United States
Environmental Protection
Agency
Office of
Research and
Development
Off ice of Sol id Waste
and Emergency
Response
EPA/540/S-92/004
April 1992
&EPA Ground Water Issue
Evaluation of Soil Venting Application
Dominic C. DiGiulio*
Introduction
The Regional Superfund Ground-Water Forum is a group of
scientists, representing EPA's Regional Superfund Offices,
organized to exchange up-to-date information related to
ground-water remediation at Superfund sites. One of the
major issues of concern to the Forum is the transport and fate
of contaminants is soil and ground water as related to
subsurface remediation.
The ability of soil venting to inexpensively remove large
amounts of volatile organic compounds (VOCs) from
contaminated soils is well established. However, the time
required using venting to remediate soils to low contaminant
levels often required by state and federal regulators has not
been adequately investigated. Most field studies verify the
ability of a venting system to circulate air in the subsurface
and remove, at least initially, a large mass of VOCs. They do
not generally provide insight into mass transport limitations
which eventually limit performance, nor do field studies
generally evaluate methods such as enhanced biodegradation
which may optimize overall contaminant removal. Discussion
is presented to aid in evaluating the feasibility of venting
application. Methods to optimize venting application are also
discussed.
For further information contact Dominic DiGiulio (405)332-
8800 or FTS 700-743-2271 at RSKERL-Ada.
Determining Contaminant Volatility
The first step in evaluating the feasibility of venting application
at a hazardous waste site is to assess contaminant volatility. If
concentrations of VOCs in soil are relatively low and the
magnitude of liquid hydrocarbons present in the soil is
negligible, VOCs can be assumed to exist in a three-phase
system (i.e., air, water, and soil), as illustrated in Figure 1. If
soils are sufficiently moist, relative volatility in a three-phase
system can be estimated using equation (1) which
incorporates the effects of air-water partitioning (Henry's
constant) and sorption (soil-water partition coefficient).
Cg
Ct
(pgKocfoc / h) + i
(1)
where:
Cg = Vapor concentration of VOCs in gas phase(mg/
cm3 air)
Ct = Total volatile organic concentration (mg/cm3 soil)
pg = Bulk density (g/cm3)
Koc = Organic carbon-water partition coefficient
(cm3/g)
foc = Fraction of organic carbon content (g/g)
Kh = Henry's Constant (mg/cm3air/mg/cm3water)
6 = Volumetric moisture content (cm3/cm3)
(|> = Volumetric air content (cm3/cm3)
Caution must be exercised when using this approach since
this relationship is based on the assumption that solid phase
sorption is dominated by natural organic carbon content. This
assumption is frequently invalid in soils below the root zone
where soil organic carbon is less than 0.1%.
Environmental Engineer, Robert S. Kerr Environmental
Research Laboratory
Superfund Technology Support Center for
Ground Water
Robert S. Kerr Environmental
Research Laboratory
Ada, Oklahoma
Technology Innovation Office
Office of Solid Waste and Emergency
Reponse, U.S. EPA, Washington, DC
Walter W. Kovalick, Jr., Ph.D.,
Director
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Air < > Water
KH
Soil
= Soil-water partition coefficient
= Henry's Constant
Water J<
Figure 1. Three phase system.
Figure 2. Four phase system.
Equation (1) can be used to evaluate individual VOC
contaminant reduction trends and attainment of soil-based
remediation standards. Vapors should be collected from
dedicated vapor probes under static (venting system not
operating) conditions. This estimate is valid only for soils in the
immediate vicinity of the probe intake. This approach
minimizes sample dilution and collection of vapor samples
under nonequilibrium conditions. It, however, necessitates
periodic cessation of venting. When the vapor concentration
for a VOC approaches a corresponding total soil
concentration, actual soil samples can be collected to confirm
remediation. This approach has several benefits over
conventional soil samples collection and analysis. At lower
VOC concentration levels, collection of static vapor samples is
likely more sensitive than soil collection and analysis due to
VOC loss in the latter procedure. Siegrist and Jenssen (1990)
demonstrated substantial VOC loss during normal soil sample
collection, storage, and analysis. Also, comparing contaminant
reduction trends strictly with soil samples is difficult due to
spatial variability in soils. No two soil samples can be collected
at the exact same location. In addition, soil gas analyses can
be accomplished more quickly and inexpensively than soil
sample collection, thus enabling more frequent evaluation of
trends. A potential disadvantage of using this approach is
inability to distinguish VOC vapors emanating from soils as
opposed to ground water. Hypothetically, soils could be
remediated to desired levels with probes still indicating
contamination above remediation standards. This concern
could be alleviated to some degree by determining the
presence of a diffusion vapor gradient from the water table
using vertically placed vapor probes.
