PB91-181750
FORCED AIR VENTILATION FOR REMEDIATION
OF UNSATURATED SOILS CONTAMINATED BY
VOC
(U.S.) Environmental Protection Agency
Ada, OK
May 91
U.S. DEPARTMENT OF COMMERCE
National Technical Information Service
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EPA/600/2-91/016
May 1991
FORCED AIR VENTILATION FOR REMEDIATION OF
UNSATURATED SOILS CONTAMINATED BY VOC
by
Jong Soo Cho
Processes and Systems Research Division
Robert S. Kerr Environmental Research Laboratory
Ada, Oklahoma 74820
ROBERTS. KERR ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
ADA, OKLAHOMA 74820
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TECHNICAL REPORT DATA
(Please read Instructions on ihe reverse before complei'
1. REPORT NO.
EPA/600/2-91/016
2.
4. TITLE AND SUBTITLE
FORCED AIR VENTILATION FOR REMEDIATION OF UNSATURATED
SOILS CONTAMINATED BY VOC
B. REPORT DA
6. PERFORMING ORGANIZATION CODE
PB91-181750
ff
ay
7. AUT.HOR(S)
Jong Soo Cho
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
P.O. Box 1198
Ada, OK 74820
10. PROGRAM ELEMENT NO.
ABWD1A
11 CONTRACT/GRANT NO.
INHOUSE
12. SPONSORING AGENCY NAME AND ADDRESS
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
P.O. Box 1198
Ma, OK 74820
13. TYPE OF REPORT AND PERIOD COVERED
Project Report
14. SPONSORING AGENCY CODE
EPA/600/15
15. SUPPLEMENTARY NOTES
Project Officer: Jong Soo Cho FTS: 743-2353
16. ABSTRACT
Parameters which were expected to control the removal process of
VOCs from contaminated soil during the SVE operation were studied
by means of numerical simulations and laboratory experiments in
this project.Experimental results of SVE with soil columns in the
laboratory indicated that the removal efficiency of VOCs from soil
columns was a complicated function of air flow and the
hydrogeometry inside. The partition process between air and the
immobile liquid was not an equilibrium one, and the interfacial
mass transfer varied with the residual amount of VOCs in the soil.
Additional experiments under various conditions should be conducted
to obtain further insight into SVE process. Two computer models
were developed to study soil air and VOC movement during the SVE
process. The first one was an analytical approximate model which
could be used for the simulation of air movement in the SVE
operation with multiple wells in homogeneous soil media. The second
-one was a numerical model in three-dimensional geometry which used
a finite difference solution scheme. A simple pneumatic pump test
was conducted, and part of test data were used for the validation
of the simple analytical model.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
COSATi Field,Group
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS i Tins Report)
UNCLASSIFIED
21 NO. OF PAGES
90
20 SECURITY CLASS (This paqc
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (R«v. 4-77) PREVIOUS EDITION i s OBSOLETE
80
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DISCLAIMER
The information in this document has been funded wholly or in part by the United States
Environmental Protection Agency. It has been subjected to the Agency's peer and administrative review
and it has been approved for publication as an EPA document. Mention of trade names or commercial
products does not constitute endorsement or recommendation for use.
QUALITY ASSURANCE STATEMENT
All research projects making conclusions or recommendations based on environmentally
related measurements and funded by the Environmental Protection Agency are required to participate in
the Agency Quality Assurance Program. This project was conducted under an approved Quality
Assurance Project Plan. The procedures specified in this plan were used with the following exceptions:
The QA/QC plan for field pneumatic tests was not made and the original QA/QC plan was not updated.
The calibration of pressure gauges was not conducted and a calibration chart for the pitot tubes supplied
by the manufacturer was used. Soil air pressures relative to the atmospheric pressure were measured
and the pressure changes with distance from the wells were observed. The pressure gauges in the range
of less than 1 inch water were very sensitive to the atmospheric pressure and unreliable under windy
conditions. The reproducibilities of the gauges in higher ranges were good and the repeated
measurement could replicate the trend of pressure changes. Information on the plan and documentation
of the quality assurance activities and results are available from the author.
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ABSTRACT
Many cases of soil vacuum extraction(SVE) applications in the field have been reported, but
very few systematic studies about physical and chemical processes in soil air are found. Parameters
which were expected to control the removal process of VOCs from contaminated soil during the SVE
operation were studied by means of numerical simulations and laboratory experiments in this project.
Experimental results of SVE with soil columns in the laboratory indicated that the removal
efficiency of VOCs from soil columns was a complicated function of air flow and the hydrogeometry
inside. The partition process between air and the immobile liquid was not an equilibrium one, and the
irrterfacial mass transfer varied with the residual amount of VOCs in the soil. Additional experiments
under various conditions should be conducted to obtain further insight into the SVE process.
Two computer models were developed to study soil air and VOC movement during the SVE
process. The first one was an analytical approximate model which could be used for the simulation of air
movement in SVE operation with multiple wells in homogeneous soil media. The second one was a
numerical model in three-dimensional geometry which used a finite difference solution scheme. A simple
pneumatic pump test was conducted, and parts of test data were used for the validation of the simple
analytical model.
This report covers a period from June 1988 to December 1990 and work was completed as
of December 31,1990.
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FOREWORD
EPA is charged by Congress to protect the Nation's land, air and water systems. Under a
mandate of national environmental laws focused on air and water quality, solid waste management and
the control of toxic substances, pesticides, noise and radiation, the Agency strives to formulate and
implement actions which lead to a compatible balance between human activities and the ability of natural
systems to support and nurture life.
The Robert S. Kerr Environmental Research Laboratory is the Agency's center of expertise
for investigation of the soil and subsurface environment. Personnel at the Laboratory are responsible for
management of research programs to: (a) determine the fate, transport and transformation rates of
pollutants in the soil, the unsaturated and the saturated zones of the subsurface environment; (b) define
the processes to be used in characterizing the soil and subsurface environment as a receptor of
pollutants; (c) develop techniques for predicting the effect of pollutants on ground water, soil, and
indigenous organisms; and (d) define and demonstrate the applicability and limitations of using natural
processes indigenous to the soil and subsurface environment, for the protection of this resource.
This report describes research conducted to develop, evaluate, and demonstrate the
efficacy of forced air ventilation of VOCs from unsaturated soils. The research assesses evaporation of
VOCs under artificially driven pressure gradients as a means of removing VOCs, which are widely
encountered as ground water pollutants.
Clinton W. Hall
Director
Robert S. Kerr
Environmental Research Laboratory
IV
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CONTENTS
Disclaimer ii
Quality Assurance Statement ii
Abstract Hi
Foreword iv
Figures vii
Abbreviations and Symbols ix
Acknowledgements x
1. INTRODUCTION 1
2. CONCLUSIONS AND RECOMMENDATIONS 3
3. BACKGROUND REVIEW 5
4. PROCESS OF SOIL VACUUM EXTRACTION 8
Soil Air Flow 8
VOC Fate and Transport 10
Parameters 12
5. EFFECT OF PARAMETERS 17
One-Dimensional Solutions 17
Analysis of SVE Processes 22
6.VOC REMOVAL RATE MEASUREMENTS 37
Soil Column Experiments 37
Removal Rate Model 39
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7.MODEL WITH SUPERPOSITION OF ANALYTICAL SOLUTIONS 51
Analytical Solutions 51
Pneumatic Pump Test 54
Simulation of Pneumatic Pump Test " 57
8.THREE-DIMENSIONAL FINITE DIFFERENCE MODEL 68
Finite Difference Solutions 68
Computer Implementation 72
References 74
VI
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FIGURES
Number
5-1.
5-2.
5-3.
5-4.
5-5.
5-6.
5-7.
5-8.
6-1.
6-2.
Pressure distribution inside soil column
Air velocity distribution inside soil column
Relative permeability of soil air with moisture content inside clay soil
Removal rate from soil column, experiment 1
Removal rate from soil column, experiment 2
Removal rate from soil column, experiment 3
Removal rate from soil column, experiment 4
Removal rates at different operating temperatures
Schematic diagram of soil column experiment
Toluene concentration in effluent air from soil column
Page
29
30
31
32
33
33
35
36
42
43
20 ml of pure toluene
6-3. Toluene concentration in effluent air from soil column 44
10 ml pure toluene following 10 ml water
6-4. Toluene concentration in effluent air from soil column 45
10 ml water following 10 ml toluene
6-5. Toluene concentration in effluent air from soil column 46
15 ml water following 5 ml toluene
6-6. Comparison of effluent concentrations from different soil columns 47
Air flow rate 10ml/min
6-7. Comparison of effluent concentrations from different soil columns 48
Air flow rate 20 ml/min
6-8. Comparison of effluent concentrations from different soil columns 49
Air flow rate 30 ml/min
VII
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6-9. Conceptual model of VOC removal from soil pores 50
7-1. Vector presentation of well screened section in three-dimensional space 59
7-2. Schematic diagram of pneumatic pump test 60
7-3. Measured pressure distribution at 15 ft depth for air injections/veil test 61
7-4. Measured pressure distribution at various depths 62
Air injection well pressure 50 inch water
7-5. Measured pressure distribution at 15 ft depth for vacuum extraction well test 63
7-6. Measured pressure distribution at 15 ft depth 64
for injection/extraction wells test
7-7. Measured pressure distribution at various depths 65
Air injection well pressure 50 inch water
Vacuum extraction well pressure -48 inch water
7-8. Isobaric contour plots of computed pressure distribution 66
7-9. Isobaric contour plots of computed pressure distribution 67
VIII
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ABBREVIATIONS AND SYMBOLS
Abbreviations
ADI : Alternative Directive Implicit
FID : Flame Inonization Detector
PVC : Polyvinyl Chloride
scfm : standard cubic feet per minute
SVE : Soil Vacuum Extraction
TCE : Trichloroethylene
VOC : Volatile Organic Contaminant
Symbols
atm : atmospheric pressure
cp : centipoise
H : Henry's law constant
Kpa : Kilopascal
L : soil column length
x : x coordinate in rectangular coordinate system
longitudinal direction of soil column
z : z coordinate in rectangular coordinate system
vertical direction in three-dimensional models
A : linear increment
V : gradient operator
3 : partial differential operator
IX
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ACKNOWLEDGEMENT
The author is deeply grateful for the help of many people: to Dr. Carl Eddington, Chemistry
Department, East Central University, Ada, Oklahoma, and Lisa Secrest, NSI/RSKERL, Ada, Oklahoma,
for the GC analysis; to Frank Blaha, U.S. Coast Guard; Frank Beck, Dominic DiGiulio, and Dr. Don
Kampbell, EPA/RSKERL; engineers in the Traverse Group Inc., and Solar Universal Technologies, Inc.,
Traverse City, Michigan, without whose help it would have been impossible to perform the pneumatic
pump test in Traverse City; to Tri Duong and Joe Blanton, NSI/RSKERL, for the implementation of
computational scheme, encoding the program in FORTRAN, and developing the graphical
postprocessor; and to the revewers who offered valuable comments and suggestions during the writing of
this report.
