co2 transport through the capillary fringe in sand

13
Pergamon 0956-053X(94)00034-4 Waste Management, Vol. 14, No. 5, pp. 421~,33, 1994 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0956-053X/94 $6.00 + .00 ORIGINAL CONTRIBUTION CO2 TRANSPORT THROUGH THE CAPILLARY FRINGE IN SAND Franfois Caron,* Steve R. Wilkinson, John Torok, Michael K. Haas, and William N. Selander AECL Research, Chalk River Laboratories, Chalk River, Ontario, Canada KOJ IJO ABSTRACT. A large part of the Carbon-14 (14C) present in Low- and Intermediate-Level Wastes (L&ILW) destined for disposal in near-surface facilities is expected to be released as carbon dioxide. Carbon-14 can be transported through unfractured porous media either by gas-phase diffusion or by dissolution and transport by groundwater. Since the exposure to the critical individual to t4C is strongly dependent upon the transport pathway, it is important to know which pathway is dominant. The objective of this work is to evaluate the influence that the capillary fringe of the water table has as a barrier to the transport of carbon dioxide from pore gases to the groundwaters. Sand columns were used to simulate a porous medium and a capillary fringe. The mass transfer rate of C02 across the capillary fringe was determined experimentally. A mathematical model representing diffusion through a semi-infinite porous medium and gas transfer across a planar interface was used to model the mass transfer process. The experi- mental results indicate that the mass transfer rate is 20-50 times slower than for an open surface. No significant influence of the grain size was found, but the results suggest that the mass transfer rate is pH-dependent between pH 6 and 7. INTRODUCTION The CANDU ® nuclear reactors produce 14C wastes originating predominantly from the neutron activa- tion of 170 present in the heavy-water moderator (I). The disposal of low-level radioactive wastes containing 14C creates the potential for radioactive gas production and subsequent release to the bio- sphere. Various chemical forms and pathways are known for 14C migration from radioactive waste dis- posal sites, and the major form is C02 gas (2-4), formed by microbial decomposition, chemical deg- radation of the wastes, and volatilization. Methane production is not expected to be important (3-5) as some of it would be consumed by methanotrophs in soils, resulting in CO 2 (6). The emphasis of this work, therefore, is on 14CO 2 gas migration. The risks associated with this contaminant are inhala- tion (if 14CO2 is present as gas) and ingestion (if RECEIVED 5 JANUARY 1994; ACCEPTED 27 MAY 1994. *To whom correspondence may be addressed. Acknowledgments--The authors wish to thank D. R. W. Killey and D. R. Lee for discussions, G. F. Keenleyside for editorial comments, and L. Nikel for minute details of the typing. Finan- cial contribution from COG (CANDU ®Owners Group) working party #49 is gratefully acknowledged. ® CANDU: CANada Deuterium Uranium. Registered trade- mark. 14CO2 is transferred to groundwaters or incorpo- rated into plants). The 14C can be ingested as car- bonate or as an organic form, which would imply that 14C is incorporated into plants and into higher trophic levels in the food chain. The aqueous path- way is more critical because of the risk conse- quences associated with ingestion. The scenario described here applies to a waste disposal site built near the ground surface in an un- fractured porous medium (sand) with a semi- permeable bottom, which is located above and near the water table. The gaseous species 14CO 2 can es- cape from the bottom of the repository to the envi- ronment by two main pathways: gas-phase migra- tion, which involves the diffusion of gaseous 14CO 2 through the unsaturated soil and into the air, and aqueous transport, which involves the dissolution of ~4C02 into the groundwater and the transporta- tion of it by aqueous migration. Gaseous migration of C02 is the dominant mech- anism in dry and unsaturated soils because of the high gas diffusivity (7). There is a fast CO 2 gaseous exchange with the small amount of liquid water in the pores, and equilibrium is usually reached within minutes. This exchange, or retardation, is more pronounced at higher water saturation and low CO 2 partial pressure (8). If a near-surface disposal site is 421

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Page 1: CO2 transport through the capillary fringe in sand

Pergamon

0956-053X(94)00034-4

Waste Management, Vol. 14, No. 5, pp. 421~,33, 1994 1994 Elsevier Science Ltd

Printed in the USA. All rights reserved 0956-053X/94 $6.00 + .00

ORIGINAL CONTRIBUTION

CO2 TRANSPORT THROUGH THE CAPILLARY FRINGE IN SAND

F r a n f o i s C a r o n , * S t e v e R . W i l k i n s o n , J o h n Torok , M i c h a e l K . H a a s , a n d

W i l l i a m N . S e l a n d e r AECL Research, Chalk River Laboratories, Chalk River, Ontario, Canada KOJ IJO

ABSTRACT. A large part of the Carbon-14 (14C) present in Low- and Intermediate-Level Wastes (L&ILW) destined for disposal in near-surface facilities is expected to be released as carbon dioxide. Carbon-14 can be transported through unfractured porous media either by gas-phase diffusion or by dissolution and transport by groundwater. Since the exposure to the critical individual to t4C is strongly dependent upon the transport pathway, it is important to know which pathway is dominant. The objective of this work is to evaluate the influence that the capillary fringe of the water table has as a barrier to the transport of carbon dioxide from pore gases to the groundwaters.

