Journal of Hydrology, 111 (1989) 133--143 133 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Nether lands

[2]

D I F F U S I O N A N D C O N S U M P T I O N OF M E T H A N E IN AN U N S A T U R A T E D ZONE IN NORTH-CENTRAL ILLINOIS, U.S .A.

ROBERT G. STRIEGL and AUDREY L. ISHII

U.S. Geological Survey, P.O. Box 25046, Mail Stop 413, Denver, CO 80225 U.S. Geological Survey, 102 E. Main St., Urbana, IL 61801 (U.S.A)

(Received October 24, 1988; accepted after revision February 20, 1989)

'U.S.A.)

ABSTRACT

Striegl, R.G. and Ishii, A.L., 1989. Diffusion and consumption of methane m an unsatura ted zone in north-central Illinois, U.S.A.J . Hydrol., 111: 133-143.

The distr ibut ion of CH 4 in unsa tura ted glacial and eolian deposits adjacent to buried low-level radioactive waste was measured, and movement of the gas from the waste source was simulated using a two-dimensional finite-difference model for gas diffusion in the unsa tura ted zone. Mean PCH 4 was greatest (1.56 Pa) in a pebbly-sand deposit 11.6 m below the land surface and 12 m from the waste, and generally decreased with increased horizontal distance from the waste. Mean PCH 4 was least (0.07 Pa) at depth of 1.8 m below land surface, regardless of distance from the waste. PCH 4 at the land surface averaged 0.17 Pa. Depth versus PCH 4 profiles suggest consumption of both waste-produced and atmospheric CH 4 in the upper unsatura ted zone, presumably by methanotroph- ic microorganisms. Numerical simulations of methane movement support the consumption obser- vation; inclusion of a term in the model for consumption of CH 4 in the upper 2 m of the unsatura ted zone resulted in simulated PCH 4 within 30% of mean PCH 4 at eleven of th i r teen sampling locations. A similar fit of the data was obtained for only four locations when consumption was not considered.

INTRODUCTION

Recent increases in the CH4 composition of the atmosphere have evoked extensive characterization of global CH4 sources and sinks (Khalil and Rasmussen, 1983; Blake and Rowland, 1986, 1988; Matthews and Fung, 1987; Mooney et al., 1987). A related area of importance is determination of how existing CH4 sinks may accomodate future CH4 increases. Microbial consump- tion of CH4 in soils was first recognized near sources of large CH4 concentra- tions (Adamse et al., 1972; Mancinelli et al., 1981). More recently, consumption of atmospheric or subatmospheric concentrations of CH4 has been observed in a v a r i e t y o f u n s a t u r a t e d s o i l s a n d c l i m a t e s ( H a r r i s s e t a l . , 1982; K e l l e r e t a l . ,

1988). H o w e v e r , t h e t a x o n o m y , t h e d e p t h d i s t r i b u t i o n , a n d t h e c o n s u m p t i v e

c a p a c i t i e s o f t h e r e s p o n s i b l e m e t h a n o t r o p h s h a v e n o t b e e n f u l l y c h a r a c t e r i z e d

( C o n r a d , 1984).

I n t h i s p a p e r w e d e s c r i b e t h e p a r t i a l - p r e s s u r e d i s t r i b u t i o n o f CH4 i n t h e

0022-1694/89/$03.50 © 1989 Elsevier Science Publishers B.V.

I 34

unsa tu ra t ed zone near buried low-level rad ioac t ive waste, define t ranspori proper t ies for CH4 in unsa tu r a t ed glacial and eol ian deposits, and present resul ts of numer ica l s imula t ions for C H 4 diffusion in a ver t ica l plane perpm> dicular to the end wall of a waste-disposal t rench. In the upper unsa tu ra t ed zone, m e t h a n o t r o p h s apparen t ly consume both waste-produced and atmospher- ic CH4; match of s imulated or PCH~ and field-measured PCH~ is a t la ined by inclusion of a first-order CH~-consumption term in the t ranspor t mode i