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SECTION 1
INTRODUCTION
Fuel leakage and spills are the most frequent sources of soil and ground-water
contamination at service stations and underground storage tank areas. A large portion of released
hydrocarbon infiltrates the subsurface and remains bound under capillary pressure as residual immiscible
phase liquid. The residual hydrocarbon serves as a continuous source for groundwater contamination.
Therefore, the reclamation of the contaminated aquifer should include removal of the long-term
contamination source. The clean-up of soil contaminated by Volatile Organic Contaminants (VOCs) is
generally an expensive operation due to the high cost associated with excavation, transportation and
disposal. Classical methods such as soil removal, forced percolation, encapsulation, or trenching are
frequently impossible or prohibitively expensive, especially in the midst of an industrial or residential area.
An alternative method to remediate soils is by the use of the soil vacuum extraction (SVE)
system. This process has proven to be inexpensive and effective for the clean up of soil and ground-
water contaminated by solvents and volatile components of petroleum products (Bennedsen, 1987;
Jafek, 1986; Agrelot etal., 1985; Malot, 1985). The cost of installation and operation of an SVE system
is usually tower than the cost of other methods (Hinchee et a/.,1987). Another major advantage is that
this method is an in-situ process. The contaminated soil remains in place and is not transported and
disposed of in other locations. The SVE system is also used for the removal of methane gas originated in
landfills (Moore et a/., 1982). Practical applications of the SVE system have been reported for the control
of methane gas migration from landfills (Moore etal., 1979). Methane and carbon dioxide generated by
microbial decomposition of organic materials can migrate a long distance from the landfill and can build
up to explosive levels. The SVE wells, sometimes with interdiction walls, are installed to prevent the
migration of methane gas (Mohsen et a/., 1980).
Many field applications have been reported since early 1980 (Bruckner, 1987; Bruckner and
Kugele, 1985; Glynn and Duchesneau, 1988; Hutzler et a/.,1988). In spite of many field applications, very
few scientific or systematic studies have been reported. Therefore, the design of the SVE system has
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been mainly dependent on experience and rough estimations. Sometimes, prototype or pilot-scale
systems are used to obtain design parameters such as well depths, well spacings, and extraction rates
(Hutzler et al., 1988). Field operations and pilot scale studies can be found in several review reports
(Dynamac, Inc., 1986; Oak Ridge National Laboratory, 1989; Hutzler et al., 1988).
This project investigated the movement of VOCs in soil air during the SVE applications.
Several physical and chemical processes are involved in the movement of VOCs in soil air, including
convective and diffusive transport, interfacial mass transfer between immiscible phases, and
biological/chemical transformations. Physical and chemical properties of soils and VOCs are expected to
control these processes. The ultimate goal of this project was to obtain knowledge on relationships
among the various properties and processes of VOC transport in soil air. These relationships were
integrated in computer models. This report includes laboratory experiments and field tests of the SVE
system under relatively simple conditions. The model development procedures are also included in this
report. Vigorous validations of models are recommended prior to public distribution.
This report consists of several sections. Section 2 includes the summary of the conclusions
of this project and recommendations for future research. In section 3, background review of the SVE
research and model development is included. In sections 4 and 5, mathematical expressions of
processes involved in SVE are derived and analyzed. In section 6, soil column experiments conducted in
the laboratory are reported. In sections 7 and 8, development of two models and a field pneumatic pump
test are included.
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SECTION 2
CONCLUSIONS AND RECOMMENDATIONS
From the experiments in laboratory, field tests, and development of models in this project,
the following conclusions are drawn:
(1) From analyses of experiments and model simulations, very valuable information could be
obtained. The observation of simulated results based on soil column experimental conditions showed
several physical and chemical properties influencing the efficiency of the SVE operation. Among VOC
chemical properties, the vapor pressure was the most sensitive factor that controlled the efficiency of
total operations.
(2) Air flow rate and liquid distribution were very important parameters which controlled the
removal rate of VOCs from soil columns. A conceptual model was proposed to describe the evaporative
process of VOCs from the residual liquid in soil pores.
(3) The pneumatic pump test gave very important information for design of SVE systems,
including the zone of influence, soil characterization and pumping efficiencies.
(4) Two computer models for soil air flow and VOC transport in the SVE system were
developed. The analytical solution model developed was very simple and easy to use. Simulations of
pneumatic pump tests with this model revealed that the model generated reasonable results and could
be used as an initial design tool. A fully three-dimensional finite difference model was developed.
Various solution methods have been tried and explicit schemes were selected to reduce the
computational time and memory requirements. A graphical postprocessor was attached to enhance the
visualization of output results.
The proposed future works are as follows:
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(1) A large number of studies on mass transfer have been reported in engineering literature,
but very few pertain to soil systems. Soil particles and pore sizes are not uniform and the Reynolds'
number is usually less than 0.1 in soil systems. The extrapolation of empirical correlations to unmeasured
operating conditions is not desirable, and further studies are required to obtain more precise correlations
suitable for soil systems. More experiments are suggested with modified columns and procedures for
quantitative analyses.
(2) The proposed model for VOC removals from soil pores needs to be verified through
additional experiments.
(3) Research on the enhancement of SVE by increased temperature is also proposed to
achieve better efficiency of SVE operations.
(4) Pneumatic pump tests are recommended under various operating conditions before full
scale implementations of SVE systems. Tracer gas tests will help further.
(5) A main reason for the lack of field scale model developments is the expense of the
model validation with field scale data. It is very costly to perform tests for the model validation, but this is
a very necessary step. A simple pneumatic pump test, like the one reported in this project, will give very
important information for model validation and optimal design of the SVE system.
(6) Additional refinement and validation of the analytical solution model are necessary for
further field applications. The finite difference model is still in the developmental stage and needs a
rigorous validation through numerical experimentations and comparison with field data. In addition to the
validation, alternative schemes should be tested to accelerate the computation.
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SECTION 3
BACKGROUND REVIEW
In this section, a small number of background reviews of the SVE process study are
included. Reviews are limited to the areas of laboratory research and mathematical model development.
Several laboratory experiments involving convective transport due to air flow inside soil
pores have been reported since 1980. Before this time, research involving soil gas movement was
restricted to diffusional transport. Laboratory research is often performed with small soil columns. Marley
and Hoag (1984) and Baehr etal. (1989) used soil columns to measure the removal rate of gasoline from
contaminated soil. They reported experiments on the removal rate of partially saturated gasoline in the
capillary fringe above the water table by steady air flow. More than 99 % removal of gasoline initially
present was observed in a reasonably short time. Aware, Inc. (1987) conducted soil column experiments
to evaluate the SVE process with various contaminant conditions and soil types. They reported 40 to
90% removal of the initial amount of VOCs applied in less than 8 days of operation in the temperature
controlled environment. They concluded that there is the possibility of success in contaminated soil
cleaning with the SVE process. Rainwater etal. (1988 a, b) reported large-sized soil column experiments
to study the volatilization mechanism in porous media and provided removal rate data of hydrocarbon
mixtures with a preliminary modeling effort. They concluded that the presence of the residual water in
porous media significantly retarded the diffusion of the hydrocarbon vapor and slowed the removal
process.
Since soil column experiments are one-dimensional, they are easy to analyze. But it is
difficult to replicate three-dimensional field conditions with one-dimensional soil columns. It is reasonable
to conduct large three-dimensional experiments with sand boxes or tanks. Texas Research Institute
(Thornton and Wootan, 1982; Wootan and Voynick, 1984) reported experiments with large sand boxes.
They studied the removal of gasoline product floating above a water table using the SVE process and
showed the possibility of the field scale application. A large volume of gasoline spilled in sand tanks was
removed by airflow and a remarkable amount of gasoline was also degraded by microbial activity.
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Johnson (1989) reported a large physical model study to examine the effectiveness of an SVE system.
He observed high hydrocarbon vapor concentration in soil air just after gasoline spillage. Water table
fluctuation made the hydrocarbon concentration decrease due to the entrapment of hydrocarbon in the
capillary fringe. He indicated the low efficiency of the SVE application for the removal of the entrapped
gasoline residual.
