United States
                    Environmental Protection
                    Agency
 Air and Energy Engineering
 Research Laboratory
 Research Triangle Park. NC 27711
                    Research and Development
 EPA/600/SR-94/201
& EPA      Project Summary
January 1995
                    Development of a
                    Lumped-Parameter  Model  of
                    Indoor  Radon  Concentrations

                    Kirk K. Nielson, Vern C. Rogers, and Rodger B. Holt
                     The report describes a simplified,
                   lumped-parameter model to character-
                   ize indoor radon concentrations from
                   data that are more readily available than
                   those required for existing mathemati-
                   cal  models.  The lumped-parameter
                   model was developed from numerous
                   sensitivity analyses with the more de-
                   tailed RAETRAD model and from analy-
                   ses of trends from empirical data sets.
                   The model analyses established radon
                   dependence on soil parameters, house
                   size,  floor cracks  and openings, and
                   indoor air  pressures. The empirical
                   analyses estimated house air infiltra-
                   tion properties, concrete slab diffusion
                   properties, sub-slab ventilation effec-
                   tiveness, and floor crack areas.
                    The  lumped-parameter  model was
                   defined by simplifying these theoreti-
                   cal and empirical trends into a single
                   equation. The equation expresses net
                   soil-related  indoor radon  concentra-
                   tions as a function of the sub-slab ra-
                   don concentration, which  defines the
                   radon source strength, and a number
                   of house parameters that characterize
                   the radon entry and accumulation char-
                   acteristics.
                    The model was  validated by com-
                   parison to radon measurements at the
                   Florida Radon Research  Program ra-
                   don test cells, by comparisons  with
                   soil radon potential mapping calcula-
                   tions, and by comparisons with indoor
                   radon data at more than  60 houses.
                   The test-cell comparisons exhibited an
                  average agreement within  3% for the
                  floating-slab cell and within 17% for
                  the slab-in-stem-wall cell. The compari-
                  sons with soli radon potential mapping
 calculations showed a relative standard
 deviation of about 30%. The compari-
 sons with house radon data depended
 on sub-slab ventilation system but av-
 eraged  within a factor of 2 for both
 slab-in-stem-wall houses and mono-
 lithic slab houses.
   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

  A lumped-parameter model has been
 developed to provide a simple means of
 estimating indoor radon concentrations from
 data that are more commonly available than
 those  required for existing, detailed math-
 ematical  models. It was developed under
 the Florida  Radon Research  Program
 (FRRP) to simplify evaluations of different
 construction options for attenuating indoor
 radon  entry and accumulation. The FRRP
 technically supports the Florida Department
 of Community Affairs development of
 radon-resistant building  construction stan-
 dards.  The lumped-parameter model con-
 sists of an empirical correlation of long-term
 average indoor radon concentrations with
 site parameters that include sub-slab radon
 levels  and soil water contents, and house
 parameters that include house  width and
 height, age, slab crack location, slab water/
cement ratio, stem-wall type, indoor pres-
sures driving air infiltration through the su-
perstructure and the slab, and  sub-slab
ventilation effectiveness. The use of default
                                                                   Printed on Recycled Paper