F1ELI] STUDY

Decomposi t ion of o rgan ic waste buried at the low-level radioact ive-waste disposal site (4l°20'N: 89°47"W) near Sheffield, Bureau County, in nor th-centra i Illinois produces CH~ tha t diffuses t h rough su r round ing unsa tu ra t ed glacial and eol ian deposits. In o rder to col lect gases from the deposits, th ree boreholus were augered to wea thered bedrock in a ver t ica l plane pe rpend icu la r to the end wall of a waste-disposal t rench, at d is tances of 12, 29, and 46m from the end wall. At the s tudy sect ion, wea thered shale is over la in by a pebbly outwash sand, which is over la in by glacial till and eol ian silt (Fig. 1). A modern soil ha.,, developed on the eol ian silt. The wa te r table is located in the wea thered shale near its con tac t with the outwash sand. Four or five gas-sampling tubes were nested in each borehole at depths of 1.g 13.6m below the land surface (Fig. I~. Boreholes were cons t ruc ted m a layered fashion; screened sect ions of g a s sampling tubes were su r rounded by washed sil ica sand, which was over la in m sequence by bentoni te , concre te grout, and sifted paren t mater ia l . The ben ton i te served to absorb excess wa te r from the grout , and the grout blocked pneumat ic communica t ion a long the borehole between layers. Gas-sampling

M[- I [ R!-I

24D

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"~ ~' ~- . . . . . . . ° " ° , , " ~GLACIAL TILL . , 'o . . . . . . . ~, , , , , ° , , " "

, . .-. . . . . . ;-. . . . : .~. t :.. :.;.... :.%.'2 ~.:;:. :..-. we..: .... '. ".':.'.'..::..: ~o :.:'e:-:.. ".':..'.'::: ~;:-'.'::; ";:.'.'. i~ .;: ~, ~_ _ ~ "-.- ~ " . . . . • "° " . "* e . ' . " " ; , . j . , "." . ' . ' . ' : : ". , : : : ": . . . . . . . . , . , . , t . . . . . . . . ; ".'" • V ' - * . ' . ' . : % " : . ' . " . " ' , ' , l , ' : . ; ° ,q lK " ' "

. ~ ~ _ ~ 1 ' ; ' ~ " ~ ; ~ ' : ! : ~ O U T W A S H S A N D :.:".:;.i;:a'.'.:'.".:;:':':°'.'.:":,';:":;'

IL~Z_zz. W L . 9 _ T _ _ H _ u E _ R T E _ D S H z A ~ ! ~ - 7 - 1 < 7 Z-_L---E-Z-~-:L:7--: .--- - - -~ ~-~:.~;~'.~g~°3::.:....~5:g'..~.::}~..:.:?{:.:.'.::'...~.~})}~:W~::~

:, 5 10 MF { f R h l. _ _ . _ _ . L . . . . J

NL] V E R I I C A L E X A G G E R A t i O N O A T U M iS SEA t F V E I

E X P L A N A T I O N

= G A S S A M P [ ff,aG L O < A I II.lr',,

Fig. 1. Lithology of cross section and locations where gas samples were collected

135

T A B L E 1

M e t h a n e par t ia l p r e s su re s in t he u n s a t u r a t e d zone (Pa).

Date Hor izon ta l d i s t ance from t r e n c h end wal l

12 m 29 m 46 m

Eolian silt, 1.8 m below the land surface 03/20-22/84 0.14 06/08/84 0.16 08/14 16/84 0.14 10/25 26/84 < 0.05 02/20-21/85 0.09 06/11 12/85 0.06 08/28/85 09/20/85 < 0.05 01/15/86 < 0.05

0.05 0.09 0.15 0.10

< 0.05 < 0.05

0.06 0.05 0.06

0.08 0.12 0,08

< 0.05 0.06 0.10 0.06

Eolian silt, 3.6 m below the land surface 01/20/84 0.12 03/20 22/84 0.18 06/08/84 0.29 08/14 16/84 0.16 10/25 26/84 0.10 02/21/85 06/11 12/85 0.23 08/2~29/85 < 0.05 09/20/85 0.05 10/30/85 < 0.05 01/15/86 0.36

