United States
Environmental Protection
Agency
Air and Energy Engineering
Research Laboratory
Research Triangle Park, NC 27711
Research and Development
EPA/600/SR-92/090 December 1992
EPA Project Summary
Simplified Modeling of Air Flow
Dynamics in SSD Radon
Mitigation Systems for
Residences with Gravel Beds
T.A. Reddy, K.J. Gadsby, H.E. Black, III, D.T. Harrje, and R.G. Sextro
The technique presently considered
most effective for mitigating residences
for radon is subslab depressurization.
Given that many such mitigation sys-
tems designed and installed by the pro-
fessional community do not perform
entirely satisfactorily, there is a need
to better understand the dynamics of
subsiab air flow. This report suggests
that subslab air flow induced by a cen-
tral suction point be treated as radial
air flow through a porous bed con-
tained between two impermeable disks.
It also shows that subslab air flow is
most likely to be turbulent under actual
field situations in houses with subslab
gravel beds, but remains laminar when
soil is present under the slab. The
physical significance of a model is dis-
cussed, and simplified closed-form
equations are derived to predict pres-
sure and flows at various distances
from a single central depressurization
point. A laboratory apparatus was built
to verify the model and experimentally
determine the model coefficients of the
pressure drop versus flow for com-
monly encountered subslab gravel ma-
terials. These pressure drop coefficients
can be used in conjunction with the
simplified model as a rational way to
assess subslab communication in
houses. Preliminary field verification
results in a house with gravel under
the basement slab are presented and
discussed.
This Project Summary was developed
by EPA's Air and Energy Engineering
Research Laboratory, Research Tri-
angle Park, NC, to announce key find-
ings of the research project that is fully
documented in a separate report of the
same title (see Project Report ordering
information at back).
Introduction
Subslab depressurization (SSD) has
been widely adapted as a radon mitigar
tion technique. This method relies upon
reducing the pressure under the slab to
values below that of the basement (or
living space in the case of slab-on-grade),
at least where soil gas flow into the base-
ment could occur. In the pre-mitigation
diagnostic phase, the degree of "connec-
tivity" under the slab as well as the per-
meability characteristics of the subslab
medium must be determined before a suit-
able SSD system can be designed. Proper
attention to these aspects will ensure that
reasonable flows, and hence the desired
degree of depressurization, will prevail at
all points under the slab.
Parallel with the above aspect is the
concern that mitigators tend to over-de-
sign SSD systems to be on the safe side.
In so doing, there is a definite possiblity
that more radon from the soil is removed
and vented to the ambient air than would
have ocurred naturally. There is thus the
need to downsize current overly robust
SSD mitigation systems and decrease
emission exhaust quantities of radon while
simultaneously ensuring that indoor radon
does not rise to undesirable levels.
One aspect of the current research is
the formulation and verification of a rapid
diagnostic protocol for subslab and wall
depressurization systems designed to con-
trol indoor radon concentrations. The for-
mulation of the diagnostics protocol con-
sists of: (1) specification of practical guide-
Printed on Recycled Paper
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lines that would enhance the effective-
ness of the engineering design of the ra-
don mitigation system, and (2) reliance on
fundamental scientific studies that provide
additional data and insight needed to de-
velop, test, and revise protocols. The re-
port addresses the latter, relying on cur-
rent data and understanding and antici-
pating that additional data will become
available to refine the approach taken here.
Specification of the Problem
In terms of modeling the induced
subslab pressure fields, the prestock con-
struction can be divided into three groups:
(1) those with a gravel bed under the
concrete slab, (2) those without, .in which
case soil is the medium under the slab,
and (3) those houses which have both. In
Group 2, the soil permeabilities are much
lower than in Group 1, and more careful
design of the mitigation system is war-
ranted. In New Jersey, houses less than
about 30 years old typically have gravel
beds about 0.05-0.1 m thick under the
slab. However other states seem to have
very different construction practices; for
example, houses In Florida are often slab-
on-grade directly on compacted fine-
grained soil which offers high resistance
to air flow.
