RADON EMANATION AND TRANSPORT I N POROUS MEDIA

by: Venn C. Rogers and K i rk K. Nielson Rogers and Associates Engineering Corp. P.O. Box 330, Sal t Lake City, UT 84110-0330

ABSTRACT

A un i f i ed model o f radon emanation and transport has been devel oped that combines the RAECOM model f o r di f fusive transport w i th new mathematical models o f advecti ve transport, moisture effects, and radon emanation. The model accounts f o r advective deplet ion i n radon source regions, and f o r t h e ef fects o f varying moistures on radon emanation, d i f fus ion, and advecti ve transport rates. Radon transport i n gas- and wa te r - f i l l ed pore space i s characterized, and exchange between the phases i s considered. Correlations are a1 so given for diffusion and permea b i l i t y coeff icients. The model provides a comprehensive assessment o f source potent i a1 s f o r indoor radon accumul at ion based on s o i l moistures, radium, emanation, and advection of s o i l gas.

INTRODUCTION

Radon emanation and transport i n soi 1 s i s i 11 ust rated schemat i c a l l y i n Figure 1. Radon i s emanated from radium-bearing minerals i n t o the s o i l pore space, followed by d i f f u s i v e and advective transport o f the radon gas i n both l i q u i d and gas phases i n t o a home, entering v i a cracks, sumps, porous bui ld ing materi a1 s, water, and other routes. Advection becomes dominant w i th proximity t o many home entry points, and exchange between a1 r and water phases i s cont i nual .

I

Rogers and Associates Engineering Corporation (RAE) i s performing a pro ject f o r the Department o f Energy t o coordinate the eight key components o f radon emanation and t ranspor t shown i n Figure 1 i n t o a uni f ied, simp1 i f i e d model.

where

D a

"w

c a

c w

x R

P

P

m

Eai r

^water

Kd

Twa

Taw

The i n the negat i ve

radon d i f f u s i o n coe f f i c i en t i n a i r , inc lud ing the to r tuos i ty factor

radon

radon

radon

radon

d i f f u s i o n coef f i c ien t i n water

concentration i n the a i r - f i l l e d pore space

concent r a t i on 1 n the water-f i l 1 ed pore space

decay constant

radium concentration I n the s o l i d matr ix

bul k dry densi ty

t o t a l poros i ty

f rac t i on o f moisture saturat ion

component of emanation coef f i c ien t t h a t i s a d i r e c t pore a i r source o f radon

Component o f emanation coef f i c ien t t h a t i s a d i r e c t pore water source o f radon

equi l i brium d i s t r i b u t i o n coe f f i c i en t f o r radium i n sol id-to-pore-1 i q u i d

t rans fer fac to r o f radon from pore 1 i q u i d t o pore a i r

t rans fer f ac to r o f radon from pore a i r t o pore l i q u i d

second term i n the brackets wi th Eai r accounts f o r radon production water from radium dissolved i n the water. The expression has a

s ign preceding i t because measurements o f R include the radium dissolved i n pore water.

- Twa - - Taw 1-m

and

It f o l 1 ows , f o r negl i g i bl e radon decay i n t h e pore 1 i q u i d ,

and Ewater components of t h e emanation c o e f f i c i e n t are shown i n &?\r and are given by

Ewater = Ew f o r m < m* m*

= EW f o r m > m*

Fair = Ea (1 - m/m*) f o r m < m*

= 0 f o r m - > m*

where, m*, Ea and Ew are constants of t he emanation c o e f f i c i e n t model (2). The term Ea i s the emanation c o e f f i c i e n t f o r no moisture, Eu i s t he emanation coef f ic ient a t saturat ion, and t he plateau i n t he E curve s t a r t s a t m*.

Combining Equations (1) and ( 2 ) , using Equations (3) and (4) and inc lud ing advection i n t h e gas phase, y i e l d s :

where

D

K '

K

u

P

E ' k

For

= pore average d i f f u s i o n c o e f f i c i e n t

= K ( 1 - m ) ~ ~

= pore gas permea b i l i t y

= pore gas v i s c o c i t y

= pore gas pressure

= [E - m(1-P)/Kd P] / ( 1 - m + ink) ( 9

r a d o n e q u i l i b r i u m d i s t r i b u t i o n c o e f f i c i e n t , water-to-air.

no advection, Equation ( 7 ) i s equal t o t h e standard radon d i f f u s i o n equation, using the pore average D a n d a n adjusted emanation c o e f f i c i e n t t h a t decoupl es Equations (1) and (2). Consequently, standard measurements (7,8) and theore t i ca l models (1,2) of D and E can be used w i t h t h e new formulat ion, and previous ana ly t i ca l and numerical radon d i f f u s i o n sol u t i ons are ap l i cab le . The computer code RAECOM (5.6) has been adapted t o solve Equation (7) inc lud ing advection, where t he l a y e r thicknesses are selected f o r constant

(dP/dx) . The devel opment i s readi 1 y extended t o mu1 t i -dimensional and time-dependent formalisms.

