmp),cden(ncmp),
+ chen(ncmp),casol(ncmp),cmdif(ncmp2)
common /cbS/ vis(nnmx),pmw(nn3)
common /cb9/ xmf(nmf)
common /cblO/ den(nn6)
common/cbl I/pex(nnslO),rxnp(nn2)
common /cb30/ ibc(nnmx)
common/cb31/source(nn2)
common /cb64/ bok(nbcmp),bom(nbcmp),krtd(ncmp)
common /cb84/ ibcxmf(nmbc),bcxmf(nmbc),dfxmf(nmbc)
Common/cb86/strl(ncmpp5),str0(ncmpp5),cmf(ncmpp5),csink(ncmpp5)
+ ,cwsink(ncmpp5),csflux(ncmpp5),cmass 1 (ncmp5),cmassO(ncmp5)
+ ,cphex(ncmpp5),crsink(ncmpp5),tmass 1 .tmassO
common /cb90/ infile,outpre,outfile
common /cb91/ cname
Dimension local arrays.
dimension omfel(ncmp),soel(nelmx),iel(nelmx)
Zero vectors and define local pointers.
if(ipt(29).ne.O) write (ipt(29),*)
+ 'Reading from Input File',infile(2)
lcsat=.false.
lprnt(3)=.true.
do 80 i= l,(ipt(3Hipt(4Hipt(5>Mpt(6)+ipt(7))*ipt(l)
80 xmf(i)=zerO
do 81 i= l,(ipt(3)+ipt(4))*ipt(l)
ibcxmf(i)=0
dfxmf(i)=zerO
81 bcxmf(i)=zerO
do85i = l,3*ipt(2)
sat(i) = zerO
85 continue
ipt02=2*ipt(0)
ipt03=3*ipt(0)
ipt!2=2*ipt(l)
ipt!3=3*ipt(l)
ipt22=2*ipt(2)
== RESTART INFORMATION ===
if(ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Restart Information'
c
c— Read two logical variables. Lctrl(26) indicates if this run
C— is a restart and lctrl(32) indicates whether the run is a
C— continuation of the previous run (lctrl(32)=t) or
C— is a new run using the previous run as initial conditions
C— (setting lctrl(32)=f resets the cumulative mass balance).
C
lctrl(32) = .false.
call commnt(13,21)
read(13,*) lctrl(26), lctrl(32)
if(lctr!(26))then
callcommnt(13,21)
read(13,*) infile(4)
open(28,nle=infile(4),status='unknown')
else
infile(4) = 'none opened'
endif
write(21,550)lctri(26),innle(4),lctrl(32)
= INITIAL PRESSURE INFORMATION ===
if(ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Initial Pressure Information'
c
c— Read an integer control variable (ipt(75)) indicating how the
c—• initial pressure distribution is to be input:
c 1 = Compute initial pressure distribution assuming Pg = 1 arm
c and Pa is hydrostatic referenced to atmospheric pressure
c at the water table. The water table is assumed to be flat;
c 2 = Input gas and aqueous pressures at all nodes;
c 3 = Assume gas and aqueous pressures are atmospheric and input
c the Darcy velocity and saturations for both the aqueous
c and gas phases. This option can only be used if the
c phase mass balance equations are not solved.
c Note: ipt(75)=3 is not a general option but is retained for
c for column simulations.
c— Error Check: ipt(75)=(l-3);
c— Write header information.
write (21,499)
call commnt(13,21)
read(13,*)ipt(75)
if (ipt(75).lt.l .or. ipt(75).gt.3) call ErrMessage (48,0,ipt(29))
write (21,500) ipt(75)
c
o— If ipt(75) = 1, then read the depth to the water table (m).
c— Compute the initial pressure distribution.
c— All pressures are gauge pressures in Pascals.
c— Write to output file.
If(ipt(75).eq. l)Then
if (ipt(29).ne.O) write (ipt(29),*)
+ 'Computing Initial Pressure Distribution'
callcommnt(13,21)
read(13,*)wtdpth
c
c— Estimate a gas phase density. Do not consider NAPL effects.
Do86i = l,ipt(l)
gmw = zerO
vpn = rone
do 87 ic = ipt(15)+l, ipt(15)+2
if(cvp(ic).gt.zerO) then
if(lctrl(10)) then
cvpt = cvp(ic)
else
cvpt = cvp(ic) + dtemp((ic-l)*ipt(89)+idepth(i))
endif
gmw = gmw + cvpt*cmw(ic)/patm
vpn = vpn - cvpt/patm
end if
87 continue
gmw = gmw + vpn * cmw(ipt(15)+3)
gmden = gmw * patm / r
gden = gmden / temp(i)
C
C—• Use Hubbert's Potential to set initial gas phase pressure.
C
pwtble = patm * (dexp(wtdpth*gden*t(22)/patm>rone)
if(znode(i).ge.wtdpth) then
p(ipt(l>i-i) = pwtble
+ + cden(ipt(15)+l) * t(22) * (znode(i)-wtdpth)
189
-------
86
else if(znodc(i),lt.wtdplh) then
p(i) = patm * (dexp(znode(i)*gden*t(22)/patm)-rone)
p(ipt(l)+i) = cdcn(tpt(15>tl) * t(22) * (znode(i)-wtdpth)
•j-pwlble
end if
continue
write (21,501) wtdpth
Endif
c— Otherwise if ipt{75) = 2, then read in initial water and gas phase
c— at all nodes,
c — One node per line, followed by water and air pressure.
c — Output all user input pressures (Pa gauge).
If(ipt(75),cq,2)Then
callcommnt(13,21)
Read (13,*) nd
Backspace 13
If (nd .11.0) Then
Read (1 3,*) nd, paq,pgas
EndDo
Else
Doi«Upt(l)
Read (13,*)nd,pOpt(l)+nd),p(nd)
EndDo
Endlf
write (21, 502)
write (21,503) (nd,p(ipt(lHnd),p(nd),nd=l,ipt(l))
Endlf
c
c — Foript(75)=3, set pressures to atmospheric conditions
lf{ipt(75),cq.3)Then
p(i) s zcrO
EndDo
Endlf
c
c— Compute initial capillary pressures.
EndDo
c
CKBMMOO.S INITIAL VELOCITY INFORMATION =
C
if (ipt(29).nc.O) write (ipt(29),*)
+ 'Reading Darcy Velocity Computation Information'
c
c— Element or nodal Darcy velocities. Read a logical variable
c— Indicating if velocities are discretized on an elemental or nodal
c— basis,
call commnt (13,21)
rcad(13,*)lctrl(18)
Write (21,504) ktrl(18)
c
c— Darcy velocity compulation approach:
c— If kttl( 1) is true then Darey velocities are determined from
c— transient pressure distributions. Write message.
lf(lcltl(l))Then
write (21,505)
Endlf
e— If lclrl(l) is false then the Darcy velocity distribution is
c—constant. Read a logical variable indicating if steady state Darcy
c—velocities are computed from the pressure field.
Icssv = .false.
lf(,not.lcirl(I))Then
call commnt (13,21)
read(13,*)Icssv
Endlf
e
c— Compute the SS Darcy velocities from input pressures when
c— letil(l )=F and kssv - true
If («not,lctrl(l) .and. Icssv) Then
write (21,506)
call VEL
Endif
_ - Read in SS Darcy velocities when lctrl(l)=F and lcssv=false.
c— First determine if Darcy velocity components are uniform. If yes,
c— then read only the 4 components, otherwise read the 4 components
• for all nodes or elements depending on the selected computation
- method.
lev =.false.
If (.not.lctrl(l) .and. .not.lcssv) Then
write (21,507)
call .commnt (13,21)
read (13,*) lev
call commnt (13,21)
If (lev) Then
read (13,*) qgx,qgz,qax,qaz
IfOctrl(18))Then
Doi = i,ipt('l)
q(i) = qgx
q(i*-iptl2) = qax
q(i+ipt!3) = qaz
EndDo
•Else
Doi-l,ipt(0)
q(i) = .qgx
q(i+ipt(0)) = qgz
q(i+ipt02) = qax
q(i+ipt03) = qaz
EndDo
Endif
Else
If(lctrl(18))Then
Doi = l,ipt(l)
read (13,*) i,q(i),q(i+ipt(l)),q(i-Hptl2),q(i+iptl3)
EndDo
Else
Doi = l,ipt(0)
read (13,*) i,q(i),q(i+ipt(0)),q(i+ipt02),q(i+ipt03)
EndDo
Endif
Endif
Endlf
c
c — Write the steady state velocity components (m/sec).
If(.not.lctrl(l))Then
If (lev) Then
write'(21,508) qgx,qgz,qax,qaz
Else
If(lctrl(18))Then
write<2.1,S09)
write (21,51 l).(i,qffl,q(i+ipt(l)),q(WptJ2),
Else
write (21,510)
write«(21,51 1) (i,q(i),q(Mpt(0)),q(i4:ipt02),
+ q(i+ipt03),i=l,ipt(0))
Endif
Endlf
Endif
c
c — Read mobile phase saturations if ipt(75)=3.
c — Note: This is not a general option but is retained for column
c — simulations. Saturations are never stacked for this case.
c — Icsat indicates uniform mobile phase saturations (true).
If (.not.Ictrl(l) .and. ipt(75).eq.3) Then
call commnt (13,21)
read(13,*) Icsat
call commnt (13,21)
If (Icsat) Then
read(13,*) sat(l),sat(l+ipt(l))
Doi = 2,ipt(l)
sat(i) = sat(l)
sat(i+ipt(l)) = sat(l+ipt(l))
EndDo
Else
Doi = l,ipt(l)
read(1 3,*) ii,s
190
-------
EndDo
Endlf
Endlf
c
c======= NAPL SATURATION AND COMPOSITION =====
c
if (ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Initial NAPL Saturation and Composition Data'
c
c — Read the number of elements containing NAPL.
c — A number less than zero indicates that a NAPL saturation is
c — uniform and contained in all elements
c — Error check: inoel<=ipt(0)
c — Print header
call commnt (13,21)
read (13,*) inoel
If (inoel .gt. ipt(0)) call ErrMessage (49,0,ipt(29))'
write (21, 5 12)
c
c — If no NAPL present, print message.
If (inoel .eq.O) write (21,513)
c
c — Error check: lctrl(24) must be true for inoel nonzero and vice
c — versa.
if(.not.lctrl(24) .and .inoel.ne.0) call En-Message (82,0,ipt(29))
if(lctrl(24) .and. inoel.eq.O) call ErrMessage (105,0,ipt(29))
c
c — If inoel<0 then read and distribute uniform NAPL sat and mole
c — fractions at all nodes.
If (inoel. It. 0) Then
call commnt (13,21)
read (13,*) soel(l),(omfel(j),j=l,ipt(15))
If (soel(l).lt.zerO .or. soel(l).gt.rone)
+ call ErrMessage (51,0,ipt(29))
sum = zerO
Doii = l,ipt(15)
sum = sum + omfel(ii)
EndDo
If (sum .ne. rone) call ErrMessage (52,0,ipt(29))
write (21,514)
write (21,515) soel(l),(omfel(j)j=l,ipt(15))
Do 146 i = l,ipt(l)
sat(ipt(2)*2+i) = soel(l)
Dol46ii =
146
xmf(ipt(10)+iiml+i) = omfel(ii)
continue
Endlf
c
c — If the number of elements with NAPL is greater than zero,
c — then for each element provide the following information:
c — ( 1 ) element number
c — (2) NAPL saturation
c — (3) mole fraction of each organic component. There must be
c — ipt(15) mole fractions specified for each element, and they
c — • must sum to 1.
c — Error Checks: element number=(l,ipt(0)); So=(0-l); sum xi = 1.
c — Distribute the element saturation to each node in the element.
If (inoel .gt.O) Then
call commnt (13,21)
write (21,516) inoel
write (21,529) (cname(icp(i+ipt(3)+ipt(4))),i=l,ipt(5))
Do 130 i = 1, inoel
read (13,*) iel(i)
If (iel(i).lt.l .or. iel(i).gt.ipt(0))
+ call ErrMessage (50,0,ipt(29))
backspace 13
read (13,*) iel(i),soel(i),(omfel(j)j=l,ipt(15))
If (soel(i).It.zerO .or. soel(i).gt.rone)
+ call ErrMessage (5 1 ,0,ipt(29))
sum = zerO
Doii = l,ipt(15)
sum = sum + omfel(ii)
EndDo
If (sum .ne. rone) call ErrMessage (52,0,ipt(29))
write (21,517) iel(i),soel(i),(omfel(j)j=l,ipt(15))
i3=iel(i)*3
ilocl = ipt22 + nodept(nodel(i3-2)) + nelpt(i3-2)
iloc2 = ipt22 + nodept(nodel(i3-l)) + nelpt(i3-l)
iloc3 = ipt22 + nodept(nodel(i3)) + nelpt(i3)
sat(ilocl) = lO.OdO + sat(ilocl) + soel(i)
sat(iloc2) = 1 (XOdO + sat(iloc2) + soel(i)
sat(iloc3) = lO.OdO + sat(iloc3) + soel(i)
Do ii=l,ipt(15)
ilocl = ipt(IO) + iiml + nodel(i3-2)
iloc2 = ipt(IO) + iiml + nodel(i3-l)
iloc3 = ipt(10) + iiml + nodel(i3)
xmf(ilocl) = lO.OdO + xmf(ilocl) + omfel(ii)
xmf(iloc2) = lO.OdO + xmf(iloc2) + omfel(ii)
xmf(iloc3) = lO.OdO + xmf(iloc3) + omfel(ii)
EndDo
130 Continue
C
C— Now adjust for the multiple entries in sat and xmf for nodes where
C— adjacent elements have nonzero organic saturations. Average
C— organic saturations over a given material
C— property block and mole fractions over the entire domain.
Doi = l,ipt(2)
ff(sat(2*ipt(2)+i).ge.lO.OdO)then
sat(2*ipt(2)+i) = sat(2*ipt(2)+i)/10.0dO
xx=dint(sat(2*ipt(2)+i))
sat(2*ipt(2)+i) = 10.0dO*(sat(2*ipt(2)+i)-xx)/xx
Endlf
EndDo
dol45i=l,ipt(l)
do!45ii=l,ipt(15)
if(xmf(ipt(10)-l-iiml-M).ge.lO.OdO)then
xmf(ipt(10)+iiml+i)=xmf(ipt(10)+iiml+i)/10.0dO
xx=dint(xmf(ipt(l 0)+iiml +i))
xmf(ipt(10)+iiml+i)
+ =10.0dO*(xmf(ipt(10)+iiml+i)-xx)/xx
end if
145 continue
Endlf
c
c— Initialize porosity and residual saturation vectors.
do!70i = l,ipt(2)
170 srw(i) = bsrw(matpt(i))
do 171 i = l,ipt(0)
171 por(i) = bphi(matel(i))
c
c— Compute initial gas and aqueous phase saturations
If(ipt(75).ne.3)Then
call SATW
Endif
If(ipt(75).eq.3)Then
do!47i=l,ipt(2)
if(ipt(3).gt.O) then
if(sat(i).gt.sat(i+2*ipt(2)))then
sat© = sat(i)-sat(i+2*ipt(2))
else
write(21,*) 'Respecify gas phase saturation'
stop
end if
else
if(sat(i+ipt(2)).gt.sat(i+2*ipt(2)))then
sat(i+ipt(2)) = sat(i+ipt(2))-sat(i+2*ipt(2))
else ',
write(21,*) 'Respecify aqueous phase saturation'
stop
end if
end if
147 continue
Endlf
c
c== BLOCK Q: OXYGEN AND NUTRIENT INITIAL CONDI-
TIONS =====
c
if(ipt(29).ne.O) write (ipt(29),*)
+ 'Reading Gas, Aqueous, and Biophase Initial Conditions'
c
c— Read a logical variable indicating if the gas phase initial
c— conditions are uniform. Skip this input if oxygen is not
c— present in the gas phase.
191
-------
write (21318)
call commnr 03,21)
if(cvp(ipt(]5>l-2),ge.zciO) then-
call commnt ( 1 3v2I)
read (13,*) lunfx
c
0 — Read the gas phase initial conditions for oxygen and nutrient.
c— Iniial conditions arc read as partial pressures (i.e. mole
c — fractions). Nutrient can only be present if oxygen is present.
rf(hinfx)Then
call commit (I3i21-)
ifl(cvp{ipt{15)+4),gc,zerO;and.Ictrl(9))then
read (13,*) xog, xng
write (21,519) xog
write (21 ,543) xng
c
c— Error Check: mole frac=(0-l)
If (xog,It.zerO .or. xog.gt.rone)
+ callErrMessage(53,0,ipt(29))
If (xng.ItzerQ .or. xng.gt.rone)
+ call ErrMessage (73,0,ipt(29)>
else
read(13,*)xog
write (21,519) xog
c
c— Error Check: mole frac=(0-l)
If (xog.lf.zetO .or. xog.gt.rone)
•f call ErrMessage (53,0,ipt(29))
end if
C
C — Assign gas phase initial conditions to the xmf vector.
if (cvp(ipt(15)+4) ge,zetO;and.lctrl(9)) then
ipto = ipt(3)-3
iplgo2=ipt(8H'pto*ipt( 1 )
if (cvp(ipt(15)+4) ,ge. zeiO) then
iptn = ipt(3)-I
iptgn2=ipt(8)+iptn*ipt(I )
dolS5i=l,ipt(l)
15S xmfti+iptgn2)=xng
end if
else
ipto = ipt(3)-2
iptgo2=ipt(8)+i|>to*ipt(l )
end if
dolS6i=l,ipt(l)
156 xmf(i+iplgo2)=xog
else
c
e— Read a vector of nonuniform initial gas phase mole fractions.
otllcommm(I3,21)
if (cvp(ipt( I 5H4),gc,zer0.and.lctrl(9)) then
iptgo - ipt(3)-3
ip(go2=ipt(8)+ip!EO*'pt( 1 )
if (cvp(ipt(15)+4) .ge. zerO) then
iptn = ipt(3)-I
ip(gn2=ipt(8)+iptn*ipt(l)
write (21,547)
dol57ii=l,ipt(l)
rcad(13,*) i, xmf(i+iptgo2), xmf(i+iptgn2)
c — Iirror Check: mole frac=(0-l )
If (xmf(i+iptgo2).l(,zeiO .or. xmf(i+iptgo2)
•»• ,gt rone) call ErrMessage (53,0,ipt(29))
If (xmf(i+iplgn2).ll,zerO .or. xmf(i+iptgn2)
+ .gt.rone) call ErrMessage (73,0,ipt(29))
1 57 continue
else
write (21 ,520)
dol5Sii=l,ipt(l)
read(I3,*) i. xmf(i«ptgo2)
e
c— Error Check: mole frac=(0-l)
If (xmli(i+iptgo2),lt.zerO .or. xmf(i+iptgo2)
+ .gt.rone) call ErrMessage (53,0,ipt(29))
1 58 continue
end if
else
iptgo = ipt(3)-2
iptgo2=ipt(8)+iptgo*ipt(l)
write (2K520)
dol59ii=l,ipt(I)
read(13,*) i, xmf(i-t-iptgo2)
c
c— Error Check: mole frac=(Qi 1)
If (xrtif(Mptgo2).It.zerO .or. xmf(i+iptgo2).gt.rone)
+ call EirMessage (53,0,ipt(29));
159 continue
ehd'if
end if-
end if
c
c— Read a logical variable indicating if the aqueous phase initial
c— conditions are uniform. Skip this input if oxygen is not present
c— in the aqueous phase.
call commnt (13,21)
if (casol(ipt(15)+2).ge.O) then
call commnt (13,21)
read (13,*) lunfx
c
c— Read the'aqueous phase initial conditions for oxygen and nutrient.
c—Inital conditions are read* as concentrations (i.e. g/L). Nutrient
c— can' only be present if oxygen is present
If (lunfx) Then
call commnt (13,21-)
' if(lctri(9)) then
read(13,*)-xoa, xna
c
c— Convert xna into a mole fraction.
xna = xna*cmw(ipt(15)+10/(cmw(ipt(15)+4)*cden(ipt(15)+l))
write (2T.543) xna
c
e— Error Check: mole frac=(0-l)
If (xna.lt.zerO .or. xna.gt.rone)
+ call ErrMessage (74,0,ipt(29))
else
read(13,*)xoa
end if
c
c— Convert xoa into a mole fraction.
xoa'= xoa*cmw(ipt(15)+l )/(cmw(ipt(15)+2)*cden(ipt(l 5)+I))
write (21,544) xoa
c
c— Error Check: mole frac=(0-1)
If (xoa.lt.zerO .or. xoa.gt.rone)
+ call ErrMessage (54,0,ipt(29))
C
C-— Assign aqueous phase initial conditions to the Xmf vector.
iptao = ipt(14)+l
iptao2=ipt(9)+iptao*ipt( I.)
if(lctrl(9))then
iptan = ipt(4)-l
iptan2=ipt(9)+iptan*ipt(I)
do!60i=l,ipt(l)
160 xmf(i+iptan2)=xna
end if
do!61i=l,ipt(I)
C
C— Initialize biophase if present (Ictrl(3)=t). Oxygen is
C— always a component of the biophase. Nutrient is present
C— in the biophase if included (lctrl(9)=t).
C
if(lctrl(3))
+ xmf(ipt( 12)+ipt( 17)»ipt( I )+i)=xoa
if(lctrl(9))
+ xmf(ipt(I2)+(ipt(17)+l)*ipt(I)+i)=xna
161 xmf(i+iptao2)=xoa
else
c
c— Read a vector of nonuniform initial aqueous component
c— concentrations (gm/l).
call commnt (13,21)
iptao = ipt(14)+l
iptao2=ipt(9)+iptao*ipt( 1)
if (casol(ipt(15)+4) .ge. zerO .and. Ictrl(9)) then
iptan = ipt(4)-l
iptan2=ipt(9)+iptan*ipt(l)
192
-------
write (21,548)
do!62ii=l,ipt(l)
read(13,*) i, xoa, xna
c
c— Convert xoa into a mole fraction.
xoa = xoa*cmw(ipt(15)+l)/(cmw(ipt(15)+2)
+ *cden(ipt(15)+l))
c
c— Error Check: mole frac=(0-1)
If (xoa.lt.zerO .or. xoa.gt.rone)
+• . call ErrMessage (54,0,ipt(29))
c
c— Convert xna into a mole fraction.
xna = xna*cmw(ipt(15)+l)/(cmw(ipt(15)+4)
+ *cden(ipt(15)+l))
c
c— Error Check: mole frac=(0-l)
If (xna.lt.zerO .or. xna.gt.rone)
4- call ErrMessage (74,0,ipt(29))
C — Initialize biophase if present (lctrl(3)=t). Oxygen is
C — always a component of the biophase. Nutrient is present
C — in the biophase if included (lctrl(9)=t).
C
if(lctrl(3))
+ xmf(ipt(12)+ipt(17)*ipt(l)+i)=xoa
if(lctrl(9))
+ xmf(ipt(12)+(ipt(17)+l)*ipt(l)+i)=xna
xmf(i+iptao2) = xoa
162 xmf(i+iptan2) = xna
else
write (21,546)
do 163 ii=l,ipt(l)
read(13,*) i, xoa
c
c — Convert xoa into a mole fraction.
xoa = xoa*cmw(ipt(15)+l)/(cmw(ipt(15)+2)
+ *cden(ipt(15)+l))
c
c — Error Check: mole frac=(0-l)
If (xoa.It.zerO .or. xoa.gt.rone)
+ call ErrMessage (54,0,ipt(29))
C
C — Initialize biophase oxygen mole fraction if needed. Oxygen is
C — always a component of the biophase. If nutrient is present
C — (lctrl(9)=t) it must be included in the biophase.