Figures 1 (a) and (b) depict the con-
struction and air flow paths expected in a
house with either gravel or soil under the
slab, when single-suction pressure is ap-
plied through the slab. (For a radon miti-
gation system using subslab pressuriza-
tion, a good approximation, would assume
similar aerodynamic effects with the direc-
tion of air flows reversed.) Since the per-
meability of the gravel bed is usually very
much higher than that of the soil below,
one could assume, except for the irregu-
lar pattern around the footing which would
occur over a relatively small length, that
the subslab air flow is akin to radial flow
between two Impermeable circular disks
with a spacing equal to the thickness of
the gravel bed. Note that this model equally
accounts for the leakage of air from the
basement which essentially occurs from
the perimeter cracks or through the base-
ment wall.
For a house without a gravel bed (Fig-
ure 1b), suction applied at a simple pen-
etration through the slab (as in Figure 1a)
Is no longer practical since the area of
depressurization is usually small. To en-
hance mitigation effectiveness, the cur-
rent practice is to increase this area either
by digging a pit below the concrete slab
or, more simply, by hollowing out a hemi-
sphere of about 0.3-0.45 m radius under-
neath the suction hole. Even under such
conditions, if the soil underneath the slab
is free of major obstructions like concrete
footings, ductwork, piping, and large rocks,
air flow can be approximated as occurring
between two impermeable circular disks
with a spacing equal to either the depth of
the pit or the radius of the hollow hemi-
sphere.
Preliminary Theoretical
Considerations
The above duscussion suggests that
flow underneath the slab be visualized as
occurring in the radial streamlines termi-
nating at the central suction point. Note
that such a reprensentation would per-
haps be too simplistic or even incorrect
for a house with a partial basement (Group
3, above). This study is limited to under-
standing the flow and pressure drop char-
acteristics through a homogeneous bed
(of either gravel or soil) with uniform bound-
ary conditions, the obvious one to start
with being a circular configuration.
The first questions relate to the nature
of the flow; i.e., is the flow is laminar or
turbulent, and where, if at all, is there a
transition from one regime to another. The
Reynolds number gives an indication of
the flow regime. Though there is an inher-
ent ambiguity in the definition of the quan-
tity characterizing the length dimension,
we shall adhere to the following definition:
Re
where q
A
va
dv
.3. JL dy.
''
(D
total volume flow rate,
cross sectional area of
the flow (for radial flow
through a circular bed
of radius r and thickness
h, A = 2 wh),
kinematic viscosity of
air,
equivalent diameter of
gravel or soil particles,
and
void fraction or porosity
of the gravel bed.
For flow through a gravel bed, some
typical values of the above parameters
could be assumed:
h = 0.1 m, dv = 0.0125 m, va (at 15°C) =
1 4.6x1 0-6m2/s, and 0 = 0.4.
The values of q encountered in practice
range from 10 to 50 l/s. The Reynolds
numbers for radial flow at different radii
have been computed under these
conditons. A safe lower limit for turbulent
flow is when Re >10, and a safe upper
limit for laminar flow is when Re < 1.
Since basements do not generally exceed
6 m in radius, subslab flow tends to be
largely turbulent when a gravel bed is
present. This by itself is an important find-
ing since earlier studies do not seem to
have recognized this fact.
Subslab flow characteristics in a house
with soil as the subslab medium have
also been investigated. Soil grain diam-
eters range from 0.06 to 2 mm, and vol-
ume flow rates in corresponding mitiga-
tion systems are typically lower, about 0.8-
6.0 l/s. Assuming typical values of h = 0.1
m.O = 0.4, and q = 2.4 l/s, the corre-
sponding Reynolds numbers for air flow
through sands of different grain diameters
have been calculated from Eq. (1). The
flow is likely to be laminar in most cases.
Mathematical Model for Radial
Flow
The core of any model is the formula-
tion of the correlation structure between
pressure drop and Re (or flow rate). For
laminar flow, Darcy's law holds, providing:
.
pf.g dx
(2)
where Pf
density of the flowing
fluid, and
g = gravitational constant.
For turbulent flows, a widely used model
J
pf.g dx
(3)
The left side is the pressure drop per
unit bed length, and a can be loosely
interpreted as the resistivity of the porous
bed to the flow of the particular fluid. The
permeability k of the porous bed is given
by: v
k="g^'a (4)
A mathematical expression can be de-
rived for the pressure field when suction
is applied at the center of the circle. Air
flows are assumed radially through a cir-
cular homogeneous gravel bed. For the
suction pressures encountered in this prob-
lem, air can be assumed to be incom-
pressible. Thus assuming a simple model
such as Eq.(3) for the pressure drop yields:
dr
(5)
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Concrete
slab
Footing
(a) House with a subslab gravel bed
Gravel bed
Ground
level
Concrete
slab
Footing
(No air flow)
Gravel Pit
(b) House with a subslab soil bed.