Sand columns were used to simulate a porous medium and a capillary fringe. The mass transfer rate of C02 across the capillary fringe was determined experimentally. A mathematical model representing diffusion through a semi-infinite porous medium and gas transfer across a planar interface was used to model the mass transfer process. The experi- mental results indicate that the mass transfer rate is 20-50 times slower than for an open surface. No significant influence of the grain size was found, but the results suggest that the mass transfer rate is pH-dependent between pH 6 and 7.

I N T R O D U C T I O N

The C A N D U ® nuclear reactors produce 14C wastes originating predominant ly f rom the neutron activa- tion of 170 present in the heavy-wa te r modera tor (I). The disposal o f low-level radioact ive wastes containing 14C creates the potential for radioact ive gas product ion and subsequent release to the bio- sphere. Var ious chemical forms and pa thways are known for 14C migration f rom radioact ive waste dis- posal sites, and the major form is C02 gas (2-4), fo rmed by microbial decomposi t ion , chemical deg- radat ion of the wastes , and volatilization. Methane product ion is not expec ted to be important (3-5) as some of it would be consumed by methanot rophs in soils, resulting in CO 2 (6). The emphasis of this work, therefore , is o n 14CO 2 gas migration. The risks associa ted with this contaminant are inhala- tion (if 14CO2 is present as gas) and ingestion (if

RECEIVED 5 JANUARY 1994; ACCEPTED 27 MAY 1994. *To whom correspondence may be addressed. Acknowledgments--The authors wish to thank D. R. W. Killey and D. R. Lee for discussions, G. F. Keenleyside for editorial comments, and L. Nikel for minute details of the typing. Finan- cial contribution from COG (CANDU ® Owners Group) working party #49 is gratefully acknowledged. ® CANDU: CANada Deuterium Uranium. Registered trade- mark.

14CO2 is t ransferred to groundwaters or incorpo- rated into plants). The 14C c a n be ingested as car- bonate or as an organic form, which would imply that 14C is incorporated into plants and into higher trophic levels in the food chain. The aqueous path- way is more critical because of the risk conse- quences associated with ingestion.

The scenario described here applies to a waste disposal site built near the ground surface in an un- f r a c t u r e d p o r o u s m e d i u m (sand) wi th a semi- permeable bot tom, which is located above and near the water table. The gaseous species 14CO 2 c a n es- cape f rom the bo t tom of the reposi tory to the envi- ronment by two main pathways: gas-phase migra- tion, which involves the diffusion of gaseous 14CO 2 through the unsaturated soil and into the air, and aqueous transport , which involves the dissolution of ~4C02 into the groundwater and the t ranspor ta- tion of it by aqueous migration.

Gaseous migration of C02 is the dominant mech- anism in dry and unsaturated soils because of the high gas diffusivity (7). There is a fast CO 2 gaseous exchange with the small amount of liquid water in the pores , and equilibrium is usually reached within minutes. This exchange , or re tardat ion, is more pronounced at higher water saturation and low CO 2 partial pressure (8). I f a near-surface disposal site is

421

Page 2: CO2 transport through the capillary fringe in sand

422 F. CARON ET AL.

located in an area with a humid climate, however, the aqueous transport scenario may be considered a major path for 14CO2 migration. The process is com- plex, and it is important to understand what hap- pens in moist soils.

In relatively dry soils, well above the water table, gas is a continuous phase and its migration is dom- inated by gas-phase diffusion (7). At lower eleva- tions near the top of the capillary fringe, water tends to fill the small pores and sits at the contact points of the soil particles. The pore space is occu- pied by gas and liquid in approximately equal amounts, forming a transition zone made of sepa- rate pockets of liquid. Neither phase is continuous, and water flow is minimal because of the phase dis- continuity. This may become a barrier to liquid flow, and the hydraulic conductivity is so low that long periods of time are required for any apprecia- ble water flow to occur (9). The gaseous diffusion process is also expected to be inhibited in this re- gion because C02 has to transfer across several gas- liquid and liquid-gas interfaces until the pores are predominantly filled with liquid. Below the transi- tion zone, in a fully saturated medium (i.e., the ten- sion-saturated region, and below the water table), dissolved CO 2 migrates by diffusion, groundwater convection, and hydrodynamic dispersion.