If soils are visibly contaminated or the presence of
nonaqueous phase liquids (NAPLs) is suspected in soils
based on high contaminant, total organic carbon, or total
petroleum hydrocarbon analysis, contaminants are likely
present in a four phase system as illustrated in Figure 2.
Under these circumstances, most of the VOC mass will be
associated with the immiscible fluid and assuming that the
fluid acts as an ideal solution, volatilization will be governed by
Raoult's Law.
P =X P°
a a a
(2)
where:
Pg = vapor pressure of component over
solution (mm Hg)
Xg = mole fraction of component in
solution
P° = saturated vapor pressure of pure
component (mm Hg)
In a four-phase system, contaminant volatility will be governed
by the VOC's vapor pressure and mole fraction within the
immiscible fluid. The vapor pressure of all compounds
increases substantially with an increase in temperature while
solubility in a solvent phase is much less affected by
temperature. This suggests that soil temperature should be
taken into account when evaluating VOC recovery for
contaminants located near the soil surface (seasonal
variations in soil temperature quickly dampen with depth). For
instance, if conducting a field test to evaluate potential
remediation of shallow soil contamination in the winter, one
should realize that VOC recovery could be substantially
higher during summer months, and low recovery should not
necessarily be viewed as venting system failure.
As venting proceeds, lower molecular weight organic
compounds will preferentially volatilize and degrade. This
process is commonly described as weathering and has been
examined by Johnson (1989) in laboratory experiments.
Samples of gasoline were sparged with air and the
concentration and composition of vapors were monitored.
The efficiency of vapor extraction decreased to less than 1%
of its initial value even though approximately 40% of the
gasoline remained. Theoretical and experimental work on
product weathering indicate the need to monitor temporal
variation in specific VOCs of concern in extraction and
observation wells.
Evaluating Air Flow
Air permeability (kg) in soil is a function of a soil's intrinsic
permeability (k) and liquid content. At hazardous waste sites,
liquid present in soil pores is often a combination of soil water
and immiscible fluids. Air permeability (k ) can be estimated
by multiplying a soil's intrinsic permeability (k) by the relative
permeability (kr).
ka=kikr
(3)
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The dimensionless ratio kr varies from one to zero and
describes the variation in air permeability as a function of air
saturation. Equations developed by Brooks and Corey (1964)
and Van Genuchten (1980) are useful in estimating air
permeability as a function of air saturation or liquid content.
The Brooks-Corey equation to estimate relative permeability of
a non-wetting fluid (i.e. air) is given by:
(4)
where:
= effective saturation
= a pore distribution parameter
The effective saturation is given by:
0-40
(5)
Where:
9
e
e
= volumetric moisture content
= total porosity
= residual saturation
The pore size distribution parameter and residual water con-
tent can be estimated using soil-water characteristic curves
which relate matric potential to volumetric water content.
When initially developing an estimate of relative permeability
for a given soil texture and liquid content, values for e, 9r, Se,
and X can be obtained from the literature. Rawls et al.
(1982) summarized geometric and arithmetic means for
Brook-Corey parameters for various USDA soil textural
classes. Figure 3 illustrates relative permeability as a function
of volumetric moisture content for clayey soils assuming e =
0.475, 9r= 0.090, and A, = 0.131.
The most effective method of measuring air permeability is by
conducting a field pneumatic pump test. Using permeameters
or other laboratory measurements provide information on a
0
0 0.1 0.2 0.3 0.4 0.5
Moisturd9)(
Figure 3. Relative permeability vs moisture content of clay.
relatively small scale. Information gained from pneumatic
pump tests is vital in determining site-specific design
considerations (e.g., spacing of extraction wells). Selecting the
placement and screened intervals of extraction and
observation wells and applied vacuum rates during a pump
test is often based on preliminary mathematical modeling.
