United States
Environmental Protection
Agency
Air and Energy Engineering
Research Laboratory
Research Triangle Park, NC 27711
Research and Development
EPA/600/SR-94/198 January 1995
&EPA Project Summary
The RAETRAD Model of Radon
Gas Generation, Transport, and
Indoor Entry
Kirk K. Nielson, Vern C. Rogers, Vern Rogers, and Rodger B. Holt
The report describes the theoretical
basis, implementation, and validation
of the RAdon Emanation and TRAnsport
into Dwellings (RAETRAD) model, a
conceptual and mathematical approach
for simulating radon (Z22Rn) gas gen-
eration and transport from soils and
building foundations to the indoor en-
vironment. It has been implemented in
a computer code of the same name to
provide a relatively simple, inexpensive
means of estimating indoor radon en-
try rates and concentrations. RAETRAD
uses the complete, multiphase differ-
ential equations to calculate radon
generation, decay, and transport by
both diffusion and advection (with
pressure-driven air flow). The equa-
tions are implemented in a steady-state,
2-dimensional finite-difference mode
with elliptical-cylindrical geometry for
maximum efficiency and modeling de-
tail.
For validation, the air flow part of
RAETRAD was compared with a 2-di-
mensional analytical calculation of air
flow through a uniform field. Variations
of less than 1% were observed between
the analytical and numerical pressure
fields. The radon generation, decay, and
transport part of RAETRAD was vali-
dated by similar comparisons with 1-di-
mensional analytical calculations for
open and concrete-covered soils. Most
radon concentration profiles and sur-
face radon fluxes for these compari-
sons were also within 1%.
RAETRAD calculations were also
compared with empirical data from two
6 x 6 m research structures with
floating-slab and slab-in-stem-wall con-
struction. The comparisons included
soil radon concentration profiles and
indoor radon concentrations under dif-
ferent air pressure and ventilation con-
ditions. The RAETRAD values were
consistently within less than 1 stan-
dard deviation of the measured data.
Indoor radon concentrations averaged
within 11% of calculated values and
had an average bias of only 3%. Com-
parisons with measurements from other
houses showed greater variations due
to assumptions about house floor slab
integrity and diffuslvity.
This Project Summary was developed
by EPA's Air and Energy Engineering
Research Laboratory, Research Triangle
Park, NC, to announce key findings of
the research project that Is fully docu-
mented in a separate report of the same
title (see Project Report ordering infor-
mation at back).
Introduction
Elevated indoor radon concentrations
usually result from elevated radon gen-
eration and mobility in soils combined with
openings or pores in the building founda-
tion. Although indoor radon levels are dif-
ficult to predict, long-term average levels
can be estimated by mathematical mod-
els, which simulate the complex processes
of radon generation, transport, and indoor
entry using soil and house parameters.
The RAETRAD model was developed
to provide a new level of simplicity in
detailed radon modeling. From
user-specified house and soil proper-
ties, RAETRAD computes detailed
Printed on Recycled Paper
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air-pressure and radon-concentration
profiles in the floor slab, foundation,
and surrounding soils, and the result-
ing radon entry rate and indoor radon
level.
RAETRAD is designed to address ques-
tions such as how strong and how close to
the house can a radon source be for par-
ticular soil and ground water conditions with-
out excessively elevating indoor radon
levels? This information is important for
planning and regulating soil excavation, for
replacement at radium-contaminated sites,
and also in regulating building construction
in areas with high-radium strata or with fill
soils of higher or lower radium concentra- •
tfon.
The RAETRAD model represents
slab-on-grade houses of different sizes and
shapes on soils with any distribution of
radon source strengths, physical proper-
ties, water contents, and gas transport prop-
erties. K was developed in part under the
Florida Radon Research Program (FRRP),
which has been cosponsored by the Florida
Department of Community Affairs and the
U.S. Environmental Protection Agency. It
has been used in the FRRP to characterize
the effects of foundation soil and fill proper-
ties on indoor radon entry, to characterize
the modes of radon entry, to characterize
soil radon potentials for mapping of their
geographic distributions, to develop simpli-
fied lumped-parameter models, and to sup-
port development of radon-protective
building construction standards.
Theoretical .Basis
RAETRAD computes radon production
from radium decay in floor slabs, founda-
tion structures, and surrounding soils. It
also computes the detailed radon interac-
tions in the solid, liquid, and gas phases
of the soils and concretes, and radon gas
transport and indoor entry by both diffu-
sion (concentration-driven) and advection
(with pressure-driven air flow). The theo-
retical equations used for defining radon
generation and transport in the foundation
and soil regions consider the effects of
moisture and the simultaneous effects of
diffusive and advective radon movement.