Many computer models have been developed for experimental data analyses. A one-
dimensional model was developed by D.J. Wilson et al. (1988) for analysis of AWARE, Inc.'s soil column
experiment (1987). This simple model was used for analysis of soil column experiments and later
expanded to two-dimensional rectangular and cylindrical coordinate systems for analysis and design of
field scale operations. This model used site-specific partition coefficients and a finite-difference scheme
with a relaxation method to solve partial differential equations. A two-dimensional, finite difference model
was reported by D.E. Wilson et a/.(1987) for simulations of sand-box experiments performed by the
Texas Research Institute (Wootan and Voysnick, 1984). This model included the airflow and transport of
gasoline components evaporated from free product over the water table. The floating gasoline product in
the capillary fringe above the water table was treated as a constant flux boundary due to evaporation.
Air flow and VOC transport in the soil system are considered as the two main processes in
SVE systems. Some models have been developed to treat the air flow only. Initially in designing an SVE
system, the airflow model is sufficient. For the prediction of clean-up time, a model developed to
describe both processes is necessary. A two-dimensional model with the axial symmetry assumption
which was limited for the single venting well was presented by Kemblowski (1989). Analytical solutions of
soil air pressure distributions were obtained in porous media confined by impervious boundaries. Only the
radial directional flow to the well was considered. In field applications of the SVE process, multiple wells
are expected to show three-dimensional configurations of the air pressure and flow velocity distributions.
Therefore, only a three dimensional model incorporating various well locations and lengths of screened
well sections can provide an optimal design. Because of the large memory and computational time, three-
dimensional models developed for SVE systems are rare. Colorado State University (Sabadell era/.,
1988) reported a three-dimensional airflow model with the finite difference method. Their model was
tested with limited field data.
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The similarity of the physical processes of SVE and ground-water pumping led to the idea of
utilization of a ground-water model as an aid in the design of soil vacuum extraction systems. Massmann
(1989) compared the soil air flow equation with the ground-water flow equation. The difference between
these equations was the air compressibility which made the flow equation nonlinear. The equation could
be linearized by substituting the density of air with an initial or averaged value. The maximum
computational error in pressure distribution due to the linearization was estimated to be 7% when the
applied vacuum pressure was 0.5 atm. Computational error was negligible with the applied vacuum of 0.2
atm or less. He concluded that computational error was negligible in the range of applied vacuum
pressure in field operations and the use of a ground-water model was a reasonable tool in the design of a
SVE system when an appropriate soil air flow model was not readily available. Application of a ground-
water flow model for simulations of the air pressure and flow velocity distributions of an SVE system was
reported by Cho and DiGiulio (1990).
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SECTION 4
PROCESS OF SOIL VACUUM EXTRACTION
The basic principle of SVE is very simple. Airflow is induced in the subsurface by a pressure
gradient applied through vertical wells or horizontal trenches. The flowing air sweeps out VOCs by
vaporizing highly volatile components from soil pores and the contaminated soil air is collected by
extraction wells. Effluent air from extraction wells is often treated by off-air treatment systems, e.g. an
activated carbon tank or catalytic converters. Atypical SVE system consists of air pumps or blowers
connected to a series of wells located in contaminated soil. The lower pressure inside the extraction well
generated by pumps causes soil air to move to the well. Sometimes air injection wells are added for the
further control of airflow.
VOC transport in convective and diffusive modes is considered as the main physical
process. When there is an induced pressure gradient, the bulk phase of soil air moves and carries a large
amount of VOCs in the convective transport mode. Especially in the close vicinity of wells and trenches, a
large pressure gradient is developed and the convective transport dominates the movement of VOCs. At
remote areas from wells, the pressure gradient becomes very small. VOC transport in this remote area is
expected to be slow because of the diffusive transport. In addition to the convective and diffusive
movements, VOC transport in soil air during SVE is expected to be influenced by other processes
including the partition process among gas, liquid and solid soil matrices, and biological/chemical
transformations. In this project, biological/chemical transformation processes of VOCs were not studied.
Soil Air Flow
The VOC concentrations in soil air are usually low and the changes in thermodynamic and
transport properties of soil air due to the VOC concentrations are not significant. Therefore, air flow can
be considered independent of the VOC concentration in soil air and treated explicitly from VOC transport.
In cases where the property changes due to the high concentrations of VOCs in soil air are significant,
iterative or updating procedures at each time step should be used to solve the coupled equations.
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Three basic equations are considered in the description of airflow, the mass balance
equation of soil air, the flow velocity due to pressure gradients, and the equation of state. Detailed
derivation of these equations is given in Massman (1989) and D.E. Wilson, et a/(1987). The mass
balance of soil air is expressed by the equation of continuity.
apa
= -VPV (4-1)
ra a t ra
where the $ is the air filled porosity in soil, p is the density of soil air, and V is the velocity vector of air
a a
flow.
The air flow velocity due to pressure gradient can be expressed by Darcy's law when the
slip flow is negligible. In the case of air flow in sand and gravel, the slippage of air on the soil wall is
negligible (Massman, 1989) and Darcy's law for the flow in porous media can be applied.
K
V Vp (4-2)
where K is the soil-air permeability tensor and n is the viscosity of air.
a a
The density of air is a function of the pressure and temperature. The relationship among
these parameters is expressed by the equation of state. One of these equations of state is the ideal gas
law, which is simple and applicable only for the gas at low pressure. The ideal gas law can be used
because the operating pressure of the conventional SVE system is close to ambient or lower. The ideal
gas law for soil air is
where MW is the molecular weight of soil air, R is the ideal gas law constant, and T is the absolute
temperature.
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By combining equations (4-1),(4-2), and (4-3), a general soil airflow equation can be
obtained.
MW p.
p K
V( ° ° Vp) (4-4)
This airflow equation is nonlinear because the air density, p , in the right hand side of the equation is a
a
function of pressure.
VOC Fate and Transport
VOCs can be present in the subsurface soil in five basic ways: (1) as a residual immiscible
liquid phase in the soil pore spaces, (2) as a floating product above the water table in the case of light
hydrocarbon and as a pooled or continuously migrating liquid of the dense nonaqueous phase moving
continuously to the bottom of the ground-water, (3) as a vapor in soil air, (4) as dissolved components in
soil pore water and ground-water, and (5) as adsorbed hydrocarbons on soil particles surfaces. When soil
air remains undisturbed after spillage and infiltration to the subsurface, it becomes saturated by VOC
vapors evaporated from the liquid phase. This highly saturated air will be removed initially after SVE
starts. As vapors are purged from soil pores, the concentration of VOCs in soil air begins to decrease as
the process shifts away from equilibrium. At this stage, the interfacial mass transfer between the liquid
and flowing air is expected to control the removal of VOCs from soil. Flowing air in the SVE system
moves much faster than the liquid phase inside soil pores. Therefore, the residual immiscible liquid, soil
pore water, and solid particles are considered as immobile phases in model developments.
The following mathematical descriptions of the VOC movement in soil air are proposed. The
convective transport by bulk air flow and diffusive transport due to the concentration gradient are the
major transport processes. The mass flux of the VOC component A is
10
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where c is the concentration of the component A in soil air, V is the velocity vector of air flow, 41 is the air
f\ a
filled porosity in soil, and D is the diffusrvity.
The mass balance of the component A in soil air becomes
-VN. +S
A a
= - V c V + V * D Vc + S (4-6)
r\ 3 A3
where S is the source/sink term of soil air.
a
The mass balance of the component A in the immobile phase becomes
9C
^-8 (4'7)
where <)> is the pore volume occupied by the immobile phase, C is the concentration in the immobile
/ A
phase, and S.is the source/sink term for the immobile phase.
The source/sink terms both in the mass balance of component in soil air and the immiscible
phase include the interfacial mass transfer and biological/chemical transformations. The interfacial mass
transfer of VOCs from the immobile phase to flowing air in soil pores will be a source term of VOCs in soil
air and a sink term of VOCs in the immobile phase. When soil pores contain static soil air, soil air is at
equilibrium with the liquid phase. Equilibrium concentrations in both phases can be related by Raoult's
law between nonaqueous liquid hydrocarbon and air. For the equilibrium between aqueous phase and
air, Henry's law is used when the solubility of the VOC is tow (Trowbridge and Malot, 1990). This
equilibrium state of the VOC in soil pores is achieved when contacting time is sufficient or the interfacial
mass transfer rate is very high. If the equilibrium cannot be maintained, the interfacial mass transfer rate
is controlled by the diffusion within each phase.
11
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Parameters
Several parameters are used in the description of the VOC movement and therefore are
needed to obtain solutions of the air flow and VOC transport equations. Properties of soil and VOCs
should be measured for the accurate design of the SVE operation on the specific site. Most
thermodynamic and transport properties of VOC components in air can be obtained from reported data.
These properties may change depending on the operating conditions of the SVE system. The property
changes by operating conditions sometimes cause considerable variations in the efficiency of SVE.
Thermodynamic and transport properties of VOCs in various conditions can be estimated from theoretical
and empirical relationships.
Soil Air Permeability
The permeability of soil air with multiphase fluids, i.e. air, water and non-aqueous liquid, in
soil pores is expressed by two terms, K , the relative permeability of air, and K. , the intrinsic permeability
rs i
of soil.
K = K K. (4-8)
a ra i v '
The intrinsic permeability of soil is obtained from hydrogeological data during site characterization
procesi
1987).
process. The relative permeability of air, K , is a function of the air saturation in soil pores (Parker et a/.,
Id
1/2. . .. 1/m. .2m
Kra=csa (1-(1'sa })
where m is a shape parameter of the soil water characteristic curve (van Genuchten, 1980), c is a
correction factor for the gas slippage (Corey, 1986) and s is the air saturation, defined as the ratio of air
3
filled porosity to total porosity. If the gas slippage effect is ignored, c = 1, then the relative permeability
becomes solely a function of the air saturation, s .
a
12
-------
Molecular Weight
The average molecular weight of air is 28.8 g/gmol. Considering all the components in soil
air, the average molecular weight becomes
MW = >"yAMW. (4-10)
a '-> ' k A v '
where MW is the molecular weight of the component A and y is the mole fraction of the component A in
soil air. In the conventional SVE application, concentrations of VOCs in soil air even in the saturated
condition are so tow that the average molecular weight of air can be used.