The transition zone, therefore, may act as an ef- fective barrier to diffusion into groundwaters. It is important to quantify the contribution of this diffu- sion barrier to mass transfer in safety assessment calculations of radioactive waste disposal facilities, since the amount of 14CO2 t ransferred to the groundwaters is not known at the present time.

In static groundwater conditions, molecular dif- fusion can be the dominant migration mechanism, and it should be constant with time and space, pro- vided that the diffusing substance is not affected by reaction with the solid phase. Migration can also be influenced by ion exchange or adsorption between the dissolved CO 2 ( H C 0 3 - , C 0 3 ) and the solid support. This effect is negligible with inorganic sil- ica sand used here (8), but it can be important if the soil contains an appreciable amount of carbonates (10). The presence of other aqueous species such as Ca 2+ , Mg 2+ , and Fe z+ is important because these ions can precipitate with carbonates.

The objective of this experimental program is to determine the mass transfer coefficient of C02 across the gas and aqueous phases in the soil and to determine whether this constitutes a significant barrier to mass transfer. The ultimate purpose is to use this information to develop a comprehensive model for Carbon-14 transport around a near-sur- face repository.

In the present experiment, sand columns were used to determine the influence of the transition

zone above the capillary fringe as a barrier to the mass transfer of C O 2. The columns were connected to a water supply. The two modes of the hysteresis curve (9) were simulated in separate experiments: the wetting mode (water rising by capillary action in the sand) and the draining mode (a sand saturated with water is drained by gravity, with residual water remaining in the pores). The zero piezometric level was held constant during the experiment to mini- mize advection, porewater migration and hydrody- namic dispersion, so molecular diffusion was ex- pected to be the dominant migration mechanism for dissolved C02. The top of the columns were con- nected to a supply of C02 maintained at a constant partial pressure. The C02 concentration was ex- pected to remain constant because the COz-water exchange is almost instantaneous, and the diffusiv- ity in the gas phase is three to five orders of mag- nitude higher than in the liquid phase (I1). The amount of C02 in the gas phase was therefore in infinite supply compared to what dissolves into the aqueous phase. The columns were equilibrated hy- drostatically prior to the beginning of the diffusion experiment. The solution of the diffusion equation in a semi-infinite medium (12) can be used to model the solute profiles in the saturated zone. Dependent variables examined in this work include the particle size of the sand, the ambient pH, and the moisture profile of the capillary fringe (i.e., the profile devel- oped by draining or wetting).

THE MATHEMATICAL MODEL AND SYSTEM PARAMETERS

A simple diffusion-driven model representing the mass transfer of a soluble gas across the interface between unsaturated and saturated porous media is formulated for columns in the wetting mode of the hysteresis curve. More than one process (advec- tion, etc.) controlled the mass transfer to the col- umns in the draining mode, and the results were too difficult to interpret, thus mathematical modelling was not attempted in this situation.

The domain of the porous media is modelled as two semi-infinite regions joined along a planar sur- face, across which exchange can occur. Both re- gions together comprise a domain infinite in extent, but the column from which the measurements are taken is finite. To determine whether the above is adequate for modelling diffusion in the experimen- tal apparatus, conditions at the top and bottom of the sand column are considered. As mentioned ear- lier, the CO 2 concentration in the soil gas is as- sumed to be the same as that in the flushing gas. Therefore, the " d r y " region (i.e., pores predomi- nantly filled with gas) is modelled as one of con- stant concentration.

Page 3: CO2 transport through the capillary fringe in sand

C O 2 T R A N S P O R T T H R O U G H T H E C A P I L L A R Y F R I N G E IN S A N D 423

The bottom of the column consists of a porous ceramic disk to hold the sand, yet water and dis- solved species are allowed to flow and diffuse through. The porous disk is located a few centime- tres below the zero piezometric level, and it could provide some resistance to diffusion. The column can be treated as infinite in this direction, as long as the aqueous C02 concentration at the porous disk is small compared to the aqueous concentration at the interface between the two regions.

These considerations lead to the following math- ematical model, based on Fick's law, which is ap- plicable over the semi-infinite region on the aque- ous side of the air-water interface:

OC 02C - - = D f o r x > 0 , t > 0 ; [1] Ot

with a far-field boundary condition given by

where C:

t:

D:

x:

Ci:

C ~ Ci as x --" +~', [21

DIC 1 concentration as a function of position x and time t (mg C/L), Time since the onset of diffusion (s), Aqueous C02 diffusion coefficient ( c m 2 / s ) ,

Axial distance in the direction of diffusion (cm), Background aqueous C02 concentration (mg C/L).

If the exchanging gas follows Henry's law (13), then

where H:

Cx:

Cd

Cg H = - - [31

Cl

Henry 's law coefficient (dimension- less), Equilibrium concentration of the compound of interest in air at the air-water interface (concentration units), and Equilibrium concentration of the un-ionized compound of interest in the liquid phase (same concentration units as Cx).