Evaluating Mass Transfer Limitations and
Remediation Time
The effects of mass transport limitations are usually
manifested by a substantial drop in soil vapor contaminant
I;
§
1
u
-Re-Start Yield Spiki
Time
Figure 4. Concentration vs. time.
concentrations as illustrated in Figure 4 or by an asymptotic
increase in total mass removal with operation time. Typically,
when venting is terminated, an increase in soil gas
concentration is observed overtime. Slow mass transfer with
respect to advective air flow is most likely caused by diffusive
release from porous aggregate structures or lenses of lesser
permeability as illustrated in Figure 5. The time required for
the remediation of heterogeneous and fractured soils depends
on the proportion of contaminated material exposed to direct
bulk airflow. It would be expected that long-term performance
of venting will be limited to a large degree by gaseous and
liquid diffusion from soil regions not exposed to direct airflow.
Regardless of possible causes, the significance of mass
transport limitations should be evaluated during venting field
tests. This can be achieved by pneumatically isolating a small
area of a site and aggressively applying vacuum extraction
until mass transport limitations are realized. Isolation can be
achieved by surrounding extraction wells with passive inlet or
air injection wells as shown in Figure 6. Quantifying the
effects of mass transport limitations on remediation time might
then be attempted by utilizing models incorporating mass
transfer rate coefficients.
The discrepancy frequently observed between mass removal
predicted from equilibrium conditions using Henry's Law
constants and that observed from laboratory column and field
studies is sometimes reconciled by the use of "effective or
lumped" soil-air partition coefficients. These parameters are
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Air Advection
A A A A A A\ S
Molecular Drrfusioi) ~\ v_z z
*T T T V T T/ >4.
Low Permeability
Strata
A A A A A A A
T T T T T T T
Air Advection
Palmer et at, 1988
Molecular Lmfi
usion
Figure 5. Effect of Low Permeability Lenses.
determined from laboratory column tests and are then used for
model input to determine required remediation times. While
this method does indirectly account for mass transport
limitations, problems may arise when one attempts to
quantitatively describe several processes with lumped
parameters. The primary concern is whether the lumped
parameter is suitable for use only under the laboratory
conditions from which it was determined, or whether it can be
transferred for modeling use in the field. Perhaps the most
direct method of accounting for mass transport limitations
would be to incorporate diffusive transfer directly into
convective-dispersive vapor transport models.
Enhanced Aerobic Biodegradation
With the exception of a few field research projects, soil
vacuum extraction has been applied primarily for removal of
volatile organic compounds from the vadose zone. However,
circulation of air in soils can be expected to enhance the
aerobic biodegradation of both volatile and semivolatile
organic compounds. One of the most promising uses of this
technology is in manipulating subsurface oxygen levels to
maximize in-situ biodegradation. Bioventing can reduce vapor
treatment costs and can result in the remediation of
0 24ft.
7.32 meters
o Venting Probe Cluster
• Passive Inlet Well
• Vent Well
A Borehole Sampling Locatk
semivolatile organic compounds which cannot be removed by
physical stripping alone.
Venting circulates air in soils at depths much greater than are
possible by tilling, and oxygen transport via the gas phase is
much more effective than injecting or flooding soils with
oxygen saturated liquid solutions.
Hinchee (1989) described the use of soil vacuum extraction at
Hill AFB, Utah for oxygenation of the subsurface and the
enhancement of biodegradation of petroleum hydrocarbons in
soils contaminated with JP-4 jet fuel. Figures 7 and 8 illustrate
subsurface oxygen profiles at the Hill site prior to and during
venting. It is evident that soil oxygen levels dramatically
increased following one week of venting. Soil vapor samples
collected from observation wells during periodic vent system
shutdown revealed rapid decreases in oxygen concentration
and corresponding CO2 production suggesting that aerobic
biodegradation was occurring at the site. Laboratory
treatability studies using soils from the site demonstrated
increased carbon-dioxide evolution with increasing moisture
content when enriched with nutrients. It is worthwhile to note
that soils at Hill AFB were relatively dry at commencement of
field vacuum extraction indicating, that the addition of moisture
could perhaps stimulate aerobic biodegradation even further
under field operating conditions.