0.07 0.05 0.06 0.05 0.18 0.05 0.05 0.06 0.05 0.05 0.14

0.07 0.05 0.14 0.18 0.06

0.15 0.05

< 0.05 < 0.05

0.05

Glacial till, 7.3 m below the land surface 03/20-22/84 0.71 0.63 0.25 06/054)8/84 0.64 0.49 0.28 08/14-16/84 0.33 0.43 0.31 10/25-26/84 0.58 0.34 02/20-21/85 0.45 0.56 0.28 06/11-12/85 0.74 0.97 0.36 08/28-29/85 0.35 0.89 0.47 10/30/85 0.32 0.80 0.43 01 / 15/86 0.73 0.68 0.38

Outwash sand, 11.6 m below the land surface 01/19/84 1.54 0.71 0.34 03/20-22/84 0.97 0.67 0.26 06/054)8/84 1.04 0.52 0.29 08/14-16/84 1.38 0.57 0.31 10/25-26/84 1.33 0.67 0.46 02/21/85 1.77 06/11-12/85 2.76 0.98 0.35 08/28~29/85 1.68 0.91 0.47

136

TABLE 1 (continued)

Date Horizontal distance from t rench end wall

12m 2 9 m 46m

10/30/85 1.18 0.82 0.44 01/15/86 0.84 0.65 0.39

Outwash sand, 13. 6 m below the land surface 01/19/84 1.55 03/20/84 1.08 06/08/84 0.99 08/16/84 1.38 10/26/84 1.18 06/12/85 2.76 08/29/85 1.77 10/30/85 1.18 01/15/86 0.84

= no sample; multiple dates indicate boreholes sampled on consecutive days.

tubes were kept closed from the atmosphere throughout the period of study. Gas samples were collected at approximately ten-week intervals during January 1984 to January 1986, and analyzed for volume fractions of N2, 02, Ar, CO2, 14CO2, CH4, C2H6, C3Hs, C4H10, and 222Rn. Detailed discussions of the geology of the study section, field installations, laboratory analytical methods, and concentrations of all gases analyzed for are found in Striegl (1988).

PCH4 is the product of the methane volume fraction and the local barometric pressure, which averaged 98,600 Pa for the period studied. Discrete measure- ments of PCH4 ranged from < 0.05 to 2.76 Pa (Table 1); the mean field-measured PCH4 ranged from 0.07 to 1.45 Pa (Table 2) for the locations sampled. Methane

TABLE 2

Mean of field-measured PCH 4 (Pa) and s tandard deviation of sample (s)

Depth below Horizontal distance from t rench end wall

12m 2 9 m 4 6 m

mean s mean s mean s

1.8 (eolian silt) 0.08 3 6 (eolian silt) 0.17 7.3 (glacial till) 0.53 11.6 (outwash sand) 1.45 13.6 (outwash sand) 1.41

0.06 0.07 0.04 0.07 0.03 0.10 0.07 0.05 0.08 0.06 0.19 0.67 0.18 0.34 0.07 0.55 0.72 0.15 0.37 0.08 0.58

137

was detected in all samples, but analyses were not quantitive for partial pressures < 0.05Pa. Greatest PCH4 was in the outwash sand in which the waste-disposal trench was completed. Less-than-atmospheric PCH4 occurred throughout the eolian silt; the smallest mean PCH4 was 0,07 Pa, in eolian silt, 29m from the trench. The glacial till excepted, mean PCH4 decreased with distance from the trench. The reason for the reversal in the PCH4 gradient in the glacial till (Table 2) is not explained, although it may be caused by possible contamination of one of the sampling locations at the 7.3m depth (Striegl, 1988). The standard deviation of PCH4 samples (Table 2) was greatest in the outwash sand at the location nearest the trench, suggesting a variable CH4 source. This was probably caused by discrete releases of CH4 from waste decomposing in breached waste-disposal containers.

