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 ------- 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 ------- 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. ------- 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 Official Business Penalty for Private Use $300 BULK RATE POSTAGE & FEES PAID EPA PERMIT No. G-35 EPA/600/SR-94/201 ------- |