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values for some of these parameters fur-
ther simplifies the model with little loss of
accuracy.
Theoretical Basis and
Development
  The lumped-parameter model was de-
veloped from numerous sensitivity analy-
ses with  the  more  detailed RAETRAD
model and from analyses of trends from
empirical data sets that characterized build-
Ing construction  and performance. The
theoretical RAETRAD analyses character-
ized radon entry  by diffusion through the
intact floor slab and by both diffusive and
advective entry through cracks and open-
Ings in  the building  floor and  foundation
walls. The RAETRAD analyses suggested
simplified approximations to express  in-
door radon as a function of radon source
strength,  house  radon entry  rates, and
 house  ventilation parameters. Radon
 source strength was defined in terms of
 sub-stab  radon concentration,  and house
 radon entry rates were defined from floor
 openings, pressure driving forces, and slab
 diffush/ity.
    From  RAETRAD sensitivity analyses,
 the interactive effects  of soil type, house
 size, ftoor crack size and  location, and
 indoor pressures were determined. House
 size had a relatively small,  inverse effect
 when the slab radon entry  rate was nor-
 malized by the house area and  sub-slab
 radon concentration. Sub-slab radon deple-
 tion from  leakage  through cracks also
 caused a small, linear dependence of slab
 radon entry on crack location. Radon en-
 try through cracks also was relatively uni-
 form for a given soil when  normalized by
 the crack  area  and sub-slab radon con-
  centration. Entry through cracks varied lin-
  early with indoor pressure and had an
  exponential  dependence  on soil type,
  which was represented by  a surrogate of
  water saturation fraction.  These  effects
  were represented by simple, fitted para-
  metric relationships that were combined
  into a single  equation to express indoor
  radon as a function of sub-slab radon, soil
  water content (a surrogate that includes
  permeability  effects),  house width,  floor
  crack location  and area fraction, indoor
  pressure (driving soil gas entry), and house
  and soil ventilation rates.
  Empirical Basis  and
  Development
     Empirical analyses of trends from prior
  data sets characterized house air infiltra-
  tion properties, concrete slab diffusion
  properties, sub-slab ventilation effective-
  ness, and ftoor crack areas. The data on
  Florida house ventilation rates suggested
a nominal 0.25 air change per hour (ach)
passive  infiltration  rate  with  an
age-dependent increase of 0.007 ach per
year. The infiltration rates were expressed
in terms of the passive, ventilating indoor
air pressure, which was estimated from
the FRRP house data to be -0.7 Pa. This
value,  combined  with  age-dependence,
corresponds to a ventilation-pressure re-
lationship of X,, = 0.31 (APV)06 + 0.007y,
where  A,, is  tne house  air  infiltration rate
(ach),  APV is the  ventilating indoor pres-
sure (Pa), and y is the age of the house
(years).
   Radon diffusion  measurements  in
Florida concrete floor slabs suggested a
correlation with their water/cement ratio
as a surrogate for their radon diffusion
coefficient.  The resulting  trend had  an
exponential-dependence  on the water/
cement ratio of the concrete.  Sub-slab
ventilation (SSV) effectiveness was ap-
proximated from reviews  of prior perfor-
 mance by an 80% effectiveness estimate
for  active  SSV  systems and approxi-
 mately 6% effectiveness for passive SSV
 systems. Floor crack areas were  recog-
 nized as being difficult to characterize
 by visual  inspection,  and to consist of
 an approximate 0.2% leakage area plus
 an  additional 0.29% that could  result
 from a hollow stem wall.
  Lumped-Parameter Model
   The lumped-parameter model used the
  combined fitting constants from the theo-
  retical and empirical analyses to  express
  the net, soil-related indoor radon as a
  function of 11 variables and 14 constants.
  The resulting  expression for the  lumped
  parameter model is
  Cnet - Cin -Coul - hp^1(APv)" + 0.007yl


  [(2x10-3 + 2,9x10-38) (4r+APe;3.:0:045068)
                    "70
  +2.9x10-V1'4W
                                  xh
where


  C.n  =
             net indoor radon concentration
             from sub-slab sources (pCi L1)
             total indoor radon concentra-
             tion (pCi L-1)
             outdoor (background) radon
             concentration (pCi L1)
             sub-slab radon concentration
             (pCi L1)
             radon  reduction factor from
             sub-slab ventilation (fssv=0.2
             for  active system, 0.936 for
             passive  system, and 1 for
             capped or no system)
 h    =   height of indoor volume (m)
 Apv  _   ventilation-driving
          indoor-outdoor pressure differ-
          ence (Pa)
 y    =   house age (years)
 8    =   1 for hollow-block stem walls
          and 0  for poured  monolithic
          stem walls
 AP  =   indoor-outdoor pressure differ-
          ence (Pa)
 S   =   sub-slab soil  water content
          (fraction of saturation)
 W   =   concrete slab water/cement
          ratio
 xcik  =   location  of  dominant crack
          from perimeter of house (m)
 xh   -   house minor dimension (width)
          (m) = rh->/7i.