C
if(Ictrl(3))
+ xmf(ipt(12)+ipt(17)*ipt(l)+i)=xoa
163 xmf(i+iptao2) = xoa
end if
end if
end if
C
C — Now assign gas phase nitrogen mole fractions for calculation
C — of initial gas phase density without organic content. This
C — neglects water vapor presence
C
if (ipt(3).gt.O) then
if(lctrl(9))then
in = ipt(3) - 2
else
in = ipt(3)-l
end if
ix = in * ipt(l)
do 165 i=l,ipt(l)
xmf(ipt(8)+ix+i) = rone
do!65ii=ipt(13),ipt(3)
if(icp(ii).ne.icp(in+l)) then
xmf(ipt(8)+ix+i) = xmf(ipt(8)+ix+i)
end if
165 continue
end if
C— Now assign aqueous phase water mole fractions for calculation
C — of initial aqueous phase density without organic content
C
if(ipt(4).gt.O) then
ix=ipt(14)*ipt(l)
do 166 i=l,ipt(l)
xmf(ipt(9)+ix+i) = rone
do 166ii=ipt(14),ipt(4)
if(icp(ipt(3)+ii).ne.icp(ipt(3)+ipt(14)+l))
+ xmf(ipt(9)+ix+i) = xmf(ipt(9)+ix+i)
166 continue
end if
C
C — Calculate the gas phase initial phase molecular weight and the
C — aqueous phase initial density for velocity calculations.
C
Ikeep = ictrl(22)
lctrl(22) = .false.
call MOLEWT
lctrl(22) = Ikeep
do!67i = l,ipt(l)
pmwO(i) = pmw(i)
1 67 denO(i) = den(4*ipt( 1 )+i)
C
C — Next calculate the equilibrium distribution of the organic
C — • components. This initial distribution occurs only in elements
C — containing NAPL. Organic components are partitioned into the gas,
C — aqueous, solid, and biophases.
igas =0
iaq = igas + ipt(3)
inapl = iaq + ipt(4)
isol = inapl + ipt(5)
ibio = isol + ipt(6)
do!64ii = l,ipt(15)
inapl = inapl +• 1
if((ipt(3).gt.0).and.(icp(igas+l).eq.ii))igas=igas+l
if((ipt(4).gt.0).and.(icp(iaq+l).eq.ii)) iaq=iaq+l
if((ipt(6).gt.O).and.(icp(isol-H).eq.ii))isol=isol+l
if((ipt(7).gt.0).and.(icp(ibio+l).eq.ii)) ibio=ibio+l
ngas = (igas- 1) * ipt(l)
naq = (iaq-l) * ipt(l)
nnapl = (inapl-1) * ipt(l)
nsol = (isol-l)*ipt(l)
nbio = (ibio-l)*ipt(l)
C
C — Compute organic equilibrium mole fractions when organic phase
C — is present.
Do!64i=l,ipt(l)
if(xmf(nnapl+i).gt.zer0) then
C
C — Compute gas phase equilibrium organic mole fractions. Allow
C- — for the possibility that there are fewer organic components
C — in the gas phase than in the organic phase.
if(ipt(3).gt.O) then
if(cvp(icp(igas)).gt.zerO) then
if(lctrl(10)) then
cvpt = cvp(icp(igas))
casolt = casol(icp(iaq))
else
cvpt = cvp(icp(igas))
+ + dtemp((icp(igas)- 1 )*ipt(89)+idepth(i))
casolt = casol(icp(iaq)) + dtemp
+ ((icp(iaq)-l )*ipt(89)+3*ipt(88)+idepth(i))
end if
if(icp(igas).eq.ii) xmf(ngas+i)
+• =xmf(nnapl+i)*cvpt/patm
end if
end if
C
C — Compute aqueous phase equilibrium organic mole fractions. Adjust
C — .for the possibility that there are fewer organic species in the
C — aqueous phase than in the organic phase
if(ipt(4).gt.O) then
if(icp(iaq).eq.ii) xmf(naq+i)
+ =xmf(nnapl+i)*casolt
end if
C
C — Set initial bio-phase organic component mole fractions equal to
193
-------
C— ihc aqueous phase mole fractions if needed.
if(lclrl(3))lhen
if(lep ,asinfc(i),csflux(i),cphex(i),i=I ,iendmb)
call commnt(28,21)
kndmb = iptC65)*5
rcad(28,602)(cmassl(i),cmassO(i),i=l,iendmb)
call commnl(28,21)
rcad(28,*) tmassl.tmassO
c
c— Read the pressure vectors.
if(ktrl
-------
c— Gas phase component boundary conditions.
c (I) Read the number of nodes for which gas phase component boundary
c conditions are specified.
c (2) For each such node, read:
c (2a) the node number
c (2b) an integer variable indicating the boundary condition
c type for all gas phase components at the node.
c 1 = constant mole fraction
c 2 = constant diffusive flux
c 3 = mixed type (contact with a known fluid).
c (2c) the boundary condition values for each component in the
c gas phase. The values are listed in sequential order
c corresponding to the component numbers. Only components
c that are present in the gas phase are listed. Component
c boundary conditions are not provided for components which
c are excluded from the gas phase (i.e. negative vapor
c pressure). Two values are needed for each boundary node.
c These values are used as needed to specify the boundary
c condition.
c 1 = specified gas phase mole fraction (partial pressure)
c in contacting fluid. The partial pressures must sum
c to one (used for first type boundary).
c 2 = user supplied value of Dm/length (m/sec).
c— Error check node numbers and BC type
c— Impose first type BCs
call commnt( 13,21)
read(13,*)ipt(20)
If(ipt(20).gt.O)Then
lerror = .false.
Doi = l,ipt(20)
ii = ipt(18) + ipt(19)
read (13,*) ibc(ii+i),ibcxmf(ibc(ii+i))
+ ,(bcxmf(icbc*ipt(l)+ibc(ii+i))
+ ,dfxmf(icbc*ipt( 1 )+ibc(ii+i)),icbc=0,ipt(3)-1)
if (ibc(ii+i).lt.O .or. ibc(ii+i).gt.ipt(l))
+ call ErrMessage (57,0,ipt(29))
if (ibcxmf(ibc(ii+i)).lt.l .or. ibcxmf(ibc(ii+i)).gt.3)
+ call ErrMessage (58,0,ipt(29))
if(lctr!(9)) then
ixmfnc = ipt(3)-l
else
ixmfnc = ipt(3)
end if
ixmfn = (ixmfnc-l)*ipt(l)+ibc(ii+i)
sum = zerO
doicbc = 0,ipt(3)-l
ixmf = icbc*ipt(l)+ibc(ii+i)
c
c— Error check: xmf = (0,1).
if( bcxmf(ixmf).lt.zerO .or. bcxmf(ixmf).gt.rone)
+ call ErrMessage (83,0,ipt(29))
if(ibcxmf(ibc(ii+i)).eq.l.and.lprnt(6)) lerror = .true.
if(ibcxmf(ibc(ii+i)).eq.l) xmf(ixmf) = bcxmf(ixmf)
if(icbc+l .nejxmfnc) sum = sum + bcxmf(ixmf)
end do
c
c- Calculate master component boundary condition in mole fractions.
c
bcxmf(ixmfn) = rone - sum
c
c— Error check: sum of specified boundary concentrations must
c—equal 1.
if(sum+bcxmf(ixmfn).ne.rone) call ErrMessage (85,0,ipt(29))
EndDo
if(lerror) call ErrMessage (127,l,ipt(29))
lerror = .false.
Endlf
c
c— Aqueous phase component boundary conditions.
c (1) Read the number of nodes for which aqueous phase component
c boundary conditions are specified.
c (2) For each such node, read:
c (2a) the node number
c (2b) an integer variable indicating the boundary condition
c type for all aqueous phase components at the node.
c 1 = constant mole fraction
c 2 = constant diffusive flux
c 3 = mixed type (contact with a known fluid).
c (2c) two boundary conditions values for each component in the
c aqueous phase. The values are listed in sequential order
c corresponding to the component numbers. Only components
c that are present in the aqueous phase are listed.
c Component boundary conditions are not provided for
c components which are excluded from the aqueous phase
c (i.e. negative solubility). Two values are needed for
c each boundary node component. These values are used as
c needed to specify the boundary condition.
c 1 = specified aqueous phase concentration (g/1)
c in contacting fluid (used for first type boundary).
c 2 = user supplied value of Dm/length (m/sec).
c— Error check node numbers and BC type
c—- Impose first type BCs
call commnt (13,21)
read(13,*)ipt(21)
If(ipt(21).gt.O)Then
lerror = .false.
ii = ipt(18) + ipt(19) + ipt(20) •
Doi = l,ipt(21)
read (13,*) ibc(ii-t-i),ibcxmf(ipt(l)+ibc(ii-H))
+ ,(bcxmf((ipt(3)+icbc)*ipt(l)+ibc(ii+i))
+ ,dfxmf(icbc*ipt( 1 )+ibc(ii+i)),icbc=0,ipt(4)-1)
if (ibc(ii+i).It.O .or. ibc(ii+i).gt.ipt(l))
+ call ErrMessage (59,0,ipt(29))
if (ibcxmf(ipt(l)+ibc(ii+i)).lt. 1 .or.
+ ibcxmf(ipt(l)+ibc(ii+i)).gt.3)
+ call ErrMessage (60,0,ipt(29))
sum = zerO
do icbc = 0, ipt(4) -1
ixmf=(ipt(3)+icbc)*ipt(l)+ibc(ii+i)
c
c— Convert specified boundary concentrations into mole fractions.
if(icbc+l.ne.ipt(14)+l) then
bcxmf(ixmf) = bcxmf(ixmf) * cmw(ipt(15)+l)
+ / (cmw(icp(ipt(3)+icbc+l)) * cden(ipt(15)+l))
sum = sum + bcxmf(ixmf)
c
c—Error check: xmf = (0,1).
if( bcxmf(ixmf).lt.zerO .or. bcxmf(ixmf).gt.rone )
+ call ErrMessage (84,0,ipt(29))
c
c— Error warning: no mass balance for first type nodes.
if( ibcxmf(ipt(l)+ibc(ii+i)).eq.l.and.lprnt(6))
+ lerror = .true.
c
c— Impose first type boundary condition.
if (ibcxmf(ipt(l)+ibc(ii+i)) .eq. 1)
+ xmf(ixmf) = bcxmf(ixmf)
end if
end do
c- Calculate master component boundary condition in mole fractions.
ixmfw = (ipt(3)fipt(14))*ipt(l)+ibc(ii+i)
bcxmf(ixmfw) = rone - sum
if (ibcxmf(ipt(l)+ibc(ii+i)) .eq. 1)
+ xmf(ixmfw) = rone - sum
EndDo
if(lerror) call ErrMessage (127,l,ipt(29))
lerror = .false.
Endlf
c— Read nodes with a constant gas phase specific discharge.
c— Units of source are m**3/sec.
c— Error check node numbers
call commnt (13,21)
read (13,*) ipt(22)
If (ipt(22) .gt. 0) Then
iptbc = ipt(18) + ipt(19) + ipt(20) + ipt(21)
Doi = l,ipt(22)
read (13,*) ibc(iptbc+i),source(i)
if (ibc(iptbc+i).lt.O .or. ibc(iptbc+i).gt.ipt(l))
+ call ErrMessage (63,0,ipt(29))
EndDo
Endlf
195
-------
Read nodes with a constant aqueous phase specific discharge.
Units of source are m**3/sec.
call commm( 13,21)
rcad(13,*)ipl(23)
lf(ipl(23),gt.O)Then
iptbc = ipl(lS) + ipt(19) + ipt(20) + ipt(21) + ipt(22)
Doi = l,ipt(23)
read (13,*) ibc(iptbc+i),source(ipt(22)+i)
if (ibe(iptbe+i),lt.O .or. ibe(iptbc+i).gt.ipt(l))
+ caUErrMessage(64,0,ipt(29))
EndOo
Endlf
Write boundary condition information.
write (21321)
write (2 1 322) ipt(l 8) ! constant gas phase pressures
If(ipt(18),gt.O)Then
write (21,523)
write (21,524) (ibc(i),p(ibc(i)),i=l,ipt(18))
Endlf
write (21325) ipt(19) ! constant aqueous phase pressures
lf(ipl(19).g».0)Thcn
write (21326)
ii = ipt(18) + i
write (21324) ibc(H),p(ipl(l)+ibc(U))
EndDo
Endlf
write (21 327) ipt(20) ! gas phase component BCs
If (ipl(20) ,gt, 0)Then
write (21,528)
write (21329) (cnamc(icp(i)),i=l,ipt(3))
Doi = l.ipt<20)
ii = ipt(!8)-t-ipt(19)
If(ipt<3).lc.2)Thcn
write (21,531) ibc(il+i),ibcxrnf(ibc(ii+i)),
•f (bcxmf(ibc(ii+iHicbc*ipt(l))
+ ,dfxmf(ibc(ii+i)+icbc*ipt(l)),icbc=0,ipt(3)-l)
Else
\vritc (21,531) ibc(!i+i),ibcxmf(ibc(ii+i)),
+ (bcxmf(ibc(l!+i)+icbc*ipl(l))
+ ,dfxmf(ibc(iiH4)+icbc*ipt(l)),icbc=0,l)
Doj = l,(ipt(3)-lV2
write (21, 532)
+ (bcxmf(ibc(iW)+icbc*ipt(l»
+ ,dfxmf(ibc(ii+i)+icbe*ipl(l)),icbc=j*2jj)
EndDo
Endlf
EndDo
Endlf
write (21333) ipl(21) 1 aqueous phase component BCs
If(ipt(21).gt.O)Then
write (21,534)
write (21,529) (cnamc(icp(H-ipt(3))),l=l,ipt(4))
Ooi-l,ipt(21)
!f(ipt(4),lc. 2)Then
write (21,531) ibc(ii+i),ibcxmf(ipt(l)+ibc(ii+i)),
(bcxmf(ibc(ii+i)+ipt(l )*(icbc+ipt(3)))
,dfxmf(ibc(ii+i)+ipt(l )«(icbc+ipt(3)))
,icbc=0,ipt(4)-l)
Else
write (21,531) ibe(ii+i),ibcxmf(ipt(l)+ibc(ii+i)),
(bexmf(ibe(ii+i)+ipt(l)*(icbc+ipt(3)))
,dfxmf(ibc(ii+i)+ipt(l)*(icbc+ipt(3)))
,icbc=0,l)
write (21, 532)
+ (bcxmf(ibc(ii+i)+ipt(I )*(icbc+ipt(3)))
+ ,dfxmf(ibc(ii+iHipl(l)*(icbc+ipt(3)))
+ ,icbc=j*2jj)
EndDo
Endlf
EndDo
Endlf
write (21336) ipt(22) ! constant gas phase flux
If(ipt(22).gt. 0>Then
iptbc = ipt(18) -1- ipt(l 9) + ipt(20) -I- ipt(21)
write (21,537)
Doi=l,ipt(22)
write (21,524) ibc(iptbc+i),source(i;)
EndDo
Endlf
write (21 ,538) ipt(23) ! constant aqueous phase flux
If(ipt(23).gt.O)Then
iptbc = ipt(18) + ipt(19) + ipt(20) + ipt(2l) + ipt(22)
write (21,539)
Doi==l,ipt(23)
write (21,524) ibc(iptbc+i),source(ipt(22)+i)
EndDo
Endlf
c
c — If constant pressure nodes are present, then update saturations.
if «ipt(18) .gt. 0 .or. ipt(19) .gt. O).and.lctrl(l)) then
call SATW
endif
c====== INITIALIZE VARIABLE3 =====
c
c — Do not perform these initializations if the run is a restart.
if(.not.lctrl(26)) then
C
C — Now assign aqueous phase water mole fractions.
C
if(ipt(4).gt.O) then
ix=ipt(14)*ipt(l)
do460i=l,ipt(l)
xmf(ipt(9)+ix-H) = rone
do460ii=l,ipt(4)
if(icp(ipt(3)+ii).ne.icp(ipt(3)+ipt(14)+l»
+ xmf(ipt(9)+ix+i) = xmf(ipt(9)+ix+i)
460 continue
C
C — Now assign gas phase water mole fractions. No gas phase water
C — vapor equilibrations are permissible when the aqueous phase is
C — absent.
C
if(ipt(3).gt.O) then
do 470 i=l,ipt(l)
ifflctrl(lO)) then
cvpt = cvp(ipt(15)+l)
else
cvpt = cvp(ipt(15)+l)
+ + dtemp(ipt( 1 5)*ipt(89)+idepth(i))
endif
470 if(cvp(ipt(15)+l).ge.zerO)
+ xmf(ipt(13)*ipt(l>l-i)
+ = xmf(ipt(9)+ix+i)*cvpt
+ /(temp(i)*cden(ipt(15)+l)*r*patm)
endif
endif
C
C — Finally assign gas phase nitrogen mole fractions.
C
if(ipt(3).gt.0)then
if(lctrl(9))then
in = ipt(3) - 2
else
in = ipt(3) - 1
endif
ix = in*ipt(l)
do475i=l,ipt(l)
xmf(ipt(8)+ix+i) = rone
do475ii=l,ipt(3)
if(icp(ii).ne.icp(in+l)) then
xmf(ipt(8)+ix+i) = xmf(ipt(8)+ix+i)
endif
475 continue
endif
endif
C
C — Compute the phase molecular weights and densities. Do not
196
-------
C— compute the phase density derivative terms on the first time
C— step unless the run is a restart.
c if(.not.lctrl(26)) then
Ikeep = lctrl(22)
lctrl(22) = .false.
call MOLEWT
Ictrl(22) = Ikeep
c else
c call MOLEWT
c end if
C
C— Compute solid phase equilibrium organic mole fractions when the
C— run is not a restart.
C
if(.not.lctrl(26)) then
if(ipt(14).gt.0.and.ipt(16).gt.0)then ;
iaq = ipt(3)
isol = ipt(3) + ipt(4) + ipt(5)
do480ii = l,ipt(15)
ngas = (igas-1) * ipt(l)
inapl = inapl + 1
if(icp(iaq+l).eq.ii) iaq=iaq+l
if(icp(isol+l).eq.ii)isol=isol+l
naq = (iaq-1) * ipt(l)
nsol = (isol-1) * ipt(l)
do480i = l,ipt(l)
if(icp(isol).eq.ii) then
if(xmf(naq+i).gt.0.dO) then
xmf(nsol+i) = bok(l)*(xmf(naq+i)*cmw(icp(isol))
+ * den(ipt(l)+i) * 1.0d3 ) ** (rone/bom(l))
else
xmf(nsol+i) = O.dO
end if
if(lctrl(19)) then
if(xmf(naq+i).gt.0.dO) then
xmf(nsol+i+ipt(l)) = xbok*bok(l)*(xmf(naq+i)
+ *cmw(icp(isol))*den(ipt(l)+i)*1.0d3)
+ **(rone/(xbom*bom(l)))
else
xmf(nsol+i+ipt(l)) = O.dO
end if
end if
end if
480 continue
end if
end if
c
c====== WELL CONDITIONS =======
c
if(ipt(29).ne.O) write (ipt(29),*)
+ ' Reading Extraction / Injection Well Conditions'
c
c— Read logical variable indicating if a well is included.
call commnt (13,21)
read (13,*) lctrl(12) ! Is a well to be simulated?
write (21,540) lctrl(12)
c
c— Read the volumetic flux (standard cubic feet per minute).
If(lctrl(12))then
call commnt (13,21)
read (13,*) qwell
c
c— Read the well radius (m); and the minimum and maximum node numbers
c— along the well screen.
c— Error Check: rwell > 0; all nodes along screen have same radius.
call commnt (13,21)
read (13,*) rwell,ii jj
if (rwell .le. zerO) call ErrMessage (65,0,ipt(29))
if (xnode(ii).ne.rwell .or. xnode(jj).ne.rwell)
+• call ErrMessage (66,0,ipt(29))
iptbc = ipt(18)+ipt(19)+ipt(20>t-ipt(21)«pt(22)+ipt(23)
ipt(24) =1 ! number of nodes along well screen.
ibc(iptbc+ipt(24)) = ii ! nodes along well screen.
If (xnode(i) .eq. rwell) Then
ipt(24) = ipt(24) + l
ibc(iptbc+ipt(24)) = i
Endlf
EndDo
ipt(24) = ipt(24) + 1
ibc(iptbc+ipt(24)) = jj ! bottom node along well screen
zwell = zerO ! determine length of well screen
Do i = l,ipt(24)-l
zwell = zwell + znode(ibc(iptbc+i+l)) - znode(ibc(iptbc+i))
EndDo
Do 350 i = 1 ,ipt(24)-1 [identify elements along the well screen
ndl = ibc(iptbc+i)
nd2 = ibc(iptbc+i+l)
Do j = l,ipt(0)
i3 = 3*(j-l)
If ((ndl .eq. nodel(i3+l) .or. ndl .eq. nodel(i3+2) .or.
+ ndl .eq. nodel(i3+3)) .and.
+ (nd2 .eq. nodel(i3+l) .or. nd2 .eq. nodeI(i3+2) .or.
+• nd2 .eq. nodeI(i3+3))) Then
ibc(iptbc+ipt(24)+i) = j
goto 350
Endlf
EndDo
350 Continue
c
c— Write well conditions.
write (21,541) qwell,rwell,zwell,ipt(24)
Do i = l,ipt(24)-l
write (21,542) ibc(iptbc+ipt(24)+i),ibc(iptbc+i),
+ ibc(iptbc+i+l)
EndDo
qwell = qwell / 2118.60dO ! convert cfm to m"3/s
Endlf
c
c—• Generate boundary condition pointers.
ipt(62) = ipt(18) + ipt(19) + ipt(20) +ipt(21)
ipt(63) = ipt(62) + ipt(22)
ipt(64) = ipt(63) + ipt(23)
C
C==== VELOCITY BOUNDARY CONDITIONS =====
C
if(ipt(29).ne.O)
+ write (ipt(29),*) 'Reading Velocity Boundary Conditions'
C
C— Read a logical variable indicating if the bottom boundary is
C— impervious.
C
if(lctrl(18)) then
call commnt (13,21)
read (13,*) lctrl(28)
C
C— Read a logical variable indicating if the R.H.S. boundary is
C— impervious.
call commnt (13,21)
read(13,*)lctrl(29)
- Read a logical variable indicating if the L.H.S. boundary is
- impervious. Note that this boundary will be adjusted in the
- presence of a well.
call commnt (13,21)
read(13,*)lctrl(30)
C— Read a logical variable indicating if the top boundary is
C— impervious.
C
call commnt (13,21)
read(13,*)lctrl(31)
write (21,555) lctrl(28),lctrl(29),lctrl(30),lctrl(31)
— If lctrl(31) is true read the length of the cap (m). The cap is
— assumed to extend from the well to the input value.
if(lctrl(31))then
call commnt (13,21)
read (13,*) caplen
write(21,556) caplen
end if
end if
197
-------
«PRINT INITIAL CONDITIONS =
C
c«=
C
If(lprnt<3»Then
if(ipt<29).nc.0> write (ipl(29),*)
•f 'Writing Initial Conditions'
callprmeO)
Endlf
c
c—Formats
499 format e/riNPUT2',69e'=')/)
SCO format emrriAL PRESSURE DISTRIBUTION ',46('=')/
+ * Pressures are defined as: ipt(75) = ',i5/
+ " 1 * compute assuming: Pg=latm' /
+ ' Pa = hydrostatic;' /
+' 2 * input Pg and Pa at all nodes;')
501 format (
+ ' Depth (o water table (m): wtdpth = ',el2.4)
HE forrrutC
+' Input initial gauge pressure (Pa) at all nodes:'/
+ • Node Aqueous Phase GasPnase')
503 format (3x,i6,4x,el2,4,4x,el2.4)
504 format f/DARCY VELOCITY COMPUTATION APPROACH ',40('=')/
+ ' Use nodal7 Darey velocities if true: lctrl(I8) =',15)
505 format (
•f-' Time dependent Darcy velocity profiles.')