METHANE TRANSPORT IN THE UNSATURATED ZONE

Conceptual CH4 transport model

Trenches were cut into unsaturated glacial and eolian deposits at the Sheffield site. At the trench closest to the study section, low-level radioactive waste was randomly placed in the excavation in an assortment of containers and covered with fill material (Striegl, 1988). Settling and decomposition of waste, and uneven compaction of fill material have created many void spaces in the trench volumes. Because of these void spaces, it is thought that there is good pneumatic communication among trenches, the atmosphere, and the surrounding geological deposits, and that the system as a whole is generally isobaric. Accumulation of water in and on waste containers causes formation of transient, localized anaerobic areas where CH4 is produced by decomposition of organic wastes. The waste-produced CH4 mixes throughout the trench volumes. Because the system is isobaric, CH4 diffuses out of the trenches and into the surrounding unsaturated geologic deposits under its partal-pressure gradient. Diffusion is relatively fast in the outwash sand compared to diffusion in the overlying till and eolian sediments. In the deep unsaturated zone, CH 4 is relatively unreactive; retardation of CH4 transport is caused mainly by the physical structure of the porous medium and by dissolution of CH4 into pore water according to its Henry's law constant. The water table, which is located near the contact of the outwash sand and the weathered shale, acts as a nearly impermeable boundary for CH4 diffusion. In the shallow unsaturated zone, PCHt is maintained at about 0.5 of the atmospheric PCH4. These small methane partial pressures cannot be explained by diffusion or by gas to water partition- ing, and are inferred to be caused by consumption of both waste-produced and atmospheric CH4 by methanotrophs.

Theoretical development and application of the CH4 transport model

The mechanism of primary importance for gas transport in the unsaturated zone is generally considered to be ordinary molecular diffusion (Keen, 1931;

138

Evans, 1965; Weeks et at., 1982). Fundamen ta l theory for o rd inary diffusion accord ing to Fick 's first and second laws is presented in Bird et al. (1960, chapters 16-19); more extens ive theore t ica l discussions of gas diffusion in porous media are found in Cunn ingham and Will iams (1980) and in Mason and Mal inuskas (1983).

T rans i en t one-dimensional diffusion of' gas A into gas B is given by Fick ,~ second law:

5 2 CA ~(-,'~ D~I~ (ix '~ 6t

where: DAB - molecu la r diffusion cons tan t for diffusion of gas A into gas B (m ~ d ~); CA = concen t r a t i on of gas A ( m o l m :~); x = dimension in the direct ion of diffusion (m); and t t ime (d).

For gas diffusion in the unsa tu r a t ed zone, Fick 's second taw (:an be general ized to include physical , chemical , and biological factors t ha t affect fYee molecu la r diffusion (see Weeks et al., 1982); the equa t ion for CH4 diffusion being:

' 6 C n a ~ c : , _ I o , , ( o . r O,,)/K.] T - + /JQ (£} DAB z OD ax e . . . . .

where; z = to r tuos i ty fac tor tor res i s tance to diffusion caused by the porous medium (dimensionless); ®D = dra ined or gas-filled poros i ty (dimensionless): O T = to ta l poros i ty (dimensionless); Ow -- OD water-fil led porosi ty (dimen- sionless); KH Henry ' s law cons tan t (dimensionless); and fl gas-consumption term [T l].

Physical factors t ha t affect diffusion in the unsa tu ra t ed zone include tem- pera ture , pressure, tor tuos i ty , and water- and air-filled porosit ies. The molecu la r diffusion cons tan t for CH4 into free a i r at STP (DaB °) is 1.69 m ~ d (Katz et aI., 1959), which can be cor rec ted to DAB =: 1.74 m ~ d ~ by:

DA, , - DAB° ( T / T ° ) '8~a (W/P) ~;~,)

(Bird et al., 1960, p. 505), where 7' and P are the mean t empera tu re (283 K) and the mean ba romet r i c pressure (98,600 Pa) at the site.