When conducting site characterization and field studies, it is
recommended that CO2 and O2 levels be monitored in soil
vapor probes and extraction well offgas to allow the
assessment of basal soil respiration and the effects of site
management on subsurface biological activity. These
measurements are simple and inexpensive to conduct and
can yield a wealth of information regarding:
1. The mass of VOCs and semivolatiles which have
undergone biodegradation versus volatilization. This
information is crucial if subsurface conditions (e.g.,
moisture content) are to be manipulated to enhance
biodegradation to reduce VOC offgas treatment costs
and maximize semivolatile removal.
2. Factors limiting biodegradation. If O and CO monitoring
Distance (feet)
0 10 20 30 40 50 60 70 80 9C
DiGiulio, 19:
Figure 6. Proposed Pilot Test Design.
Figure 7. Oxygen concentration in vadose zone before venting.
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Distance (feet)
0 10 20 30 40 50 60 70 80 90
Oxygen Concentration in Vadose Zone After Venting
Figure 8. Oxygen concentration in vadose zone after venting.
reveals low O2 consumption and CO2 generation while
readily biodegradable compounds persist in soils, further
characterization studies could be conducted to determine
if biodegradation is being limited by insufficient moisture
content, toxicity (e.g. metals), or nutrients.
3. Subsurface air flow characteristics. Observation wells
which indicate persistent, low O2 levels may indicate an
insufficient supply of oxygenated air at that location
suggesting the need for air injection, higher extraction
well vacuum, additional extraction wells, or additional
soils characterization which may indicate high moisture
content or the presence of immiscible fluids impeding the
flow of air.
Location and Number of Vapor Extraction Wells
One of the primary objectives in conducting a venting field
test is to evaluate the initial placement of extraction wells to
optimize VOC removal from soil. Placement of extraction
wells and selected applied vacuum is largely an iterative
process requiring continual re-evaluation as additional data
are collected during remediation. Vacuum extraction wells
produce complex three-dimensional reduced pressure zones
in affected soils. The size and configuration of this affected
volume depends on the applied vacuum, venting geometry
(e.g., depth to water table), soil heterogeneity, and intrinsic
(e.g., permeability) and dynamic (e.g., moisture content)
properties of the soil. The lateral extent of this reduced
pressure zone (beyond which static vacuum is no longer
detected) is often termed the radius or zone of influence
(ROI). Highly permeable sandy soils typically exhibit large
zones of influence and high air flow rates whereas less
permeable soils, such as silts and clays, exhibit smaller zones
of influence and low air flows.
Measured or anticipated radii of influence are often used to
space extraction wells. For instance, if a ROI is measured at
10 feet, extraction wells are placed 20 feet apart. However,
this strategy is questionable since vacuum propagation and
air velocity decrease substantially with distance from an
extraction well. Thus, only a limited volume of soil near an
extraction well will be effectively ventilated regardless of the
ROI. Johnson (J.J., 1988) describes how the addition of 13
extraction wells within the ROI of other extraction wells
increased blower VOC concentration by 4000 ppmv and mass
removal by 40 kg/day. They concluded that the radius of
influence was not an effective parameter for locating
extraction wells and that operation costs could be reduced by
increasing the number of extraction wells as opposed to
pumping at higher rates with fewer wells.
Determining the propagation of induced vacuum requires
conducting pneumatic pump tests in which variation in static
vacuum is measured in vapor observation wells at depth and
distance from extraction wells. Locating extraction and
observation wells along transects as illustrated in Figure 4
minimizes the number of observation wells necessary to
evaluate vacuum propagation at linear distances from
extraction wells. Pressure differential can be observed at
greater distances than would otherwise be possible in other
configurations.
Propagation of vacuum in soils as a function of applied
vacuum can be determined by conducting pneumatic pump
tests with incrementally increasing flow or applied vacuum.
Vacuum is increased after steady state conditions (relatively
constant static vacuum measurements in observation wells)
exist in soils from the previously applied vacuum. A step pump
test will indicate a significant increase in static vacuum or air
velocity with increasing applied vacuum near an extraction
well. However, at distance from an extraction well, a
significant increase in static vacuum will not be observed with
an increase in applied vacuum. Pneumatic pump tests allow
determination of radial distances from extraction wells in which
air velocity is sufficient to ensure remediation.