506 formate
+' Steady state Darcy velocity profile is generated from the'/
+ ' user defined initial pressure distribution:')
507 format(
+•' User defined steady state velocities:')
508 formate
+•' Constant steady state Darcy velocity components'/
+ ' gas phase velocity, x(orr) component: vgx =',e!2.4/
+ ' gas phase velocity, z component: vgz =',e!2.4/
•f' aqueous phase velocity, x component vax =',e!2.4/
+ ' aqueous phase velocity, z component: vaz =',e!2.4)
509 formate
•(•' Oas Phase Aqueous Phase'/
+" Node x-dir z-dir x-dir z-dir')
510 formate
•f.' Oas Phase Aqueous Phase'/
+ ' Element x-dir z-dir x-dir z-dir')
511 format e3x,i5,5x,4el 2.4)
512 format e/'lNITIAL NAPL SATURATION AND COMPOSITION ',36('='))
513 formate
+ ' No NAPL is present')
514 formate
•f * Uniform NAPL saturation and mole fractions in all elements',/
+ * NAPL sat Component mole fractions')
515 format (3x,6ecl2.5,lx))
516 formate
+ * Number of elements with NAPL present: inoel =',i5,/
+ • Element NAPL sat Component mole fractions (l-ipt(15))')
517 format e2x,i6,2x,6(el2.5,lx))
518 format e/'OAS, AQUEOUS, AND BIOPHASE PHASE INITIAL CONDI-
TIONS '
+ ,24('='))
519 formate
t' Uniform gas phase oxygen mole fraction: xog = ',e!2.4)
543 formate
+ 'Uniform gas phase nutrient mole fraction: xng =',e!2.4)
544 formate
+ ' Uniform aqueous phase oxygen mole fraction: xoa =',e!2.4)
545 format e
+ ' Uniform aqueous phase nutrient mole fractiomxna =',e!2.4)
546 formate
+' Non-uniform aqueous phase oxygen mole fraction')
547 format(
+' Non-uniform gas phase oxygen and nutrient mole fraction')
548 format(
+' Non-uniform' aqueous phase oxygen and nutrient mole fraction')
520 format(
+ ' Non-uniform gas phase oxygen mole fraction')
521 format (/'BOUNDARY CONDITIONS ',56('='))
522 format(
•f' Number of nodes with constant gas pressure: ipt(IS) = ',i5)
523 format(
-f' Node Constant gas phase pressure (Pa gauge)')
524 format (3x,i5,14x,e 12.4)
525 formate
+ ' Number of nodes w/constant aqueous press.: ipt(19) =',i5)
526 format (
+ ' Node Constant aqueous phase pressure (Pa gauge)')
527 format (
+ ' Number of nodes W/gas phase component' /
+•' boundary conditions: ipt(20) = ',15)
528 forrhatC Gas phase BCs:' /
+' Nbde^ BC type BC values for gas phase components' /
•H' in pairs (concentratibn:Drri/!ength)')
529' format (2'0x,a!3,1 Jx.alS)
531 format (3x,i.'),6'x,il,4x,2(el2.4,':',el0.4,2x))
532 format(I:9x,2(el2.4,':',el0.4,2x))
533 format (
+ ' Number of nodes w/aqueous phase' /
+ ' component boundary conditions: ipt(21) =',i5)
534 format (' Aqueous phase BC:' /
+ ' Node BC typfe BC values for aqueous phase components'/
+' frr pairs (concentrafion:Dm/Iength)')
536 formate
+ ' Number of nodes w/constant gas phase flux:ipt(22) =',i5)
537 format (
+' Node Constant gas phase flux (scms)')
538 format (
+ ' Numberof nodes w/constant aq. phase flux:ipt(23) =',15)
539 format (
+' Node Constant aqueous phase flux (cms)')
540 format (/'EXTRACTION / INJECTION WELL DATA ',43('=')/
+ ' Include an extraction/injection well: lctrl(12) =',15)
541 format(
+ ' Volumetric fluid extraction rate (scfm): qwell =',e!2.4/
+' Well radius (m): rwell = ',e!2.4/
+ ' Length of well screen (m): zwell =',e!2.4/
+ ' Number of nodes along well screen: ipt(24) =',i5 /
+ ' Element and node numbers along well screen:'/
-1-' Element Element nodes along well screen')
542 format (9x,i6,I8x,2i8)
550 format (/'RESTART INFORMATION ',56('=')/
+ ' Run is a restart: lctrl(26) =',15/
+ ' Restart data: (unit 28) = ',a20/
+' Run is a continuation: lctrl(32) = ',15)
555 format (/'VELOCITY BOUNDARY CONDITIONS',48('=')/
+ ' Bottom boundary is impervious: lctrl(28) = ',15/
+ ' R.H.S. boundary is impervious: lctrl(29) = ',15/
+ ' L.H.S. boundary is impervious: lctrK30) = ",!5/
+' Note: L.H.S. is adjusted when a well is present'/
+ ' Top boundary is impervious: lctrK31) =',15)
556 format(
+ ' Top boundary is covered from x = 0 to: caplen =',e!2.4)
601 format(3el5.8,ilO)
602 formate5el5.8)
return
end
Subroutine - mobil.f
198
-------
C —
c
C mobil.f - This subroutine computes capacity coefficients, and
C aqueous and gas phase mobility terms in stacked
C storage.
C
c : :
subroutine mobil (iter)
include 'dimen.inc'
common /cbl/ matel(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
•f matpt(nn6)
common /cb2/ p(nn3)
common /cb2b/ pt(nn3)
common /cb3/ sat(nnstk3)
common /cb3b/ satt(nnstk3)
common /cb4/ satk(nnstk2),cc(nnstk)
common /cb5a/ bphi(nmblk),bpermh(nmb!k),bpermv(nmblk)
common /cb5b/ bvgn(nmblk),bvga(nmblk),bvgm(nmblk),bsrw(nmblk)
common /cbfi/ pmob(nnstk4)
common /cb6b/por(nelmx),srw(nnstk)
common /cb8/ vis(nnmx),pmw(nn3)
C
C— Dimension local arrays.
C
dimension c(3)
data ccmin / 1 .Od-7 /
c
c— Branch computations for single and multiple material property
c— blocks uniform material properties
if (ipt(26) .eq. 1) then ! uniform material properties.
c
c— Update chord slope approx for capacity coeffs, no stacking.
do!0i = l,ipt(l)
if (iter .eq. l)then
cc(i) = -ccmin
else
x = p(2*ipt(l)+i) - pt(2*ipt(l)+i)
if(x.ne. O.OdO)then
cc(i) = (sat(ipt(2)+i) - satt(ipt(2)+i)) / x
if (dabs(cc(i)) .It. ccmin) cc(i) = -ccmin
else
cc(i) = -ccmin
endif
endif
c
c—• Compute relative permeability.
c(l) = 1 .OdO / (1 .Odd - srw(i))
c ! van Genuchten function
c(2)=1.0dO/bvgm(l)
sweff = (sat(ipt(2)+i) - srw(i)) * c(l)
steff= (sat(ipt(2)+i)+sat(ipt(49)+i) - srw(i)) * c(l)
pmob(2*ipt(2)+i) = dsqrt(sweff) * (l.OdO - (l.OdO - ! kra
+ sweff**c(2)) ** bvgm(l)) ** 2
pmob(i) = dsqrt(l.OdO-steff) * (l.OdO ! krg
+ - steff**c(2)) ** (2*bvgm(l))
c
c— Compute mobilities. Note 'bpermh' is an anisotropy factor.
pmob(3*ipt(2)+i) = bpermv(l) ! aq. z-dir
+ * pmob(2*ipt(2)+i) *wvis
pmob(2*ipt(2)+i) = bpermh(l) * pmob(3*ipt(2)+i)! aq. x-dir
if (lctrl(20)) then ! include Klinkenberg adjustment
pmob(ipt(2)+i) =bpermv(l) * pmob(i) * vis(i) *
+ (1 .OdO + b/(patm+p(i)))
else
pmob(ipt(2)+i) = bpermv(l) * pmob(i) * vis(i) ! gas z-dir
endif
pmob(i) = bpermh(l) * pmob(ipt(2)+i) t gas x-dir
10 continue
c
c— Multiple material property blocks.
else
c
c— Update chord slope approx for capacity coeffs.
do 20 i = l,ipt(l)
do 20 j = 0,nodept(i+l)-nodept(i)-l
jj = nodept© + j
if (iter .eq. l)then
cc(jj) = -ccmin
else
x = p(2*ipt(l)+i) - pt(2*ipt(l)-ri)
if(x.ne. O.OdO)then
cc(jj) = (sat(ipt(2)+jj) - satt(ipt(2)+Jj)) / x
if(dabs(cc(jj)).lt. ccmin) cc(jj) =-ccmin
else
cc(jj) = -ccmin
endif
endif
c
c— Compute relative permeability.
mprop = matpt(jj)
c(l) = 1.0dO/(1.0dO - srw(jj))
c(2) = 1 .OdO / bvgm(mprop)
sweff = (satOpt(2Mj) - srwOJ)) * c(l)
steff = (sat(ipt(2)+jj)+sat(ipt(49)+jj) - srwQj)) * c(l)
sweff = dminl (sweff, 1 .OdO)
• steff=dmin 1 (steff, 1 .OdO)
steff= dmaxl(steff,xround)
sweff = dmaxl(sweff,xround)
pmob(2*ipt(2)+ii) = dsqrt(sweff) ! kra
+ * (1 .OdO - (1 .OdO -sweff**c(2)) ** bvgm(mprop)) ** 2
pmobQj) = dsqrt(l.OdO-steff) ! krg
+ * (1 .OdO - stefi**c(2)) ** (2*bvgm(mprop))
c
c— Compute mobilities. Note 'bpermh' is an anisotropy factor.
pmob(3*ipt(2)+jj) = bpermv(mprop) ! aq. z-dir
+ * pmob(2*ipt(2)+jj) * wvis
pmob(2*ipt(2)+jj) = bpermh(mprop) ! aq. x-dir
+ * pmob(3*ipt(2)+jj)
if (lctrl(20)) then ! include Klinkenberg adjustment
pmob(ipt(2)+ij) = bpermv(mprop) * pmobflj) * vis(i) *
+ (1 .OdO + b/(patm+p(i)))
else
pmob(ipt(2)+jj) = bpermv(mprop) * prnobQj) *
H- vis(i) ! gas z-dir
endif
pmob(jj) = bpermh(mprop) * pmob(ipt(2)+jj) ! gas x-dir
20 continue
endif
return
end
Subroutine - molewt.f
C — __
c
C MOLEWT.f - Subroutine which computes the fluid phase molecular
C weights, densities, and mass densities.
C
C Required Control Flags:
C
C lctrl(l) - logical variable controlling presence of flow
C solution
C lctrl(l) = .true. - compute flow solution
C lctrl(l) = .false. - skip flow solution
C lctrl(22) - logical variable controlling execution of
C solution for dden
C lctrl(22) = .true. - compute dden
C lctrl(22) = .false. - skip dden
C
199
-------
c
c-
c
subroutine MOLEWT
include Mimen inc'
Declare »nd define common block variables.
common/cb2/ p(nn3)
common /cb6e/ temp(nnmx)
common fcb7b/ cmw(ncmp),cvp(ncmp),cden(ncmp),
+ chen(ncmp),casol(ncmp),cmdif(ncmp2)
common /cb8/ vis
-------
C— Declare and define common block variables.
C
common /cbl/ matel(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ matpt(nn6)
common /cblc/ xnode(nnmx),znode(nnmx),rbar(nelmx),area(nelmx)
common /cb2c/ q(ne!4)
common/cb3/ sat(nnstkS)
common /cb3b/ satt(nnstk3)
common /cb6d/ dtemp(nzmax6),idepth(nnmx)
common /cb7b/ cmw(ncmp),cvp(ncmp),cden(ncmp),
+ chen(ncmp),casol(ncmp),cmdif(ncmp2)
common/cb9/ xmf(nmf)
common /cb9b/ xmft(nmf)
common /cblO/ den(nn6)
common /cbl I/ pex(nnslO),rxnp(nn2)
common /cb62/ rxn(nmf),cex(nmfs)
common /cb62b/ rhsex(nmfs)
common /cb63/ kex(ncmp5),kmax(ncmp5)
common /cb64/ bok(nbcmp),bom(nbcmp),krtd(ncmp)
C
C— Dimension local arrays.
C
dimension qaveg(nnmx),qavea(nnmx),xl(nnmx)
C
C— Klen is the dimension used to calculate the exchange coefficient
C— bounds. Ordinarily this is not used and the exchange coefficients
C—• are bounded using the element dimension. However for column
C— experiments, the column dimension may be appropriate and should
C— be entered here in meters. Otherwise set klen to a negative
C— number.
C
data klen/-O.lOdO/
data limag, limao, limgo, limab, limas /
+ .true., .true., .true., .true., .false./
C
C— This statement sets upper limits on exchange coefficients.
C— Limits are expressed in the fraction of equilibrium it is
C— possible to approach over one element. Limits are is order:
C— gas/aqueous, aqueous/NAPL, gas/NAPL, aqueous/biophase,
C— and aqueous/solid.
C
doli = l,ipt(l)
xl(i) = zerO
qaveg(i) = rone
qavea(i) = rone
1 continue
do2i = l,ipt(0)
i3=i*3
n3=nodel(i3)
n2=nodel(i3-l)
nl=nodel(i3-2)
darea = dsqrt( 2.0dO * area(i))
if(klen.lt.zerO) then
xl(nl) = dmaxl( xl(nl), darea)
xl(n2) = dmaxl( xl(n2), darea )
xl(n3) = dmaxl( xl(n3), darea)
else
xl(nl) = klen
xl(n2) = klen
xl(n3)=klen
end if
if(lctrl(18))then
qelgl = dsqrt( q(nl)**2 -t- q(nl+ipt(l))**2) / darea
qelg2 = dsqrt( q(n2)**2 +• q(n2+ipt(l))**2) / darea
qelg3 = dsqrt( q(n3)**2 + q(n3+ipt(l))**2) / darea
qelal = dsqrt( q(nl+ipt(40))**2 + q(nl+ipt(41))**2) / darea
qela2 = dsqrt( q(n2+ipt(40))**2 + q(n2+ipt(41 ))**2) / darea
qela3 = dsqrt( q(n3+ipt(40))**2 + q(n3+ipt(41))**2) / darea
qaveg(nl) = dminl( qaveg(nl), qelgl)
qavea(nl) = dminl( qavea(nl), qelal )
qaveg(n2) = dminl( qaveg(n2), qelg2)
qavea(n2) = dminl( qavea(n2), qela2)
qaveg(n3) = dminl( qaveg(n3), qelgS )
qavea(n3) = dminl( qavea(n3), qela3 )
else
qelg = dsqrt( q(i)**2 + q(i+ipt(0))**2 ) / darea
qela = dsqrt( q(i+ipt(67))**2 + q(i+ipt(68))**2) / darea
qaveg(nl) = dminl( qaveg(nl), qelg )
qavea(nl) = dminl(qavea(nl), qela)
qaveg(n2) = dminl( qaveg(n2), qelg)
qavea(n2) = dminl ( qavea(n2), qela)
qaveg(n3) = dminl (qaveg(n3), qelg)
qavea(n3) = dminl( qavea(n3), qela )
end if
2 continue
C
C— Compute the phase mass exchange. Initially iterate over just
C— the mobile phases and then add NAPL, solid, and biophases.
C— Aqueous/gas exchange is controlled by the aqueous phase
C— mole fractions. NAPL/gas and NAPL/aqueous exchange are controlled
C— by the mole fractions in the respective mobile phases.
C— Solid/aqueous mass exchange is governed by the solid phase
C— loading. Aqueous/ biophase mass exchange is governed by the ;
C— biophase mole fractions. For now this routine is not stacked. ;
C— Stacking will arise when the exchange coeficients are correlated
C—• with velocities or material properties.
C
ipt2x2 = ipt(49)
ipt2x4 = ipt(51)
ipt2x5 = ipt(52)
ipt2x6 = ipt(53)
ipt2x7 = ipt(54)
ipt2x8 = ipt(55)
ipt2x9 = ipt(56)
ipt2 = ipt(2)
iptl=ipt(l)
C
C— Zero the exchange vectors.
C
do 90 i = 1,10*ipt2
90 pex(i) = zerO
do91i = l,ipt(61)*ipt2
cex(i) = zerO
91 rhsexffl = zerO
C
C— Begin iterations over the various components. First the organic
C— components.
C
icg = 0
ica = 0
icn = 0
ics = 0
icb = 0
do!00iexc=l,ipt(15)
ic = icp(iexc)
if(icp(icg+l).eq.ic) then
icg = icg + 1 .
igc = icp(icg)
end if
if(icp(ipt(3)+ica+l).eq.ic) then
ica = ica + 1
iac = icp(ipt(3)+ica)
end if
if(icp(ipt(3)+ipt(4)+icn+l).eq.ic) then
icn = icn + 1
end if
if(icp(ipt(3)+ipt(4)+ipt(5)4ics+1 ).eq.ic) then
ics = ics + 1
isc = icp(ipt(3)-Hpt(4)+ipt(5)+ics)
end if
if(icp
-------
C— Iterate oxer the nodes, Iniiial temperature dependent parameters.
C
JolOOi = l,ipt(l)
if(lctrj(10))thcn
cvpt s cvp(ic)
casollFCasol(ie)
else
itcmp ~ (ic-l)*ipt(89)+idepth(i)
cvpt ~ cvp(ic) 4> dtempCitcmp)
itcmp s jtempf3*ipt(88)
casolt = casol(ic) + dtemp(itemp)
end if
do 100 ii = 0,nodcpt(i+l)-nodept(i)-l
islk = ii + nodepl(i)
C
C— Initialize saturations. Control NAPL exchange with NAPL
C—saturations from the previous time step.
C
sgconl«sat(istk)
snt = salt(ipt2x2+istk)
C
C— Calculate terms when NAPL is present.
C
if((snt,gt.zerO).and.(xmft(i+in),gt,zerO))then
C
C— Calculate gas phase exchange when the gas phase is present.
C
if(ipt(3),gt.0.and.igc.eq.ic)then
C
C— PUT USER DEFINED GAS/NAPL MASS TRANSFER COEFFI-
CIENT FUNCTION HERE.
C— ASSIGN IT TO KGO TO UTILIZE BUILT-IN CONTROL.
C
if(limgo) then
kgo = kex(5*(ic-l)+3)
C
C— Gaj/NAPL control on mass transfer coefficient with the greater of
C— the gas phase advcclive velocity or diffusional velocity.
C
kgo « dminU kgo, -{ dmaxl( qaveg(i),
+ cmdif(2*ic-iyxl(i)**2) * d1og(
+ kmax
-------
C— exceed the amount of organic component available from the NAPL
C
xfluxl = pexao*t(8)
xflux2 = den(ipt(40)+i)*snt*xmf(i+in)
if(xfluxl.gt.xflux2) then
xlimit = xflux2 / xfluxl
pexao = xlimit * pexao
cexao = xlimit * cexao
end if
pex(ipt2+istk) = pex(ipt2+istk) + pexao
C
C— Update aqueous/NAPL phase mass exchange.
C
pex(ipt2x6+istk) = pex(ipt2x6+istk)+pexao*cmw(ic)
C
C— Update NAPL/aqueous component mole exchange.
C '
cex(ins+istk) = cex(ins+istk) - pexao
C
C— Update NAPL/aqueous phase mole exchange.
C
pex(ipt2x2+istk) = pex(ipt2x2+istk) - pexao
C
C— Update NAPL/aqueous phase mass exchange.
C
pex(ipt2x7+istk) = pex(ipt2x7+istk)-pexao*cmw(ic)
C
C— Update right hand side terms.
C
rhsex(iasn-istk) = rhsex(ias-!-istk)
+ + cexao * casolt * xmf(in+i)
end if
else
C
C— Calculate aqueous/gas exchange where NAPL is absent and both
C— mobile phases are present.
C
if((ipt(3)+ipt(4)).ne.ipt(3).and.igc.eq.iac)then
C
C— PUT USER DEFINED AQUEOUS/GAS MASS TRANSFER COEFFI-
CIENT FUNCTION
C— HERE. ASSIGN IT TO KAG TO UTILIZE BUILT-IN CONTROL
C
if(limag) then
kag = kex(5*(ic-l)+l)
C
C— Gas/aqueous control on mass transfer coefficient with the greater
C— of the gas or aqueous phase advective velocity or diffusional
C— velocity.
C
kag = dminl( kag,-(dmaxl( qaveg©
+ , qavea(i), cmdif(2*ic-l)/xl(i)**2
+ , cmdif(2*ic)/xl(i)**2)
+ * dlog(kmax(ic))))
C
C— PUT USER DEFINED AQUEOUS/GAS MASS TRANSFER COEFFI-
CIENT FUNCTION
C— HERE. ASSIGN IT TO KAG TO BYPASS BUILT-IN CONTROL
C
else
kag = kex(5*(ic-l)+l)
end if
C
C— Calculate constants.
C
sdgas = den(i)
sdaq = den(iptl+i)
keqag = patm*casolt/cvpt
C
C— Update left hand side terms for aqueous phase equations.
C
cexag = sdaq * kag
if(sgcont.lt.sgtest) cexag = zerO
cex(ias+istk) = cex(ias+istk) + cexag
C
C— Update aqueous/gas phase mole exchange.
C
pexag = cexag * (keqag*xmf(ig+i) - xmf(ia+i))
pex(ipt2+istk) = pex(ipt2+istk) + pexag
C— Update aqueous/gas phase mass exchange.
C
pex(ipt2x6+istk) = pex(ipt2x6+istk)+pexag*cmw(ic)
C— Update gas/aqueous phase mole exchange.
C
pex(istk) = pex(istk) - pexag
C
C— Update gas/aqueous phase mass exchange.
C
pex(ipt2x5+istk) = pex(ipt2x5+istk)-pexag*cmw(ic)
C— Update the right hand side terms for the component transport
C— equations.
C
rhsex(igs+istk) = rhsex(igs+istk) - pexag
rhsex(ias-Mstk)
+ = rhsex(ias+istk) + cexag*keqag*xmf(ig+i)
end if
end if
C
C— Calculate the exchange terms when adsorption is considered.
C— Use Freundlich isotherms for the equilibrium solid phase loading.
C— Adsorption can only occur if the aqeous phase is present. Only
C— include adsorption when NAPL is not present
C
if((ipt(6).gt.0).and.(ipt(4).gt.0).and.iac.eq.isc)
+ then
C
C— Set the aqueous phase mole fraction for aqueous/solid exchange
C— to zero if it is nonpositive.
C
if(xmf(ia+i).Ie.zerO) then
xmfa = zerO
else
xmfa = xmf(ia+i)
end if
C
C— PUT USER DEFINED AQUEOUS/SOLID MASS TRANSFER COEFFI-
CIENT FUNCTION
- HERE. ASSIGN IT TO KSA TO UTILIZE BUILT-IN CONTROL
C
if(limas) then
ksa = kex(5*(ic-l)+5)
C
C— Aqueous/solid control on mass transfer coefficient with the
C— greater of the aqueous phase advective velocity or
C— diffusional velocity.
C
ksa = dminl( ksa, -(dmaxl( qavea(i),
+ cmdif(2*ic)/xl(i)**2)
+ *dlog(kmax(ic+4*ipt(65)))))
C
C— PUT USER DEFINED AQUEOUS/SOLID MASS TRANSFER COEFFI-
CIENT FUNCTION
C— HERE. ASSIGN IT TO KSA TO BYPASS BUILT-IN CONTROL
C
else
ksa=kex(5*(ic-l)+5)
end if
C
_ - Calculate constants. This form puts the mass transfer resistance
C—• for solid/aqueous interactions into the aqueous phase
C
C
C— Set the aqueous phase equilibrium mole fraction to zero if the
C— solid phase mass fraction is nonpositive.
