EPA/600/A-93/253
Measurements of Soil Permeability and Pressure Fields
in EPA's Soil-gas Chamber
by: Ronald B. Mosley
U.S. Environmental Protection Agency
Air and Energy Engineering Research Laboratory
Research Triangle Park, NC 27711
Richard Snoddy and
Samuel A. Brubaker, Jr.
Acurex Environmental Corp.
P.O. Box 13109
Research Triangle Park, NC 27709
ABSTRACT
EPA's soil-gas chamber was designed to study the production
and transport of radon and other potential indoor air pollutants
originating in soils. This chamber is instrumented to measure
distributions of radon and pressure fields. It is also
instrumented to measure moisture distributions and their resulting
influence on soil permeability. An analytic solution for advective
flow in the soil-gas chamber is presented which includes the
effects of moisture-dependent spatial variations of the
permeability. Measurements of the pressure field are compared with
the model calculations. Relatively good agreement between the
measurements and calculations is obtained except in the region near
the water level where the boundary conditions are not rigorously
satisfied.
This paper has been reviewed in accordance with the U.S.
Environmental Protection Agency's peer and administrative review
policies and approved for presentation and publication.
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Introduction
In an effort to better understand the mechanisms of transport
and entry of radon and other soil contaminants into the indoor air
environment, EPA has constructed and instrumented a soil chamber to
simulate and study these mechanisms. This paper will report some
early results from these studies. This facility has been discussed
elsewhere (1) and will not be described in detail here. Because it
is believed that advective transport is usually the dominant
mechanism for pollutant entry into indoor air (2-9), this paper
will concentrate on the advective aspects of radon transport. It
will first present a model using analytic solutions to describe the
advective flow including the effects of moisture dependent
permeability. Preliminary measurements will also be compared to
the model predictions.
Some developments presented in three previous papers (10-12)
will be combined to derive a solution to the advective transport
equation that is applicable to the soil research chamber at EPA's
Air and Energy Engineering Research Laboratory (AEERL). Reference
(10) presented an analytic solution for advective flow of soil gas
into an infinitely long porous cylinder buried parallel to the
surface of the soil. The physical properties of the soil,
including the permeability, were assumed to be uniform and
isotropic. Reference (11) modified the model from reference (10)
to account for the effects of moisture variation with depth on the
permeability of the soil. Reference (12) modified the solution for
the semi-infinite block of soil with uniform permeability to
satisfy the boundary conditions at the vertical walls of the
research chamber at AEERL. This paper combines these three methods
of solution to yield an analytic solution for pressures and flows
that is applicable to the research chamber even when permeability
varies with the moisture in the vertical direction.
Development of the Equations
The steady state flow of radon in soil gas, which is treated
as incompressible in the applicable pressure range, is described by
three equations:
V- —VP = 0 (1)
V
v = - — VP (2)
2
-------
V-D.VC-—-VC-XC+G = 0. (3)
e e
Equation (1) is the continuity equation, equation (2) is Darcy's
law, and equation (3) represents the diffusion, advection, decay,
and generation of radon in the soil gas. A solution to equation
(1) can be obtained (10) for the case in which the permeability and
gas viscosity are independent of position. However, even if the
physical properties of the soil are highly uniform, the soil
moisture will have a vertical distribution due to the influence of
gravity. Since the permeability varies markedly with moisture
content, the permeability can be expected to vary with depth in the
soil. This is particularly true near a zone of saturation such as
near the water table.
In order to take advantage of the previously mentioned
solution, a coordinate transformation will be applied in which
5 ¦
and
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Using the above assumptions, the solution from reference (10)
can be written as
ln V+(Q+Jif>h2-b'2)2
P(Z.
This solution applies for an infinitely long cylinder in a semi-
infinite block of soil in the new coordinate system. For the
solution to be applicable to the soil research chamber, it not only
must be transformed back to the original reference frame, but it
also must be made to satisfy the boundary conditions imposed by the
finite size of the experimental chamber. This latter task will be
accomplished by applying the classic method of images to simulate
the influences of the vertical walls of the chamber. Because flow
near the bottom of the chamber will be dominated by the changing
permeability, the boundary condition on velocity at the bottom
surface of the chamber has not been rigorously pursued.