DIFFUSION, PERMEABILITY, AND EMANATION COEFFICIENTS

Site-speci f ic measurements of D and K are most desirable f o r obtaining input data f o r t he radon transport models. RAE has accumulated an extensive s o i l data base inc luding D and K measured values as wel l as values o f many other nuclear, physical , and geological parameters. I n addit ion, model s have been developed t o cal cul a te D and K from basic data and f i r s t pr inciples. The random-pore combi nat ion model t h a t was devel oped ear l i e r (2.3) was modif ied and extended t o a1 so include the ca lcu lat ion o f s o i l permeabil i t i e s i n a s imi l ar manner.

I n the K calculations, s o i l s were modeled t o contain log-normal s ize d i s t r i butions o f cyl i ndr i cal pores w i th uniform surface water f i l m s t h a t could vary from dryness t o saturation. Contiguous pore space contained a l l possi bl e random combinations o f the pore sizes, both i n ser ies and pa ra l l e l configurations. Ind iv idual cy l i nd r i ca l pore permeabi l i t ies were computed from the r a d i i ( r ) o f the a i r - f i l l e d pore spaces as r2/8, fo l lowing the funct ional s i ze-dependence used by Youngqui s t (10). The resu l t ing permeabil i t i e s o f indiv idual pore segments were combined f o r the en t i re s o i l i n the same way as pore d i f f us ion coef f i c ien ts were previously combined t o estimate bulk s o i l radon d i f f us ion coeff ic ients. The resu l t ing permea b i l i t y cal cul a t i ons are i l l u s t r a t e d by the black dots i n Figure 4. Gas permeabi l i t ies var ied slowly wi th moisture, increased rap id ly w i th the geometric standard deviat ion o f t he grain-size d is t r ibu t ion , and increased as the square o f the average p a r t i c l e * "leter.

I n addit ion t o f i e l d measurement, 1 aboratory measurements o r compl ex model calculations of D and K, empirical corre lat ions have a1 so been used. These correlat ions have the advantage o f being simple and easy t o use, w i t h a minimum amount o f information needed. One cor re la t ion frequent ly used f o r D i s (5)

Since tha t corre lat ion was developed, RAE has measured over 1500 addit ional D measurements f o r the Department of Energy's Urani um M i l 1 T a i l i ngs Remedi a1 Action Program. Most o f these 0 ' s were measured a t high compactions. Consequently, Equation (10) has been modified as fol lows t o inc lude the effects o f high compactions:

where

d = geometric mean p a r t i c l e diameter (urn).

A port ion o f the 0 values i n the data base are p lo t ted i n Figure 5, along with correl a t ion curves for a 1 ow compaction, 1 arge-grai ned materi a1 and a high-compaction, small -grained materi a1 . The h i gher compact f on reduces the value o f D a t 1 ow mof stures.

A s imi l ar correl a t ion has been devel oped f o r s o i l , permeabil f t ies . It f s

where

d' = geometric mean p a r t i c l e diameter (cm) = 0.0001d.

Equation (12) applies t o s o i l s whose p a r t i c l e d i s t r i b u t i o n can be approximated by a 1 og-normal d i s t r i but i on w i th a geometric standard deviation. S, of ten.

For other val ues o f S, Equation (12) must be mu1 t i p 1 ied by

The corre lat ion values for K are a1 so p lo t ted i n Figure 4 f o r several values o f dl. Curves are given for an S of ten and o f f ive.

Possi bl e ani sot ropy o f radon d i f f u s i on coef f ic ients o f s o i l s was examined by conducting 1 aboratory d i f f us ion measurements on s o i l s f n both the d i rec t ion of the compactive force and perpendicular t o the compactive force. Six d i f f e ren t s o i l s were prepared by compacting t o 95 percent o f standard Proctor density, and then pressing a 10-cm diameter thin-walled d i f f us ion tube i n t o the s o i l e i ther para l le l o r perpendicular t o the d i rec t ion o f compaction. Eighteen time-dependent radon d i f f us ion measurements (7) on the resul t i n g s o i l cyl i nders gave an average d i ff usion coef f i c f ent r a t i o (perpendi cul ar/para'H e l ) o f 1.2 + 0.3, ind icat ing only a marginal increase i n d i f f u s i o n along the bedding plane. This could s t i l l be greater i n some undisturbed so i l s , but i s probably ins ign i f i can t i n re-compacted s o i l s i n construction excavations.

Over 50 s imi la r laboratory air-permeabil i ty measurements were conducted on f i ve of the same s o i l samples. The average r a t i o o f air-permeabil i t i e s (perpendi cul ar/paral l e l t o compaction) was 6 + 6, ind ica t ing a somewhat more s i gni f i cant increase i n permea bi 1 i ty a1 ong thebeddi ng p l ane. Thi s r a t i o a1 so may be greater i n undisturbed soi ls , but may be important even i n some re-compacted soi 1 s .