After the initial placement of extraction wells has been
established based on the physics of air flow, an initial applied
vacuum must be selected to ensure optimal VOC removal. In
regard to mass transfer considerations, the vent rate should
be increased if a significant corresponding mass flux is
observed. Even though an increased venting rate may not
substantially increase the propagation of vacuum with
distance, air velocity will increase near the extraction well. If
most contaminants are in more permeable deposits, an
increase in applied vacuum will increase mass removal
eventually to a point of diminishing returns or until the system
is limited by diffusion. Note that this strategy is for
optimization of volatilization not biodegradation. Optimizing in-
situ biodegradation often necessitates reducing air velocity in
soil. As a result, vapor treatment costs are minimized but
overall mass flux decreases. Thus, in-situ biodegradation of
VOCs minimizes overall costs but may extend venting
operation time.
During a field test, it is desirable to operate until mass
transport limitations are realized in order to evaluate the long
term performance of the technology. This can be achieved by
isolating small selected areas of a site by the use of passive
air inlet wells. When attempting to evaluate diffusion limited
mass removal in isolated areas, applied vacuum should
remain high and the distance between passive inlet and
extraction wells should be minimized. Too often, venting field
tests are conducted for relatively short periods of time (e.g.,
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2-21 days) which only results in assessment of air
permeability and initial mass removal. Longer field studies
(e.g., 6 months -12 months) enable better insight into mass
transfer limitations which eventually govern venting
effectiveness.
Screened Interval
The screened interval of extraction wells will play a significant
role in directing air flow through contaminated soils. Minimum
depths are recommended by some practitioners for venting
operation to avoid short-circuiting of airflow. However, the
application of venting need not be limited by depth to water
table since horizontal vents can be used in lieu of vertically
screened extraction wells to remediate soils with shallow
contamination. Often, it is desirable to dewater contaminated
shallow aquifer sediments for venting application. For
remediation of more permeable soils with deep contamination,
an extraction well should be screened at the maximum depth
of contamination or to the seasonal low water table,
whichever is shallowest, to direct air flow and reduce short-
circuiting. For less permeable soils, or for more continuous
vertical contamination, a higher and longer screened interval
may be useful. In stratified systems, such as in the presence
of clay layers between more permeable deposits, more than
one well will be required, each venting a distinct strata.
Screening an extraction well over two strata of significantly
different permeability will result in most air flow being directed
only in the strata of greater permeability. It is important to
screen extraction wells over the interval of highest soil
contamination to avoid extracting higher volumes of air at
lower vapor concentration.
During venting, the reduced pressure in the soil will cause an
upwelling of the water table. The change in water table
elevation can be determined from the predicted radial
pressure distribution. Johnson et al. (1988) indicated that
upwelling can be significant under typical venting conditions.
Water table rise will cause contaminated soil lying above the
water table to become saturated, resulting in decreased mass
removal rates. Ground water upwelling due to venting system
operation can be minimized with concurrent water table
de watering.
Placement of Observation Wells
Observation wells are essential in determining whether
contaminated soils are being effectively ventilated and in the
evaluation of interactions among extraction wells. The more
homogeneous and isotropicthe unsaturated medium, the
fewer the number of vapor monitoring probes required. To
adequately describe vacuum propagation during a field test,
usually at least three observation well clusters are needed
within the ROI of an extraction well. At least one of these
clusters should be placed near an extraction well because of
the logarithmic decrease in vacuum with distance. The depth
and number of vapor probes within a cluster depends on the
screened intervals of extraction wells and soil stratigraphy.
However, vertical placement of vapor probes might logically
be near the soil-water table interface, soil horizon interfaces,
and near the soil surface. As previous mentioned, the use of
air flow modeling can assist in optimizing the depth and
placement of vapor observation wells and in the interpretation
of data collected from these monitoring points.
When constructing observation wells it is desirable to minimize
vapor storage volume in the screened interval and sample
transfer line. This will minimize purging volumes and ensure a
representative vapor sample in the vicinity of each observation
well. Analysis of soil gas in an on-site field laboratory is
preferred to provide real time data for implementation of
engineering controls and process modifications. It is
recommended that steel canisters, sorbent tubes, or direct GC
injection be used in lieu of Tedlar bags when possible
because of potential VOC loss through bag leakage or
diffusion within the teflon material itself. This problem may
lead to erroneous analytical results and the potential of a false
negative indication of soil remediation at low soil gas
concentrations.
Summary/Conclusions
While the application of soil vacuum extraction is conceptually
simple, its success depends on understanding complex
subsurface physical, chemical, and biological processes
which provide insight into factors limiting venting performance.