Figure 1. A subslab mitigation system and air flows in the basement of a house. Note that part of the
air flowing through the subslab bed originates from the basement and the rest from the
ambient air.
where p(r) is the pressure of air at a
radial distance r from the center, and pa is
the density of air.
Integrating Eq. (5), and using the bound-
ary conditions r = ro and p = pa at the edge
of the disk, yields:
Since the pressure drop is often mea-
sured in units of head of water, it is more
convenient to modify Eqs. (5) and (6) to:
Pa /_q_f j_
' pw ' Wi/ " 1-b
P(r)-Pa
pa-g
'_g_)b. J_. (ri-b _roi-b)
'2nh/ 1-b
(6)
P(r)-Pa =
Pw.g
(r -TO ) (7)
On the other hand, during laminar flow,
Darcy's Law holds and exponent b=1. Un-
der these circumstances, integrating Eq.
(5) with b = 1 and inserting the appropri-
ate boundary conditions, yields:
P(r)-pa _
Pw.g
= a
Pw
-9-
2nh
1n i
(8)
It is easy to modify these equations to
apply to outward radial flow as encoun-
tered in houses where subslab pressur-
ization is used. The boundary conditions
are still the same, but now the pressure at
the entrance of the suction pipe is higher
than ambient pressure and the quantity
[p(r) - pj is positive and represents the
pressure above the ambient pressure.
If parameters a and b are constant for a
given bed material and can be determined
by actual experiments in the field, they will
serve as indices for mitigation system de-
sign.
Laboratory Apparatus
The soundness of the mathematical deri-
vation presented above needs to be evalu-
ated, and the numerical values of the em-
pirical coefficients of Eq. (3) needs to be
determined. To this end, a laboratory
model consisting of a 2.4 m diameter cir-
cular section that is 0.15 m deep was
constructed. The top and bottom imper-
meable disks were 0.02 m thick plywood,
and a wire mesh at the outer periphery of
the disks was used to contain the gravel
between the disks. The apparatus allowed
experiments to be conducted with a maxi-
mum disk spacing (or depth of gravel bed)
of 0.095 m. An open-cell foam sheet 0.025
m thick was glued to the underside of the
top plywood disk. During the experiments,
heavy weights were placed on top of the
plywood disk which compressed the open-
cell foam enough to effectively eliminate
gaps between the disk and the gravel top
that could short-circuit the air flow. This
guarantees that air flow occurs through
the bed and not over it.
The volume of the packed bed is ap-
proximately 0.43 m3 which, for river-run
gravel, translates into a net weight of about
700kg(1530lb).
A 0.038 m diameter hole at the center
of the top disk served as the suction hole.
Nine holes, were drilled on three separate
rays of the top disk, and a polyvinyl chlo-
ride (PVC) pipe of 0.012 m inner diameter
with chamfered ends was press-fit into
these holes. Pressure measurements at
these nine holes would then yield an ac-
curate picture of the pressure field over
the entire bed.
We choose a predetermined total air
flow rate and gradually control the speed
of the suction fan to achieve this flow. The
pressure measurements (representative of
the corresponding static pressure inside
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the porous bed) at each of the nine taps
are taken with all other taps closed. This
completes a series of readings pertaining
to one run. In subsequent runs, the total
air flow rate is set to another predeter-
mined value and the series of readings
are repeated.
Experimental Results and
Analysis of Radial Flow
Table 1 summarizes the different ex-
periments performed using the laboratory
apparatus. For example, Experiments A
involved river run gravel of nominal diam-
eters of 0.012 and 0.019 rn, referred to as
small and large gravel, respectively. Ex-
periments A1 and A2 differ only in the
spacing between the plywood disks; i.e.,
the thickness of the bed was altered. Ex-
periment A1 involved three runs each with
a different total volume flow rate, the val-
ues of which are also given in Table 1.
The flow regime (as specified by the cor-
responding calculated Reynolds number)
was found to be turbulent throughout the
radial disk.
The values of the mean gravel diameter
and the porosity of the bed are required
for computing the Reynolds number [given
by Eq. (1)]. Least-square regression for
both the constant 'a' and exponent 'b' was
performed on the observed experimental
pressure drop data using Eq. (7). R2 val-
ues were very high (Table 2), and better
fits cannot realistically be expected (given
the measurement errors in the readings,
we may in fact be overfitting in the sense
that we are trying to assign physical mean-
ing to random errors).