Tor tuos i ty , r. is a fac tor tha t cor rec t s for the increased res i s tance t{} diffusion tha t is caused by the physical s t ruc tu re of the medium, Three empir ical (Wesseling, 1962; Grable and Siemer, 1968; Lai et al., 1976) and three theore t ica l (Marshall , 1959; Mil l ington, 1959; Mil l ington and Quirk, 1960) fo rmula t ions for to r tuos i ty were eva lua ted to de te rmine the fo rmula t ion that best r epresen ted all geologic deposi ts and wa te r - sa tu ra t ion condi t ions at the cross sect ion studied. The Mi l l ing ton (1959) formulat ion:

.: O~ I:~ (-i)

most accu ra t e ly represen ted the cross section. Measured porosi t ies as well as to r tuos i ty using the Mi l l ing ton (1959) fo rmula t ion for the geologic deposits m the cross sect ion are listed in Table 3.

TABLE 3

Porosities and tortuosities of geologic deposits

139

Deposit Total Drained Tortuosity porosity porosity ~ = O~/3 O T O D (Millington, 1959)

Eolian silt 0.43 0.30 0.755 Glacial till 0.32 0.02 0.684 Outwash sand 0.35 0.29 0.705

The concentra t ion of C H 4 (CA; mol m 3 of unsaturated zone gases) can be defined from the ideal gas law as:

CA -- P A / R T (5)

where: PA the partial pressure of gas A (the product of the measured volume fraction and the barometric pressure) (Pa); R gas constant (8.314 Pa m3/K mol); T temperature (mean temperature of the unsaturated zone) (K).

Chemical factors that affect PCH 4 distribution in the unsaturated zone include part i t ioning of the gas among phases, and oxidation. Because all surfaces are covered by at least a few molecular layers of water in the gas - water-solid matrix, CH 4 was assumed to part i t ion primarily to water according • to its Henry's law constant (KH), which is 2.97 × 104 at 283K (Perry et al., 1984). Oxidation of CH4, which was considered to be primarily mediated by microorganisms, was included in the gas-consumption term ft. For regions where consumption of C H 4 does not occur, insertion of the defined terms DA~, ~, OD, OT, CA, KH into eqn. (2) allows for its solution. No values for the CHcconsumption term were available for incorporat ion into the t ransport equation. It was therefore necessary to i teratively arrive at fl by repeated computer simulation until a best match between mean field-measured PCH4 and simulated PCH4 was found.

Numer ica l solution

Movement of CI-I 4 in the unsaturated zone was simulated by finite-difference solution of the two-dimensional equivalent of eqn. (2) using the method of preconditioned conjugate gradients (Ishii et al., 1989). The cross section was represented by a 36 × 53 grid that was subdivided vertically into three layers to delineate outwash sand, glacial till, and eolian silt. Physical characterist ics of each layer were assumed to be isotropic, having the porosities and tortuosi- ties listed in Table 3. The upper boundary of the grid was the land surface, having a constant PCH 4 of the 0.17 Pa. The lower boundary was the water table, which was fixed at the contact between the outwash sand and underlying weathered shale. Because gas diffusion into water is approximately 104 times

140

s lower t h a n in to a i r - f i l led pore spaces , the w a t e r t ab l e was r e g a r d e d as an i m p e r m e a b l e bounda ry . The wes t b o u n d a r y i nc luded the t r e n c h end wall , wh ich was r e g a r d e d as h a v i n g a c o n s t a n t P C H 4. Dr i l l i ng in to the was te to co l l ec t s amples for d e t e r m i n a t i o n of a source P C H 4 was no t pe rmi t t ed . However , the a v e r a g e of two PCH4 m e a s u r e m e n t s f rom the t r e n c h cap ( < 0.5 m above was te ) was 2.6 Pa. F o r mode l ing purposes , a source of 3.0 Pa of CH 4 a t the t r e n c h endwa l l was used. This va lue was se lec ted because : (a) i t was the sma l l e s t PCH4 source v a l u e t h a t r e su l t ed in a fit of the da ta ; (b) m e a s u r e d PCH4 va lues a t the t r e n c h cap were be tween 2 and 4Pa ; and (c) the model was r e l a t i v e l y i n sens i t i ve to P C H 4 sources be tween 3 and 10Pa. A zero-flux b o u n d a r y was l oca t ed 10 m beyond the most d i s t a n t borehole ; t h a t d i s t a n c e was sufficient to p r ec lude a r t i f i c i a l b o u n d a r y effects caused by the n u m e r i c a l s i m u l a t i o n in the cross sect ion. S i m u l a t i o n s were for a pe r iod of 15 years , the a p p r o x i m a t e age of the was t e -d i sposa l t rench .