When the inverse transformation is carried out and an infinite
number of image solutions are superposed to simulate the effects of
the walls of the chamber, the resulting pressure can be written as
(8)
P?ln(
(4hi-x) 2 + (r+$)2
(4hi-x)2+(r-$)2
where
-i
(9)
and C (2)=1.64. The flow streamlines are given by
4
-------
ijr (x,y) =
Is
n
toy*
AD
tan"1
r*)2] [x2+(r-$)2]
fV l4hi+x)T {11)
T [ (4M+x)2+(r+)2] [ (4hi+x)2+(r-Q)2]
(ihi-x)T }
T [(4^i-x)2+(r+)2] [ (4/3i-x)2+(r-)2]
and the vertical component is given by
v(
y n [x2+(r+)2] [x2+(r-4>)2]
(4hi+x)2[i+24^r-ri +
i [ (4hi+x) 2+ (T+$)2] [ (4hi+x) 2+ (r-O)2]
(4Ai-x)2[l+2 4^Mr-r] +4>2-r2
k(y)
i [ {4hi-x) 2+ (T+<1>)2] [ (4hi-x) 2+(r-4>)2]
Upon integrating equation (12) over the soil surface, the total
rate of flow is obtained as
Q=
471 Lk0p'
(13)
Equation (13) provides a means of measuring k0. However, sinceP'
contains the ratio k(h)/k0, information about the variation of
permeability with depth is required. Using a measured moisture
profile, an empirical model by Rogers and Nielsen (13) can be used
to calculate the permeability. This empirical model relates the
permeability to the moisture content as
5
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Jc=Jc0exp (-12 s4)
(14)
When s, the fraction of moisture saturation, is measured as a
function of depth in the soil, the vertical permeability profile
can be computed. Knowing the moisture content at depth h allows
the ratio k(h)/k0 to be evaluated as
=exp[-12s* (h) ] . (15)
K
Equations (9) and (13) can then be solved for the permeability at
the surface of the soil as
- a*
' 4 71 LP,
In
I(h) +\jI2 (h) -i?/2 C (2) J2WexP(-24s<)
1(h) -\Jl2 (h) -b'2) 8 h*
(16)
Moisture and Permeability Measurements
Soil moisture was measured with a Troxler Sentry 200-AP
moisture monitor. This device consists of a sensor which moves
vertically inside a hollow polyvinyl chloride (PVC) tube in the
soil. It measures the percent water by volume in the soil to an
accuracy of 0.2% by measuring the effective capacitance of the
surrounding soil. Moisture measurements were taken 0.15 m apart at
four different locations within the chamber.
The measured moisture profiles are illustrated in Fig. 1.
Note that the moisture approaches zero near the surface where
evaporation occurs. From about 0.4 m to 1.2 m the moisture remains
nearly constant at about 15% of saturation. At depths greater than
1.2 m, the moisture increases rapidly to saturation at about 1.9 m
which is near the water level.
The permeability as computed from the empirical model of
Rogers and Nielsen is shown in Fig. 2 This figure illustrates that
the permeability is relatively independent of moisture until the
level reaches about 0.2 of saturation. For levels above 0.2, the
permeability decreases very rapidly with increasing moisture. An
initial estimate of k0 is given by
Jc0 = 3 . 86xl0"6e2d4/3 (17)
where d is the average diameter of soil particles that pass through
a No. 4 mesh screen. For the present soil, d = 3.8x10'" m. This
estimate was used to compute the profiles shown in Fig. 2. The
permeability profile as a function of depth is then used to
evaluate the transformation in equations (4) and (5) as well as to
compute 1(h) in equation (9). A more rigorous value of k0 can be
obtained from equation (16). More appropriately, linear regression
is applied to the measured flow/pressure relationship and the
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resulting slope used to compute k0 from
Jt0 = —K—
0 4 nL
J(A) +y/l2(A) -Jb
/2
1(A) -V^I2(^) -b/2J
+ (2) j2 (A) exp{-24s4 (A)}
8 A2
slope.
(18)
Figure 3 shows the flow rate as a function of the applied pressure.