C
if(xmf(is-H).le.zerO) then
efrac = zerO
else
efrac = (( xmf(is+i) / bok(l)) ** bom(l))
+ / ( cmw(ic) * den(iptl+i) * 1.0d3 )
end if
sdaq = den(iptl+i)
203
-------
C— Update left hand side terms for aqueous phase equations.
ccxas * sdaq * Icsa
cex(ias+lstk) = cex(iastislk) + cexas
C
C— Update left hand side terms for solid phase equations.
C
cex(lss+istk) * zerO
C
C— Update aqueous/solid phase mole exchange. Tnis ibrm puts the
C— mass transfer resistance for solid/aqueous interactions into
C— (he aqueous phase.
C
pexas = cexas*(efrac-xmfa)
pcx(ipt2+istk) = pex(ipt2+istk) + pexas
C
C— Update solid/aqueous phase mass exchange. This form puts the
C— mass transfer resistance for solid/aqueous interactions into
C— the aqueous phase.
C
pcx(ip!2x8+istfc) = pex(ipt2x8+istfc)-pexas*cmw(ic)
C
C— Update aqueous/solid phase mass exchange. This form puts the
C— mass transfer resistance for solid/aqueous interactions into
C— the aqueous phase.
C
pcx(ipl2x6+islk) = pex(ipt2x6+istk)+pexas*cmw(ic)
C
C— Update right hand side terms, first for the aqueous phase and
C— then the solid phase,
C
rhscx(iss+istk) = rhsex(iss+istk) - pexas
rhscx(ias+istk) = rhsex(iastistk) +• cexas * efrac
C
C— Calculate terms for two compartment sorption model. This can
C— only be used for one organic component. The slow compartment
C— terms have been caluclated above (ipt(6)=l), the fast compartment
C— terms are calculated below (ipt(6)=2).
C
if«ipt(6).cq,2).and.letrl(19))then
C
C— PUT USER DEFINED AQUEOUS/SOLID MASS TRANSFER COEFFI-
CIENT FUNCTION
C— HERE. ASSIGN IT TO KS A TO UTILIZE BUILT-IN CONTROL.
C
ifClimas) then
ksa = xkex*kex(5*(ic-l)+5)
C
C— Aqueous/solid control on mass transfer coefficient with the
C— greater of the aqueous phase advective velocity or
C— diffusions! velocity.
C
ksa = dininl( ksa, -( dmaxl(
+ qavea(i), cmdif(2'ic)/xl(i)**2)
•f * dlog(kmax(ic+4*ipt(65)))))
C
C— PUT USER DEFINED AQUEOUS/SOLID MASS TRANSFER COEFFI-
CIENT FUNCTION
C— HERE. ASSIGN IT TO KSA TO BYPASS BUILT-IN CONTROL.
C
else
ksa = xkex*kex(5*(ic-l)+5)
end if
C
C— Set the aqueous phase equilibrium mole fraction to zero if the
O— solid phase mass fraction is nonpositive.
C
iftxmfl(is-t-i+iptl).le,zer0) then
efrac = zcrO
else
efrac = ((xmf(is+i+iptl )/(xbok*bok(l)))
+. **(xbom*bom(l)))
+ / ( cmw(ic) * den(iptl+i) * 1 .Od3)
end if
ccxas = sdaq * ksa
ccx(iastistk) = cex(ias+istk) + cexas
ccx(iss+istk+ipt2) = zerO
pexas s eexas*(efrac-xnifa)
pex(ipt2+istk) = pex(ipt2-Msfk) + pexas
pe*(fpt2x8+istfc)
= p*ex(ipt2x8+istk) - pexas*cmw(ic)
pex(ipt2x64-istk)=pex(ipt2x6+istk)+pexas*crhw(ic)
rnsex(is^istk-Hpt2)
+ = fhsex(i^s+iitk4-ip't2) - pexas
rfisex(iaS+istk)=rh'sex(ias+istk) + cexa'S * efrac
eridif
Sndif
C— Calculate aquebusTbiophaSe rhble transfer only if NAPL is absent
C— and the biofea'ctioh terms are riot in'sefted directly ihto the
C— aqueous phase equations.
if(lctrl(3)) then
C— PUT USER DEFINED AQUEOUS/BlOPHASE MASS TRANS-
FER COEFFICIENT
c— FUNCTION HERE. ASSIGN rr TO ftAfi TO UTILIZE BUILT-
IN coNf R'OL.
c
if(limabj then
kab = kex(5*(ic-i)+4)
C
- Aqueous/biophaSe control oil mass transfer coefficient with the
C— greater of the aq'ireous pha'se advecfive velocity or
C— aqueous phase diffusiohal velocity.
C
kab = dminU kab, -(dmaxl( q'a'vea(i)',
+ cmdif(2*ic)/xl(i)**2)
+ *dlog(kmax(ic+3*ipt(65)))))
C
C— PUT USER DEFINED AQUEOUS/BIOPHASE MASS TRANS-
FER COEFFICIENT
C— FUNCTION HERE. ASSIGN IT TO KAB TO UTILIZE BUILT-
IN CONTROL.
C
else
kab = kex(5*(ic-l)+4)
end if
C
C— Calculate cbnsfahis".
C
sdaq = deh(ipti+i)
C
C— This form assumes that biophase exchange is controlled in the
C— aqueous phase.
C
sdb = sdaq
C
C— Update left hand side terms for aqueous phase equations. The
C— bibmass term a'ccounts for the volume of the reactive phase
C— properly.
C
cexab = kab * sdb
C
C— Update aqueoUs/biophase phase mole exchange.
C
if(.not.lctrl(16))then
C
C— Set the aqueous and bio phase mole fractions to zero if they
C— are nonpositive.
C
if(xmf(ia+i).le.zerO) then
xmfa = zerO
else
xmfa = xmf(ia+i)
end if
if(xmf(ib+i).le.zerO) then
xmfb = zerO
else
xmfb = xmf(ib+i)
end if
pex(ipt2+istk) = pex(ipt2+istk)
+ - cexab * (xmfa - xmfb)
C
C— Update aqueous/biophase phase mass exchange.
C
204
-------
pex(ipt2x6+istk) = pex(ipt2x6+istk)
+ - cmw(ic) * cexab * (xmfa - xmfb)
C
C— Update biophase/aqueous phase mole exchange.
C
pex(ipt2x4+istk) = pex(ipt2x4+istk)
+ + cexab * (xmfa - xmfb)
C
C— Update biophase/aqueous phase mass exchange.
C
pex(ipt2x9+istk) = pex(ipt2x9+istk)
+ + cmw(ic) * cexab * (xmfa - xmfb)
C
C— Update the right hand side terms for the component transport
C— equations.
C I
rhsex(ias+istk) = rhsex(ias+istk)
+ + cexab * xmf(ib+i)
rhsex(ibs+istk) = rhsex(ibs+istk)
+ + cexab * (xmfa - xmfb)
C
C— Do not consider aqueous/biophase phase mole exchange, however
C— include the bioreaction loss.
C
end if
end if
100 continue
C
C— Now calculate mass exchange for oxygen. Mass exchange
C— for oxygen is only considered for bioventing simulations. First
C— compute pointers.
C
if(lctrl(3)) then
ico = ipt(15) + 2
C
C— Consider moist gas phase.
C
if(icp(ipt(13)+2).eq.ico) then
igo = (ipt(13)-H)*ipt(l)
igos = (ipt(13)+l)*ipt2
C
C— Consider dry gas phase.
C
else
igo = ipt(13)*ipt(l)
igos = ipt(13)*ipt2
end if
iao = ipt(9) + (ipt(14)-H)*ipt(l)
ibo = ipt(12) + ipt(17)*ipt(I)
iaos = ipt(3)*ipt2 + (ipt(14}il)*ipt2
ibos = (ipt(3)+ipt(4)+ipt(5)+ipt(6))*ipt2 + ipt(17)*ipt2
C
C— Iterate over the nodes.
C
do200i = l,ipt(l)
if(lctrl(10)) then
cvpt = cvp(ico)
casolt = casol(ico)
else
itemp = (ico-l)*ipt(89)+idepth(i)
itemp2 = (ico-l)*ipt(89)+3*ipt(88)+idepth(i)
cvpt = cvp(ico) + dtemp(itemp)
casolt = casol(ico) + dtemp(itemp2)
end if
C
C— PUT USER DEFINED AQUEOUS/BIOPHASE MASS TRANS-
FER COEFFICIENT
C— FUNCTION HERE. ASSIGN IT TO KABO TO UTILIZE BUILT-
IN CONTROL.
C
if(limab) then
kabo = kex(5*(ic-l)+4)
C
C— Aqueous/biophase control on mass transfer coefficient with the
C— greater of the aqueous phase advective velocity or
C— aqueous phase diffusional velocity.
C
kabo = dminl( kabo, -(dmaxl( qavea(i),
+ cmdif(2*ic)/xl(i)**2 ) * dlog(kmax(ic+3*ipt(65)))))
C
C— PUT USER DEFINED AQUEOUS/BIOPHASE MASS TRANS-
FER COEFFICIENT
C— FUNCTION HERE. ASSIGN IT TO KABO TO BYPASS BUILT-
IN CONTROL.
C
else
kabo = kex(5*(ic-l)+4)
end if
C
C— Turn off aqueous/biophase oxygen exchange if the aqueous phase
C— oxygen mole fraction is negative.
C
if(xmf(iao+i).lt.zerO) kabo = zerO
C
C— PUT USER DEFINED AQUEOUS/GAS MASS TRANSFER COEFFICIENT
C— FUNCTION HERE. ASSIGN IT TO KAGO TO UTILIZE BUILT-
IN CONTROL.
C
if(Iimag) then
kago = kex(5*(ic-l)+l)
C
C— Gas/aqueous control on mass transfer coefficient with the greater
C— of the gas or aqueous phase advective velocity or diffusional
C— velocity.
C
kago = dminl( kago, -(dmaxl( qaveg(i)
+ , qavea(i), cmdif(2*ic-l)/xl(i)**2, cmdif(2*ic)
+ /xl(i)**2) * dlog(kmax(ic))))
C
C— PUT USER DEFINED AQUEOUS/GAS MASS TRANSFER COEFFICIENT
C— FUNCTION HERE. ASSIGN IT TO KAGO TO BYPASS BUILT-
IN CONTROL.
C
else
kago = kex(5*(ic-l)+l)
end if
C
C— Turn off gas/aqueous oxygen exchange if the gas phase
C— oxygen mole fraction is negative.
C
if(xmf(igo+i).lt.zerO) kago = zerO
C
C— Calculate constants. Use aqueous phase properties for the biophase
C
keqag = patm*casolt/cvpt
sdaq = den(iptl+i)
C
C— This form assumes that exchange is into a biophase, the size of
C— which is determined by the maximum allowable biomass. Aqueous
C— phase material properties are used to determine the volume of the
C— biophase.
C
sdb = sdaq
C
C— Update left hand side term for the aqueous phase equations.
C— First consider aqueous/gas oxygen mole exchange.
C
cexago = sdaq * kago
do 200 ii = 0, nodept(i+l)-nodept(i)-l
istk = ii + nodept(i)
sgcont = sat(istk)
if(sgcont.lt.sgtest) cexago = zerO
cex(iaos+istk) = cex(iaos+istk) + cexago
C
C— Then consider aqueous/biophase oxygen mole exchange. The biomass
C— term accounts for the volume of the reactive phase properly.
C
cexabo = kabo * sdb
C
C— Update aqueous/gas phase mole exchange.
C
pexago = cexago * (keqag*xmf(igo+i) - xmf(iao+i))
pex(ipt2+istk) = pex(ipt2+istk) + pexago
C
C— Update aqueous/gas phase mass exchange.
C
205
-------
pex(ipt2xfrtistk) = pex(ipt2xfrfistk) H- pexago*cmw(ico)
C
C— Updntc aqucous/biophase phase mole exchange.
C
if(,Bot.fcttI(16))thett
C
C — Scl the aqueous and bio phase mole fractions to zero if they
C— are nonpositive,
C
lf(xmf(iaKrt0.k!,zetO) then.
else
xmfa=xmf(iao+i)
end if
i(l(xmf(ibo+i).lc,zerO) then.
else
xmf(ibo+i)i
end if
pexabo - cexabo * (xmfa - xmJb)
pexflpG+istk) » pex(ipt2+istk) - pexabo
C
C— Update aqucous/biophase phase mole exchange.
C
pcx(ipt2x6+istk) = pex(ipt2x6+istk) - pexabo*cmw(ico)
C
C — Update biophase/aqueous phase mole exchange.
C
pex(ipt2x4+istk) = pex(ipt2x4+istk) + pexabo
C
C~ Update biophase/aqueous phase mass exchange.
C
pcx(ipt2x9+istk) * pex(ipt2x9+istk) +• pexabo
C
C — Do not consider aqueous/biophase phase mole exchange, however
C— include the biorcaction loss.
C
end if
C
C — Update gas/aqueous phase mole exchange.
C
pcx(istk) = pex(istk) - pexago
C
C — Update the right hand side terms for the component transport
C— equations,
C
rhsex(igostistk) =rhsex(igos+istk) - pexago
rhsex(iaos+istk)
•<• s rhscxflaos+istk) +• cexago * keqag * xmf(igo+i)
if(.noUctrl(16)) tlien
rhscx(iaos+is:k) = rhscx(iaos+istk)
•(- +• cexabo * xmfb
rhscx(ibos+!stk) = rhsex(ibos+istk)
+ + cexabo * ( xmfa - xmfb )
end if
200 continue
C
C — Now calculate mass exchange for the nutrient. Mass exchange for
C— nutrient is only considered for bioventing simulations. First
C— compute pointers.
C
if(fcttl(9))tncn
ign = ipt(9)-ipt(l)
ian = ipt(10)-ipt(l)
ibn « ipt(12) + ipt(l) * (ipt(7)-2)
igns-(ipl(3)-l)*ipt2
ians = (ipt(3)+iptW-l)*ipt2
ibns = (ipt(3)+ip!(4)+ipt(5Hipt(6>ipt(7)-2)*ipt2
C
C — Iterate over the nodes.
C
do2IOi=l,ipt(l)
if
-------
C— biomass term accounts for the volume of the reactive phase
C— properly.
C
cexabn = kabn * sdb
C
C— Update aqueous/gas phase mole exchange.
C
pexagn = cexagn * (keqag*xmf(ign+i) - xmf(ian+i))
pex(ipt2+istk) = pex(ipt2+istk) + pexagn
C
C— Update aqueous/gas phase mass exchange.
C
pex(ipt2x6+istk) = pex(ipt2x6+istk)+pexago*cmw(icn)
C
C— Update aqueous/biophase phase mole exchange.
C
if(.not.lctrl(16))then
C
C— Set the aqueous and bio phase mole fractions to zero if they
C— are nonpositive.
C
if(xmf(ian+i).Ie.zerO) then
xmfa = zerO
else
xmfa = xmf(ian+i)
end if
if(xmf(ibn+i).Ie.zerO) then
xmfb = zerO
else
xmfb = xmf(ibn+i)
end if
pexabn = cexabn * (xmfa - xmfb)
pex(ipt2+istk) = pex(ipt2+istk) - pexabn
C
C— Update aqueous/biophase phase mole exchange.
C
pex(ipt2x6+istk)
+ = pex(ipt2x6+istk) - pexabn * cmw(icn)
C
C— Update biophase/aqueous phase mole exchange.
C
pex(ipt2x4+istk) = pex(ipt2x4+istk) + pexabn
C
C—• Update biophase/aqueous phase mass exchange.
C
pex(ipt2x9+istk) = pex(ipt2x9+istk) + pexabn
end if
C
C— Update gas/aqueous phase mole exchange.
C
pex(istk) = pex(istk) - pexagn
C
C— Update the right hand side terms for the component transport
C— equations.
C
rhsex(igns+istk) = rhsex(igns+istk) - pexagn
rhsex(ians+istk) = rhsex(ians+istk)
+ + cexagn * keqag * xmf(ign+i)
if(.not.lctrl(16)) then
rhsex(ians+istk) = rhsex(ians+istk)
+ + cexabn * xmfb
rhsex(ibns+istk) = rhsex(ibns+istk)
+• -i- cexabn * (xmfa - xmfb)
end if
210 continue
end if
end if
C
C— Calculate water mass exchange between the aqueous and gas phases.
C— This is done only when both mobile phases are present and water is
C— present in the gas phase. The presence of NAPL has no effect
C— on this term. Gas phase mole fractions controls water mole
C— exchange.
C
icw = ipt(15) + 1
icl = icp(ipt(13)+l)
if((icl.eq.icw).and.(ipt(3)+ipt(4)).ne.ipt(3))then
igw = ipt(13)*ipt(l)
iaw = ipt(9) -t- ipt(14)*ipt(l)
igws = ipt(13)*ipt2
do300i = l,ipt(l)
if(lctrl(10)) then
cvpt = cvp(icw)
else
itemp = (icw-l)*ipt(89)+idepth(i)
cvpt = cvp(icw) + dtemp(itemp)
end if
keqw = cvpt/patm
C
C— PUT USER DEFINED GAS/AQUEOUS MASS TRANSFER COEFFICIENT
C— FUNCTION HERE. ASSIGN IT TO KGAW TO UTILIZE BUILT-
IN CONTROL.
C
if(Iimag) then
kgaw = kex(5*(ic-l)+l)
C
C— Gas/aqueous control on mass transfer coefficient with the greater
C— of the gas or aqueous phase advective velocity or diffusional
C— velocity.
C
kgaw = dminl( kgaw, -< dmaxl( qaveg(i)
+ , qavea(ij, cmdif(2*ic-l)/xl(i)**2, cmdif(2*ic)
+ /xl(i)**2) * dlog(kmax(ic))))
C
C— PUT USER DEFINED GAS/AQUEOUS MASS TRANSFER COEFFICIENT
C— FUNCTION HERE. ASSIGN IT TO KGAW TO BYPASS BUILT-
IN CONTROL.
C
else
kgaw = kex(5*(ic-l)+l)
end if
C
C—• Update constants.
C
sdgas = den(i)
sdaq = den(iptl+i)
C
C— Update left hand side terms for gas phase equations
C
cexagw = sdgas * kgaw
do 300 ii = 0,nodept(Hi)-nodept(i)-1
istk = ii + nodept(i)
sgcont = sat(istk)
if(sgcont.lt.sgtest) cexagw =zerO
cex(igws+istk) = cex(igws+istk) + cexagw
C
C— Update aqueous/gas phase mole exchange.
C
pexagw = cexagw * (keqw*xmf(iaw+i) - xmf(igw+i))
pex(ipt2+istk) = pex(ipt2+istk) - pexagw
C
- Update aqueous/gas phase mass exchange.
C
pex(ipt2x6+istk) = pex(ipt2x6+istk) - pexagw*cmw(icw)
C
C— Update gas/aqueous phase mole exchange.
C
pex(istk) = pex(istk) + pexagw
C
- Update gas/aqueous phase mass exchange.
C
pex(ipt2x5+istk) = pex(ipt2x5+istk) + pexagw*cmw(icw)
C
- Update the right hand side terms for the gas phase transport
C—• equations. The aqueous phase does not have a water transport
C— equation since the effect of water mass exchange is accounted
C— for through the phase exchange terms.
C
rhsex(igws+istk) = rhsex(igws+istk)
+ + cexagw * keqw * xmf(iaw+i)
300 continue
end if
return
end
207
-------
ijie *• napjs,f
c
c
c
c
C Arguments: jconv - integer flag for global convergence
C
C Required Control Hi(gs:
C
C
C
c
c
c
c
c-
NAPLSJ - Subroutine which updates the NAPL
saturations using the finite element method.
1(16) - convergence criterion for immobile phases
Control Flags computed internally in routine:
ipt(38) - flag specifying time step modification
subroutine NAPLS(konv)
include 'dimcn.lnc'
C
C — Pccliira jind deli ne common block variables.
C
common /cbl/ matel(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ matpt(nn6)
common fcblc/ abyl2(nelmx),aby30(nelmx)
common /cb3/ sat(nnstk3)
common /cb3b/ satt(nnstk3)
common /cbfib/ porfnclmx),srw(nnstk)
common /cblO/ den(nnS)
common /cblOb/ dden(nn6),pmwt(nn3),dent(nn6)
common /cbl l/pex(nnslO),rxnp(nn2)
common /cWO/ a(icnl),rhs(nsolve),w(icnl)
C
C— Set pointers,
C
fpt(38)=0
mssjpt(49)
insm = ipt(54)
C
C — Begin iterations.
C
do400itnapl=l.ipt(33)
dollOi = l,ipt<2)
tlis(i) = zerO
110 a(i) = zcrO
do I20i=l,ipl(0)
C
C— Set the pointers to the local nodes II, 12, and 13. The
C— postscript s is for stacked local nodes, and p is for phase
C — Compute constants.
C
ie!3 = i*3
icll = ie!3-2
icl2 = ic!3-I
ilsnodcHiell)
1 1 s = nodepl(i I } i- nc!pt(iel 1 )
ilpsm = insm4 Us
12-nodcl(iel2)
i2s = nodep«i2>tnelpt(iel2)
i2psm — insm + i2s
i3s = nodepl(i3)+nclpt(iel3)
i.lpsm = insm + i3s
dl =ronc
d2 s rone
03 = rone
term = por(i)'aby30(i)/l(8)
C
C— Compute the mass matrix.
C
a! I =Merm*( 3.0dO*dl + d2+ d3)
al2 = term*( dl+ d2+ d3/2.0dO)
al3sterm*( dl+ d2/2.0dO + d3 )
all=al2
«22 m term*( dl + 3.0dO*d2 + A3 )
43)
a31,=al3
s33i=term*,( dH- 4213,OdO*d3)
'mass* matrix.
aU=aH+aJ24-al3
a!2 = zerO
aJ3 = zerO
a22 = a
a21 = zerO
a23 = zerO
a31=zerO
a32 = zerO
C— Now compute the right hand side terms.
,.. . 2 = por(i)*abyl2(i)
if(ipt(5).gt.l)then
rhsl = pex(ilpsm)
rhs2 = pex(i2psm)
rhs3 = pex(i3psm)
else
rhsl =pex(ilpsm)
rhs2 = pex(i2psm)
rhs3 = pex(i3psm)
end if
fl = term!2 * ( 2.0dO*rhsl + rhs2 + rhs3)
f2 = term!2*( rhsl+2.0dO*rhs2+ rhs3)
f3 = term!2*( rhsl+ rhs2 + 2.0dO*rhs3)
^
C— Assemble global matrix and right hand side vector. Note that
C— the left hand side matrix is diagonal due to mass lumping and
C— the solution is therefore explicit.
C
120
C
C—
c—
c
a(i2s) = a(i2s) + a22
a(i3s) = a(i3s) + a33
rhs(ils) = rhs(ils) + fl
rhs(i3s) = rhs(i3s) + f3
continue
Solve for saturations. Skip any node where the NAPL saturation
is zero. Determine the max norm of the updated solution.
dsat = zerO
satmax = smino
do!50i=l,ipt(l)
do!50ii = 0, nodept(i+l)-nodept(i)-l
imat = nodept(i)+ii
isat = imat + ins
satold=sat(isat)
if(sat(isat).gt.smino) then
if(a(imat).ne.zerO) then
sat(isat) = (dent(ipt(l)*5+i)*satt(isat)
+ + rhs(imat)/a(imat))/den(ipt(l)*5+i)
satmax = dmaxl(satmax,dabs(sat(isat)))
dsat = dmaxl(dsat,dabs(sat(isat)-satold))
end if
else
C
C — Set NAPL saturation equal to zero when it falls below zero.