  The factor C^, fsStf, and h  directly multi-
ply the net indoor radon concentration pre-
dicted by the lumped-parameter model.
The  ventilation-driving  indoor pressure,
APV, also directly affects the indoor radon
level with the nominal  age  dependence.
The remaining terms account for particu-
lar mechanisms or variations in indoor ra-
don entry. The first term in the brackets is
a product of crack area fraction (2x10'3 +
2.9 x 10'38) and radon entry velocity. The
1/70 term approximates diffusive  entry
through  the crack and the  APexp(-3-
0.045e6S) term approximates advective
entry through the crack. The second ma-
jor term  in the brackets accounts for ra-
don diffusion through the slab and depends
on the water/cement ratio of the concrete.
The third term in the brackets slightly in-
creases  the  effect of  radon diffusion
through  the slab due to slab crack  loca-
tion, and the last term  in brackets slightly
 increases the diffusive entry through the
 slab for  small structures.
   For the reference house conditions used
 previously (AP = -2.4Pa), the lumped-pa-
 rameter model estimates that slightly over
 half of the" radon  entry'Dccurs by advec-
 tion through floor cracks and openings for
 a monolithic slab house, and about two-
 thirds occurs by  advection  through the
 openings for a slab-in-stem wall (SSW)
 house. To estimate absolute indoor  radon
 concentrations, the sub-slab radon con-
 centration can  be represented by  mea-
 sured values or calculated from surrogates
 such as radon flux or  soil-gas radon con-
 centrations.

 Model Validation
    Calculated indoor/sub-slab radon ratios
 (Cno,/Csub)  from the  lumped-parameter
 model were compared with measured data
 from the FRRP test cells, with reference
 data used to generate soil radon potential