An earlier study found exponent b to be
1.56 for the cylindrical disk model. This is
generally borne out in the present study
where b = 1.6 for the small river-run gravel
and b - 1.4 for the large gravel.
The values of permeability of the po-
rous bed calculated following Eq. (4), in-
cluded in Table 2, show a threefold differ-
ence between small and large gravel sizes.
The numerical values seem to correspond
to those cited in the radon literature.
Field Verification
The irregular boundary conditions and
the non-homogeneity in subslab beds that
arise in practice are, however, not easily
tractable with a simple expression such
as Eqs. (7) and (8). Resorting to a nu-
merical computer code may be the only
rigorous way to predict pressure fields un-
der actual situations. This section shows
that the simplified approach nevertheless
has practical relevance in that it could be
used to determine areas under the slab
with poorer connectivity.
Table 1. Summary of the different experiments using river-run gravel performed with the
laboratory apparatus
Experiment
A1
A2
A3
Gravel size
(nominal
diameter)
(m)
0.012
0.012
0.019
Disk
spacing
(m)
0.075
0.10
0.10
No. of
runs
3
2
4
Total flow
rate
(l/s)
20.5
30.1
37.3
22.1
31.4
11.2
15.2
17.6
20.8
Table 2. Summaryol'variouslaboratoryexperiments performed'andthe physical'parameters deduced
in the framework of the study using river-run gravel
Experiment
A1+A2
A3
Diameter of
particles
nominal
(m)
0.012
0.019
measured
(m)
0.011
0.022
Measured
porosity
0.374
0.424
r?
0.99
0.99
Pressure
drop
exponent
1.60
1.40
Permeability
of bed
(m2)
9.4x10's
34x10-*
The house under investigation (H21) has
a partial basement with a gravel bed un-
der the basement slab. As shown in Fig-
ure 2, the basement (though rectangular)
is nearly square (6.45 x 7.60 m). It has
two sides exposed to the ambient air above
grade, while the other two sides are adja-
cent to slab-on-grade construction. One
suction hole of 0.1 m diameter was drilled
at roughly the center of the basement
slab to which a temporary mitigation sys-
tem was installed. Though 19 holes were
drilled through the slab (Figure 2), two of
them (holes 11 and 12) were found to be
blocked beneath the slab. Consequently,
data from only 17 holes have been used
in this study. This blockage was later found
to be due to the presence of an oversized
footing for a support column.
Three sets of runs were carried out
which, depending on the air flow rate
through the single suction pipe, are termed:
1) 28 l/s - high flow, 2) 23.4 l/s - medium
flow, and 3) 18.1 l/s - low flow.
Note that the analytical expression for
the pressure field under turbulent flow
given by Eq. (7) is strictly valid for a circu-
lar disk with boundary conditions at r = ro
and p = pa. The rectangular basement is
approximated by a circle of 3.5 m mean
radius. Also included the extra path length
of ambient air flowing down the outer base-
ment wall, going under the footing, and
flowing through the subslab gravel into
the suction hole. This is about 2 m. Con-
sequently, ro = 5.5 m. The effective thick-
ness of the°subslab gravel bed, h, is ab-
out 0.05 m.
The gravel under the slab, though river-
run, was highly heterogeneous in size and
shape. In general, its average size was
slightly less than 0.012 m. However, the
properties of the 0.012 m gravel deter-
mined experimentally in the laboratory (see
Table 2) were used.
Figure 3(a) shows the observed and
calculated pressure drops for the low flow
rate. Readings from holes 13 and 14 are
lower, and poorer connectivity to these
holes is suspected; i.e., some sort of block-
age in this general area. Agreement be-
tween model and observation is striking,
given the simplification in the model and
also the various assumptions outlined
above. This was also true for the other
two flow rates chosen.
Figure 3(a) indicates the non-uniform
areas under the slab. A better way of
illustrating how well the model fares against
actual observations is shown in Figure
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-6.45m-
6
§
K
Figure 2. The basement slab of House H21 showing the relative positions of the subslab penetrations.
The mitigation system suction hole is marked +.
3(b). The solid line represents the model
predictions while observations are shown
by discrete points. Again, the predictive
ability of this modeling approach is satis-
factory, and certain holes have pressure
drop values higher than those predicted
by the model.