Optimizing venting performance is critical when attempting to
meet stipulated soil-based clean-up levels required by
regulators. The first step in evaluating a venting application is
to assess contaminant volatility. Volatility is a function of a
contaminant's soil-water partition coefficient and Henry's
constant if present in a three-phase system, and a
contaminant's vapor pressure and mole fraction in an
immiscible fluid, if present in a four phase system. Volatility is
greatly decreased when soils are extremely dry. As vacuum
extraction proceeds, lower molecular weight organic
compounds preferentially volatilize and biodegrade.
Decreasing mole fractions of lighter compounds and
increasing mole fractions of heavier compounds affect
observed offgas concentrations. Understanding contaminant
volatility is necessary when attempting to utilize offgas vapor
concentrations as an indication of venting progress.
The significance of mass transport limitations should be
evaluated during venting field tests. Long term performance of
venting will most likely be limited by diffusion from soil regions
of lesser permeability which are not exposed to direct airflow.
Mass transport limitations can be assessed by isolating a
small area of a site and aggressively applying vacuum
extraction. Simplistic methods to evaluate remediation time
should be avoided. One of the most promising uses of vacuum
extraction is in manipulating subsurface oxygen levels to
enhance biodegradation. When conducting field studies, it is
recommended that CO2and O2 levels be monitored in vapor
probes to evaluate the feasibility of VOC and semivolatile
contaminant biodegradation.
Air permeability in soil is a function of a soil's intrinsic
permeability and liquid content. Relative permeability of air
can be estimated using relationships developed by Brooks
and Corey (1964) and Van Genuchten (1980). The most
effective method of measuring air permeability is by
conducting pneumatic pump tests. Information gained from
pneumatic pump tests can be used to determine site-specific
design considerations such as the spacing of extraction wells.
Measured or anticipated zones of influence are not particularly
useful in spacing extraction wells. Extraction wells should be
located to maximize air velocity in contaminated soils.
-------
Pneumatic pump tests with increasing applied vacuum may be
useful in determining radial distances from extraction wells in
which air velocity is sufficient to ensure remediation.
Screened intervals should be located at or below the depth of
contamination. In stratified soils, more than one well is
necessary to ventilate each strata. At least three observation
well clusters are usually necessary to observe vacuum
propagation within the radius of influence of an extraction well.
Logical vertical placement of vapor probes might be near the
soil-water table interface, soil horizon interfaces, and near the
soil surface.
References
(1) Brooks, R.H., and Corey, AT., 1964. Hydraulic
Properties of Porous Media, Colorado State University,
Fort Collins, CO., Hydrol. Pap. No. 3, 27 pp.
(2) Hinchee, R.E., 1989. Enhanced Biodegradation through
Soil Venting, Proceedings of the Workshop on Soil
Vacuum Extraction, Robert S. Kerr Environmental
Research Laboratory, Ada, Oklahoma, April 27-28, 1989.
(3) Johnson, J.J., 1988. In Situ Air Stripping: Analysis of
Data from a Project Near Benson, Arizona, Master of
Science Thesis, Colorado School of Mines, Colorado.
(3) Johnson, P.C., Kemblowski, M.W., and Colthart, J.D.,
1988. Practical Screening Models for Soil Venting
Applications, NWWA/API Conference on Petroleum
Hydrocarbons and Organic Chemicals in Groundwater,
Houston, TX, 1988.
(4) Johnson, R.L., 1989. Soil Vacuum Extraction: Laboratory
and Physical Model Studies, Proceedings of the
Workshop on Soil Vacuum Extraction, Robert S. Kerr
Environmental Research Laboratory, Ada, Oklahoma,
April 27-28, 1989.
(5) Rawls, W.J., Brakensiek, D.L, and Saxton, K.E., 1982.
Estimation of Soil Water Properties, Transactions of the
ASAE, 1982, pp. 1316-1328.
(6) Siegrist, R. L, and Jenssen, P. C., 1990. Evaluation of
Sampling Method Effects on Volatile Organic Compound
Measurements in Contaminated Soils, Environ. Sci.
Technol., Vol. 24, No. 9, p. 1387-1392.
(7) Van Genuchten, M.T., 1980. A Closed-Form Equation for
Predicting the Hydraulic Conductivity of Unsaturated
Soils, Soil Sci. Soc. Am. J., 44:982-898.
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