Viscosity of Gas Mixture
The viscosity of a gas mixture can be obtained from (Reid et al, 1977)
n=2 ~ (4'11>
2 yA 6AB
where
AR ~~ 1/2
[8(1 + MW/MWJ ]
A D
Like the molecular weight of air, the average viscosity of air can be used for the SVE application.
Dlffuslvltv In Gas Mixture
The molecular diffusion coefficient of a single component in a gas mixture can be obtained
from the Stefan-Maxwell equation (Hirschfelder et al., 1954). The diffusivity of component A in soil can be
obtained from the tortuosity for wet soil (Bruell and Hoag, 1986). The tortuosity, T, is defined as the ratio
of D/(D <)> ), where D is the molecular diffusion coefficient in air, and has the relationship with porosities as
f\ 9 f\
follows:
13
-------
(4-12)
where is the air-filled porosity and $ is the total porosity (Millington and Quirk, 1961).
3
Vapor Pressure and Aqueous Solubility
The vapor pressure of a pure component A at the given temperature can be obtained from
Antoine's equation (Reid et al, 1977).
where p is the vapor pressure, T is the absolute temperature, and a, p, 7 are constants for the VOC
f\
component A. The vapor pressure is very sensitive to the temperature.
The partial pressure of the component A in a gas mixture which is at equilibrium with a liquid
mixture can be obtained from Raoult's law.
(4-14)
where the p. is the vapor pressure of the pure component A at a given temperature and x is the mole
fraction in liquid phase. Henry's law expresses the relation between the partial pressure and the aqueous
phase concentration of a component which has a low solubility, like TCE and hydrocarbons in petroleum
products. The Henry's law constant can be obtained from Gossett (1987).
H = exp (co - £/T) (4-15)
where T is the absolute temperature, and co and 5 are constants.
14
-------
When immiscible liquid phases of mixed components exist, aqueous solubilities are
complicated functions of compositions in immiscible phases and should be estimated from the
thermodynamic correlations (i.e., UNIFAC, Reid et a/.,1977).
Interfaclal Mass Transfer
Two basic theories about interfacial mass transfer, the film theory and the penetration
theory, have been widely accepted. The film theory assumes instant equilibrium between the contacting
phases and concludes that the mass transfer coefficient is proportional to the diffusivity (Skelland, 1974).
The penetration theory assumes a finite contacting time between two phases and shows that the mass
transfer coefficient is proportional to the square root of the diffusivity (Skelland, 1974). Estimated values
of interfacial mass transfer coefficients from both theories showes little difference (Skelland, 1974).
One of the empirical correlations for the interfacial mass transfer between immiscible phases
is the first order kinetics expression. In this model, the rate of mass exchange between immiscible
phases is expressed by the mass transfer potential and the mass transfer coefficient. The difference of
the concentration at equilibrium and the actual concentration in the main body is defined as the mass
transfer potential. The mass transfer rate is expressed as
KG(CA-CA) (4-16)
where c is the concentration of A at equilibrium, c is the actual concentration in the main body of
A A
fluid, and K- is the mass transfer coefficient (Bird et a/., 1960). The mass transfer coefficient, KL,, is
Ca o
expected to be a function of Reynolds' number, Schmidt's number, and the air saturation, 6 , which is
cl
the ratio of the air filled porosity to the total porosity of soil.
KQ = KQ(Re, Sc, ea) (4-17)
Reynolds' number of soil air, Re, is given by
15
-------
D Vpadp
Re E- (4-18)
a
where V is the air flow velocity and d is a characteristic length (i.e. particle diameter, diameter of residual
blobs). Schmidt's number, Sc, is another dimenstonless term, which is
where D. is the diffusion coefficient of the component A in soil air.
16
-------
SECTION 5
EFFECT OF PARAMETERS ~
Analytical solutions in one-dimensional systems have been obtained for the soil airflow and
contaminant transport equations under simplifying assumptions and were applied for the analysis of soil
column operations. Effects of parameters on the VOC movement were studied through simulations and
comparisons with soil column experiments.
One-Dimensional Solutions
Air Flow
At steady state with a constant permeability and viscosity of soil air, the mass balance
equation of soil air, equation (4-4), becomes
V(PVp) = 0 (5-1)
d
Substitution of the density with an averaged value made the above equation a linearized Laplace
equation.
V2p = 0 (5-2)
When the ideal gas law is used in place of density, the equation becomes a nonlinear partial differential
equation.
V (pvp) = 0 (5-3)
In the one-dimensional coordinate system, these equations become
17
-------
2
0 (5-4)
for the linearized equation and
2. 2.
=0 (5-5)
ax2
for the nonlinear equation. Applicable boundary conditions are as follows;
p = p. at x=0 (5-6a)
= Poutatx=L (5-6D)
The pressure distribution obtained from the linearized equation is
(5'7)
and from the nonlinear equation is
From Darcy's law for the fluid flow in porous media, the airflow velocity obtained from
equation (5-7) is
V
Ka pi n - pout
x 11 L
(5-9)
and from the nonlinear equation, it is
18
-------
K (p. - p )
V =-fr ' " °Ut (5-10)
X *S» "I 2 ' 2 2 .X
Pin + (Pout Pin >L
The airflow velocity is a function of location when the nonlinear equation is used. It has a constant value
when the linearized equation is used.
Transport of Component
The mass balance equation of the component A in soil air without any transformations due
to biochemical/chemical reactions in one-dimensional coordinate system becomes
2
8c ac. a c
dX
with the initial condition
c =c. att=t (5-12a)
A Ao 0
and boundary conditions
c = 0 for x=0, clean air entrance (5-12b)
- = 0 for x = L, no concentration gradient (5-12c)
9x
The following conditions are assumed to obtain the one-dimensional solution. A constant
tortuosity and air saturation values are assumed, neglecting the fact that VOCs and water are
continuously evaporated as air flows through soil pores. The pressure drop through the soil column is
negligible and the airflow velocity is assumed to be constant through the column, as equation (5-9), and
remains unchanged through the experiment. The vapor pressures of VOCs remain constant through the
19
-------
experimental period until all the separate phase liquid evaporates. The temperature is constant,
neglecting the heat of evaporation. Then the transport equation of component A in gas phase can be
rewritten as follows.
ac a c 3c
D^--V A-+a-pcA (5-13)
at .2 ax K A
oX
KQ CA K
where V = V /4> , a = , and p = . The analytical solution of this equation can be obtained from
x a t)' T" B(X>t) (5'14)
A(x,t) = exp(-pt){1 -1/2 erfc( x' Vt
-1/2 exp(Vx/D) erfc(
-
2(Dt)°-5
2(Dt)'
B3(x,t)/B4(x)
20
-------
and
(U-V) (V+U)X-2UL 2L- x - Ut
2(U+V) 6XP( 2D 2(Dt)0'5
(U-V) .(V- U) x- 2UL
V2
- x+Ut
-)exp(-UL7D)
V
The mass balance of component A in the immobile phase is
(5-15)
with the initial condition
21
-------
The analytical solution for this equation can be obtained by the integration of the right hand
side from t=t to the time t at the location x.
o
where c is from equation (5-14).
Analysis of SVE Processes
Density Effects
The pressure distribution varies with location inside soil columns, but is not a function of the
air permeability at steady state. The pressure and corresponding velocity distributions obtained from the
linearized and nonlinear equations are in Figures 5-1 and 5-2. Figure 5-1 shows a small difference
between calculated pressures from the linearized and nonlinear equations. The maximum difference is
about 20% when the ratio of the inlet pressure, p. , and the outlet pressure, p , is 0.6. But the
corresponding air flow velocity in Figure 5-2 shows a large difference between calculated values from the
linearized and nonlinear equations. When the pressure ratio is 0.9, the maximum difference is about 10
%, and it is about 70 % at the location of the lowest pressure when the pressure ratio is 0.6. The error in
the airflow velocity calculated from two equations generates errors in the estimation of the convective
movement term in the transport equation. Therefore, one should be very careful when the linearized
equation is used.
Air Porosity
The air porosity has significant effects on air flow and VOC transport. The relative
permeability of soil air is a function of the air saturation as shown in equation (4-5). If the liquid saturation,
including the water and immiscible nonaqueous phases, is high, then the relative permeability becomes
so small that a large pressure drop is expected. The relative permeability with respect to water saturation
in clay soil is plotted in Figure 5-3. The effect of air porosity on VOC transport impacts the diffusivity
22
-------
through equation (4-12), so does the interfacia! mass transfer from the immobile phase to the air flow
through equation (4-17). The liquid saturation also is considered to determine the effective interfacial
area for the mass transfer. As the liquid saturation increases above the residual saturation, the mass
transfer coefficient is expected to increase due to the increased interfacial area between contacting
phases. After passing the maximum point, the interfacial area decreases, and so does the mass transfer
coefficient. The change of contacting area is considered to be a complicated function of the
hydrogeometry inside soil pores (Hunt etal., 1988), and is expected to vary continuously as the removal
process of VOCs and soil water continues. Additional efforts should be made in this area of research.
Systematic studies in the laboratory and field should be conducted to gain better knowledge of the
process.