The slope is found to be 1.60x10'® m4 s kg'1. Equation (18) then
yields k0 = 3.l7xl0'11 m2, with = l.85xl0'5 kg m'1 s 1, L = 0.66 m,
h = 0.965 m, b' =0.0254 m, and £(2) = 1.64.
Pressure Measurements
The permeability profiles in Fig. 2 are also used to compute
the pressures and streamlines given by equations (8) and (10),
respectively. Calculated pressure contours in the measurement
plane are illustrated in Fig. 4. For a comparison, the upper
portion of the figure shows the pressure contours when permeability
is constant (k0) throughout the region. The lower portion of the
figure shows the pressure contours when the permeability varies as
shown in Fig. 2. Significant differences in the pressure contours
are apparent where the moisture content increases dramatically.
The pressure differences are not effectively transmitted through
regions of high moisture near the bottom of the chamber. The
strong influence of moisture is perhaps even more apparent in the
stream function illustrated in Fig. 5. The upper portion of the
figure corresponds to the case of constant permeability, while the
lower portion corresponds to variable permeability shown in Fig. 2.
Note how flow is excluded from the bottom portion of the chamber
where the permeability is low due to high moisture content. This
result is consistent with observations in Fig. 4.
Fig. 6 shows pressure distribution in the horizontal direction
at five different vertical levels. Each vertical level was chosen
to correspond to a row of measurement probes in the chamber. The
center row contains the suction tube located at x = 0. Note that
the greatest pressure variations occur near the suction tube. As
might be expected, the pressure decreases more quickly in the
direction of the open surface. The symbols in this figure
represent measurements of the pressure. Generally, the agreement
between measurements and predictions is good. The agreement is no
worse than about 14% except for certain points located in the
bottom row and a few points on the extreme right side of the
chamber. Certain evidence, such as frequently collecting water in
the sampling lines, suggests that the soil near the right wall of
the chamber may contain higher moisture contents than the rest of
the soil at the same level. Consequently, the moisture profile
and the resulting permeability profile near the right wall of the
chamber may not correspond to those in Figs. 1 and 2 that were used
7
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to compute the pressure. The closest moisture measurement column
is located about 0.8 m from the pressure sensors at the right side.
The model underpredicts the pressure somewhat near the bottom where
the moisture is highest. The principal reason for this
underprediction may be that the solution does not rigorously
satisfy the boundary condition of zero vertical flow at the bottom
surface of the chamber. This slight underprediction of the
pressure in this region should have little influence on other
physical quantities such as total flow rate and radon migration,
since the low value of permeability in the lower region of the
chamber forces the flow to go to zero at depths somewhat above the
bottom surface of the chamber.
Discussion and Conclusions
A model is presented to describe advective flow in AEERL's
soil-gas research chamber. The model satisfies the appropriate
boundary conditions at the vertical walls of the chamber and
accounts for the effects of variations in permeability with the
moisture content of the soil. It was seen that the lower
permeability due to moisture caused a greater fraction of the total
pressure drop to occur near the central porous tube. While the
model generally shows good agreement with pressure measurements,
there are two regions in which some deviations occur. The model
tends to overpredict the pressure at the sensor locations near the
right wall of the chamber. This is the region where higher-than-
normal levels of moisture were suspected. Local measurements of
permeability tended to support this conclusion. The model tends to
underpredict the pressure at the sensor locations near the bottom
of the chamber. This is the region in which the solution is less
rigorous in the sense that the condition of zero vertical flow at
the surface is not imposed on the solution. For convenience, the
rationale was used that, since the low values of permeability in
that region would prevent any gas flow, it would not be necessary
to impose a no flow condition on the solution. As was seen by the
streamlines (Fig. 5) , no flow occurs near the bottom of the
chamber. While this lack of rigor leads to a modest error (100%)
in the local pressure field, it probably has no significant effect
on pollutant transport because negligible flow occurs in this
region anyway. In order to confirm these assumptions, the solution
will be modified in the future to satisfy the boundary conditions.
If necessary, this will be done with numerical solutions.
In the present case, it is found that incorporation of the
effects of moisture on permeability improves the mathematical
representation of the pressure field by as much as 2 5%. However,
sandy soils probably exhibit the least effects of the moisture
profile. Moisture retention in most soils is expected to be
greater than for sands. Consequently, the effect of the moisture
profile is probably minimal in the present case. The moisture
effects contained in this solution should take on greater
significance for clay soils.