C
150
C
sat(isat) = zerO
end if
continue
Return when NAPL has only one component.
if(ipt(5).eq.l)then
ipt(38) = 1
208
-------
return
endif
C
C— Check convergence with the relative change in state variable for
C— the multicomponent case.
C
if(dsat/satmax.le.t(15)) then
if(ipt(28).gt.O) then
write(ipt(28),*)' NAPL saturation iterations =', itnapl
endif
if(itnapl.le.ipt(34)) ipt(38) = 1
return
endif
400 continue
write(*,*) 'Maximum iterations exceeded in NAPLS; ', itnapl-1
iconv = iconv + 1
return
end
Subroutine - naplx.f
C
C
C NAPLX.f - Subroutine which updates the NAPL phase
C mole fractions using the finite element method.
C
C Arguments: iconv - integer flag for global convergence
C
C Required Control Flags:
C
C t( 16) - convergence criterion for immobile phases
C Ictrl(S) - logical variable controlling type of FEM
C solution for transport
C Ictrl{8)= .true. - use mass lumping
C lctrl(S) = .false. - full FEM solution
C
C
subroutine NAPLX(iconv)
include 'dimen.inc'
character*10 cname(ncmp)
C
C— Declare and define common block variables.
C
common /cbl/ matel(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ matpt(nn6)
common /cble/ abyl2(nelmx),aby30(nelmx)
common/cb3/ sat(nnstk3)
common /cb6b/ por(nelmx),srw(nnstk)
common/cb9/ xmf(nmf)
common/cb9b/ xmft(nmf)
common /cblO/ den(nn6)
common /cbl II pex(nnslO),rxnp(nn2)
common /cb40/ a(icnl),rhs(nsolve),w(icnl)
common /cb41/ irn(icnl),icn(icnl),iw(icnl,8),ikeep(icnl,5)
common /cb41b/ nbw(0:2),ia
common /cb62/ rxn(nmf),cex(nmfs)
common /cb91/ cname
C
C— Set pointers.
C
in = ipt(40)
ins = ipt(49)
C
C— Now sequentially solve for the NAPL mole fractions.
C
do 200 icnapl = l,ipt(5)
iptc = ipt(58) + icnapl
icpt = (iptc-l)*ipt(l)
icpts = (iptc-l)*ipt(2)
C
C— Zero the finite element matrices.
C
do210i = l,ipt(2)
rhs(i) = zerO
nrow = (i-l)*nbw(l)
do210j=l,nbw(l)
210 a(nrow+j) = zerO
C
C— Compute the local finite element matrices.
C
do 220 i = l,ipt(0)
C
C— Set the pointers to the local nodes 11,12, and 13. The
C— postscript s is for stacked local nodes, p is for phase, and
C— c is for component. Compute constants.
C
ie!3=i*3
iell =ieI3-2
iel2 = ie!3-l
il=nodel(iell)
ils = nodept(il)+nelpt(iell)
ilp = in + il
ilps = ins + ils
ilc = icpt + il
ilcs = icpts + ils
i2 = nodel(ie!2)
i2s = nodept(i2)+nelpt
-------
b31=b!3
b32 = b23
b33 = tenn30*(pexl
C
C~— Lump the "mass" matrix.
C
if(lctrl(S)) then
all sa
a2l szcrO
+ pex2 + 3.0dO*pex3)
end if
C
C— Now compute the right hand side terms.
C
lcrmI2 = porfi)*abyl2(i)
rhsl =cex(ilcs)
rhs3=ccx(i3cs)
n « tcnnl2 * ( 2.0dO»rhsl + rhs2 + rhs3)
R « tcrmlZ * ( rhsl + 2,OdO*rhs2 + rhs3 )
rhsl + rhs2 + 2.0dO*rhs3)
• Assemble global matrix and right hand side vector in banded form.
irowl=(il-l)*nbw(l)
irow2 = (i2-l)*nbw{l)
Irow3*(i3-l)*nbw(l)
koll2*icom+(!2-il)
icol2I=ico122 + (il-i2)
Icol23 = icol22+(i3-i2)
icol33
tbl 1 sail + l(10)*bll
ab21=«21+t(10)*b21
ab3l=a3H-t(10)*b31
220
C
C —
C —
C
a(irowl -t-icolll) = a(irowl -t-icolllj + abll
a(trowl +ico!12)=a(irowl -Hcoll2) + abl2
n(irowl +icoll3) = a(irowl+icoll3) + abl3
a(irow2 + ico!21 ) = a(irow2 + ico!21 ) + ab21
a(irow2 + ico!22) - a(irow2 -f- ico!22) + ab22
a(irow2 + ico!23) = a(lrow2 +• ico!23) + ab23
a(irow3 + Icol31) = a(irow3 + ico!31) + ab31
a(irow3 + ico!32) = a(irow3 + ico!32) + ab32
a(irow3 4- ico!33) = a(iro%v3 + ico!33) + ab33
riis(il) = rlis(il) + fl -bll *xmft(ilc)
-bl2*xmft(i2c)-bl3*xnift(i3c)
rhs(i2) * rhs(i2) + tl - b21 * xmft(ilc)
-b22*xmft(i2c)-b23*xmft(i3c)
rhs
-------
Subroutine - prnt.f
c—
c
C PRNT.f - outputs current values of selected variables
C defined in the logical array'Iprnt'.
C
C Required Control Flags:
C
C Ictrl(l) - logical variable controlling presence of flow
C solution
C lctrl(l) = .true, -computeflow solution
C lctrl(l) = .false. - skip flow solution
C lctrl(2) - logical variable controlling presence of transport
C solution
C lctrl(2) = .true. - compute transport solution
C lctrl(2) = .false. - skip transport solution
C Ictrl(3) - logical variable controlling inclusion of
C biodegradation
C lctrl(3) = .true. - include biodegradation
C lctrl(3) = .false. - neglect biodegration
C lctrl(lS) - logical variable denoting type of q calculation
C lctrl(18) = .true.-nodelFEMq
C lctrl(18) = .false. - element average q
C lctrl(19) - logical variable controlling type of sorption
C lctrl(19) = .true. - two compartment sorption
C lctrl(19) = .false. - single compartment
C sorption
C lctrl(23) - logical variable controlling the printing of
C contour plot data
C lctrl(23) = .true. - print contour plot data
C lctrl(23) = .false. - do not print contour
C plot data
C
C
subroutine PRNT (its)
include 'dimen.inc'
character*20infile(4),outpre,outfile(8+ncmp)
character* 10 cname(ncmp)
common /cbl/ matel(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ matpt(nn6)
common /cblc/ xnode(nnmx),znode(nnmx),rbar(nelmx),area(nelmx)
common/cb2/ p(nn3)
common /cb2c/ q(ne!4)
common/cb3/ sat(nnstk3)
common /cb6b/ por(nelmx),srw(nnstk)
common /cb7b/ cmw(ncmp),cvp(ncmp),cden(ncmp),
+ chen(ncmp),casol(ncmp),cmdif(ncmp2)
common /cb9/ xmf(nmf)
common /cblO/ den(nn6)
common /cb 10b/ dden(nn6),pmwt(nn3),dent(nn6)
common /cbl II pex(nns 10),rxnp(nn2)
common /cb64/ bok(nbcmp),bom(nbcmp),krtd(ncmp)
common /cb64b/ bsden(nmblk)
common /cb86/ Strl(ncmpp5),str0(ncmpp5),cmf(ncmpp5),csink(ncmpp5)
+ ,cwsink(ncmpp5),csflux(ncmpp5),cmassl(ncmp5),cmassO(ncmp5)
+ ,cphex(ncmpp5),crsink(ncmpp5),tmassl,tmassO
common /cb90/ infile,outpre,outfile
common /cb91/ cname
C
C— Dimension local arrays, rcont, contr, and xm are dimensioned
C— with two less than maximum number of output columns divided by
C— 10. Currently dimensioned to support 132 column output maximum.
C
dimension tp(nnstk3),rcont(l l),xm(l 1)
character contr(l 1)*10
C
C— Nout + 2 is the number of output columns desired in outpre.con
C— Currently set to 5 columns for 80 column output. Set nout to 6
C— for 132 column output.
C
data nout/3/
C
C— Print header and time.
C
write (21,500) its,t(9),t(9)/60.0dO,t(9)/3600.0dO,t(9)/.8640d5
C— Print nodel gas phase pressure.
C
if(Iprnt(9))then
Doi = l,ipt(l)
tp(i) = (patm+p(i)) / patm
EndDo
callfprnt(21,tp(l),ipt(l),
+ '@ Nodal gas phase pressure (atm)')
endif
C
C— Print nodel aqueous phase pressure.
C ...
if(lprnt(10))then
Doi = l,ipt(l)
tp(i) = (patnH-p(ipt(l)-t-i)) / patm
EndDo
caUfprnt(21,tp(l),ipt(l),
+ ' @ Nodal aqueous phase pressure (atm)')
endif
C
C— Print nodel capillary pressure.
C
if (lprnt(l 1)) call fprnt (21,p(2*ipt(l)+l),ipt(l),
+ ' @ Nodal gas/aqueous capillary pressure (Pa)')
C
C— Print gas phase mass or molar density.
C
if(lprnt(12))then
if(lprnt(8))then
call fprnt (21,den(l),ipt(l),
+ ' @ Gas phase molar density')
else
call fprnt (21,den(3*ipt(l)+l),ipt(l),
+ ' @ Gas phase mass density')
endif
endif
C
C— Print aqueous phase mass or molar density.
C
if(lprnt(13))then
if(lprnt(8))then
call fprnt (21,den(ipt(l)+l),ipt(l),
+ '@ Aqueous phase molar density')
else
call fprnt (21,den(4*ipt(l)+l),ipt(l),
+ '@ Aqueous phase mass density')
endif
endif
C
C— Print NAPL phase mass or molar density.
C
if(Iprnt(14))then
if(lprnt(8))then
call fprnt (21,den(2*ipt(l)+l),ipt(l),
+ ' @ NAPL phase molar density')
else
call fprnt (21,den(5*ipt(l)+l),ipt(l),
+ '@ NAPL phase mass density')
endif
endif
C
C— Print gas phase component output.
C
if(lprnt(15))then
do!0i=l,ipt(3)
ic=icp(i)
iptc=(i-l)*ipt(l)
if(lprnt(8)) then
call rprnt(21,xmf(iptc+l),ipt(l),
+ ' @ Nodal gas phase component mole fractions:'
+ //cname(ic))
else
do!5ii = l,ipt(l)
211
-------
1 5 lp(ii) * xmf{iptc+ii) * den(ii) * cmw(ic)
callfprnt(2|,lp(l)>ipt(l),
+ ' @ Nodal gas phase component concentrations (g/j):
t //ename(ic))
end if
10 continue
cnJif
C
C— Print aqueous phase component output.
C
if(lpmtpt(4)+ipt(5)
ic=icp(i)
if(lpnit(8))tlicn
call fprm(21,xmf(iptc+l),ipt(l),
+ ' • Nodal NAPL phase component mole fractions: '
+ //cnamc(ic))
else
do35ii=l,ipt(l)
35 tp(ii) = xmf(iptc+ii) * den(ipt(40)+ii) * cmw(ic)
callfpfnt<21,tp(l),ipt(l),
+ '© Nodal NAPk phase component concentrations (g/L): '
+ /fcnanxKlc))
end if
30 continue
cndif
C
C — Print solid phase mass loadings,
C
if(lpml(18))lhen
do 40 i=l+ipt(3)+ipt(4)+ipt(5),ipt(3)+ipt(4>l-ipt(5)H-ipt(6)
Ie=iep(i)
iptc=KM)*ipt{l)
if fktrl(19)) then
if(i-!pl(3)-ipt(4Hpt(5),eq.l)then
call fprnt(21,xmf(iptc+l),ipt(l),
+ ' ® Nodal slow solid phase component moss '
•*• //"loading gm/gm (slow compartment): '
•f //cnametic))
45 lp(ii) * xmf(iptc+ii)*(rone-xden)
call fprnl(21,tp(l),ipt(l),
+ '@ Notlal slow solid phase component mass '
+ //"loading gm/gm(bulk): '
+ //cnamc(ic))
else if (i.ipt(3).ipt(4).ipl(5).eq,2) then
ieaicp(i-l)
call fprnt(21,xmf(iptc+l),ipt(l),
+ ' @ Nodal fast solid phase component mass '
+ //"loading gm/gm(fast compartment): '
+ //cnamc(ic))
do50ii = l,ipt(l)
50 tp{ii) m xmf(ipte+ii)*xden
caHfprnt(2I,tp(l),ipt(I),
•*• '© Nodal fast solid phase component mass '
+ If loading gm/gm(bulk): '
+ //cnamc(ic))
.do55ii = l,ipt(l)
55 jp(ii) = xmf(iptc+ii)*xden
+ + xmf(iptc-ipt(l)+ii) * ( rone - jtden )
callfprrit(21,tp(l),ipt(|),
+ "@ Np.dal total solid phase component mass '
t //' loading gm/gm(bulk): '
t //cname(ic))
end if
else
call fprnt(21,xrnf(iptctl),ipt(l),
t ' <§ Nodal splid phase cpmppnent mass '
+ //'loading gm/gm(bu!kj: '
+ //cnam.e(ic))
end if
40 continue
endif
C
- Print biophase phase mole fractions.
C
if(lprnt(19))then
do 60 i=l+ipt(3)+ipt(4)+ipt(5)+ipt(6),
+ ipt(3)tipt{4)t"Pt(5)tipt(6)4-ipl(7)-l
ic=icp(i) "
iptc=0-))*ipKD
if(lprnt(8))then
call fprnt(21,xmf(iptc+l),ipt(l),
+ '@ ^odal bio-phase component mole fractions: '
+ //cname(ic))
else
do65ii = l,ipt(l)
65 tp(ii) = xmf(iptc+ii) * den(ipt(l)+ii) * cmw(ic)
callfprnt(21,tp(l),ipt(l),
+ '@ Nodal bio-phase component concentrations (g/L):
+ //cname(ic))
endif
60 continue
call fprat(2 1 ,xmf(ipt(l )+iptc+ 1 ),ipt( 1 ),
+ ' @ Nodal bio-phase biomass concentration')
endif
c
c — Compute and print an element average total organic soil
c — • concentration.
c
If (lprnt(29).or.lcon(!8)) then
Do jel = 1 ,ipt(0) Hoop over number of elements
n3=(jel-l)*3
xl = rbarfjel) * area(jel) * third
x = xl * por(jel)
iptlxS = ipt(41)
il = node!(n3+l) ! element node numbers
\2 = npdel(n3+2)
|3=nodel(n3+3)
igl = il ! nodel gas phase storage locations
ial = ipt(l )+igl ! nodel aqueous phase storage locations
ia2 = ipt(l)+ig2
ia3 = ipt(l)+ig3
inl = ipt(l)+ial ! nodel napl phase storage locations
in2 = ipt(l)+ia2
in3 =ipt(l)+ia3
ndstkl = nodept(il) + nelpt(n3+l) ! node position in stack
ndstk2 = nodept(i2) + nelpt(n3+2)
ndstk3 = nodept(i3) + nelpt(n3+3)
igls = ndstkl ! gas phase stacked node numbers
ig2s = ndstk2
ig3s = ndstkS
ials = ipt(2)+igls ! aqueous phase stacked node numbers
ia2s = ipt(2)+ig2s
ia3s = ipt(2)+ig3s
inls = ipt(2)+ials ! napl phase stacked node numbers
in2s = ipt(2)+ia2s
in3s = ipt(2)+ia3s
Wnapl = x * ( ! mass of napl
den(iptlx3+inl)*sat(inls) +
den(iptl x3+in2) * sat(in2s) +
den(iptlx3+in3)*sat(in3s))
Onapl = Wnapl ! mass of organic in napl
212
-------
Waq = x * ( ! mass of aqueous phase
+ den(iptlx3+ial)*sat(ials) +
+ den(iptlx3+ia2) * sat(ia2s) +
+ den(iptlx3+ia3) * sat(ia3s))
Oaq = zerO ! mass of organic in aqueous phase
Doi = l,ipt(14)
ipipt3 = i + ipt(3)
ic = icp(ipiptS)
iaqc = (ipipt3-l)*ipt(l)
Oaq = Oaq + krtd(ic) * x * cmw(ic) * (
+ den(ial) * sat(ials) * xmf(iaqc+il) +
+ den(ia2) * sat(ia2s) * xmf(iaqc+i2) +,
+ den(ia3) * sat(ia3s) * xmf(iaqc+i3))
EndDo
Wgas = x*( ! mass of gas phase
+ den(iptlx3-Higl)*sat(igls) +
+ den(iptlx3+ig2) * sat(ig2s) +
+ den(iptlx3+ig3) * sat(ig3s)) '
Ogas = zerO ! mass of organic in gas phase
Doi = l,ipt(13)
igasc = (i-l)*ipt(l)
ic = icp(i)
Ogas = Ogas + x * cmw(ic) * (
+ den(igl) * sat(igls) * xnrf(igasc+il) +
+ den(ig2) * sat(ig2s) * xmf(igasc+i2) +
+ den(ig3) * sat(ig3s) * xmf(igasc+i3))
EndDo
Wsld = bsden(matel(jel))*rbar(jel)*area(jel) ! mass of solid
Osld = zerO ! mass of organic in solid phase
Doi = l,ipt(16)
ipiptS = i + ipt(59)
ic = icp(ipipt5)
isc = (ipipt5-l)*ipt(l)
If(xbok.gt.zerO)then
If(i.eq.l)then
solden = (rone-xden)*bsden(matel(i))
Else If (i.eq.2) then
isum = ipt(3)+ipt(4)+ipt(5)
ic = icp(isum+i-l)
solden = xden*bsden(matel(i))
End If
Osld = Osld + solden*
+ ( xmf(isc+i 1) + xmf(isc+i2) + xmf(isc+i3) )
+ *xl
Else
Osld = Osld + bsden(matel(jel)) *
+ (xmf(isc+il) + xmf(isc+i2) + xmf(isc+i3))
+ *xl
Endlf
EndDo
c tp(jel) = 1 .d6*(Onapl+Oaq+Ogas+Osld)/CWnapl+Waq+Wgas+Wsld)
tp(jel) = l.d6*(OnapI+Oaq+Ogas+Osld)/(Ws!d)
EndDo
If (lprnt(29)) call fprnt (21,tp(l),ipt(0),
+ '@ Element average total organic soil concentration (ppm)')
Endlf
C
C— Print nodel gas phase saturation.
C
if(Iprnt(20))then
if(ipt(l).eq.ipt(2)) then
call fprnt (21,sat(l),ipt(l),' @ Gas phase saturation')
else
call fprnt2 (21,sat(l),ipt(2),'@ Gas phase saturation'
+ ,matpt,nodept,ipt(l))
end if
end if
C
C— Print nodel aqueous phase saturation.
C
if(lprnt(21)) then
if(ipt(l).eq.ipt(2)) then
call fprnt (21,sat(ipt(l)+l),ipt(l),
+ ' @ Aqueous phase saturation')
else
call fprnt2 (21,sat(ipt(2)+l),ipt(2),
+• '@ Aqueous phase saturation',matpt,nodept,ipt(I))
end if
C— Print nodel NAPL phase saturation
C
if(Iprnt(22)) then
if(ipt(l).eq.ipt(2)) then
call fprnt (21,sat(ipt(40)+l),ipt(l),
+ '@ NAPL phase saturation')
else
call fprnt2 (21,sat(ipt(49)+l),ipt(2),
+ '@ NAPL phase saturation',matpt,nodept,ipt(l))
end if
end if
C
C— Print gas phase Darcy velocities.
C
if(lprnt(23))then '•
C
C— Print nodal Darcy velocities.
C
if(lctrl(18))then
call fprnt (21,q(l),ipt(l),
+ '@ Nodal gas phase x Darcy velocity (m/sec)')
call fprnt (21,q(ipt(l)+l),ipt(l),
+ ' @ Nodal gas phase z Darcy velocity (m/sec)')
C
C— Otherwise print element Darcy velocities.
C
else
call fprnt (21,q(l),ipt(0),
+ '@ Element gas phase x Darcy velocity (m/sec)')
call fprnt (21 ,q(ipt(0)+l ),ipt(0),
+ ' @ Element gas phase z Darcy velocity (m/sec)')
end if
end if
C
C— Print aqueous phase Darcy velocities.
C
if(lpmt(24))then
C
C— Print nodal Darcy velocities.
C
if(lctrl(18))then
call fprnt (21,q(ipt(40)+l),ipt(l),
+ ' @ Nodal aqueous phase x Darcy velocity (m/sec)')
call fprnt (21,q(ipt(41)+l),ipt(l),
+ '@ Nodal aqueous phase z Darcy velocity (m/sec)')
else
call fprnt (21,q(ipt(67)+l),ipt(0),
+ ' @ Element aqueous phase x Darcy velocity (m/sec)')
call fprnt (21,q(ipt(68)-H),ipt(0),
+ ' @ Element aqueous phase z Darcy velocity (m/sec)')
end if
end if
C— Write contour information.
C
if(lctrl(23)) then
ipcon = 0
if(lcon(2)) then
ipcon = ipcon + 1
contr(ipcon) = * gas p '
end if
if(Icon(3)) then
ipcon = ipcon + 1
contr(ipcon) =' aq p '
end if
if(Icon(4)) then
ipcon = ipcon + 1
contr(ipcon) = ' cap p '
end if
if(lcon(5)) then
ipcon = ipcon +1
contr(ipcon) = * gas den '
end if
if(lcon(6)) then
ipcon = ipcon -f 1
213
-------
contrQpcon) =' aq dcij *
cndif '
ipcon s ipcon + J
contr(ipcon) '-' nap! pt(71).and.
+ i.gt.ipt(69)-fipt(70)) then
contr(i-ifiisl+l) =' NAPL '
clseif(i.le.ipt(69)+ipl(70)+ipt(71)+ipt(72).and.
+. i.gt.ipt(69)+ipt(70)+ipt(71)) then
comr(i-ifirst*l) =' solid '
else
contr(i-ilirst+-I) =' biophase'
end if
S3 continue
wrile(24,*)' elapsed time=',t(9)
writc(24,*)'
+ (conlr(i-ifirsn-l ),i=ifirst,ilast)
wrilc(24,*)' x z ',
•f (cnamc(icp(ipt(61 )+i)),i=ifirst,ilast)
if(Icon(l))then
write(24,*) ' x& in m; composition in mole fractions'
, ' solid phase loading in g/g; biomass in g/L'
else
write(24,*) ' x,z in ny, comppsifiqn in gni/]L'
, ' solidphase loading In, g/g; bioniass in g/L'
end if
do90i = J
,
ifQcon(l))then
xm(iirifirst-H) = rone
else
C— Convert gas phase mole fractions into concentrations (g/L) if
""• lcon(l) = false.
if(ii.le.ipt(69)) then
xm(ii-ifirst+l) = den(i)*cmw(icp(ipt(61)+ii))
C — Convert aqueous and biophase mole fractions into concentrations
C — (g/L) if lcon(l) = false. Biomass is always gm/L.
ej§e,if((ii.le.ipt(69)+ipt(70).and.ii.gt.
ipt(69)).br.(ii.le.ipt(74)..aiid.ii
.gt.ipt(74)-ipt(73))) then
if(jcp(ipt(61)tii).eq.ipt(65)+J)then
xm(iHlr?.t-H) = rone
else''
" "jtm(ii-ifirsH-l) = den{ipt(l)+i)
" * cmw(icp(ipt(61Hii))
end if
C— Convert NAPL mole fractions to concentrations (g/L).
C
else if (ii.Je.ipt(69)+ipt(70)tipt(71).and.
+ ii.gt.ipt(69)+ipt(70)) then
xm(ii-ifirst+l) = den(ipt(40)+i)
+ * cmw(icp(ipt(61)+ii))
C
C— Solid phase loadings are always g/g.
