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
Penalty for Private Use
$300
     BULK RATE
POSTAGE & FEES PAID
 EPA PERMIT NO. G-35
EPA/60Q/SR-92/090

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