Results of numerical modeling

The d i s t r i b u t i o n of P C H , in the cross sec t ion was first s i m u l a t e d w i t h o u t fl i nc luded in the model . Resu l t s of t h a t s i m u l a t i o n for the t h i r t e e n l o c a t i o n s sampled a re l i s t ed in the l e f t -hand co lumns of Tab le 4. The s i m u l a t e d PCH~ va lues m a t c h the m e a n f ie ld-measured PCH4 va lues (cen t re co lumns , Tab le 4) poor ly . The m e a n d e v i a t i o n of the s i m u l a t e d P C H 4 va lues from the mean P C H 4 va lue s is 92%; s i m u l a t e d PCH4 va lues are w i th in 30% of the mean P C H 4 va lue s a t on ly four of t h i r t e e n loca t ions .

S a t i s f a c t o r y two- d imens iona l s i m u l a t i o n ( r igh t -hand columns, Table 4) of the f i e ld -measured P C H 4 d i s t r i b u t i o n r equ i r ed the i nc lus ion of a t e rm to a c c o u n t for c o n s u m p t i o n of CH 4 in the uppe r u n s a t u r a t e d zone. Va lues of 0.25 d 1 for fl, and of 2 m for the t h i c k n e s s of the zone of CH4 consumpt ion , were d e t e r m i n e d by r e p e a t e d n u m e r i c a l s i m u l a t i o n of CH, m o v e m e n t un t i l the sma l l e s t v a l u e s t h a t a ch i eved a fit of the f ie ld-measured PCH4 d i s t r i b u t i o n were

TABLE 4

Simulated PCH 4 and mean of field-measured PCH4 at the locations samples (Pa)

Depth below land surface

Horizontal distance from trench end wall

12 m 29 m 47 m

NI 1 X 2 I a NI X I NI X I

1.8 m (eolian silt) 0.29 0.08 0.10 0.19 0.07 0.08 0.18 0.07 0.08 3.6 m (eolian silt) 0.39 0.17 0.19 0.20 0.07 0.09 0.19 0.08 0.08 7.3 m (glacial till) 0.71 0.53 0.53 0.32 0.67 0.21 0.29 0.34 0.19 11.6 m (outwash sand) 1.54 1.45 1.46 0.82 0.72 0.73 0.60 0.37 0.50 13.6 m (outwash sand) 1.36 1.41 1.30

1NI = simulated PCH4, methane consumption not included in the model. 2~ = mean of field-measured PCH4. aI = simulated PCH4, methane consumption included in the model.

141

found. Mean deviation of the simulated PCH 4 values from the mean field-meas- ured PCH4 is 18%; simulated PCH4 values are within 30% of the mean PCH 4 values at eleven of thir teen locations.

CONCLUSIONS

The movement of C H 4 in the unsaturated zone near a buried CH4 source was simulated using a two-dimensional finite-difference solution for ordinary molecular diffusion. Diffusion of C H 4 w a s inhibited by the physical s tructure of the medium and by dissolution of CH 4 into infiltrating water. CH4 consump- tion in the upper unsaturated zone also was observed.