Soil Column Experiments
Soil column experiments reported by AWARE, Inc. (1987) were used for additional analyses
of the SVE process with the mathematical model. Trichloroethylene (TCE) was used in column
experiments of four separate runs with two different types of soil, the New Jersey Cohansey sand and the
Tennessee Loess soil. New Jersey sand was used in experiments 1 and 2, and Tennessee soil was used
in experiments 3 and 4. Each experiment was spiked with a different amount of TCE. Experimental
conditions and properties of soil and chemicals are listed in Tables 5-1 and 5-2.
In experiment 1, TCE amounting to 8 times more than the solubility limit of the water content
inside the column was applied. The existence of free pure TCE could be assumed. The flow rate at the
outlet was 0.14 cm/min, which was the average value maintained during the experiment. At this flow rate,
the pressure drop was negligible because of the tow moisture content inside soil. The mass transfer
coefficients were assigned to fit the experimental observations by means of the least square optimization
method. Plots of calculated removal rates and measured values are in Figure 5-4. After the high initial
removal rate because of the saturated condition in soil air, the removal rate reached a steady state in a
short time. This steady state was maintained for about 400 days, then the removal rate dropped sharply
when the TCE concentration fell below its solubility in water. The effluent concentration and removal rate
continuously decreased until all TCE disappeared from the soil column. One check on the numerical
technique is the calculation of the conservation of mass. Normally, a small amount of mass is either
generated or destroyed due to numerical truncation in the mathematical algorithms. To check these
23
-------
calculations, mass balance was calculated at day 400. The total amount removed was calculated to be
98 % and the calculated remaining in the soil column was 4 % of initial mass which suggests a 2 % error
in mass balance. In the AWARE, Inc.'s report, a large mass balance error could be found, which is
suspected to be caused by poorly maintained analytical procedures.
The operating condition of experiment 2 was the same as that of experiment 1, except for
the different applied concentration of TCE. TCE saturated water solution was spiked on the soil column in
experiment 2. Therefore, the driving potential for the interfacial mass transfer continuously decreased as
the operation continued because the concentration in the water solution continuously decreased. The
removal rate never reached the steady state, but decreased continuously until all of the TCE in soil
disappeared (Figure 5-5). The maintained airflow rate in the column was 0.155 cm/min. With this air flow
rate, the pressure drop through the soil column was negligible.
Soil columns for experiments 3 and 4 had a different soil type which had less permeability
than that used in experiments 1 and 2. The initial water contents were greater than in previous runs. The
initial amount of TCE in column of experiment 3 was above the solubility limit and TCE existed in a pure
product form. The removal rate reached a steady state in a short time after air started to flow (Figure 5-6).
The total clean-up time was shorter than that of experiment 1 due to the small initial TCE amount. In 150
days, the removed mass of TCE reached 97% of the initial mass. The mass balance error was 3%.
The column in experiment 4 was almost saturated by water and the required pressure drop
was calculated as almost 0.5 atm. over a one foot column to maintain the air flow rate at 0.177 cm/min.
This large pressure drop is impractical in a field operation. The initial TCE was in a saturated water
solution, and the operation never reached the steady state (Figure 5-7).
All of the mass transfer coefficients were adjusted to fit the experimental data. The values of
the mass transfer coefficients for experiments 3 and 4 were different from those of experiments 1 and 2,
where different types of soil have been used. Even though some difference existed among the adjusted
values, the empirical relationships like the ones in the chemical engineering literature could not be
derived mainly due to the lack of experimental data.
24
-------
Temperature Effect on the Removal Efficiency
To investigate the temperature effect on the performance of the SVE process, soil column
experiment 1 reported by Aware, lnc.(1987) was simulated at different temperatures. Thermodynamic
and transport properties of TCE at several temperatures are enlisted in Table 5-3. The mass transfer
coefficients were calculated from the penetration theory of the interfacial mass transfer.
In comparing property changes at different temperatures in Table 5-3, the largest
differences are found in vapor pressures. At a 15 °C increase of temperature in ambient condition, the
vapor pressure becomes doubled. The major contributing factor on the performance of the SVE process
is the vapor pressure. Figure 5-8 shows that the removal rate can be doubled when the operating
temperature increases 15°C. It may be worthwhile to consider increased temperature operation.
25
-------
TABLE 5-1. Characteristics of Soil Columns
Properties
a 27
Intrinsic Permeability(cm x10 )
a 3
Soil Particle Density (g/cm )
a 3
Soil Bulk Density (g/cm )
blnitial Water Content (%)
Initial VOC Content (^g/g soil)
Initial Amount of Soil (g)
Diameter of Soil Column (cm)
°Pressure at Exit (Kpa)
c -17
Mass Trans. Co. K_(sec x10 )
Run1
4.34
2.68
1.46
4.1
8850
2600
6.35
101
8.9
Run2
4.34
2.68
1.45
17.4
15
2680
6.35
101
8.75
Run3
1.09
2.66
1.43
10.2
4010
2600
6.35
101
1.27
Run4
1.09
2.66
1.43
24.4
4.2
2470
6.35
63
1.75
a: estimated values
b: Aware, Inc. (1987)
c: adjusted values to fit the experimental result
26
-------
TABLE 5-2. Chemical Properties and Operating Conditions
aMolecular Weight of TCE
^CE Liquid Density(g/cm )
a 2
Diffusivity (cm /sec)
Q
Vapor Pressure (Kpa)
a 3
Aqueous Solubility(g/cm )
a 3
Henry's Law Constant (Kpa/(gmol/cm ))
aViscosity of Air at 20°C (cp)
Initial Pressure inside column (Kpa)
Entering Air Pressure (Kpa)
Mole Fraction of TCE in Entering Air
Temperature ( K)
131.4
1.46
-2
8.0x10
7.73
.3
1.1x10
7.1 4x1 03
0.01846
101.3
101.3
0.0
293
a: Chemical Engineers' Handbook (1973)
b: Aware Inc. (1987)
27
-------
TABLE 5-3. Properties of TCE at Various Temperatures
Temperature
°K
278
293
308
g
Diffusivity
(cm /sec)
-2
7.30x10
8.00 x10"2
8.73 x10"2
b
Viscosity
cp
1.75x10
1.85X10"2
1.92x10"2
c
Vapor Pres.
Kpa
3.57
7.75
1.54
d
Henry's Law
g
Kpa/(g/cm )
g
2.98x10
7.22 x103
1.60 x104
"G
(cm/sec)
-7
8.12x10
8.90 x10'7
9.70x10"7
arReidetal. (1977)
b: Reid etal. (1977)
c: equation (4-13)
d: equation (4-15)
28
-------
1.00
CD
Po«t - « pin
0.50
x/L
Figure 5- f. Pressure distribution inside soil column
Calculated from nonlinear equation
Calculated from linear equation
-------
co
o
Figure 5-2. Air velocity distribution inside soil column
Calculated from nonlinear equation
Calculated from linear equation
-------
Moisture (6)
Figure 5-3. Relative permeability of soil air with moisture content inside clay soil
31
-------
CO
ro
V . JLU-
0.08-
V-
»*»
«ti
o
* 0.06-
V
m J
4-*
10
(A
* 0.04-
Iv
>
o
El
V
tf
0.02-
0.00-
b^.Mt««a_.«« L ^.J
vvjmputcoi
D Experimental
»
8 ^
-
D
1
1
^ 1
DL
1 1 1 1 1 1 II 1
II II II I 1
0 50 100 150 200 250 300 350 400 45
Days
Figure 5-4. Removal rate from soil column, experiment 1
-------
w
CO
0.005
0.004-1-
^
o
tJ
S 0.003
ro
>
O
3
0)
0.0024-
o.ooi4-
0.000
D D
Computed
Experimental
0 5
Figure 5-5. Removal rate from soil column, experiment 2
40 45 50
-------
co
0.10
0.08
«fl
\
* 0.06+
4J
IT)
OS
IT)
>
O
8
V
Pi
0.04 +
0.02-1-
0.00
D
Computed
D Experimental
H 1 1 h
20 40 60
80
Days
100 120 140 160
Figure 5-6. Removal rate from soil column, experiment 3
-------
CO
en
0.05
0.00
Computed
Experimental
n
15
Days
20
n
25
D
30
Figure 5-7. Removal rate from soil column, experiment 4
-------
0.20
0.15--
*
I
0.10--
o
t>
0.05--
0.00
4-
-4-
T - 35 C
T - 20 C
T - 5 C
50 100 150 200 250 300 350 400 450 500
Days
Figure 5-8. Removal rates at different operating temperatures
36
-------
SECTION 6
VOC REMOVAL RATE MEASUREMENTS
One of the major controlling processes in SVE is the partitioning among gas, liquid and solid
soil phases. Usually, local equilibrium is assumed between flowing air and less mobile liquid /solid
phases (Pfannkuch, 1984). When convective movement dominates the transport of contaminant and its
rate is fast, the local equilibrium assumption is not accurate and a kinetics model seems to be more
proper in description of sorption processes (Cho and Jaffe, 1988). Several physical and chemical
properties of soil and contaminants will affect the interfacial mass transfer rate. Experimental
investigations of two parameters, the air flow rate and the liquid distribution including the nonaqueous
phase liquid and water, on the removal rate of VOCs from soil pores are presented.
Soil Column Experiments
Nine soil columns made of 2 inch, Schedule 80, PVC pipe were used. Each column had a
soil packed section 28 to 30 cm long and two additional empty sections with a cap on each end. Brass
fittings were attached on the top and bottom sections of the columns. Both 1/4 inch I.D. plastic and
copper tubings were used. Plastic tubings were used in the place where VOCs did not come in contact.
The Oil-Creek sand was packed in the columns. The sand was white-colored, and uniformly sized with a
very small amount of organic content on surface. These columns were set up in a constant temperature
room.