Steady-state radon entry rates and in-
door radon concentrations are computed
in a two-step process that involves first
solving the air-pressure and airflow distri-
butions in the soil and foundation regions,
and then solving the corresponding radon
concentration profiles, considering the lo-
calized radon generation rates, decay
rates, and transport rates by diffusion and
advection. The air pressure distributions
under and near the house are solved with
LaPlace's equation applied to discrete re-
gions to represent specified floor, footing,
and soil materials. The resulting localized
airflow velocities are used in the corre-
sponding radon calculations in computing
simultaneous diffusive and advective ra-
don transport. The equations are solved
numerically in elliptical-cylindrical geom-
etry to represent houses of different sizes
and with varying rectangular aspect
(length/width) ratios. Radon entry rates
into a house are computed by integrating
the total radon transport across the floor
surface area. Indoor radon concentrations
also are estimated from the computed en-
try rates by dividing by the house volume
and its air ventilation rate.
Implementation
The differential equations describing air
flow and radon generation and transport
are solved numerically by finite-difference
techniques. The house floor slab, foot-
ings, and soil layers are divided into nu-
merous, user-defined mesh units for these
analyses. Several analytical functions in
RAETRAD enhance its computational effi-
ciency and simplify its user interface. The
numerical calculations of air flow and radon
transport through floor cracks are acceler-
ated by use of analytical functions to esti-
mate the mesh-equivalent permeabilities
and radon diffusion coefficients for the speci-
fied cracks, rather than using finely-graded
numerical meshes to represent them. Ana-
lytical functions are also used to define
soil radon diffusion coefficients and air
permeabilities when measured values are
unavailable. These use soil porosities,
water contents, and textures to define the
radon transport properties from empirical
correlations with measured data. In addi-
tion to modeling symmetric cracks in the
floor slab, RAETRAD also accommodates
asymmetric openings such as utility pen-
etrations that do not match the elliptical
symmetry computed for the equivalent rect-
angular house shape. These are repre-
sented by multiple numerical calculations
that determine transverse leakage terms
for the discrete-point floor openings.
The numerical-analytical calculations are
performed by computing all finite-difference
coefficients for each model mesh unit and
solving the equations simultaneously by a
non-iterative matrix inversion technique.
The resulting computer code is relatively
small and efficient and operates in a Win-
dows® environment on an IBM®-compatible
personal computer. Typical execution times
are on the order of 1-2 minutes or longer,
depending on the complexity of the prob-
lem being solved and the speed of the
computer. A user interface provides que-
ries for definition of an input file and se-
lection of appropriate input parameters.
House parameters include area, volume,
shape, ventilation rate, indoor air pres-
sure, foundation depth, floor slab open-
ings, and concrete properties. Soil
parameters include layer thicknesses and
localized values of soil density, moisture,
radium concentration, and radon emana-
tion coefficient. Certain properties, such
as radon diffusion coefficient and air per-
meability, can be left unspecified for use
of default values estimated within the com-
puter code.
Comparisons with Analytical
Data
The RAETRAD code was validated and
benchmarked by several comparisons with
analytical calculations and with empirical
radon data. The analytical validations in-
cluded comparison with a 2-dimensional
air pressure field calculated for a simple
uniform 15 x 31 ft (4.6 x 9.4 m) soil space
with two different pressures applied at its
top surface. Relative standard deviations
of less than 1% were obtained between
the RAETRAD calculations and the ana-
lytical pressure field at the 1-, 2-, 4-, 8-,
and 15-ft (0.3-, 0.6-, 1.2-, 2.4-, and 4.6-m)
depths below the pressure boundary.
Analytical validations with 1 -dimensional
radon generation and diffusion from an
open soil and a concrete-covered soil sug-
gested the utility of defining a small (0.1-ft
or 0.3-m) mesh unit at the top of the soil
profile to minimize the effects of mesh
spacing. In these comparisons, both soil
radon profiles and surface radon fluxes
agreed consistently within less than 1%.
Additional 1-dimensional validations in-
cluded a uniform soil with radon genera-
tion, diffusion, and advective transport. In
this case, the air flow velocities were forced
by an external definition of a uniform pres-
sure gradient, since RAETRAD is designed
to compute drily realistic, 2-dimensional
pressure profiles. Again, agreement was
within less than 1% for all cases of air
flowing into the soil profile. When air was
drawn from the profile, a depletion of the
profile was observed that caused a maxi-
mum error of 4% for the case that was
analyzed. This error was reduced by con-
sidering a thicker soil profile and was ex-
aggerated if a thin soil layer was
considered.
Comparisons with Empirical
Data
Comparisons of RAETRAD calculations
with empirical radon measurements uti-
lized two test-cell structures (6 x 6 m)
constructed in South-Central Florida and
monitored primarily by Southern Research
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Institute (SRI). One of these structures
(test cell 1) utilized floating-slab floor con-
struction with concrete-block stem walls
over a concrete footing. The other struc-
ture had similar footings and stem walls,
but its floor slab was poured to extend
into a course of chair blocks at the top of
the stem wall. Both cells had identical
wood-frame superstructures, without win-
dows, that were sealed with 2-3 cm of
polyurethane foam to minimize air infiltra-
tion. Soil densities, radium concentrations,
radon emanation coefficients, and mois-
tures were measured in this project from
numerous cores collected around and un-
der the test cells. SRI provided measured
soil radon and air permeabilities, and in-
door pressures, air ventilation, and radon
concentrations.