PCH 4 versus depth profiles, and numerical simulations of CH 4 movement, indicate that both waste-produced and atmospheric CH4 were consumed. This suggests that soil methanotrophs not only have the capacity to utilize atmo- spheric methane as a carbon source, they also increase populations opportunis- tically to utilize C H 4 increases from other sources. At a depth of 1.8 m below the land surface, partial pressure of waste-produced and atmospheric CH4 were reduced to about 0.07Pa; essentially no waste-produced CH 4 escaped to the atmosphere at the cross section studied. Although the volumes of C H 4 produced at lowqevel radioactive-waste disposal sites such as the site near Sheffield are small when compared to CH~ production at landfills (Bingemer and Crutzen, 1987), it is evident that methanotrophs in the upper unsaturated zone have the potential for consumption of greater volumes of CH4 than were found at the study section. This is because PCH4 was reduced to the similar values regardless of C H 4 concentrat ions in underlying deposits. Maximum consump- tive capacities of soil methanotrophs need to be defined.

Assuming that values reported for methane consumption in freshwater (Rudd and Hamilton, 1975; Harri ts and Hanson, 1980) were transferable to soils, Conrad (1984) calculated that at least 107 cells per cm 2 of land surface would be necessary to explain the decomposition of CH4 that is observed in soils. Conrad's calculated methanotroph density was qualified by statements that (a) perhaps the freshwater values were not transferable to soils and (b) the depth distribution of methanotrophs in soils is yet unknown. We estimate that C H 4 consumption occurs to a depth of about 2 m at the Sheffield site, much greater than the I cm depth that has been observed for H2 and CO consumption in soils (Liebl and Seiler, 1976). Although the estimated depth of 2 m may partly be caused by a response of methanotrophs to the C H 4 s o u r c e at decomposing waste, it is unlikely that any induced increase in the depth of C H 4 consumption would be in the range of two orders of magnitude. It is apparent that depths of CH4 consumption need to be directly measured before any generalizations about methanotroph densities in unsaturated zones can be made.

REFERENCES

Adamse, A.D., Hoeks, J., DeBont, J.A.M. and Van Kessel, J.F., 1972. Microbial activities in soil near natural gas leaks. Arch. Microbiol., 83:32 51.

Bingemer, H.G. and Crutzen, P.J., 1987. The production of methane from solid wastes. J. Geophys. Res., 92: 2182-2187.

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Bird, R.B., Stewart, W.E. and Lightfoot, E.N., 1960. Transport Phenomena. Wiley, New York, N.Y., 780 pp.

Blake, D.R. and Rowland, F.S., 1988. Continuing worldwide increase in tropospheric methane, 1978 to 1987. Science, 239: 1129-1131.

Blake, D.R. and Rowland, F.S., 1988. Continuing worldwide increase in troposheric methane, 1978 to 1987. Science, 239: 1129-1131.

Conrad, R., 1984. Capacity of aerobic microorganisms to utilize and grow on atmospheric trace gases. In: M. Klug, and C. Reddy, (Editors), Current Perspectives in Microbial Ecology. Am. Soc. Microbiol., Washington, D.C., pp. 461-467.

Cunningham, R.E. and Williams, R.J.J., 1980. Diffusion in Gases and Porous Media. Plenum, New York, N.Y., 275 pp.

Evans, D.D., 1965. Gas Movements. In: C.A. Black (Editor), Methods of Soil Analysis. Am. Soc. Agron., Madison, Wisc., pp. 319-330.

Grable, A.R. and Siemer, E.G., 1968. Effects of bulk density, aggregate size, and soil water suction on oxygen diffusion, redox potentials, and elongation of corn roots. Soil Sci. Am., Proc., 32: 180-186.

Harriss, R.C., Sebacher, D.I. and Day, F.P., 1982. Methane flux in the Great Dismal Swamp. Nature, 297: 673~74.

Harrits, S.M. and Hanson, R.S., 1980. Stratification of methane-oxidizing organisms in Lake Mendota, Madison, Wisconsin, Limnol. Oceanogr., 25: 412-421.

Ishii, A.L., Healy, R. W. and Striegl, R.G., 1989. A numerical solution for the diffusion equation in hydrogeologic systems. U.S. Geol. Surv., Water Resour. Inv. Rep., 89-4027, 86 pp.