Pure toluene was used as the VOC in the vacuum extraction experiment in soil columns.
The properties of pure toluene are listed in Tables 5-2 and 5-3. Pure toluene was applied on the top of
the soil packed section of the column drop by drop through a hypodermic syringe to minimize the
disturbance of soil packing. The same method was used for water application for the control of water
content. After application of each liquid, a 24 hour equilibrium period was set to achieve uniform
distributions of each liquid.
37
-------
The airflow rate was monitored with a rotameter and adjusted as necessary with two needle
valves. The vacuum pressure and the pressure drop through the column were measured with
manometers. An in-house vacuum line was attached to the column for the vacuum source. The vacuum
pressure and corresponding air flow rate fluctuated about 10 % from the set point. Air was saturated with
moisture by passing through water baths before entering columns to minimize the water content change
in the soil. A schematic diagram of the column is in Figure 6-1.
Samples of effluent air from each column were taken directly by a gas-tight chromatograph
syringe and injected into an HP 5840A gas chromatograph equipped with an FID. A 6 ft, 1/4 inch O.D.
custom packed stainless steel column (Supelco, EPA method 602) was used for analysis of toluene
concentration in air. Nitrogen served as the carrier gas at a flow rate of 36 ml/min. The injector and FID
temperatures were set at 110°C and 150°C, respectively. The column oven temperature was fixed at
90°C. A specialty gas mixture (blend 3, Scott Specialty Gas) was used as a standard for calibration.
Results and Discussions
Two major parameters investigated in this experiment were the air flow rate and liquid phase
contents of the immiscible nonaqueous VOCs and water in soil. In Figures 6-2 to 6-5, toluene
concentrations in the effluent air from columns are plotted. The effluent concentration decreased as the
time passed even in the case where only pure toluene was applied (Figure 6-2). This decrease of effluent
concentration suggests that the interfacial mass transfer is a function of residual liquid contents inside
soil pores. Also these decreasing rates of effluent concentrations varied with respect to the air flow rate.
At a lower flow rate, the effluent concentration change was slower than at the higher air flow rate. These
trends were maintained through different water content and distributions inside the soil columns (Figures
6-2 through 6-5). To verify the effect of VOCs and water distribution effects on the removal, the effluent
concentration changes at different initial liquid conditions are plotted in Figures 6-6 through 6-8. Through
the entire experiments, the amount of toluene in each column was far above the water solubility limit and
therefore toluene existed as an immiscible nonaqueous liquid. The vapor pressure was expected to be
that of pure toluene. Even with those facts, the effluent rate was affected seriously by the water content
in the soil. In Figures 6-6 and 6-7, the increased water content shows a serious reduction of removal rate
at the same air flow. This phenomenon indicates decreased effects of water contents at the higher air
flow rate and this may be due to the entrapment of residual VOCs inside soil pores by water and thereby
38
-------
reducing the contacting area between the air and immiscible liquid phase. However, this could not be
verified (Figure 6-8).
Even though the air flow rate and the liquid distribution of VOCs and water were distinctive
parameters verified through these experiments, it was not possible to obtain quantitative correlations
among them. The main reason was that throughout these experiments, mass balance checks of VOCs
and water could not be performed. Another problem found during the experiments was redistribution of
VOCs and water inside soil columns. It was detected that liquids, including toluene and water moved
upward as air flowed up from the bottom of the column and accumulated in the upper part of the soil
packed section of column. Redistribution of liquids and experimental results suggest the necessity for a
new design of soil column and experimental procedures which include the control and measurement of
liquid content changes.
Removal Rate Model
A similarity of physics involved in the moisture removal from wet solid by dry air and the
VOC removal from soil pores by uncontaminated air suggests the same conceptual model for mass
removal. A two-period model was developed for the moisture removal from wet solid (Chemical
Engineers' Handbook, 1973). The model consists of the constant rate period and the falling period. The
constant rate period is at the first stage of the drying process in which the moisture removal rate remains
constant and is mainly controlled by external factors like air flow, temperature, and the moisture content
in the air (line BC in Figure 6-9).
The falling rate period represents the second stage of the removal process in which the
removal rate decreases as the moisture content reduces after a critical point (line CD in Figure 6-9). In
this stage, the moisture removal rate is controlled by internal factors such as the liquid diffusion, the
capillary flow of liquid, or the flow by shrinkage of solid. The capillary movement of liquid water due to the
change of the suction potential by evaporation of moisture inside pores is expected to control the drying
rate of sand soil or granular materials by air flowing through pores. The moisture removal rate is
approximated by first order kinetics.
39
-------
The removal rate of VOCs can be expressed with the same concepts of physical process.
During the first stage after air flow begins, the removal rate of VOCs from soil pores remains constant
until the VOC content is reduced to a critical value.
ac
= -S, when C.sC (critical amount) (6-1)
/ o\ 1 AC
At the second stage, after the critical point of the VOC content has been reached, the removal rate
decreases as the VOC content decreases. It is expressed by a first order kinetics model.
3C
3t Kl'CA-CA,e)whenWCe (6'2)
where K = -7-= - = - r , and C = obtainable lowest amount of the VOC content under the given operating
1 (CA,c * CA,e > A'e
conditions.
The solution of equation (6-2) for the falling rate period can be obtained.
/ Q _ Q \fC -C ^
t __ A, c A, e A, c A, e
~
(CA c- CA e>
The semilogar'ithmic plot of -r~ ' vs. t should give a straight line and the slope of the curve is related to
(CA 'CA,e)
the constant rate. The constant rate S., and the coefficient, K , are expected to be complex functions of
the liquid saturation, e and various operating conditions.
K1=K1(Re,Sc,ep (6-4)
40
-------
e/=i-ea (6-5)
The mass transfer coefficient in equation (4-17) is a function of K as
c,K) (6-6)
41
-------
IV)
VACUUM
SAMPLING PORT
Figure 6-1. Schematic diagram of soil column experiment
-------
1.5E-004
tto
S l.OE-004
o
o
o
<«
J_»
(0
(-1 diO
S i o
-------
I.DC, UU1
tt
6 l.OE-004
i
CJ (
0
£ 1
CO
(H
O)
g 5.0E-005
o
o
n npj_nnn
°Flow Rate 10 ml/min
0 00 Flow Rate 20 ml/min
o 0 Flow Rate 30 ml/min
o ° o
o
o Q) o
P o
f *
o
0
0
o o
0 . o
' ° ". « «, 9 S.
0
100 200
Time (hr)
300
Figure 6-3. Toluene concentration in effluent air from soil column
10 ml pure toluene following 10 ml water
-------
1 .cFC, VfU'l
r «
bfl
l.OE-004
d
o
j_j
j*
CO <
(-.
J_)
d \
0 Flow Rate 10 ml/min
Flow Rate 20 ml/min
0 Flow Rate 30 ml/min
a
o
o
o
0) TO
^ 5.0E-005 - *fc °
o ,F
' «
n npj_nnn
00 o o o
0 o o o
0
, ° ^ ' a , 8 8, ft * ,
0
100 200
Time (hr)
300
Figure 6-4. Toluene concentration In effluent air from soil column
10 ml water following 10 ml toluene
-------
Oi
I .OTj UU1
\
ofl
l.OE-004
C
o (
cO
"3
0)
£ 5.0E-005
<3 '
i
n nirj-nnn
Flow Rate 5 ml/min
o Flow Rate 10 ml/min
Flow Rate 20 ml/min
0 Flow Rate 30 ml/min
1 o
"o o
0 -
- : .
r o
0 ' o
« *
f \ o
' x^
?6- «.».. ° o
. f o? 8o* «; ?, » {.
0
100 200
Time (hr)
300
Figure 6-5. Toluene concentration In effluent air from soil column
15 ml water following 5 ml toluene
-------
I.5E-004
.OE-004
C!
o
i-4
J->
cd
*-.
*j
C!
O)
o
d
o
u
(D
5.0E-005
O.OE+000
o
0
o
20 ml Pure Toluene
15 ml Water, 5 ml Toluene
o
o
o
_L
o
o
o
100 200
Time (hr)
300
Figure 6-6. Comparison of effluent concentrations from different soil columns
Air flow rate 10 ml/min
-------
1.5E-004
Ofl
l.OE-004
d
o
C
o
O
5.0E-005
O.OE+000
o
o
o
o
o
o 20 ml Pure Toluene
15 ml Water, 5 ml Toluene
o
o
o
; °\
o
o
0
100 200
Time (hr)
300
Figure 6-7. Comparison of effluent concentrations from different soil columns
Air flow rate 20 ml/min
-------
(D
1.5E-004
bfl
E3 l.OE-004
d
o
i»
j-j
cd
5.0E-005
0
0
O.OE+000
0)
0
0
o
o 20 ml Pure Toluene
15 ml Water, 5 ml Toluene
0
100 200
Time (hr)
300
Figure 6-8. Comparison of effluent concentrations from different soil columns
Air flow rate 30 ml/min
-------
en
o
£
t3
o
6
B
' Constant
Rate
Critical Point, c
Falling Rate
Time
Figure 6-9. Conceptual model of VOC removal from soil pores
-------
SECTION 7
MODEL WITH SUPERPOSITION OF ANALYTICAL SOLUTIONS
The development of a three-dimensional analytical approximate model to simulate the air
flow during the SVE operation and a simple pneumatic pump test conducted on an aviation gasoline
contaminated site are presented in this section. This model adopted a superposition method of the
analytical solutions from potential theory in a three-dimensional space. This analytical model is only
applicable to homogeneous media. Pneumatic pump tests were conducted to obtain soil air flow
characterization around an air injection and vacuum extraction well in relation to a field demonstration
project of a bioremediation. The operating condition of the test was very favorable to the application of
SVE. The information obtained was very valuable and showed the importance of the pneumatic pump
test prior to the design of a full scale operation. A part of the test results were used for the validation of
the model.