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maps, and with measured data from FRRP
demonstration and evaluation houses. The
test-cell data were compared for each of
eight sets  of conditions,  involving both
floating-slab and SSW construction, and
indoor  pressures from passive to -50  Pa.
The ratios of calculated/measured C^/C^
ratios varied by about 40-50%, but aver-
aged 0.97  for the floating-slab cell and
0.83 for the SSW cell.
  Comparisons of  calculated C^/C^ ra-
tios with soil radon potentials calculated
for maps for Alachua County, Florida, had
an overall  relative standard deviation of
30%, with most of the differences occur-
ring with the dry,  sandy-soil profiles. In
general, the comparison showed a posi-
tive bias for the lumped-parameter model
that was associated with  inherent differ-
ences  between the  lumped-parameter
model  and the radon mapping algorithm.
Since neither explicitly defines fill soil  lay-
ers or detailed crack properties, these are
represented implicitly, as required for the
different purposes of characterizing  soil
radon  potentials for mapping and house
radon  resistance for the  lumped-param-
eter model.
  For  comparisons of calculated C^/C^
ratios with  FRRP house data, information
was compiled from 20 houses studied by
Geomet Technologies, Inc., 13 houses
studied by Florida Solar  Energy Center,
and 30 houses studied by Southern  Re-
search Institute. The houses varied from
new to 36 years old, were almost entirely
slab-on-grade, and included a nearly equal
mix of  SSW and monolithic slab-wall con-
struction. Many had SSV systems installed,
including both suction-pit and ventilation-
mat designs.
  Net  indoor radon data  were obtained
by subtracting outdoor radon concentra-
tions from  measured indoor values. The
outdoor concentrations were  estimated
from a set of theoretical,  1-dimensional
diffusion-dispersion calculations to  de-
velop  a correlation based on sub-slab
radon  levels  and  soil properties. The
 theoretical calculations used a reference
 set of atmospheric dispersion data and
 boundary conditions  for normal  turbu-
 lence conditions, and led to the correla-
 tions  Cout « 0^(9x10'5-8.7x10-5S). This
 relationship corresponds  to about 0.1
 pCi L1  outdoors for  a sub-slab radon
 concentration  of 2,000 pCi  L1 in sandy
 soil.
   Measured C^C^ ratios for both SSW
 and monolithic slab houses were highest
 for  houses with no  SSV  system, were
 slightly  lower for  houses with  a  passive
 SSV system, and were significantly lower
 for  houses with  active  SSV systems.
 Houses with capped  SSV systems were
 erratic,  being  higher than those without
 SSV systems for SSW houses and lower
 than those without SSV systems for mono-
 lithic slab houses. Calculated CM/Csub ra-
 tios, using best-estimate input parameters,
 were lower than measured ratios for all of
 the SSW and monolithic slab houses by a
 factor that averaged  0.5+0.3 among the
 SSV categories. The only  exception was
 the capped-SSV case for monolithic-slab
 houses, where a 3-fold higher calculated
 value raised the average ratio to 1.1+1.2
 for the SSV categories if it is included.
   Alternative estimates of floor crack and
 opening areas were  explored as  a pos-
 sible  explanation  of the higher observed
 indoor radon concentrations. Estimates of
 the areas required to give  agreement be-
 tween the lumped-parameter model and
 the measured  data were excessive. Alter-
 native estimates of concrete water/cement
 ratios to explain the  differences  may be
, plausible, however. Average water/cement
 ratios of 0.64  to 0.70 were  estimated  to
 explain the respective passive-SSV and
 active-SSV data for both SSW and mono-
 lithic  houses.  For  no-SSV houses, how-
 ever,  higher water/cement ratios of 0.77
 were  required. Another explanation of the
 discrepancy may be the void  volume  of
 the SSV systems, in  which  the sub-slab
 radon concentrations typically were mea-
 sured. These sub-slab volumes may have
 lower concentrations  than the soil pore
volumes in contact with most of the slab,
therefore giving  a high estimate for the
measured C^/C.^, ratio.
Conclusions  and
Recommendations
  The lumped-parameter model combines
theoretical and empirical trends to form a
simple expression to estimate indoor ra-
don  concentrations for  Florida slab-on-
grade houses. The expression retains the
fundamental,  parametric dependencies of
the more detailed models and data sets. It
agrees with FRRP  radon test cell data
within averages of 3-17%, and with indoor
radon data from  over 60 houses within
about  a factor  of two  (houses being
higher). Its agreement with  radon  map-
ping calculations is within about 30%, ow-
ing to fundamental differences in the
purposes of the two algorithms being com-
pared.
  The present analyses suggest several
parameters to be included in future new
house evaluation projects. These include
outdoor radon concentrations (for obtain-
ing net indoor levels), concrete slab diffu-
sion  properties (water/cement ratio,
diffusion coefficient, or density), and sur-
face soil radon fluxes (as possible surro-
gates for sub-slab radon on undeveloped
land). The analyses also suggest poten-
tial improvements in the lumped-param-
eter model.  These include improved,
alternative definitions of floor crack and
opening areas and their  associated per-
meability,  an  improved correlation for pre-
dicting   concrete  diffusivity,   and
representation of sub-slab void volumes
associated with SSV systems for their ef-
fects on sub-slab radon measurements.
Even without these changes, however, the
lumped-parameter model is useful for pre-
dicting indoor radon concentrations from
a minimum of readily obtainable param-
eters. It also  is useful for interpreting and
coordinating  data from  the  FRRP  New
House Evaluation Project and for provid-
ing additional focus for that project.

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   K. Nielson, V.C. Rogers, and R. Holt are with Rogers and Associates Engineering
     Corp., Salt Lake City, UT 84110-0330.
   David C. Sanchez is the EPA Project Officer (see below).
   Tha complete report, entitled "Development of a Lumped-Parameter Model of
     Indoor Radon Concentrations," (Order No. PB95-142048; Cost: $27.00, 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, NC 27711
United States
Environmental Protection Agency
Center for Environmental Research Information
Cincinnati, OH 45268

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EPA/600/SR-94/201

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