An alternate approach, to the one
adopted here and described above, would
be not to assume specific gravel bed co-
efficients but to determine them from re-
gression. This entails using Eq. (7) and
the data set of actual observations and
determining the parameters a (and per-
meability k) and b by regression. Such an
approach yielded a value of k which is
practically identical to that of the 0.012 m
gravel determined experimentally in the
laboratory apparatus. This suggests that
even a visual inspection of the porous
material under the slab can be an indica-
tor good enough for a mitigator to select a
standard bed material from a table before
using the physical properties of the mate-
rial to get a sound estimate of what the
suction pressure ought to be in order to
generate a certain pressure field under
the slab. The need to categorize com-
monly found subslab materials, deduce
their aerodynamic pressure drop coeffi-
cients in laboratory experiments, and tabu-
late them seems to be worth investigating.
Summary
Important features of the study are:
(1) The general problem of radon miti-
gation system design is outlined,
and the scope and limitations of
prior studies are discussed both in
this aspect and at a more funda-
mental aerodynamical level. The
first need should be to determine
the nature of air flow below the
concrete slab and how it is likely to
affect the pressure drop versus flow
correlation for given subslab condi-
tions.
(2) The suggestion of a prior study,
that flow under the slab of a house
during mitigation using subslab de-
pressurization (and pressurization)
be likened to radial flow between
two impermeable disks, is sup-
ported.
(3) It is shown that subslab air flow
under actual operation of mitigation
systems is likely to be turbulent if a
gravel bed is present and laminar
in the presence of soil.
(4) A mathematical treatment, to ana-
lytically predict the pressure field in
homogeneous circular porous beds
when subjected to a single central
suction hole, is presented.
(5) A laboratory apparatus that can du-
plicate conditions which occur in
practice under slabs of real houses
being mitigated for radon using de-
pressurization (or pressurization) is
described.The experimental proce-
dure followed to measure the pres-
sure field of turbulent airflow (from
which the regression coefficients of
the pressure drop versus flow cor-
relation can be determined) is out-
lined.
(6) Preliminary field verification results
of the modeling approach in a
house with gravel under the base-
ment slab are presented and dis-
cussed. A striking conclusion of the
study is that even a visual inspec-
tion of the porous material under
the slab may be an indicator good
enough for a sound engineering
design, if used in parallel with the
modeling approach and given a
table containing the aerodynamic
pressure drop coefficients of com-
monly found subslab material.
Future Work
Logical extensions of this study would
involve applications of this methodology
to houses with (1) homogeneous beds but
with irregular boundaries, and (2) non-
homogeneous porous beds. One approach
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10 11 12 13 14 15 16 17 18 19
Hole number
(a) Pressure drop vs. hole number.
150
a observed
— calculated
Distance, m
(b) Pressure drop vs. distance.
Figure 3, Comparison of observed and estimated pressure drops in House H21 using coefficients of
0.012m gravel. Data of holes 11 and 12 are not included.
is to develop a computer program using
numerical methods (either finite element
or finite difference could be used) to solve
the basic set of aerodynamic and mass
conservation equations.
Although the above approach offers
great flexibility, it is not used easily by
non-experts. Developing engineering
guidelines for practitioners based on such.
a code demands a certain amount of ef-
fort and practical acumen. It would be
wiser to define a few "standard" basement
shapes, subslab conditions, and mitiga-
tion pipe locations; develop simplified
closed-form solutions of these cases; and
then compare these solutions with actual
measurements taken in the field. If such
an approach does give satisfactory engi-
neering accuracy, its subsequent use as
an engineering design tool, well within the
expertise of the professional community,
seems promising.
•U.S. Government Printing Offies: 1993 — 750-071/60176
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T. Reddy, K. Gadsby, H. Black III, D. Harrje, and R. Sextro are with Princeton
University, Princeton, NJ 08544.
Ronald B. Mosley Is the EPA Project Officer (see below).
The complete report, entitled "Simplified Modeling of Air Flow Dynamics in SSD
Radon Mitigation Systems for Residences with Gravel Beds," Order No. PB92-
195635/AS; Cost: $19.50 subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Air and Energy Engineering Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC27711
United States
Environmental Protection Agency
Center for Environmental Research Information
Cincinnati, OH 45268
Official Business
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$300
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