8
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References
1. Menetrez, M.Y., Mosley, R.B. , Snoddy, R. , Ratanaphruks, K. , and
Brubaker, S.A., Jr. Evaluation of radon movement through soil
and foundation substructures. Presented at the 1993
International Symposium on Measurement of Toxic and Related
Air Pollutants, Durham, NC, May 4-7, 1993.
2. Bruno, R.C. Sources of indoor radon in houses: a review.
JAPCA, v. 33, no. 2, pp. 105-109, 1983.
3. Nero, A.V. and Nazaroff, W.W. Characterizing the source of
radon indoors. Radiat, Prot. Dosim. v. 7, pp. 23-39, 1984.
4. Nazaroff, W.W. and Doyle, S.M. Radon entry into houses having
a crawl space. Health Phys., v. 48, pp. 265-281, 1985.
5. Akerblom, G., Anderson, P., and Clavenajo, B. Soil gas radon -
a source of indoor radon daughters. Radiat. Prot. Dosim. v.
7, pp. 49-54, 1984.
6. Nazaroff, W.W., Feustel, H. , Nero, A.V., Revzan, K.L.,
Grimsrud, D.T., Essling, M.A., and Toohey, R.E. Radon
transport into a detached house with a basement. Atmospheric
Environment, v. 19, no. 1, pp. 31-46, 1985.
7. Sextro, R.G., Moed, B.A., Nazaroff, W.W., Revzan, K.L., and
Nero, A.V. Investigation of soil as a source of indoor radon.
In: Radon and Its Decay Products: Occurrence, Properties, and
Health Effects: Hopke, P., ed. ; ACS Symposium Series 331;
American Chemical Society: Washington D.C., pp. 10-29, 1987.
8. Turk, B.H., Prill, R.J., Grimsrud, D.T., Moed, B.A., and
Sextro, R.G. Characterizing the occurrence, sources, and
variability of radon in Pacific Northwest USA homes. J. Air
Waste Manage. Assoc. v. 40, pp. 498-506, 1990.
9. Garbesi, K., Sextro, R.G., Fisk, W.J., Modera, M.P., and
Revzan, K.L. Soil-gas entry into an experimental basement:
model measurement comparison and seasonal effects. Eviron.
Sci. Technol. v. 27, no. 3, pp. 466-473, 1993.
10. Mosley, R.B. A simple model for describing radon migration and
entry into houses. In: Cross, F.T. , ed. , Indoor Radon and Lung
Cancer: Reality or Myth?; Part 1, Battelle Press, Columbus,
OH, V. 1, pp. 337-356, 1992.
11. Mosley, R.B. Model based pilot scale research facility for
studying production, transport, and entry of radon into
structures. In: Proceedings: the 1992 international Symposium
on Radon and Radon Reduction Technology: vol. 1. EPA-600/R-93-
083a (NTIS PB93-196194) , pp. 6-123 thru 6-140, May 1993.
12. Mosley, R.B. An analytical solution to describe the
pressure/flow relationship in EPA's soil-gas chamber.
Presented at the 1993 International Symposium on Measurement
of Toxic and Related Air Pollutants, Durham, NC, May 4-7,
1993 .
13. Rogers, V.C. and Nielsen, K.K. Correlation of Florida soil-gas
permeabilities with grain size, moisture, and porosity. EPA-
600/8-91-039 (NTIS PB91-211904), June 1991.