Analytical Solutions
Various solution methods have been developed to solve the partial differential equations
including numerical and analytical techniques. In general, there are two methods in numerical
techniques. The first one is the total domain discretization method which includes the finite difference and
finite element techniques. In this method, the boundary conditions are satisfied and the solutions inside
the boundary are obtained by approximation at the grid points. The other methods are to obtain exact
solutions satisfying the differential equations inside the domain and to approximate boundary conditions
by summation or integration of exact solutions on the boundary. The latter includes the boundary element
method and superposition method of exact solutions. The numerical technique of the total domain
discretization method has a long history and is well established. A limitation to the large scale application
of these methods is the excessive memory and computational time requirements (Frind and Verge,
1978). A major advantage is the ease of handling heterogenous media. The boundary element method
and superposition method of exact solutions require less memory and computational time because they
need approximations only on the boundaries (Hess, 1973). Another advantage is that computed data
51
-------
points are not limited on the grid points, as with the finite difference and finite element methods. A
disadvantage is their limited applicability to heterogenous media. Complex heterogenous media requires
the discretization of the whole domain to be satisfied by the approximation method, and in this case, the
finite difference and finite element methods are superior to the boundary element method.
At the steady state, the equation describing the pressure distribution of soil air is
VK pvp = 0 (7-1)
3
where K is the soil-air conductivity tensor which is a function of location and direction due to soil
3
heterogeneity and anisotropy. Along with this pressure equation, proper sets of boundary conditions are
needed for the problem domain. The first boundary is the constant pressure condition at the soil surface
exposed to the atmosphere.
P=PC (7-2)
The second one is the zero flux boundary for the impermeable layer.
V K p = 0 (7-3)
3
The last one is the continuous flux condition along the interfaces between layers of different
permeabilities.
VKa1p = VKa2p
The superposition of exact solutions is only possible only for the linear equations. By
applying the Kirchoff transformation on equation (7-1) as follows,
(7.5)
52
-------
where pr is a reference pressure (i.e., atmospheric pressure), the equation becomes a Laplace type
equation.
v2
m = 0 (7-6)
where m can be defined as the discharge potential at location x. Boundary conditions become as follows:
Constant pressure boundary,
Ka 2 2
~(P-P) (7-7)
No flux boundary,
Vm= 0 (7-8)
Continuous flux boundary between layers of different permeabilities
(K . K .) _ _
f\ 1 rtr 2 2
m1 - mg = (p - pr) (7-9)
which means the potential jump at the interface when the location vector, x, crosses the boundary from
medium 1 to medium 2.
One of the exact solutions which satisfy the equation (7-6) is the point source
where Q is the source strength and r is the distance from the source point. A finite length well in the
subsurface can be modeled as a line source with finite length. The discharge potential at x due to the line
source becomes
53
-------
m = -
where L is the length of the well. When the source strength Q is of zeroth order with respect to well
length, the equation (7-11) becomes
m Q in U+V' !; (7-12)
4it u + v + 2 h
where u, v, h are lengths of vectors defined in Figure 7-1. Another useful solution for equation (7-6) is the
point dipole which is defined as a point potential of combined point source and point sink of same
strength at an infinitesimally short distance. The potential at x due to a point dipole is
(7-13)
where q is the dipole strength, c, the unit orientation vector of dipole, r, the vector from dipole point to
location x, and r, the length of vector r. Potentials due to the line dipole and dipole panel can be obtained
by an integration method (Haitjema, 1985).
Boundary conditions can be satisfied by superposition of line and panel dipoles on
boundaries. Unknown variables are the strength terms for sources and dipoles. These unknowns can be
obtained by solving simultaneous equations satisfying boundary conditions and potential values at
selected control points. Selection of control points can be optimized from the numerical analysis (Hess,
1973).
Pneumatic Pump Test
Site Characterization
A series of pneumatic pump tests were conducted on an aviation gasoline contaminated
site. The soil type at the site was categorized as a fine sand which had a grain size of 0.35 mm average
54
-------
and 90% in the range of 0.1 to 1 mm. The intrinsic permeability of this sand was reported as 5.2x 10"10 ft2
(Ostendorf, et al., 1989). The thickness of this sand layer was about 47 ft and a thick clay layer was
located underneath. The water table was 17 ± 2 ft from the soil surface and the ground-water flow
direction was northeast.
Test Design
An injection well and an extraction well were installed 20 ft apart. Both wells were made of 5
Inch schedule 40 PVC pipe and had a 1 ft screened section 15 ft from the soil surface. Each well was
connected to a separate blower pump. To control the pressure and airflow into/out of the well, a by-pass
line, which had a opening to the atmosphere with a ball valve, was attached to each connecting pipe.
Several different pressures and airflow rates could be applied to each well by controlling valve openings.
The pressure inside the well was measured by a pressure gauge installed on the top of each well. The
volumetric flow of air inside the well was measured with pilot tubes installed on 4 inch schedule 40 PVC
pipe that connected the well and the blower pump. The maximum capacity of blower pumps was 176
scfm at the positive pressure of 52.3 inch water inside the injection well. The pressure distribution in the
subsurface around the well was measured with Magnahelic pressure gauges. Gauges were connected
through quick release connectors on probe clusters located 5,10,12.5,15, and 30 ft away from the
injection well along the straight line between injection and extraction wells. Each cluster had three
probes. Each probe had a screened opening at the bottom of 1/4 inch O.D. copper tubing and a quick
release connector at the top. The length of probes was 3,10, and 15 ft. The schematic diagram of the
test system is shown in Figure 7-2.
Test Results
A series of tests of air injection, extraction, or combined operations were conducted. The
same procedure was applied to each set of tests. The blower pump connected to the well was powered
on and the pressure and airflow were controlled by the control valve. Due to the high permeability and
tow moisture content in the soil, the transient pressure change around the well reached the steady state
very rapidly. Only the pressure distribution at the steady state could be obtained.
55
-------
In Figure 7-3, pressure distributions at a depth of 15 ft are plotted against distances from the
injection well with various well pressures. As we expect, the pressure change is large within 15 ft from the
well; beyond this distance, the pressure gradient is small. Because the airflow is proportional to the
pressure gradient, the horizontal air flow velocity decreases sharply as the distance from the well
increases. The vertical pressure gradient and airflow in that direction also"decreases as the distance
from the well increase. In Figure 7-4, the pressure distribution of the soil in the case of 42 inch water
injection well pressure is shown.
In Figure 7-5, vacuum pressure distributions at a depth of 15 ft are shown for various
vacuum pressures applied. The same trend of pressure changes and air flow velocity changes can be
seen from the figure. Conventionally, field engineers set up a pilot scale test of a single extraction well
and measure the pressure distribution and estimate the zone of influence from the measured pressure
distribution. The most important factor in determining the zone of influence and the well interval should be
the pressure gradient and the air flow velocity. For our study case, the wells should be spaced less than
30 ft apart to induce sufficient airflow in the contaminated zone.
The pressure distribution at a depth of 15 ft for the combined operation of injection and
extraction wells with various combinations of positive and negative pressures inside the wells is shown in
Figure 7-6. The maximum injection pressure was 52 inch water with the volumetric airflow of 176 scfm.
The pressure at the extraction well was -48 inch water and the volumetric flow was 140 scfm. A small
horizontal pressure gradient at a depth of 15 ft exists, and horizontal airflow can be expected. But the
pressure gradient is very small compared to the total pressure difference between two wells (100 inch
water). The horizontal airflow and the removal rate of VOCs in that direction are expected to be low.
Figure 7-7 shows the pressure distribution at different depths at maximum capacity operation. Large
vertical pressure gradients in the vicinities of the wells (within 5 ft) are seen and large volumes of airflow
in vertical direction around the wells can be expected. At the midpoint, a very small vertical gradient and
air flow exist. Therefore, it is not efficient to induce horizontal air flow with distantly located wells and
large pressure differences.
Very important information could be obtained from pneumatic pump tests. Design
parameters in the SVE system should include the zone of influence in which the pumps can produce
sufficient air flow. The conventional method of measuring the zone of influence with soil vacuum pressure
56
-------
with one well can overestimate the size of effective area of SVE. Major factors in determining the zone of
influence should be the pressure gradient and corresponding airflow.
The pumping efficiency could be measured from the tests. A single high vacuum pumping
well does not have a larger zone of influence than the tow vacuum pumping well because a large air flow
exists only in the vicinity of the well. Therefore, operating multiple low vacuum wells may be more
efficient than operating a single high vacuum well.
Combined operation of extraction and injection wells could induce horizontal airflow, but still
a large vertical flow is expected in the vicinity of the wells. Therefore, the system should be carefully
engineered to obtain reasonable efficiency. A tightly covered soil surface may help inducing more
horizontal flow.
Additional field tests are suggested to measure the pressure distribution of the operation
with a tightly covered soil surface and also with various lengths and locations of well screens.
Simulation of Pneumatic Pump Test
The pneumatic pump test conducted could be simulated by the model using the
superposition of line sources representing wells. Applicable boundary conditions were the constant
pressure at the soil surface and the impermeable boundary on water table. With the atmospheric
pressure as the reference pressure, the first boundary condition became
= zsurface
and the second boundary condition became
-ir"""-W (7-15>
These two boundary conditions could be easily satisfied by the method of images. By locating mirror
images of sources with opposite strength, the first boundary condition could be satisfied at the soil
57
-------
surface. Mirror imaged wells with the same strength could satisfy the boundary condition at the water
table. Source strengths could be obtained by solving simultaneous equations yielding the desired well
pressure at selected control points on well surface. The zeroth order well strength expression was used
for this simulation.