Katz, D.L., Cornell, D., Vary, J.A., Kobayashi, R., Elenbaas, J.R., Poettmann, F.H. and Weinaug, C.F., 1959. Handbook of Natural Gas Engineering. McGraw-Hill, New York, N.Y., 802 pp.

Keen, B.A., 1931. The Physical Properties of the Soil. Longmans Green, Toronto, Ont., 380 pp. Keller, M., Goreau, T.J., Wofsy, S.C., Kaplan, W.A. and McElroy, M.B., 1983. Production of nitrous

oxide and consumption of methane by forest soils. Geophys. Res. Lett., 10: 1156--1159. Khalil, M.A.K. and Rasmussen, R.A., 1983. Sources, sinks, and seasonal cycles of atmospheric

methane. J. Geophys. Res., 88:5131 5144. Lai, S-H., Tiedje, J.M. and Erickson, A.E., 1976. In situ measurement of gas diffusion coefficient

in soils. J. Soil Sci. Soc. Am., 40: 3~. Liebl, K.H. and Seiler, W., 1976. CO and H 2 destruction at the soil surface. In: H.G. Schlegel, G.

Gottschalk, and N. Pfenning, (Editors), Production and Utilization of Gases. Goltze KG, Gottingen, pp. 215-229.

Mancinelli, R.L., Shulls, W.A. and McKay, C.P., 1981. Methanol oxidizing bacteria used as an index of soil methane content. Appl. Environ. Microbiol., 42: 70-73.

Marshall, T.J., 1959. The diffusion of gases through porous media. J. Soil Sci., 10: 7942. Mason, E.Z. and Malinuskas, A.P., 1983. Gas Transport in Porous Media: The Dusty Gas Model.

Chem. Eng. Monogr. 17, Elsevier, New York, N.Y., 194 pp. Matthews, E. and Fung, I., 1987. Methane distribution from natural wetlands: global distribution,

area, and environmental characteristics of sources. Global Biogeochem. Cycles, 1: 61~8. Millington, R.J., 1959. Gas diffusion in porous media. Science, 130: 100-102. Millington, R.J. and Quirk, J.M., 1960. Permeability of porous solids. Trans. Faraday Soc., 57:

212-227. Mooney, H.A., Vitousek, P.M. and Matson, P.A., 1987. Exchange of materials between terrestrial

ecosystems and the atmosphere. Science, 238: 926-932. Perry, R.H., Green, D.W. and Maloney, J.O., 1984. Perry's Chemical Engineers' Handbook,

McGraw-Hill, New York, N.Y., 6th ed. Rudd, J.W.M. and Hamilton, R.D., 1975. Factors controlling methane oxidation and the distribu-

tion of methane oxidizers in a small stratified lake. Arch. Hydrobiol., 75: 522-538. Seller, W., 1984. Contribution of biological processes to the global budget of CH 4 in the atmosphere.

In: M. Klug, and C. Reddy (Editors), Current Perspectives in Microbial Ecology. Am. Soc. Microbiol. Washington D.C., pp. 468-477.

Seiler, W., Conrad, R. and Scharffe, D., 1984. Field studies of methane emission from termite nests

143

into the atmosphere and measurements of methane uptake by tropical soils. J. Atmos. Chem., 1: 171-186.

Stallard, R.F., Keller, M. and Mitre, M., 1988. Methane consumption by tropical soils: The effects of forest clearing. EOS Trans. Am. Geophys. Union, 69: p. 1223.

Striegl, R.G., 1988. Distr ibut ions of gases in the unsa tura ted zone at a low-level radioactive-waste disposal site near Sheffield, Ilinois. U.S. Geol. Surv. Water-Resour. Inv. Rep., 88-4025, 69 pp.

Weeks, E.P., Earp, D.E. and Thompson, G.M., 1982. Use of atmospheric fluorocarbons F-11 and F-12 to determine the diffusion parameters of the unsa tura ted zone in the Southern High Plains of Texas. Water Resour. Res., 18:1365 1378.

Wesseling, J., 1962. Some solutions of the steady state diffusion of carbon dioxide through soils. Neth. J. Agric. Sci., 10: 109-117.