9
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Nomenclature
h*b
b' k0 f , the transformed radius of the cylinder (m)
h-b y
C the activity concentration (Bq m'3)
d the average diameter of soil particles that penetrate a No. 4
mesh screen (m)
De the effective diffusion coefficient (m2 s"1)
G the radon generation rate (Bq m'3 s"1)
h the depth of the cylinder (m)
i a summation index (unitless)
i
k k(y), the permeability of the soil (m2)
k0 the soil permeability at the soil surface (m2)
k(h) the soil permeability at the level of the cylinder (m2)
k'(y) dk/dy is the derivative of the permeability (m)
L the length of the central section of the cylinder (m)
P pressure (Pa)
Pc the pressure applied at the central cylinder (Pa)
P1 a pressure coefficient (Pa)
Q the gas flow rate (m3 s"1)
s the fraction of moisture saturation
t an integration variable (m)
v the superficial velocity (m s'1)
x the horizontal Cartesian coordinate (m)
y the vertical Cartesian coordinate (m)
r k(y)f-iT£T
{k(y>
e the soil porosity (unitless)
C the Riemann zeta function
X the decay constant for radon (s'1)
|i the viscosity of the soil gas (kg m'1 s"1)
$ the transformation coordinate corresponding to x (m)
¦^o
cp the transformation coordinate corresponding to y (m)
h
tp^ k0f ^ , the transformed depth of the cylinder (m)
J ic (y)
ijr the stream function (m2 s"1)
the stream function evaluated at the origin (m2 s'1)
d the partial derivative symbol
10
-------
0.5-
E
Q.
-------
0.5-
1.5-
0 0.5 1
1.5 2 2.5 3 3.5
Permeability (1011m2)
Figure 2. Permeability profiles for the soil-gas chamber
12
-------
12-
10-
o>
E
£
o
Li.
0 20 40 60 80 100
Pressure (Pa)
Figure 3. Plot of the total flow/pressure relationship.
13
-------
.0.2
Q.
0.4
0.6
0.5'
0.3
0.3
Length
o-o
0.2
0.3"
—0.1
Length
Figured Pressure contours for the soil-gas chamber. The top corresponds to
constant permeability, and the bottom corresponds to variable permeability.
14
-------
0.5
0.5
0.4
0.4
0.3
0.3
£
Q_
0
~
0.2
0.2
Length
0.8
0.8
£
Q_
0)
~
0.6-
Length
Figure 5. Calculated streamlines for the soil-gas chamber. The top corresponds to
constant premeability, and the bottom corresponds to variable permeability.
15
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0.3-
0.2-
0.1-
0.4-
0.2-
0.6
0.3-
0.6-
0.3-
1
2
-1.5
1.5
2
-0.5
0.5
1
0
Horizontal distance (m)
Figure 6. Pressure as a function of horizontal position at five different depths in the soil-gas chamber.
Curves represent calculations while symbols represent measurements.
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at7^ot T-> 11in TECHNICAL REPORT DATA „
I\xL (Please read /nuructions on the reverse before completin'
1. REPORT NO. 2.
EPA/600/A-93/253
3.
4. TITLE AND SUBTITLE
Measurements of Soil Permeability and Pressure
Fields in EPA's Soil-gas Chamber
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
R. B. Mosley (EPA) and R. Snoddy and S. A.
Brubaker Jr. (Acurex)
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING OROANIZATION NAME AND ADDRESS
Acurex Corporation
P.O. Box 13109
Research Triangle Park, North Carolina 27709
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-D2-0063, Task 1/023
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Air and Energy Engineering Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Published paper; 5-8'93
14. SPONSORING AGENCY CODE
EPA/600/13
15.supplementary notes project officer is Ronald B. Mosley, Mail Drop 54, 919/
541-7865. Presented at 1993 International Radon Conference, Denver, CO, 9/20-23/
cn
j The paper discusses the measurement of soil permeability and pressure
fields using EPA's soil-gas chamber, designed to study the production and transport
of radon and other potential indoor air pollutants originating in soils. The chamber
is instrumented to measure distributions of radon and pressure fields and also
moisture distributions and their resulting influence on soil permeability. An analytic
solution for advective flow in the soil-gas chamber is presented which includes the
effects of moisture-dependent variations of the permeabilityow£tfc position., Measure-
ments of the pressure field are compared with model calculations. Relatively good
agreement between the measurements and calculations is obtained, except near the
water level where boundary conditions are not rigorously satisfied.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b. 1 DE NTI F 1 E RS/OPEN ENDED TERMS
c. cosati Field/Group
Pollution Pressure Field Detec-
Radon tion
Measurement Moisture
Soils Mathematical Models
Permeability
Test Chambers
Pollution Control
Stationary Sources
13 B
07B 17K
14G 07D
08G.08M 12A
14 B
13. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
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