C
else
xm.(ii-ifirst+l) = rone
end if
end if
95 cojjtjnue
90 writs(2^,550) xno,de(i),znodleG),(xmfQ+icp(ipt(61)
+ +ipt(74)+ii))*xm(ii-ifirst+l ),ii=ifirst,ilast)
if(ipass.gt.l)then
ifirst = iflrst + nout
ilast = minO(ipt(74),ilast + nout)
end if
80 continue
end if "
if(lcon(13).or.lcon(14).or.lcon(15))then
write(24,*j' elapsed time=',t'(9)
ipcon = 0
if(lcon(13)) then
ipcon = ipcon + 1
contr(ipcon) = ' gas sat '
end if
if(lcon(14)) then
ipcon = ipcon + 1
contr(ipcon) = ' aq sat '
end if
if(lcon(15» then
ipcon = ipcon -f 1
contr(ipcon) = ' napl sat'
end if
write(24,*)' x z ',(contr(i),i=l,ipcon)
if(ipt(l).eq.ipt(2))then
write(24,*)' x,z in m'
else
write(24,*)' x,z in m; sat stacked'
end if
do lOOi = l,ipt(l)
do 100 istk = 0, nodept(i+l)-nodept(i)-l
ipcon = 0
if(lcon(13))then
ipcon = ipcon + 1
214
-------
rcont(ipcon) = sat(nodept(i)+istk)
end if
if(Icon(14))then
ipcon = ipcon + 1
rcont(ipcon) = sat(nodept(i)+istk+ipt(2))
end if
if(lcon(15))then
ipcon = ipcon -1-1
rcont(ipcon) = sat(nodept(i)+istk+ipt(49))
end if
100 write(24,550) xnode(i),znode(i),(rcont(ii),ii=l,ipcon)
end if
if(Icon(16).or.lcon(17)) then
ipcon = 0
if(lcon(16))then
ipcon = ipcon + 1
contr(ipcon) =' gas qx '
ipcon = ipcon + 1
contr(ipcon) = ' gas qz '
end if
if(lcon(17))then
ipcon = ipcon 4- 1
contr(ipcon) = ' aq qx '
ipcon = ipcon + 1
contr(ipcon) =' aq qz '
end if
write(24,*)' elapsed time=',t(9)
write(24,*)' x z ',(contr(i),i=l,ipcon)
if(Ictrl(18))then
write(24,*) 'x,z in m; nodal q in m/s'
dol!0i = l,ipt(l)
ipcon = 0
if(lcon(16)) then
ipcon = ipcon + 1
rcont(ipcon) = q(i)
ipcon = ipcon + 1
rcont(ipcon) = q(i+ipt( 1))
end if
if(lcon(17)) then
ipcon = ipcon + 1
rcont(ipcon) = q(i+ipt(40))
ipcon = ipcon + 1
rcont(ipcon) = q(i+ipt(41))
end if
110 write(24,550) xnode(i),znode(i),(rcont(ii),ii=l ,ipcon)
else
write(24,*)
+ 'x,z in m (element centroids); element q in m/s'
doll5i = l,ipt(0)
ipcon = 0
if(Icon(16))then
ipcon = ipcon + 1
rcont(ipcon) = q(i)
ipcon = ipcon + 1
rcont(ipcon) = q(i+ipt(0))
end if
if(lcon(17)) then
ipcon = ipcon + 1
rcont(ipcon) = q(i+ipt(67))
ipcon = ipcon + 1
rcont(ipcon) = q(i+ipt(68))
end if
ie!3 = i*3
iell=ie!3-2
iel2 = ie!3-l
il = nodel(iell)
i2 = nodel(ie!2)
i3 = nodel(iel3)
xel = third*(xnode(il)+xnode(i2)+xnode(i3))
zel = third*(znode(il)+znode(i2)+znode(i3))
115 write(24,550) xel,zel,(rcont(ii),ii= 1 ,ipcon)
end if
end if
If(lcon(18))then
write(24,*)' elapsed time=',t(9)
write(24,*)' x z Total organic soil cone'
write(24,*) 'x,z in m (element centroids); cone (ppm)'
Doi = l,ipt(0)
ieI3 = i*3
iell=iel3-2'
iel2 = ie!3-I
il=nodel(iell)
i2 = nodel(ie!2)
i3 = nodel(ie!3)
xel = third*(xnode(il)+xnode(i2)+xnode(i3))
zel = third*(znode(il)+znode(i2)+znode(i3))
write(24,550) xel,zel,tp(i)
EndDo
Endlf
end if
C
C— Generate a restart file if desired.
C
if(lctrl(5)) then
rewind(27)
write(27,556) '# ipt(i),i=0,7'
write(27,549) (ipt(i),i=0,7)
write(27,556) '#,t(8),t(2),t(9),its'
write(27,551) t(8),t(2),t(9),its '
write(27,556) '# strl(i),strO(i),cmf(i),csink(i),cwsink(i)'
write(27,556) '# crsink(i),csflux(i),cphex(i),i=l,',ipt(65)+5
write(27,555) (strl (i),strO(i),cmf(i),csink(i),cwsink(i)
+ ,crsink(i),csflux(i),cphex(i),i=l ,ipt(65)+5)
write(27,556) '#cmassl(i),cmassO(i),i=l,',ipt(65)*5
write(27,555)(cmassl(i),cmassO(i),i=l,ipt(65)*5)
write(27,556) '#tmassl,tmassO'
write(27,555) tmassl.tmassO
write(27,556)'#p'
iendl = ipt(41)
write(27,549) iendl
write(27,555) (p(i),i=l,iendl)
write(27,556)'#sat'
iend2 = ipt(50)
write(27,549) iend2
write(27,555) (sat(i),i=l,iend2)
write(27,556) '# xmf'
iendS = ipt(61)*ipt(l)
write(27,549) iend3
write(27,555) (xmf(i),i=l,iend3)
write(27,556)'#pex'
iend4 = ipt(52)
write(27,549) iend4
write(27,555) (pex(ipt(52)+i),i=l ,iend4)
close(27)
open(27,fi!e=outfile(7),status='unknown')
end if
500 format (/72('*')/' Solution at:'/
+ ' time step number =',i5 /
+ ' time in seconds =',e!2.5 /
+ ' time in minutes =',e!2.5/
+ ' time in hours =',e!2.5 /
+ ' time in days =',e!2.5/72('*'))
549 format(8i!0)
550 format(8e!5.7)
551 format(3el5.8,ilO)
555 format(5e!5.8)
556 format(a,ilO)
c
return
end
c _ .
subroutine fprnt (nu,var,ilen,label)
character label*(*)
real*8 var(ilen)
write (nu, 100) label
write (nu,101) (i,var(i),i=l,ilen)
100 format (/a)
101 format (4(i5,':',ell.5,lx))
return
end
subroutine fprnt2 (nu,var,ilen2,label,matpt,nodept,ilenl)
character Iabel*(*)
real*8 var(i!en2)
integer matpt(ilen2),nodept(ilen2+l ),idum(5000)
write (nu, 100) label
215
-------
iJum{noJcpl(i)) = i
if(nQdcr»|(i-t-l).nodepl(i).gU) then
do 60 li = 1, npd£ptfitl)-npdepl(iH
60 idum
-------
c
c
c
c
c
c
c
c
c
c-
lctrl(8) - logical variable controlling type of FEM
solution for transport
lctrl(8)= .true. - use mass lumping
lctrl(8) = .false. - full FEM solution
!ctrl(19)- logical variable controlling type of sorption
lctrl(19) = .true. - two compartment sorption
lctrl(19) = .false. - single compartment
sorption
subroutine SOLID(iconv)
include 'dimen.inc'
character* 10 cname(ncmp)
C
C— Declare and define common block variables.
C
common /cbl/ matel(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ matpt(nn6)
common /cble/ abyl2(nelmx),aby30(nelmx)
common /cb6b/ por(nelmx),srw(nnstk)
common /cb7b/ cmw(ncmp),cvp(ncmp),cden(ncmp),
+ chen(ncmp),casol(ncmp),cmdif(ncmp2)
common/cb9/ xmf(nmO
common/cb9b/ xmft(nmf)
common /cb40/ a(icnl),rhs(nsolve),w(icnl)
common /cb41/ irn(icnl),icn(icnl),iw(icnl,8),ikeep(icnl,5)
common /cb41b/ nbw(0:2),ia
common/cb62b/rhsex(nmfs)
common /cb64b/ bsden(nmblk)
common /cb91/ cname
C
C— Set pointers and sequentially solve for the solid phase
C— mass loadings.
C
iptl = ipt(l)
ipt2 = ipt(2)
do200ics = l,ipt(6)
iptc = ipt(59) + ics
icpt = (iptc-l)*iptl
icpts = (iptc-l)*ipt2
ic = icp(iptc)
C
C— If two compartment sorption is considered, do not advance the
C— component identifier.
C
if((ics.eq.2).and.lctrl(19)) ic = icp(iptc-l)
C
C—Zero the finite element matrices..
C
do 210 i = I,ipt2
rhs(i) = zerO
nrow = (i-l)*nbw(l)
do210j= l,nbw(l)
210 a(nrow+j) = zerO
C
C— Compute the local finite element matrices.
C
do220i = l,ipt(0)
C
C—
C—
C—
C
C
C-
C—
C
If two compartment sorption is considered, reset the solid phase
mass density for the slow and fast compartments. Ipt(6)=l for the
slow compartment and ipt(6)=2 for the fast compartment.
if«ics.eq.l).and.lctrl(19)) then
solden = (rone-xden)*bsden(matel(i))
else if((ics.eq.2).and.lctrl(19)) then
solden = xden*bsden(matel(i))
else
solden = bsden(matel(i))
end if
Set the pointers to the local nodes 11,12, and 13. The
postscript s is for stacked local nodes, p is for phase, and
c is for component. Compute constants.
ieI3 = i*3
iell=ie!3-2
ie!2 = ie!3-l
il=nodel(iell)
ils = nodept(il)+nelpt(iell)
ilcs = icpts + ils
i2 = nodel(ie!2)
i2s = nodept(i2)+nelpt(ieI2)
i2cs = icpts + i2s
i3=nodel(ie!3)
i3s = nodept(i3)+nelpt(iel3)
i3cs = icpts + i3s
terml = aby30(i)/t(8)
C
C— Compute the lumped mass matrix.
C
if(Ictrl(8)) then
amass = lO.OdO * terml
else
aon = terml*5.0dO
aoff = terml *2.50dO
end if
C
C—
C—
C
- Compute the exchange terms. First consider phase mass transfer.
- This term is updated after a complete pass through all the
- components and phases.
term2 = aby!2(i) * por(i) * cmw(ic) / solden
rhsl =rhsex(ilcs)
rhs2 = rhsex(i2cs)
rhs3 = rhsex(iScs)
fl = term2 * ( 2.0dO*rhsl + rhs2 + rhs3 )
f2 = term2*( rhsl + 2.0dO*rhs2 + rhs3 )
f3 = term2 * ( rhs 1 + rhs2 + 2.0dO*rhs3)
Assemble lumped global matrix Note that the left hand side matrix
is diagonal due to mass lumping and the solution is explicit.
if(lctrl(8)) then
a(il) = a(il) +amass
a(i2) = a(i2) + amass
a(i3) = a(i3) + amass
else
Assemble global matrix in banded form.
irowl = (il-l)*nbw(l)
irow2 = (i2-l)*nbw(l)
irow3 = (i3-l)*nbw(l)
icolll = 1 + nbw(0)
icol!2 = icoll 1 + (i2 - il)
icoll3 = icollH-(i3-il)
icoI22 = icolll
ico!21 = ico!22 + (il -12)
ico!23 = ico!22 + (i3 - i2)
icoI33 = icolll
icoI31=ico!33 + (il-i3)
ico!32 = ico!33 + (i2 - i3)
a(irowl + icoll 1) = a(irowl + icoll 1) + aon
a(irowl + icoll 2) = a(irowl + icoll 2) + aoff
a(irowl + icoll 3) = a(irowl + icoll 3) + aoff
a(irow2 + ico!21) = a(irow2 + ico!21) + aoff
a(irow2 + ico!22) = a(irow2 + ico!22) + aon
a(irow2 + ico!23) = a(irow2 + ico!23) +• aoff
a(irow3 + ico!31) = a(irow3 + icol31) + aoff
a(irow3 + ico!32) = a(irow3 + ico!32) + aoff
a(irow3 + ico!33) = a(irow3 + ico!33) + aon
end if
C—• Assemble right hand side.
rhs(il) = rhs(il) + fl
rhs(i2) = rhs(i2) + f2
rhs(i3) = rhs(i3)+f3
220 continue
:— Solve for solid phase mass fractions. Determine the max norm of
'•— the updated solution.
if(lctrl(8)) then
217
-------
dxmf » zcrO
xmfmax = xround
do230i=l,iptl
xmfold=xmf(icpt+i)
ill(a(i).nc,zerO) then
xmf(icpH-i) - xmft(icpt+i) + rhs(i)/a(i)
xmfmax = dmaxl(xmfmajc,dabs(xmf(icpH-i)))
dxmf = dmaxl (dxmf,dabs(xmf(icpt+i)-xmfold))
end if
250 continue
else
C
C— Collapse full matrix into sparse form used by Harwell. Also
C — scale array by dividing rows through by the diagonal value.
C
in = 0
(Io260irow= l.ipll
nrow - (irow-l)*nbw(l)
aii = rone / a(nrow+l+nbw(0))
rhs(irow) = rhs(irow) * aii
if (a(nrow+icol) ,ne. zerO) then
a(ia) = a(nrawticol) * aii
irn(is) 3 irow
icn(i») = icol+irow-nbwCO)-l
cndif
260 continue
C
C— Solve the linear system using Harwell routines.
C
callma28ad(ipt(l),ia,a,icnUrn,irnl,icn,u,ikeep,iw,w,iflag)
if (iflag .It. Q) then
write (ipt(28),'?) 'iflag return frpmharwell is ',iflag
write (ipt(28),*) 'solid component is: ', cname(ic)
end if
call ma28cd (ipt(l),a,icnl,icn,ikeep,rhs,w,mtype)
C
C— Update the solution and determine the max noim of the updated
G— solution.
C
dxmf = zerO
xmfmax = xround
do 270 i = l+icpt,iptl+icpt
xmfold = xmf(i)
xmf(i) = xmft(i) + rhs(i-icpt)
xmfmax = dmaxl(xmfmax,dabs(xmf(i)))
270 dxmf = dmaxl(dxrnf,dabs(xmf(i)-xmfold))
end if
C
C— Check convergence with the relative change in state variable.
C
if(dxiru7xmfrnax.gt.t(16)) SCOOT = iconv f 1
200 continue
return
end
Subroutine - tlhs.f
c-
c
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
TLHS.f - Subroutine which forms the left hand side of the
finite clement equations for the two dimensional
component mass balance equations. Linear triangles
arc used for the basis and weighting functions.
Arguments: iphasc - integer scalar denoting the phase
gas phase: iphasc = 1
aqueous phase: iphase = 2
komp - integer scalar denoting the component
gas phase: icomp = icp(l)-icp(ipt(3))
aqueous phase: icomp = icp(ipt(3)+l) to
icp(ipt(4))
ixc - integer pointer for principal component
number
nxc - integer pointer for principal component
location in xmf
Required Control Flags:
ipt(27) - integer variable indicating type of domain
ipt(27) = 0 - xz domain
ipt(27) = 1 - rz domain
lcirl{4) - logical variable controlling printing of
clement dimcnsionless numbers
lctrl(4) = .true, - print element
dimensionless numbers
lctrl(4) * .false. - skip element
dimcnsionless numbers
klrl(S) - logical variable controlling type of FEM
solution for transport
lclrl(8)= ,irue. - use mass lumping
ktrl(8) s .false. - full FEM solution
IctrKIS) - logical variable denoting type of q calculation
lctrl(18) = .true. - nodel FEM q
lclrl(18) = .false. - element average q
lctrK2!) - logical variable controlling calculation of
the hydrodynamic dispersion tensor
lctrl(21) = .true. - calculate tensor
lctrl(21) = .false. - read tensor as input
Control Flags computed internally in routine:
t(2Ji - maximum gas phase cell Peclet number
t(24) - maximum aqueous phase cell Peclet number
t(25) - maximum gas phase cell Courant number
t(26) - maximum aqueous phase cell Courant number
Note: Component balance equations are not needed for
nitrogen ia the gas phase and water in the
aqueous phase
subroutine TLHS(iphase,icomp,ixc,nxc)
include 'dimen.inc'
Declare and define common block variables.
common /cbl/ matel(nelmx),nodel(nel3),nodept(nnmx),nelpt(nel3),
+ matpt(nn6)
common /cblc/ xnode(nnmx),znode(nnmx),rbar(nelmx),area(nelmx)
common /cbld/gama(nel3),beta(ne!3)
common /cble/ abyl2(nelmx),aby30(nelmx)
common /cb2c/ q(ne!4)
common/cb3/ sat(nnstk3)
common /cb6b/ por(nelmx),srw(nnstk)
common /cb7b/ cmw(ncmp),cvp(ncmp),cden(ncmp),
+ chen(ncmp),casol(ncmp),cmdif(ncmp2)
common/cb9/ xmf(nmf)
common /cb9b/ xmft(nmf)
common /cblO/ den(nn6)
common /cbl I/ pex(nnslO),rxnp(nn2)
common /cb30/ ibc(nnmx)
common /cb32/ bcf(nn2)
common /cb40/ a(icnl),rhs(nsolve),w(icnl)
common /cb41/ irn(icnl),icn(icnl),iw(icnl,8),ikeep(icnl,5)
common/ cb41b/ nbw(0:2),ia
common /cb62/ rxn(nmf),cex(nmfs)
common /cb62b/ rhsex(nmfs)
common /cb64/ bok(nbcmp),bom(nbcmp),krtd(ncmp)
common /cb70/ d(nmd),tort(nelmx),bdist(nmblk),bdisl(nmblk)
218
-------
common /cb84/ ibcxmf(nmbc),bcxmf(nmbc),dfxmf(nmbc)
common /cb85/ flux(ncmpp5),sflux(ncmpp5),first(ncmp)
C— Compute terms which are not component dependent. These
C— terms are only calculated once per iteration for each phase.
C— Note that for mobile phases, saturation is stacked (i.e.
C— discontinuous) while phase molar density not stacked (i.e.
C— continuous).
C
C— Zero the global matrix and right hand side vector.
C
do 110i= l,ipt(l)
rhs(i) = zerO
nrow = (i-l)*nbw(l)
do 110j = l,nbw(l)
110 a(nrow+j) = zerO
C
C— Set pointers, iptc points to the correct location in icp.
C— icpt and icpts point to the correct location in xmf,
C— and stacked xmf storage respectively, ippt and ippts point to
C— the correct location in nonstacked and stacked phase storage.
C— ic is the identity of the icomp component in the iphase phase.
C— iptco points to the organic phase components.
C
ipml = iphase-1
iptc = ipml *ipt(3)+icomp
icpt = (iptc-l)*ipt(l)
icpts = (iptc-l)*ipt(2)
ippt = ipml*ipt(l)
ippts = ipml *ipt(2)
ic = icp(iptc)
iptl=ipt(l)
iptO = ipt(0)
C
C— Compute the local finite element matrices.
C
do!20i=l,ipt(0)
C
C— Set the pointers to the local nodes il,i2, and i3. The
C— postscript s is for stacked local nodes, p is for phase, and
C— c is for component. Compute constants.
C
ieB = i*3
ieIl=ie!3-2
iel2 = ie!3-l
il=nodel(iell)
ils = nodept(il)+nelpt(iell)
ilc = icpt + il
ilcs = icpts + ils
ilp = ippt + il
ilps = ippts + ils
i2 = nodel(ie!2)
i2s = nodept(i2)+nelpt(ie!2)
i2c = icpt-H2
i2cs = icpts + i2s
i2p = ippt + i2
i2ps = ippts + i2s
i3 = nodel(ie!3)
i3s = nodept(i3)+nelpt(ie!3)
i3c = icpt + i3
i3cs = icpts + i3s
i3p = ippt +13
i3ps = ippts + i3s
sdl=sat(ilps)*den(ilp)
sd2 = sat(i2ps)*den(i2p)
sd3 = sat(i3ps)*den(i3p)
dl = den(ilp)
d2 = den(i2p)
d3 = den(i3p)
term30 = por(i)*aby30(i)
terml2 = por(i)*aby!2(i)
term = term30/t(8)
C
C— If an element has gas saturations below sgtest skip
C— calculation of the local element matrix
C
if((iphase.eq.l).and.((sat(ils).ltsgtest).or.
+ (sat(i2s).lt.sgtest).or.(sat(i3s).lt.sgtest))) goto 120
C
C—
C—
C—
C
c
C— Consider equilibrium sorption in the aqueous phase.
if(iphase.eq.2) then
term = term * krtd(ic)
end if
Compute the mass matrix. These terms are constant for a given
phase and component unless the phase density or saturation
is updated.
all=term*(3.0dO*sdl + sd2 + sd3 )
a!2 = term*( sdl + sd2 + sd3/20dO)
a!3 = term*( sdl + sd2/2.0dO+ sd3 )
a21=a!2 |
a22 = term*( sdl + 3.0dO*sd2 + sd3 )
a23 = term*( sdl/2.0dO+ sd2 + sd3 )
a31=a!3
a32 = a23
a33 = term*( sdl + sd2 +3.0dO*sd3 )
C
C— Lump 'mass' matrix if lctrl(S) = true.
C
if(lctrl(8)) then
all=all+aI2 + al3
a!2 = zerO
a!3 = zerO
a22 = a21+a22 + a23
a21 = zerO
a23 = zerO
a33 = a31+a32 + a33
a31=zerO
a32 = zerO
endif
C
C—
C
c
c—
c
Assign the Darcy velocities.
if(lctrl(18))then
Compute the stiffness matrix using nodal Darcy velocities.
iptq = ipml*ipt(40)
dqxl =q(iptq+il)*den(ilp)
dqx2 = q(iptq+i2)*den(i2p)
dqx3 = q(iptq+i3)*den(i3p)
dqzl = q(iptq+iptl+il)*den(ilp)
dqz2 = q(iptq+iptl+i2)*den(i2p)
dqz3 = q(iptq+iptl+i3)*den(i3p)
termq = rbar(i) / 24.0dO
sumlx = termq * (2.0dO*dqxl + dqx2+ dqx3)
sum2x = termq * ( dqxl + 2.0dO*dqx2 + dqx3)
sum3x = termq *( dqxl + dqx2 + 2.0dO*dqx3)
sumlz = termq * (2.0dO*dqzl + dqz2+ dqz3)
sum2z = termq *( dqzl+ 2.0dO*dqz2 + dqz3)
sum3z = termq * ( dqzl + dqz2 + 2.0dO*dqz3)
bll = sumlx * beta(iell) + sumlz * gamaflell)
b!2 = sumlx * beta(ie!2) + sumlz * gama(ieI2)
b!3 = sumlx * beta(ie!3) + sumlz * gama(ie!3)
b21 = sum2x * beta(iell) + sum2z * gama(iell)
b22 = sum2x * beta(ie!2) + sum2z * gama(ie!2)
b23 = sum2x * beta(ie!3) + sum2z * gama(ie!3)
b31 = sum3x * beta(iell) + sum3z * gama(iell)
b32 = sum3x * beta(ie!2) +• sum3z * gama(ie!2)
b33 = sum3x * beta(ie!3) + sum3z * gama(ie!3)
else
-— Compute advective terms using element Darcy velocities.
termq = rbar(i) / 24.0dO
suml = termq * (2.0dO*den(ilp)+den(i2p)+den(i3p))
sum2 = termq * (den(ilp)+2.0dO*den(i2p)+den(i3p))
sum3 = termq * (den(ilp)+den(i2p)+2.0dO*den(i3p))
^— Assign the Darcy velocities. Use q here since the saturations and
" porosities are dropped from the preceding terms.