Field soil sampling at the test cell site
extended only to 4-7 ft (1.2-2.1 m) depths
for most cores; hence deeper soil regions
were extrapolated from existing moisture
and radium data. Calculated radon con-
centration profiles were within 4.4% of the
means of measured values under test cell
1, compared to a 34% root-mean-square
uncertainty among the measured values.
Calculated radon profiles were within 18%
of the means of measured values under
test cell 2, compared to a 42%
root-mean-square uncertainty among the
measured values. Measured soil air
permeabilities differed from values calcu-
lated from soil density, moisture, and tex-
ture by 42% based on composite averages
at four depths. Excluding a heterogeneous,
low-permeability layer under part of the
site, the agreement was improved to 24%
relative standard deviation.
Indoor radon in the test cells was ana-
lyzed by RAETRAD to compare with mea-
surements before and after drilling a center
hole in each of their slabs. For the initial
slab conditions, RAETRAD computed 97
pCi L'1 in test cell 1, only 2% above the
mean of the measured values, 95 ± 44
pCi L'. The radon computed by RAETRAD
for test cell 2 was 20 pCi L1, which was
10% below the mean of the measured
values, 22 ± 7 pCi L1. With a 10-cm
center hole in each slab, test ceil 1 was
computed to have an indoor radon con-
centration of 212 pCi L'1, which was 17%
below the mean of the measured values,
255 ± 78 pCi L1. Test cell 2 with a'center
hole had a computed radon concentration
of 87 pCi L1, which was 18% above the
mean of the measured values, 74 ± 33
pCi L1. Computed air pressure and radon
concentration profiles under test cell 1 had
relative standard deviations from measured
values of 11 and 12%, respectively, which
were smaller than the standard deviations
among the replicate measurements. Com-
puted air pressure and radon concentra-
tion profiles under test cell 2 had relative
standard deviations from measured val-
ues of 25 and 20%, respectively, which
also were smaller than the standard de-
viations among the replicate measure-
ments.
Additional comparisons of RAETRAD
calculations with radon measurements
in the test cells were performed with
test cell 2 at indoor pressures of -10
and -20 Pa instead of its pas-
sive-condition pressure of -0.6 Pa. For
the -10 Pa condition, test cell 2 was
computed to have an indoor radon con-
centration of 51.5 pCi L1, which was 3%
higher than the measured 50 pCi L1
value. For the -20 Pa condition, an in-
door radon concentration of 42.9 pCi L1
was computed by RAETRAD, 14% lower
than the measured value of 50 pCi L''.
Collectively, the six model comparisons
with indoor radon measurements in the
test cells had an average difference of
11%, with an average bias of -3%.
Comparisons of RAETRAD calculations
with indoor radon measurements in 50
FRRP demonstration houses exhibited
much larger variations (geometric stan-
dard deviations of 2.8) and a bias of a
factor of 0.56 below the measured values.
This was attributed to the much less de-
tailed characterization of the houses, pri-
marily with respect to the concrete slab
integrity and diffusivity. Significant unob-
served holes or cracks (>50 cm2) near
utility penetrations or by walls, bathtubs,
or other features could cause this much
bias, as could a 3-fold higher radon diffu-
sion coefficient than was used for the floor
(0.001 cm2 s'1). Observations and mea-
surements support either of these possi-
bilities.
Conclusions
RAETRAD provides a relatively simple,
2-dimensional numerical-analytical simu-
lation of steady-state radon generation and
movement into rectangular-equivalent
slab-on-grade houses. It combines detailed
airflow and radon source, transport, and
decay calculations to accurately assess
the effects of soil moisture, radon source
distribution, and other soil and house vari-
ables of interest. Validations with
special-case analytical calculations dem-
onstrated accuracy to within approximately
1 %. Comparisons with empirical data from
FRRP test-cell structures demonstrated
accuracy that was well within the uncer-
tainty of the empirical measurements. Ap-
plication to other houses was limited by
assumptions about their floor slab integ-
rity and diffusivity.
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KirkK. Me/son, Vern C. Rogers, Vern Rogers, and Rodger B. Holt are with Rogers
and Associates Engineering Corp., Salt Lake City, UT 84110-0330.
David C. Sanchez is the EPA Project Officer (see below).
The complete report, entitled "The RAETRAD Model of Radon Gas Generation,
Transport, andIndoor Entry," (OrderNo. PB95-1'42030; 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
Official Business
Penally for Private Use
$300
EPA/600/SR-94/198
BULK RATE
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EPA
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