Figure 7-8 shows the simulated pressure distribution with measured point values for
injection well operation. Figure 7-9 shows the combined operation of injection/extraction wells operation.
The model simulation seems reasonably good. Calculated airflows were within ±20 % of measured
-10 2
values. The calculated value of the intrinsic permeability from the pneumatic pump test was 7.0x10 ft
-10 2
which was comparable with the reported value, 5.2x10 ft (Ostendorf et al, 1989).
58
-------
u
X
Figure 7-1. Vector presentation of well screened section in three-dimensional space
59
-------
Blower
.Ball
en
o
injection j vaire Wel, Pressure
\ I * ?G3U8e
^BF~"~~
^m^~~~~ *
4 Inch Schedule 40 /
PVC Pipe '
5 Inch '^
Schedule 40
PVC Pipe
Pressure Pi
ft)
t*
: Cluster
1/4 Inch S*
OD Copper
Tubing
Connector
1
? StL
m
Blower
Extraction
i
0.3m
T
\7
Figure 7-2. Schematic diagram of pneumatic pump test
-------
50
a: Well Pressure -50 inch H O
2
h: Well Pressure -42 Inch HO
c: Well Pressure -36 inch HO
d: Well Pressure -24 inch HO
e: Well Pressure -16 inch HO
1t
10 12 14 16 18 20 22
Distance from Well (ft)
Figure
7-3. Measured pressure distribution at 15 ft depth lor air injection wed test
-------
to
a: Depth 15 ft
b: Depth 10ft
c: Depth 3 ft
Distance from Well (ft)
Figure 7-4. Measured pressure distribution at various depths
Air injection well pressure 50 inch water
-------
CD
a: Well Pressure 44 inch HO
b: WEII Pressure 36 inch HO
c: Well Pressure 24 inch HO
d: Well Pressure 16 inch
e: Well Pressure 4 inch HO
10 12 14 16 18 20 22 24 26 28 30
Distance (ft)
Figure 7-5. Measured pressure dlslribullon at 15 It depth tor vacuum extraction well lest
-------
-50
a: Well Pressures 50, -48 inch HO
b: Well Pressures 36, -36 inch HO
£
c: Well Pressures 24, -24 inch HO
10 12
Distance From Well (rt)
14
16
18
20
Figure 7-6. Measured pressure distribution at 15 ft depth for injection/extraction wells test
-------
10
84-
64-
1
VI
V)
24-
04-
-24-
-44-
0
1
a: Depth 15 ft
b: Depth 10ft
c: Depth 3 ft
4-
10 12
Distance from Well (ft)
14
16
Figure 7-7. Measured pressure distribution at various depths
Air injection well pressure 50 Inch water
Vacuum extraction well pressure -48 inch water
18 20
-------
0.00 0.75 1.50 2.25 3.00 3.75 4.50 5.25 6.00 6.75 7.50 8.25 9.00
0.00 0.75 1.50 2.25 3.00 3.75 4.50 5.25 6.00 6.75 7.50 8.25 9.00
INJECTION
Horizontal Distance from Injection Well
Figure 7-8. Isobarte contour plots of computed pressure distribution
Measured pressure (inch water)
0.00
-------
0.00 0.75 1.50 2.25 3.00 3.75 4.50 5.25 6.00 6J5 7.50 8.25 9.00
0.35 0.06 -0.2 .,
0.00
0.00 0.75 1.50 2.25 3.00 3.75 4.50 5.25 6.00 6.75 7.50 i8.25 9.00
INJECTION ' EXTRACTION
Horizontal Distance from Injection Well
0.00
Figure 7-9. Isobarte contour plots of computed pressure distribution
Measured pressure (inch water)
-------
SECTION 8
THREE-DIMENSIONAL FINITE DIFFERENCE MODEL
A computational model has been developed to simulate the soil vacuum extraction process
in field scale. This model consisted of a soil air flow equation, the contaminant transport equation and the
mass balance equation of residual hydrocarbon inside soil matrices. The general air flow equation was
transformed to a Laplace type equation to obtain the soil air pressure distribution and the airflow rate.
The calculated airflow velocity was used in the transport equation to describe the convective movement
of contaminant along with the bulk airflow. In addition to the convective movement, the transport
equation included the diffusive movement and the interfacial mass transfer between the air and the
residual hydrocarbon contacting the flowing air. The mass balance equation for the residual hydrocarbon
was also used. The numerical method to solve these differential equations with boundary conditions was
the finite difference method in a three-dimensional space domain and the unsteady state time process.
Finite Difference Solutions
Soil Air Flow
The soil air flow arrives at steady state quite rapidly after the SVE system is initiated by
pumping the air into/out of the subsurface. The contaminant movement usually is a non-steady state
problem until all the contaminant mass is removed from the system. Therefore it is a reasonable to
assume that the air flow is at steady state during the operating period. The mass balance equation of soil
air at steady state may be expressed from equation (4-4)
P K
Vp) = 0 (8-1)
68
-------
This equation is non-linear due to the dependence of the density of air on the pressure. The equation
becomes linear when the viscosity and density terms are replaced by constant values. In this case, the
equation becomes
V (Kgvp) = 0 " (8-2)
If the pressure dependence of density should be included, the equation becomes
= 0 (8-3)
By applying a Kirchoff type transformation like
m = K or m = K (p - p ) for the equation (8-2) (8-4a)
dp a avr V
and
K
K p or m r3- (p2 - p2) for the equation(8-3) (8-4b)
do a 2 r
where p is a reference pressure, the soil air flow equations become
V2 m = 0 (8-5)
which is a Laplace equation. The airflow velocity becomes
V = K Vp = Vm for the linear equation (8-6a)
3
V = Vm for the nonlinear equation (8-6b)
P
69
-------
The proper boundary conditions are
1. constant pressure boundary
which is
p = p (8-7a)
3
m = m (8-7b)
a
2. no air flow boundary or no pressure gradient
_iE_ =o (8-8a)
ax.
which is
am am ap =Q (8.8b)
ax. ap ax.
The equation (8-5) with boundary conditions (8-7) and (8-8) is a linear Laplace equation and can be
solved by a standard numerical technique.
The finite difference method with central spatial difference scheme was adopted to solve this
air flow equation. Replacing equation(8-4) with the difference operator results in the following difference
equation,
. m. ...-2m... +171...
2 i +1, j, k i ,j ,k i -1.| ,k
v m p
(A Xp
m. ... - 2 m. . . + m. .
i.j+1.k i ,] ,k i .]
(A y)2
70
-------
m. . . j - 2 m. . . + rn
- LJJM-O (8.g)
(A z)
Let M+1 , N+1 , and L+1 be the numbers of nodes in x, y, and z directions, respectively. By applying the
above finite difference operator on all the interior nodal points, excluding the boundary points, w, where
specific conditions are assigned, total number of linear algebraic equations becomes (M-1) x (N-1) x (L-1)-
w. The number of equations increases rapidly as the nodal points increases. For example, 1 00x1 00x1 00
system generates 100,000 simultaneous algebraic equations which need a tremendous amount of
computational time. In this project, the point Jacob iterative method was selected to solve the equations
because it uses considerably less CPU memory than the direct solution method, allowing the large
physical problems to be simulated. Additional refinement adopting various preconditioner and accelerator
schemes is needed to make the program more stable and faster.
Transport Equation
The contaminant transport in soil air is assumed due to diffusion, convection/, and the
interfacial mass transfer between the gas and the residual hydrocarbon inside the soil matrix.
Mathematical expressions that represents these are equations (4-6) and (4-7) for mass balances of
VOCs and equation (4-8) for interfacial mass transfer. Without considering the biological or chemical
transformation of hydrocarbon in the gas and the residual hydrocarbon phase, these equations become
(8-10)
ac
= -K(c-c) (8-11)
V at
Several finite difference schemes have been developed to solve these convective diffusion
equations. In this project period, two simple schemes have been tested, the explicit method and the
alternating direction implicit schemes. Only the explicit scheme was implemented in the program. With
the explicit scheme, the equations above become
71
-------
n+1 n
fa At -i - ~A-/ i- ra- --A, v-^gx^
(V *a° V (KG(C
- V + (V *° (K(C -
and
Cn+1 Cn
i A A. *
which allows computing the concentration c and C for all nodes at the future time step t+At explicitly.
The advantage of the explicit scheme over the implicit scheme is that each node is computed explicitly
and the computations need less memory and processor time. The disadvantage is that the selection of
time step increment is severely dictated by the stability conditions. Usually, the ADI scheme is
unconditionally stable and has second-order convergence error. When using the ADI scheme, one would
have to invert a set of three tridiagonal matrices for each time step.
Computer Implementation
Very often the modeling of fluid flow and contaminant transport in the subsurface is dictated
by availability of computer resources. Because of limited computational resources at Kerr Laboratory, the
point Jacob! method for the air flow equation and the explicit scheme for the VOC transport equation
were selected. Both methods require less memory and computational time; but because of the limited
time step allowed for stability, they may not be suitable for the long period of simulation.
Currently, the algorithms and controlling program discussed above are implemented in
FORTRAN 77 on an Apollo DN4500 using Unix system V as the primary operating system. The sampling
array used by this model is 101x101x51 which calculates to 520,251 physical nodes. Given this amount
of nodes, the program requires approximately 10 Megabytes (MB) of memory which is not suitable for
personal computers. Through implication, a larger model would require even greater memory to function.
72
-------
Provided with the main program is a postprocessor program which is for the graphical
display of data generated by the main program. It is specifically designed with an XWindows interface,
and will require an XWindows server be available to run the postprocessor.
73
-------
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74
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