219
-------
c
c—
c—
f*__jr
c
iplq=i + ipml*ipt(67)
qx = q(iptq)
qzsq(iptq+iptQ)
Compwt? Ihe stiffness matrix. First compute the advective terms.
These terms are co.nstanj unless the phase density or Darcy
velocity is updated.
blgl
b2g2
b3g3
bll-
b!2 =
b!3 =
b32
b33
end if
= beta(iell)*qx + gama(iell)*qz
= bcta(ici2)*qx + gama(iel2)*qz
= beta(+sat(i3ps))*por(i)
H *cmdif(2*(ic-l)+iphase)*lort(i)
id = (iphas«-U*ip((68)
dlt=d(td+3*i-2) + dm
S*(ic-l)+(iphasc-l)*4
d(idpt-t-l)
d21=d!2
else
tdpt
dll
d21=d(idpt+3)
end if
C
C—• Compute ibe maximum clement Peclet and Courant number if desired.
C
if(ktil(4))then
pclcn = dsqrt(2.0dO*area(i))
pcsat = third*(sat(ilps>t-sat(i2ps)+sat(i3ps))
pcpore = por(i)
if(letrl{18))thcn
qx - third*(q(iptq+il)+q(iptq-t-i2>Kl * su?n / (12.0dQ. * area(i))
dlbgl=dH *b.etaflell) + d21 *gama(iell),
d2bgl = d!2 * heta((iell) + d22 * gama(iell)
dlbg2 = dl 1 * b,e,t.a(iei2). -t d?l * gama(ie!2)
d2bg2 = d!2 * bet.a.(ie.l2) + d22 * gama(iel2)
dlbg3 = dU * beta(ie,l3),,+ d21 * gama(iel3),
d2bgj = d!2 * ^eta(iel3) + d22 * gama(iel3).
bll = bll + sum,* (beta(iell) * dlbgl + garna(iell) * d2bgl)
b!2 = b!2 + sum * (beta(iel2).* dlbgl- -fc gama(iel2) * d2bgl)
b.;3 = b!3 + sum * (beta(ie,13) * dlbgl -I- gama(ieI3) * d2bgl)
b,21 = b21+ sum * (beta(ieU) * dlbg2 + gama(iell) * d2bg2)
b22 = b22 + s,um * (beta(ie!2) * dlbg2 +• gama(ie!2) * d2bg2)
b23 = b?3 + s'um.* (beta(ie!3) * dlbg2 + gama(ieB) * d2bg2)
b31 = b31 + sum * (beta(iell) "• dlbg3 + gama(iell) * d2bg3)
b32 = b32 + sum * (beta(ie!2) * dlbgS + gama(ie!2) * d2bg3 )
b33 = b33 + sum * (beta(ie!3) * dlbg3 + gama(iel3). * d2bg3)
C— Compute the exchange terms. First consider phase mass transfer.
C— This term is updated a,fter; a complete pass through all the
;— components and phases. Include the reaction, term in the aqueous
C— pha^e.
if(iphase.eq.2.and.lctrl{3>.aji.d.lctrl(16)>th,en
pex.1 = pexfilpa) -t (rxnp(il) - rxn(ilc))/por(i).
pex2 = pex.(i2ps) + (rxnp(i2) - rxn(i2c))/por(i)
pex3 = pex(i3ps) + (rxnp(i3) - rxn(i3c))/por(i)
else
pexl = pex(ilps)
pex2 = pex(i2ps)
pex3 = pex(i3ps),
end if
pterml = term3.Q *( pexl +pex2 +pex3/2.0dO)
pterm2 = term30*(pexl + pex2/2.0dO + pex3 )
pterm3 = term30 * (pex l/2.0dO + pex2 + pex3 )
bll=bll+term30*(3.0dO*pexl + pex2 +pex3 )
b!2 = b!2 +pterml
b!3=bl3 + pterm2
b21 = b21 + pterml
b22 = b22 + term30*(pexl + 3.0dO*pe"2 + Pex3 )
b23 = b23 + pterm3
b31=b3l+pterm2
b32- = b32 -b pterrnS.
b3.3==b33 + term3Q*(pexl +pex2 +3.0dQ*pex3)
C
C— Now include the lumped component exchange terms.
C
cexl = cex(ilcs)
cex2 = cex(i2cs)
cex3 = cex(i3cs)
ctermi = termS.O *- (cexl + cex2 + cex3/2.0dO)
cterm2 = term30*(cexl t cex2/2.0dO + cex3 )
cterm3 = term3Q*(cex!/2.0d0 + cex2 +cex3 )
bll=bll+term30*(3.0dO*cexl + cex2 +cex3 )
b!2 = b!2 +ctermi
bl3=b!3 + cterm2
b21 =b21 +cterinl
b22 = b22 + term30 * ( cex 1 + 3.0dO*cex2 + cex3 )
b23 = b23 + ctermS
b31 = b31 +cterm2
b32 = b32 + ctermS
b33 = b33 + term30*(cexl +cex2 +3.0dO*cex3)
Now compute the right hand side terms. These terms are constant
unless the phase saturation or contacting phase composition is
C— updated.
C
rhsexl = rhsex(ilcs)
rhsex2= rhsex(i2cs)
rhsex3= rhsex(iScs)
fl = term!2 * (2.0dO*rhsexl + rhsex2 + rhsexS )
f2 = terml2*( rhsexl+2.0dO*rhsex2+ rhsex3)
O = terml2*( rhsexl + rhsex2 + 2.0dO*rhsex3 )
C
C— Assemble global matrix and right hand side vector in banded form.
C
= (il-l)*nbw(l)
= (i2-l)*nbw(l)
C
y"i
C—
220
-------
C
C —
irow3 = (i3-l)*nbw(l)
icolll = I + nbw(0)
icoll2 = icolll + (i2-il)
icol!3 = icolll +(i3-il)
ico!22 = icolll
icol21 =icoI22 + (il -i2)
icol23 = icoI22 + (i3-i2)
ico!33 = icoll I
icolSl = ico!33 + (il - i3)
ico!32 = ico!33 + (i2 - i3)
abll =all + t(IO)*bll
abl2 = aI2 + t(10)*bI2
abl3 = aI3 + t(10)*b!3
ab21 = a21 + t(10)*b21
ab22 = a22 + t(10)*b22
ab23 = a23 + t(10)*b23
ab31=a3I +t(10)*b31
ab32 = a32 + t(10)*b32
ab33 = a33 + t(10)*b33
a(irowl + icoll 1) = a(irowl + icoll 1) + abl 1
a(irowl + icoI12) = a(irowl + icol!2) + ab!2
a(irowl +icol!3) = a(irowl +icolI3) + ab!3
a(irow2 +• ico!21) = a(irow2 + ico!21) + ab21
a(irow2 + ico!22) = a(irow2 + ico!22) + ab22
a(irow2 + icoI23) = a(irow2 + ico!23) + ab23
a(irow3 + icoI31) = a(irow3 + icoDl) + ab31
a(irow3 + ico!32) = a(irow3 + ico!32) + ab32
a(irow3 + ico!33) = a(irow3 + ico!33) + ab33
rhs(il) = rhs(il) + fl - bl 1 * xmft(ilc) - b!2 * xmft(i2c)
-b!3*xmft(i3c)
rhs(i2) = rhs(i2) + f2 - b2I * xmft(ilc) - b22 * xmft(i2c)
- b23 * xmft(i3c)
rhs(i3) = rhs(i3) + f3 - b31 * xmft(ilc) - b32 * xmft(i2c)
- b33 * xmft(i3c)
Insert third type boundary condition here when the flow solution
is not included. First look at the three sides.
ilbc = ilp
i2bc = i2p
i3bc = i3p
if(ibcxmf(i 1 bc)+ibcxmf(i2bc)+ibcxmf(i3bc).ge.4) then
if(((ibcxmf(ilbc)+ibcxmf(i2bc).eq.6).or.
(ibcxmf(i 1 bc)+ibcxmf(i2bc).eq.4))
.and.(xnode(il).eq.xnode(i2)
.or.znode(il).eq.znode(i2))) then
if(ipt(27).eq.l)then
weight = xnode(i 1) + xnode(i2)
weightl = xnode(il) / weight
weight2 = xnode(i2) / weight
else
weightl = O.SOdO
weight2 = O.SOdO
end if
dx = xnode(i2)-xnode(il)
dz = znode(i2)-znode(il)
rlen = dsqrt(dx**2+dz**2)
if(ipt(27).eq.l)then
rrad = pi*(xnode(il)+xnode(i2))
rlen = rlen*rrad
end if
qnorm = zerO
if(lctrl(18)) then
qx=q(iptq+il)*weightl+q(iptq+i2)*weight2
qz=q(iptq+iptl+il)*weightl+q(iptq+iptl+i2)*weight2
end if
if(dx.gt.zerO) then
qnorm=(dx*qz)/rlen
else
qnorm=(-dx*qz)/rlen
end if
if(dz.gt.zerO) then
qnorm = qnorm + (dz*qx)/rlen
else
qnorm = qnorm + (-dz*qx)/rlen
end if
if(dabs(qnorm).lt.(den(ilp)*dfxmf(ilc)*weightl+
den(i2p)*dfxmf(i2c)*weight2)) then
C—
C
dfx 1 =den(i 1 p)*dfxmf(i 1 c)*rlen*weightl
dfx2=den(i2p)*dfxmf(i2c)*rlen*weight2
else
dfx 1= zerO
dfx2 = zerO
end if
abc31 = den(ilp)*qnorm*rlen*weightl
abc32 = den(i2p)*qnorm*rlen*weight2
if(ibcxmf(ilfac)+ibcxmf(i2bc).eq.4)then
a(irowl + icoll 1) = a(irowl + icoll 1) + 1<10) * dfxl
rhs(il) = rhs(il) + dfxl * (bcxmf(ilc)-xmft(ilc))
a(irow2 + ico!22) = a(irow2 + ico!22) + 1(10) * dfx2
rhs(i2) = rhs(i2) + dfx2 * (bcxmf(i2c)-xmft(i2c))
Save the flux terms for the mass balance. Also compute the
surface flux for output.
if(.not.lctrl(l))then
flxmf = xmf(ilc)
f2xmf = xmf(i2c)
fsave = abc31 * flxmf + abc32 * f2xmf
+• + dfx 1 * (bcxmf(i 1 c)-xmf(i 1 c))
+ + dfx2 * (bcxmf(i2c)-xmf(i2c))
flux(5+ic) = flux(5+ic) +• fsave
if(znode(il).eq.zer0.and.znode(i2).eq.zerO)
+ sflux(5+ic) = sflux<5+ic) +• fsave
C
C — Compute the flux for the master component.
C
if(icomp.eq.l)then
fsave = abc31 * xmf(nxc+il) + abc32 * xmf(nxc+i2)
flux(5+ixc) = flux(5+ixc) + fsave
if(znode(i 1 ).eq.zer0.and.znode(i2).eq.zerO)
+ sflux(5+ixc) = sflux(5+ixc) + fsave
end if
end if
else if(.not.lctrl(l).and.
+ ibcxmf(i 1 bc)+ibcxmf (i2bc).eq.6) then
a(irowl + icoll 1) = a(irowl + icoll 1) + 1(10) * abc31
rhs(il) = rhs(il) + abc31*(bcxmf(ilc)-xmft(ilc))
a(irow2 + ico!22) = a(irow2 + ico!22) + 1(10) * abc32
rhs(i2) = rhs(i2) + abc32*(bcxmf(i2c)-xmft(i2c))
C
C —
C — •
C
Save the flux terms for the mass balance. Also compute the
surface flux for output.
fsave = abc31 * bcxmf(ilc) + abc32 * bcxmf(i2c)
flux(5+ic)
= flux(5+ic) + fsave
if(znode(i 1 ).eq.zer0.and.znode(i2).eq.zerO)
sflux(5+ic) = sflux(5+ic) + fsave
+
+
C
C — Compute the flux for the master component.
C
if(icomp.eq.l) then
fsave = abc31*bcxmf(nxc+il) + abc32*bcxmf(nxc+i2)
flux(5+ixc) = flux(5+ixc) + fsave
if(znode(i 1 ).eq.zer0.and.znode(i2).eq.zerO)
+ sflux(5+ixc) = sflux(5+ixc) + fsave
end if
end if
end if
if(((ibcxmf(i 1 bc)+ibcxmf(i3bc).eq.6).or.
+ (ibcxmf(ilbc)+ibcxmf(i3bc).eq,4))
+ .and.(xnode(il).eq.xnode(i3)
+ .or.znode(il).eq.znode(i3))) then
if(ipt(27).eq.l)then
weight = xnode(il) + xnode(i3)
weightl = xnode(il) / weight
weights = xnode(iS) / weight
else
weightl = O.SOdO
weights = O.SOdO
end if
dx = xnode(i3)-xnode(il)
dz = znode
-------
rrad = pl*(xnoflc(il)+xnode(i3))
rkn = rlen*rrad
end if
qnorm = zerO
ifllctrKtS)} then
qx=q(iptq+il)*weighU+q(iptq+i3)*weight3
qz=q(iptq+ipt 1+i 1 )*weighl l+q{iptq+ipt 1 +i3)*weight3
end if
ifltdx.gt.zerO) then
qnorm={dx*qz)/rleti
else
qnorm=(-dx*qzyrlen
end if
if(dz,gt,zcrO) then
qnorm = qnorm +• (dz*qxyrlen
else
qnorm = qnorm + (-dz*qx)/rlen
end if
if(dabs(qnorm).lt.(den(ilp)*dfxmf(ilc)*weightl+
f]cn{t3p)'dfxmf(i3c)*weight3)) then
dfxl=dcn(ilp)*dfxmf(ilc)*rlcn*weightl
dfx3=den{i3p)*dfxmf(i3c)»rlen*weight3
else
dfxlszetO
df*3 = zerO
end if
abc31 = den(ilp)*qnorm*rlen*weightl
abc33 = den{i3p)*qnorm*rlen*weight3
if(ibcxmf(ilbc)+ibcxnif(i3bc),eq.4) then
a(!rowl + icolU) = aprowl + icoll 1) + 1(10) * dfxl
rhs(iI) = rhs(il)-)-dfxl*(bcxmf(ilc)-xraft(ilc))
a(irow3 •»• ico!33) = a(iro\v3 + ico!33) + 1(10) * dfx3
rhs(i3) = rhs(i3) + dfx3 * (bcxmf(i3c)-xmft(i3c))
Save the (lux terms for the mass balance. Also compute the
surface flux for output,
if(.not,lctrl(l)) then
flxmf=xmf
-------
c
c-
c
c
c-
c
120
else if(.not.Ictrl(l).and.
ibcxmf(i2bc)+ibcxmf(i3bc).eq.6) then
a(irow2 + icoI22) = a(irow2 + ico!22) +1(10) * abc32
rhs(i2) = rhs(i2) + abc32*(bcxmf(i2c)-xmft(i2c))
a(irow3 + icoI33) = a(irow3 + ico!33) +1(10) * abc33
rhs(i3) = rhs(i3) + abc33*(bcxmf(i3c)-xraft(i3c))
Save the flux terms for the mass balance.
fsave = abc32 * bcxmf(i2c) + abc33 * bcxmf(i3c)
flux(5+ic) = flux(5+ic) + fsave
if(znode(i2).eq.zer0.and.znode(i3).eq.zerO)
sflux(5+ic) = sflux(5-ric) + fsave
Compute the flux for the master component.
if(icomp.eq.l)then
fsave = abc32*bcxmf(nxc+i2) + abc33*bcxmf(nxc+i3)
flux(5+ixc) = flux(5+ixc) + fsave
if(znode(i2).eq.zer0.and.znode(i3).eq.zerO)
sflux(5+ixc) = sflux(5+ixc) + fsave
end if
end if
end if
end if
continue
Calculations for first type boundary conditions.
ibcn = ipt(18) + ipt(19) 4-ipt(20)*ipml
do 26 i = 1, ipt(19+iphase)
nbc = ibc(ibcn+i)
inode = ibcxmf(ippt+nbc)
C
C— Skip specification of first type boundary condition if the node
C— number is zero.
C
if(inode.eq.l)then
C
C— Compute flux at first type nodes for mass balance before the
C— boundary condition is imposed. Computing the mass balance here
C— lags the mole fractions one sweep.
C
if(lprnt(6)) then
fsave = O.dO
do800irow=l,iptl
if(irow.le.nbw(0)) then
jstrt = nbw(O) + 1 - irow
jend = nbw(l)
else if(irow.ge.iptl-nbw(0)) then
jstrt = 1
jend = nbw(l) - nbw(O) + iptl - irow
else
jstrt = 1
jend = nbw(l)
endif
sum = zerO
do 805 j= jstrt jend
805 sum = sum + a(nbw(l)*irow+j)
+ * xmf(icpt+irow-nbw(0)+j)
800 fsave = fsave + (sum-rhs(irow)) * t(8)
if(.not.lctrl(l)) then
flux(ic+5) = flux(ic+5) + fsave
if(znode(nbc).eq.0.dO)
+ sflux(ic+5) = sflux(ic+5) + fsave
endif
first(iptc) = first(iptc)+(sum-rhs(irow)) * t(8)
endif
C
C— Impose first type boundary conditions.
C
rhs(ibc(ibcn+i)) = zerO
nbwO = nbw(0)
nbwl = nbw(l)
do27j = l,nbw(l)
a((nbc-l)*nbwl+j) = zerO
27 continue
a((nbc-l)*nbwl+l+nbwO) = rone
end if
26 continue
C
C— Use solution from flow section to impose boundary fluxes for third
C— type boundaries. First type pressure nodes.
C
if(Ictrl(l))then
do28i = l,ipt(18+ipml)
nbc = ibc(i+ipml *ipt(18))
nbcp = nbc + ippt
irowbc = (nbc-l)*nbw(l)
icolbc = 1 + nbw(0)
nbcpc = icpt + nbc
if(ibcxmf(nbcp).eq.3) then
porsum = zerO
do 32 ipor = 1, nodept(i+1 )-nodept(i)
32 porsum = porsum + por(matpt(nodept(i)+ipor))
porsum = porsum/dble{nodept(H-l)-nodept(i))
a(irowbc + icolbc) = a(irowbc + icolbc) +1(10)
+ * bcf(nbcp) * den(nbcp)
rhs(nbc) = rhs(nbc) + bcf(nbcp) * den(nbcp)
+ * (bcxmf(nbcpc) - xmft(nbcpc))
end if
28 continue
C
C— Third type nodes with constant volumetric flux.
C
do 29 i = 1, ipt(22+ipml)
nbc = ibc(i+ipml*ipt(22)+ipt(62))
nbcp = nbc + ippt
irowbc = (nbc-l)*nbw(l)
icolbc = 1 + nbw(0)
nbcpc = icpt + nbc
if(ibcxmf(nbcp).eq.3) then
porsum = zerO
do 33 ipor = 1, nodept(i+l)-nodept(i)
33 porsum = porsum+por(matpt(nodept(i)+ipor))
porsum = porsum/dble(nodept(i+l)-nodept(i))
a(irowbc + icolbc) = a(irowbc + icolbc) +1(10)
+ * bcf(nbcp) * den(nbcp)
rhs(nbc) = rhs(nbc) + bcf(nbcp) * den(nbcp)
+ * ( bcxmf(nbcpc) - xmft(nbcpc) )
endif
29 continue
C
C— Well nodes.
C
do31i = l,ipt(24)
nbc = ibc(i+ipt(64))
nbcp = nbc + ippt
irowbc = (nbc-l)*nbw(l)
icolbc = 1 + nbw(0)
nbcpc = icpt + nbc
if(ibcxmf(nbcp).eq.3) then
porsum = zerO
do 34 ipor = 1, nodept(i+l)-nodept(i)
34 porsum = porsum + por(matpt(nodept(i)+ipor))
porsum = porsum/dble(nodept(i+l)-nodept(i))
a(irowbc + icolbc) = a(irowbc + icolbc) +1(10)
+ * bcf(nbcp) * den(nbcp)
rhs(nbc) = rhs(nbc) + bcf(nbcp) * den(nbcp)
+ * (bcxmf(nbcpc) - xmft(nbcpc))
endif
31 continue
endif
C
C— Collapse full matrix into sparse form used by Harwell. Also
C— scale array by dividing rows through by the diagonal value.
C
ia = 0
do 30 irow = l,ipt(l)
nrow = (irow-l)*nbw(l)
if(a(nrow+l+nbw(0)).eq.zerO) a(nrow+l+nbw(0)) = rone
aii = rone / a(nrow+l+nbw(0))
rhs(irow) = rhs(irow) * aii
do30icol=l,nbw(l)
if (a(nrow+icol) .ne. zerO) then
ia = ia + 1
223
-------
a(la) = s(nrow+icol) * aii
irn(ia) = irow
icnfin) = icol+irow-nbw(0)-l
endif
30 continue
return
end
Subroutine - trans.f
c-
c
c
c
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c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
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c
c
c
c
c
c
c
c
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c-
TRANS.f - Subroutine which solves the component molar balance
equations. Solution is done sequentially starting
with the most volatile component and moving to the
least volatile.
Arguments: its - integer time step number
iconv - integer flag for global convergence
Required Control Flags:
t(14) - convergence criterion for mole fractions
1(23) • maximum gas phase cell Peclet number
1(24) - maximum aqueous phase cell Peclet number
1(25) - maximum gas phase cell Courant number
1(26) - maximum aqueous phase cell Courant number
!pt{32) - maximum component balance iterations, also used as
the criterion for decreasing dt in component balance
routines
ipt(35) - maximum number of iterations in component balance
routines for increasing dt
kttl(3) - logical variable controlling inclusion of
biodcgradation
ldrl(3) = .true. - include biodegradation
lctrl(3) = .false. - neglect biodegration
lctrl(4) - logical variable controlling printing of
clement dimensionless numbers
ktrl(4) = .true. - print element
dimensionless numbers
lclrl(4) = .false. - skip element
dimensionless numbers
letrl(9) - logical variable denoting presence of nutrient
lctrl(9) ~ .true. - nutrient considered
lctrl(9) = .false. - nutrient not considered
IclrlllS) - logical variable controlling time series output
!clrt(15) = .true. - output time series
lctrl(15) - .false. - do not output time series
lclrl(21) - logical variable controlling calculation of
the hydrodynamic dispersion tensor
Ictrl(2I) = .true. - calculate tensor
lclrl(21) = .false, - read tensor as input
Control Flags computed internally in routine:
ipt(37) - (lag specifying time step modification
C
c-
c
subroutine TRANS(its,ibconv)
include 'dimcn.inc'
character* 10 cname(ncmp)
Declare and define common block variables.
common/cb.V sat(nnstk3)
common /cb3b/ satt(nnstk3)
common /eb7W cmw(ncmp),cvp(ncmp),cden(ncmp),
t chcn85/ flux(ncmpp5},sflux(ncmpp5),first(ncmp)
common /cb91/ cname
data Iplot / .false. /
C
C— Initialize variables as needed.
C
ipt(37)=0
iptl=lpt(l)
ipt2 = ipt(2)
ipt3 = ipt(3)
C
C— Determine which mobile phases are present.
C
imobl=l
imob2=2
if(ipt(3).eq.O) imobl=2
if(ipt(4).eq.O) imob2=l
C
C— Update the biological reaction terms. These terms are lagged one
C— time step.
C
if(lctrl(3).and.Ictrl(16)) then
iconv = 0
if(ipt(28).gt.O) write(ipt(28),*)' BIO lagged'
call BlO(iconv.ibconv)
else
if(Ictrl(3).and.ipt(28).gt.O)write(ipt(28),*)
+ ' BIO separate phase included'
end if
C
C— Begin iterations over the set of component balance equations.
C
ipass = 0
do200it=l,ipt(32)
iconv = 0
C
C— Zero the component mass flux entry for the mass balance.