Emanation coef f i cients have been measured f o r several d i f f e ren t s o i l types, because the RAE data base for E consisted mainly o f values f o r uranium ores, uranium m i l l t a i l i n g s , and phosphogypsum. The new E values were measured on s o i l s documented i n the data base t o f a c i l i t a t e fu r the r development o f the emanation coe f f i c i en t model (1). The new values are shown i n Figure 6. The fit t o a r e l a t i v e l y narrow normal d i s t r i b u t i o n i s encouraging, especi a1 l y considering the widely diverse s o i l s used for the measurements. These data ind icate t h a t a best-estimate defaul t value o f E f o r normal s o i l s i s 0.22, i f s i te -spec i f i c data are not available.

SUMMARY

A simp1 i f i e d model has been devel oped f o r radon emanation and transport through a two-phase medium i n the pore spaces o f earthen materials. The model expl i c i t e l y considers radon emanation i n t o the water and the a i r pore regions, radon d i f f us ion through the pore water and a i r regions, radon and radium absorption i n the water, radon transfer between the pore water and a i r , and advection i n the a i r region. The one-dimensional steady-state formal ism i s presented and has been encoded i n t o the RAECOM computer code.

The DIFPERM code f o r ca lcu la t ing d i f f us ion and permeabil i ty coef f i c ien ts from basic p r inc ip les i s described and new corre lat ions f o r D and K are presented. It i s a1 so shown tha t horizontal permeabil i t i e s are s l i g h t l y greater than ver t i ca l permeabil i t ies, but the d i f ference i s not as evident i n the D measurements. Several new E measurements have also been made f o r a wide var ie ty o f so i ls . The geometric mean o f the E measurements i s 0.22.

ACKNOWLEDGMENT

This work i s supported by DOE Grant DE-FG02-88ER60664.

REFERENCES

1. Thamer, B.J., and Nielson, K.K., The Ef fects o f Moisture on Radon Emanation. Bureau o f Mines o f Report 184-82, 1982.

2. Niel son, K.K., and Rogers, V.C. A Mathematical Model f o r Radon D i f fus ion i n Earthen Material s. NUREG/CR-2765. U.S. Nucl ear Regul atory Commission, Washington, D.C., 1982.

3. Nielson, K.K., Rogers, V.C., and Gee, G.W. Di f fus ion o f Radon Through Soils: A Pore D is t r i bu t i on Model. Soi l Sci Soc. Am. J. - 48: 482-487, 1984.

Rogers, V.C., and Nielson, K.K. A Complete Descr ip t ion of Radon D i f f us i on i n Earthen Materials. In: Proceedings o f the Symposium on Uranium M i l 1 Ta i l i ngs Management, F^Ft Coi l i ns , Col orado, 1981. pa 247.

Rogers, V.C., e t a1 . Radon Attenuat ion Handbook f o r Uranium M i l l Ta i l i ngs Cover Desi gn. NUREG/CR-3533. U.S. Nucl ear Regul a to ry Commission, Washington, D.C., A p r i l 1984.

Rogers, V.C., e t al . Radon Attenuat ion Effectiveness and Cost Optimization o f Composite Covers f o r Urani um M i l 1 T a i l i ngs. UMTRA-DOE/ALO-165, U.S. Department of Energy, Washington, D.C . , June 1981.

Kal kewarf , P.R., e t a1 . Comparison of Radon D i f f us i on Coef f i c ien ts Measured by Transient-Di f f us i on and Steady State Laboratory Methods. NUREG/CR-2875. U.S. Nuclear Regul a to ry Commi ssion, Washington, L C . , November 1982.

Nielson, K.K., e t a1 . Radon Emanation Character is t ics o f Uranium M i l l Tai l ings. In: Proceedings of t h e F i f t h Symposium on Uranium M i l l Ta i l i ngs Management, F o r t Col l ins, Colorado, 1982. p. 355.

Rogers, V.C., e t a1. The E f fec ts o f Advection on Radon Transport Through Earthen Materi a1 s. NUREG/CR-3409, U.S. Nucl ear Regul a to ry Commi s s i on, Washington, D.C., October 1983.

10. Youngquist, G.R. D i f f u s i o n and Flow o f Gases i n Porous Sol ids. In: F l ow Through Porous Media, Arneri can Chemical Society, Washington, D.E, 1970. p a 58-69.

SOLID MINERAL GRAINS

NTERGRANULAR PORE SPACE HOME

FIGURE I. Physical mechanisms o f radon generation and transport.

OPEN PORE AREA- . .

AIR

4 UNIT CROSS SECTIONAL AREA

>

FIGURE 2. Volume o f unsaturated porous material radium i s in the solid grains and interstitial water.

MOISTURE SATURATION (m)

FIGURE 3. Components o f the emanation c o e f f i c i e n t as a funct ion o f moisture.

0.1 mm, S=10

-8 - .

0.001 mm, S=10

-1 1 I . . . I . . . I 9 ' .

0.0 0.2 0.4 0.6 0.8 1 .O

MOISTURE SATURATION (m)

Figure 4. Air permeabi 1 i t y for various soi 1 types. Data points are model calculations . Curves are correlation values. Geometric mean par t i c l e diameters, and geometric standard deviations, S , are given for each so i l type.

Crt 4J c w