C
do 130 i=3,ncmpp5
sflux(i)=zerO
130 flux(i)=zerO
C
C— Update the biological phase mole fractions every iteration when
C— considering a separate biophase.
C
if(lctrl(3).and..not.lctrl(16)) call BlO(iconv.ibconv)
C
C— Update the phase molecular weights and densities every iteration.
C
call MOLEWT
C
C— Update the phase mole exchange terms every iteration.
C
call MPEX
ipass = ipass + 1
do 100iphase = imobl,imob2
t(22+iphase) = zerO
t(24+iphase) = zerO
C
C— iptp+1 is the first entry of phase vectors, iptps+l is the first
C— entry of stacked phase vectors,
C
ipml = iphase-1
C
C— Use DISPER.f to compute the dispersivities if desired.
C
224
-------
if (lctrl(21)) call DISPER(iphase)
do 110 icomp = 1 ,ipt(2+iphase)
C
C— ic is the identity of the icomp component in the iphase phase,
C— iptct-1 is the first entry of the icomp component in the iphase
C— phase.
C
ic = icp(ipml*ipt3+icomp)
iptc = ipt(7+iphase)+(icomp-l)*ipt(l)
C
C— Compute the pointers to the principal component of each phase.
if(iphase.eq.l)then
if(Ictrl(9))then
ixc = icp(ipt3-l)
nxc = (ipt3-2)*ipt(l)
else
ixc = icp(iptS)
nxc = (ipt3-l)*ipt(l)
end if
else if(iphase.eq.2) then
ipt314 = ipt3 + ipt(14)
ixc = icp(ipt314+1)
nxc = (ipt3+ipt(14))*ipt(l)
end if
C
C— Skip the principal component of each mobile phase (i.e. nitrogen
C— for the gas phase and water for the aqueous phase)
C
if(ic.eq.ixc)goto 110
C
C— Use TLHS.f to form and assemble the finite element matrices.
C
call TLHS(iphase,icomp,ixc,nxc)
C
C— Solve the linear system using Harwell routines.
C
call ma28ad(ipt( 1 ),ia,a,icnl,irn,irnl,icn,u,ikeep,iw,w,iflag)
if (iflag.lt. 0)then
write (ipt(28),*) 'iflag return from harweil is '.iflag
write (ipt(28),*) 'trans phase/component are: '.iphase
+ ,' ',cname(ic)
end if
call ma28cd (ipt(l),a,icnl,icn,ikeep,rhs,w,mtype)
C
C— Update the solution and determine the max norm of the updated
C—• solution.
C
dxmf = zerO
xmfmax = xround
do 210 i = l+iptc,ipt(l)+iptc
xmfold=xmf(i)
xmf(i) = xmft(i) + rhs(i-iptc)
xmfmax = dmaxl(xmfmax,dabs(xmf(i)))
210 dxmf = dmaxl(dxmf,dabs(xmf(i)-xmfold))
C
C— Check convergence with the relative change in state variable.
C— Update the solution.
C
if(dxmf/xmfmax.gt.t(14)) iconv = iconv + 1
110 continue
C
C— Update the mole fraction of the principal component of each
C— phase by the mole fraction constraint after all the components
C— of that phase have been updated.
C
do300i=l,ipt(l)
xmf(nxc+i) = rone
do 300 ii=l,ipt(2+iphase)
if(icp(ipt3*ipml+ii).ne.ixc) then
ipt7p = ipt(7 + iphase)
xmf(nxc+i) = xmf(nxc+i)
+ -xmf(ipt7p+(ii-l)*iptl+i)
end if
300 continue
100 continue
C
C— Update the NAPL mole fractions. This is only needed
C— If there is more than 1 organic component.
C
if(ipt(5).gt.l)then
call NAPLX(iconv)
end if
C
C— Update the solid phase mass fractions.
C
if(ipt(6).gt.O) call SOLID(iconv)
C
C— Transport equation set is converged if each component equation
C— has converged (i.e. iconv = 0).
C
if (iconv.eq.O) then
C
C— Use NAPLS.f to update the organic phase saturation
C
if(Ictrl(24)) call NAPLS(iconv)
C
C— Reset mobile phase saturation if the flow simulator is not
C—• being used.
C
if(.not.lctrl(l)) then
do!75i=l,ipt(2)
ipt49 = ipt(49)
if(ipt(3).gt,0) then
if(sat(i).gt.zerO) then
sat(i) = sat(i)+satt(ipt49+i)-sat(ipt49-H)
if(sat(i).It. zerO)then
sat(ipt2+i) = sat(ipt2+i) + sat(i)
sat(i)'=zerO
endif
else
sat(ipt2+i) = sat(ipt2+i) + satt(ipt49+i)
+ - sat(ipt49+i)
endif
else
sat(ipt2+i) = sat(ipt2+i) + satt(ipt49+i)
+ - sat(ipt49+i)
endif
175 continue
endif
C
C— Increase the time step if the number of iterations is less than
C— orequaltoipt(35).
C
if(it.Ie.ipt(35))ipt(37)=l
C
C—• Write plotting data. This is restricted to 6 components from both
C— mobile phases.
C
if(Ictrl(15)) then
if(lprnt(26)) then
if(mod(its,ipt(84)).eq.O) Iplot = .true.
else if(.not.lprnt(26)) then
if (int(t(9)/t(28)).gt.int((t(9)-t(8))/t(28)))
+ Iplot = .true.
endif
ifflplot) then
Iplot = .false.
if(lprat(28)) then
write(26,776) t(9)
+ ,(xmf(icp(i)),i=ipt(61 )+2*ipt(74)+2
+ ,ipt(6I)+2*ipt(74)+2*(ipt(81)+ipt(82)),2)
else
write(26,776) t(9)
+ ,(xmf(icp(i)) * cmw(icp((icp(i)-1 )/ipt( 1 )+l))
+• * den(icp(i)-ipt(l)*((icp(i)-l)/ipt(l)))
+ ,i=ipt(61)+2*ipt(74)+2
+ ,ipt(61)+2*ipt(74)+2*ipt(81),2)
+ ,(xmf(icp(i)) * cmw(icp((icp(i)-1 )/ipt(!)+!))
+ * den(icp(i)-ipt(l)*(((icp(i)-l)/ipt(l))-l))
+ ,i=ipt(61)+2*ipt(74H2*ipt(81)+2
+ ,ipt(61)+2*ipt(74)+2*(ipt(81)+ipt(82)),2)
endif
end if
end if
C
225
-------
C— Print diagnostic information.
C
if(ipl(28),£t.0)then
wriic (ipt(28),800) its,t(9),it,t(8)
800 format ('Transport sol at time step =',i6,
+ ' timc=',cl0.3/
+• ' iterations for convergences'44,2x,
+ 'withtimestep=',el0.3)
if(lctrl(4))then
if(imv*I,eq,l)then
wriic (ipl(2S).S01) 'Gas',t<23),t(25)
SOI format(2x>a,' phase:'/
+ 4x,'Max cell peclet number: ',e!2.4/
+ 4x,'Max cell courant number:',el2.4/
+ 6x,'Notc - does not consider exchange')
end if
if(imob2,eq,2) then
write (ipt(28),801)' Aqueous',t(24),t(26)
end if
end if
end if
C
C— Return to MISER,f with a converged transport solution.
C
return
end if
200 continue
C
C— Reduce .(he time step if the maximum number of iterations was
C— reached without convergence. Reset the xmf and sat vectors.
C— Return to MIS.ER.f to begin time step again.
C
ipt(37)=-l
write(ipt(28),*)' Time step reduction it>=',ipt(32)
write(ipt(28),*)' .elapsed time:',t(9),' .time step:', t(8)
end if
do230i=l,ipt(l)*ipt(58)
230 xmf(i)=xmft(i)
do235i=l,ipt(41)
235 sat(i)=satt(i)
C
C— Reset the molecular weights, molecular densities, mass densities,
C— ,mass exchange terms, and bio terms.
C
callMOLEWT
callMPEX
if(lctrl(3)) call BIQ(iconv,ibconv)
999 return
776 format(7eU.4)
end
Subroutine - vel.f
C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c-
VEL,f - Subroutine which computes the mobile phase specific
discharge. This routine is not called when constant
velocity simulations are being run. Specific discharges
arc clement constants using averaged nodal properties.
Storage is as follows: qx gas phase
qz gas phase
qx aqueous phase
qz aqueous phase
Required Control Flags:
letrl( 1 8) - logical variable denoting velocity discretization
lclrl(I8) = . true. -node!
ktrl{ 18) = . false. -elemental
subroutine vcl
include Vlimen inc'
C
C — Declare and define common block variables.
C
common /cbl/ matel(nelmx),nodel(ncl3),nodept(nnmx),nelpt(nel3),
+ matpt(nn6)
common /cblc/ xnodc(nnmx),znode(nnmx),rbar(nelmx),area(nelmx)
common /cbld/ gama(nel3),beta(nel3)
common /eblc/ aby !2{nelmx),aby30(nelmx)
common /cb2/ p(nn3)
common /cb2c/ q(nc!4)
common /cb2d/ pmwO{nnmx),denO(nnmx)
common /cb3/ sat(nnsik3)
common /cb57 pmob(nnstk4)
common /cbfib/ por(nclmx),srw(nnstk)
common /cb6c/ temp(nnmx)
common /cblO/ dcn(nnfi)
common /eb30/ ibc(nnmx)
common /cb32/ bcf(nn2)
common /cb40/ a(icnl),rhs(nsolve),w(icnl)
common /cb41/ im(icnl),icn(icnl),iw(icnl,8),ikeep(icnl,5)
common /cMlb/ nbw(0:2),ia
C — Dimension local arrays.
C
dimension rhsx(nnmx),rhsz(nnmx),az(icnl),irnz(icnl),icnz(icnl)
+ ,ikeepz(icnl,5),wz(icnl)
if(lctrl(18)) goto 200
C
C — Initialize variables.as needed.
C
iptl=ipt(l)
ipt2 = ipt(2)
do 10 i=l,ipt(0)*4
q(i)=zerO
10 continue
C
C — Iterate over the mobile phases
C
iptOx2 = ipt(67)
imobl=l
imob2=2
if(ipt(3).eq.O) imobl=2
if(ipt(4).eq.O) imob2=l
do 100 iphase = imobl,imob2
C
C— Set pointers, ip points to non-stacked phase properties, ipq
C — points to q, ip2 points to den, ip2s points to pmob.
C
ipml = iphase-1
ip = ipml *ipt(l)
ipq = ipml * iptOx2
ip2 = ipml * ipt(40)
ip2s = ipml * ipt(49)
ip3d = ipml *ipt(l) + ipt(41)
Compute q element by element. First set node numbers.
do 100 i=l,ipt(0)
ix = i + ipq
iz = ix + ipt(O)
ie!3 = i*3
iell-iel3-2
iel2 = ie!3-l
il=nodel(iell)
226
-------
C
C —
C—
C —
C
C
C —
C —
C
i I s = nodept(i 1 )+nelpt(iel 1 )
ilx = ip2s + ils
ilz = ilx + ipt(2)
12 = nodel(ie!2)
i2s = nodept(i2)+nelpt(iel2)
i2x = ip2s + i2s
i2z = i2x + ipt(2)
i3 = nodel(ieB)
i3s = nodept(i3)-t-nelpt(ie!3)
i3x = ip2s +• i3s
i3z = i3x + ipt(2)
Average mobilities and densities, obtaining centroid values
for each element. Mobilities are stacked. Mass densities
are used for this expression.
xmob = third * (pmob(ilx) + pmob(i2x) + pmob(i3x))
zmob = third * (pmob(ilz) + pmob(i2z) + pmob(i3z))
If an element has a gas saturation below sgtest, set the mobility
of that element equal to zero.
if(iphase.eq.l)then
if((sat(ils).lt.sgtest).or.(sat(i2s).lt.sgtest)
.or.(sat(i3s).It.sgtest)) then
xmob = zerO
zmob = zerO
end if
else
if((sat(ils+ipt2).It.srw(ils)+srwmin)
.or.(sat(i2s+ipt2).lt.srw(i2s)+srwmin)
.or.(sat(i3s+ipt2).lt.srw(i3s)+srwrnin)) then
xmob = zerO
zmob = zerO
end if
end if
dl = den(il+ip3d)
d2 = den(i2+ip3d)
d3 = den(i3+ip3d)
C — Calculate element average density in a manner consistent with
C — the calculation of the pressure gradient.
C
davgx = (dl*dabs(beta(iell)) + d2*dabs(beta(ie!2))
+ + d3*dabs(beta(iel3)))/(dabs(beta(iell))+
+ dabs(beta(iel2))+dabs(beta(iel3)))
davgz = (dl*dabs(gama(iell)) + d2*dabs(gama(iel2))
+ + d3*dabs(gama(iel3)))/(dabs(gama(iell))+
-1- dabs(gama(ieI2))+dabs(gama(iel3)))
C
C — Calculate pressure heads.
C
pi = p(il-t-ip)
p2 = p(i2+ip)
p3=p(i3+ip)
hi = pi - dl*t(22)*znode(il)
h2 = p2 - d2*t(22)*znode(i2)
h3 = p3 - d3*t(22)*znode(i3)
C
C — Compute specific discharge.
C
q(ix) = -xmob * davgx * (( hl*beta(iell) + h2*beta(ie!2)
+ + h3*beta(ie!3))/(ZOdO*area(i)))
q(iz) = -zmob * davgz * (( hl*gama(iell) + h2*gama(ie!2)
+ +h3*gama(iel3))/(2.0dO*area(i)))
100 continue
return
C
C — Finite element q computation. First, initialize q with
C — zeros.
C
200 do 210 i=l,ipt(42)
q(i)=zerO
210 continue
C
C — Now iterate over the mobile phases.
C
imobl=l
imob2=2
if(ipt(3).eq.0)imobl=2
if(ipt(4).eq.O) imob2=l
do 220 iphase = imobl,imob2
C
C— Zero the local finite element matrices.
C
do230i = l,ipt(l)
rhsx(i) = zerO
rhsz(i) = zerO
nrow = (i-l)*nbw(l)
do230j = l,nbw(l)
az(nrow+j) = zerO
230 a(nrow-l-j) = zerO
C
C—• Set pointers, ip points to non-stacked phase properties, ipq
C— points to q, ip2 points to den, ip2s points to pmob.
C
iptl=ipt(l)
ipt2 = ipt(2)
ipml = iphase-1
ip = ipml *ipt(l)
ip2 = ipml * ipt(40)
ip2s = ipml * ipt(49)
ip3d = ipml * ipt(l) + ipt(41)
do 240i=l,ipt(0)
C
C— Set the pointers to the local nodes 11,12, and 13. The
C— postscript s is for stacked local nodes, and p is for phase
C— Compute constants.
C
ie!3=i*3
iell=ie!3-2
ie!2 = ie!3-l ,
il =nodel(iell)
ils = nodept(il)+nelpt(iell)
ilx = ip2s + ils
ilz = ilx + ipt2
i2 = nodel(ieI2)
i2s = nodept(i2)+nelpt(ieI2)
i2x = ip2s + i2s
i2z = i2x + ipt2
i3 = nodel(ieB)
i3s = nodept(i3)+nelpt(ie!3)
i3x = ip2s + i3s
i3z = i3x + ipt2
C
C— If an element has a gas saturation below sgtest or an aqueous
C— saturation below srw+srwmin, skip calculation of the local
C— element matrix.
C
ifftiphase.eq. 1 ).and.((sat(i 1 s).lt.sgtest)
+ .or.(sat(i2s).lt.sgtest).or.(sat(i3s).It.sgtest)))
+ goto 240
if((iphase.eq.2)
+ .and.((sat(ils+ipt2).lt.srw(ils)+srwmin)
+ .or.(sat(i2s+ipt2).lt.srw(i2s)+srwmin)
+ .or.(sat(i3s+ipt2).lt.srw(i3s)+snvmin)))
+ goto 240
C
C— Compute the left hand side matrix.
C
C
C—
C
aoff=aby!2(i)
aon = 2.0dO * aoff
Calculate pressure heads.
pi =p(il+ip)+patm
p2 = p(i2+ip)+patm
p3 = p(i3+ip)+patm
dl =den(il+ip3d)
d2 = den(i2+ip3d)
d3 = den(i3+ip3d)
if(iphase.eq.l) then
dglO = pmwO(il)*patm/(r*temp(il))
dg20 = pmwO(i2)*patm/(r*temp(i2))
dg30 = pmwO(i3)*patm/(r*temp(i3))
227
-------
c
c-
c
bl =pl/(dglO'l(22))-znode(il)
h2 - p2/(dg20*l<22)) - znode(i2)
h3 * p3/(dg30*l{22» - znode(i3)
else
hi =pl -dl*t<22)* (znode(il)-wtdpth)
h2 = p2 - d2»l(22) * Cznode(i2)-wtdpth)
h3 =p3 - d3*t{22) * (znode(i3)-wtdptb)
end if
• Calculate mobility terms for the right hand side.
pmlx=:2.0d0*pmob(ilx) +
pm3x
pmob(i2x) +
pmob(i2x) +
pmob(i3x)
pmob(i3x)
pmobfl 1 x) + pmob(i2x) + 2.0dO*pmob(i3x)
= 2.0dO*pmob(ilz) + pmob(i2z) + pmob(i3z)
pm2z " pmobfi 1 z) + 2.0dO*pmob(i2z) + pmob(i3z)
pm3z= pmob(i 1 z) + pmob(i2z) + 2.0dO*pmob(i3z)
C
C— Calculate pressure gradient terms for the right hand side.
C
if(iphuc.eq,l)then
term = -K22) » rbat (i) / 48.0dO
eke
term = -rbar(i)/48.0dO
end if
dpx * (hl*beta(iell)*dglO + h2*betaGel2)*dg20
+ 4- Ii3*bcta(iel3)*dg30) * term
dpz = (hl*gama(iell)*dglO + h2*gama(ie!2)*dg20
4- 4- ])3*gama(iel3)*dg30) * term
flx = pmlx*dpx
f2x = pm2x * dpx
f3x * pm3x * dpx
flz = pmlz*dpz
f2zspm2z*dpz
f3z s pm3z • dpz
C
C— Calculate mobility/gravity terms for the right hand side.
C
iftiphase cq 1) then
tcrm=:t<22) * aby!2(i)/2.0dO
dmlz = pmob(ilz) * ((patm'dl /(pl*dglO))-rone)*dglO
dm2z=pmob(i2z) * (( patm*d2 / ^p2*dg20)) - rone)*dg20
dm3z = pmob(i3z) * ((patm*d3 / (p3*dg30)) - rone)*dg30
flz » flz -t- term * ( 2.0dO*drnlz + dm2z+ dm3z)
f2z = f2z + term * (dmlz + 2,OdO*dm2z + dm3z)
fjz « f3z + term * (dmlz + dm2z + 2.0dO*dm3z)
else
term=abyl2(i)/2.0dO
dmlz = pmob(ilz) * (dl - denO(il)) * t(22)
dm2z = pmob(i2z) * (d2 - denO(i2)) * t(22)
dm3z = pmob(i3z) * (d3 - denO(i3)) * t(22)
fl z = f Iz + term * (2,OdO*dmlz+dm2z + dm3z)
flz = f2z •»• term * (dmlz + 2.0dO*dm2z + dm3z)
f3z = f3z + term * < dmlz + dm2z + 2.0dO*dm3z)
end if
C
C— Now assemble the global matrix and right hand side vector in
C— banded form.
C
rhsx(il)5trhsx(il) + flx
ihs.Mi3) = rhsx(i3) + Ox
irawl=(il-l)*nbw(l)
= 02-l)*nbw(l)
(i3-l)*nbw(l)
icol22
ico!21=icoi22 + (il-i
icol31
icol334-(il-i3)
ico!33-Ki2-i3)
a(iroiyl r)-icpll2)
a(irow) +icoll3)
a(irow2tipoJ21)
a(irow2 + jco!22)
a,(irow2-*-icp!23)
a(irow3-i-!coJ31)
a(irow3 4- icp)32)
a(irow3 + ico!33)
continue
= a(iro>v J + ippl!2) -h aoff
=a(irowj + icpjj 3) + aoff
= a(irow2 +• i,c,pl21) + aoff
= a(irpw2 + icol22) + aon
= a(itow2 * ico!23) + apff
=.a(irow3 + icp]31) + aoff
= a(irow3 + iso!32) + aoff
= a(irow3 + ico!33) + aon
240
C
C— $e.t up temporary mass matrix,
C
do25i = l,ipt(l)*nbw(l)
25 az(i) = a(i)
C
C— Impose boundary conditions.
C
nbwO = nbw(0)
nbwl =nbw(l)
dp26j=l,ipl(J)
Ivelx = .false.
)velz=.false.
C
C— No z-velocity normal to the bpt(om.
C
if(lctrj<28).and.znode(i).eq.znods(ipt(l)))then
rhsz(i) = zerO
Ivelz = .true.
end if
C
C— No x-velpcity nprmal tp the R.H.S. boundary.
C
if(lctrl(29).and.xnode(i).eq.xnode(ipt(l)))then
rhsx(i) = zerO
Ivelx = .true.
end if
C—
C
C
No x-velocity normal tp the L.H.S. bpundary. Npte that this
bpundary will be adjusted in the presence of a well.
if(lctrl,(30).and.xnpde(i).eq.xnode(l))then
rhsx(i) = zerO
Ivelx = .true.
C
C— Adjust velpcity boundary condition in the presense of a well.
C
if(!ctr!a2)) then
do28iwell=l,ipt(24)
inw = ibc(ipt(64)+iwell)
if(inw.eq.i) then
if(iphase,eq.l)then
rhsxO) = bcf(inw)
else if(iphase.eq.2.and.qwell.lt.zerO) then
rhsx(i) = bcf(inw+ipt(l))
28
C
C—
27
end if
end if
continue
end if
end if
No z-velocity normal to the top. This boundary extends from the
well to caplen.
if(lctrl{31 ).and.znpde(i).eq.znode(l)
.and.xnode(i).le.caplen) then
rhsz(i) = zerO
Ivelz = .true.
end if
if(lvelx.or.lvelz) then
do27j = l,nbw(l)
if(lvelx) a((i-l)*nbwl+j) = zerO
if(lvelz) az((i-l)*nbwl+j) = zerO
cpntinue
if(lvelx) a((i-l)*nbwl+l+nbwO) = rpne
if(lvelz) az((i-l)*nbwl+l+nbwO) = rone
end if
Ivelx = .false.
228
-------
Ivelz = .false.
26 continue
C
C— Collapse full matrix into sparse form used by Harwell. Also
C— scale array by dividing rows through by the diagonal value.
C
ia = 0
iaz = 0
do260irow = l,ipt(l)
nrow = (irow-l)*nbw(l)
if(a(nrow+l+nbw(0)).eq.zerO) then
a(nrow+l+nbw(0)) = rone
rhsx(irow) = zerO
end if
if(az(nrow+l+nbw(0)).eq.zerO)then
az(nrow+l+nbw(0)) = rone
rhsz(irow) = zerO
end if
aii = rone / a(nrow+l+nbw(0))
aiiz = rone / az(nrow+l+nbw(0))
rhsx(irow) = rhsx(irow) * aii
rhsz(irow) = rhsz(irow) * aiiz
do270icol=l,nbw(l)
if (a(nrow+icol) .ne. zerO) then
ia = ia + 1
a(ia) = a(nrow+icol) * aii
icn(ia) = icol+irow-nbw(0)-l
irn(ia) = irow
endif
if (az(nrow+icol) .ne. zerO) then
iaz = iaz + 1
az(iaz) = az(nrow+icol) * aiiz
icnz(iaz) = icol+irow-nbw(0)-1
irnz(iaz) = irow
endif
270 continue
260 continue
C
C— Solve the linear system using Harwell routines.
C
callma28ad
-------
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