This expression is strictly valid for unreactive gases. However, C02 dissociates into bicarbonate and carbona te ions, and this react ion is pH- dependent. The partition between CO2(g ) and the

undissociated species n2co3*(aq), 2 however, obeys Henry's law with a value of H = 1.2 at 298 K (14). To relate C02~g) with the total DIC in solution, H must be corrected for pH. The fraction of union- ized carbonic acid in solution, et o, is given by (14):

~0 = (I + 10 (pH-pKI) + IO[2pH-(pK'+pK'-)I) -1 , [4]

in which pK 1 = 6.3 and pK 2 = 10.3 are the nega- tives of common logarithms of the first and second dissociation constants of carbonic acid (14). The pH-dependent Henry's law conditional coefficient H c, therefore, is defined as

H c = etoH, [5]

which is a dimensionless ratio of C02 concentration in air (Cg) over total DIC concentration in solution (Co). Equation 1, combined with 5, can be solved with an interface condition representing a chemis- try-dependent flux F across the air-water interface (13) given by

F = - D ~ x = K L - C a t x = 0 , [6]

where KL, expressed in velocity units (cm/s), rep- resents the C02 mass transfer coefficient across the air-water interface. Using Laplace transforms, the solution to Eq. 1 with boundary conditions in Eqs. 2 and 6 is

- exp[KLx/D + KL2t/D] [71

x erfc +KL ,x>~O.

To make Eq. 7 applicable to a porous medium, the parameters must be adjusted for the current situa- tion: C refers to the DIC concentrations in porewa- ter, and KL represents a transport coefficient across the capillary fringe instead of across an open air- water surface. Values for Cg were calculated using the ideal gas law at 298 K and were converted to units of mg C/L in the gas phase. These units are the same as those measured in aqueous concentrations in the experiment. The diffusion coefficient D in- cludes the effect of the tortuosity of the porous sand because the diffusing substance has to travel around the sand particles, resulting in a longer diffusion path. The correction factor for tortuosity is given by (15)

DIC stands for Dissolved Inorganic Carbon, defined as the sum of all dissolved carbonate species: C02(aq), H2C03, HC03 , C032 .

2 H2CO3*(aq) is defined as the sum of the " t r u e " carbonic acid HzCO3(aq) and dissolved C02 since both are undistinguishable analytically.

Page 4: CO2 transport through the capillary fringe in sand

424 F. C A R O N ET AL.

D O

D - T2 , [8] thus obta ined ref lects only the bulk behav iour across the air-water interface of the capillary fringe.

where D ° is the diffusion coefficient of dissolved C02 in pure water (D ° = 2 x 10 -5 cm2/s (I1)), and the value of the dimensionless tortuosity factor rz was selected to be 1.5, which is reasonable for a loose pack of well-sorted sand (15), thus D = 1.33 × 10 -5 cmZ/s.

The dissolution of COE in water lowers the pH. One way to maintain the correct pH value was to bubble the gas mixture (P~co2) = 0.2 and 0.04 atm; see Table 1) through fresh pH 6 and 7 buffers at 25°C until a constant DIC measurement (i.e., equi- librium) was reached. The values of Co, pH, and H c (from Eqs. 4 and 5) thus obtained are shown in Ta- ble la, along with the main characteristics of the columns. Calculations using the Gibbs free energy (AG °) of the reaction of C02 dissolution in phos- phate buffers and water produce values of pH and Co (total DIC) in agreement with these numbers.

The background aqueous concentrat ions C,- in Table 2 are averages of DIC measurements taken before the exper iment began. These concentrat ions are essentially due to water being initially in equi- librium with normal atmospheric C02 concentra- tions. The sand used was thoroughly cleaned (see next section), and carbonate release or pick-up was not observed.

Mass exchange takes place across the transition zone which could be described as several gas-liquid interfaces. Measurements of moisture content in the sand column show a transition zone of approx- imately 5 cm in thickness over which pore air is gradually displaced by porewater . The exact loca- tion of the air-water interface (where x = 0) is dif- ficult to define and it is not important for modelling. The model does not reflect the details of the capil- lary fringe structure as this zone is treated as a pla- nar interface. The C02 mass transfer coefficient KL

MATERIALS AND EXPERIMENTAL PROCEDURE

Description of the Column An example of the sand column is illustrated in Fig. 1. The column consisted of a 6.35 cm (21/2 ") I.D. x 33 cm (13") long po lycarbona te tube filled with sand. The column had a double jacketed wall to permit the circulation of water from a constant tem- perature bath held at 25°C (-+I.0°C). The bot tom assembly consis ted of a ceramic pressure plate (Soilmoisture Corp., 0.5 bar) supporting the sand and was connected to a reservoir of aqueous phos- phate buffer (pH 6 or 7). The reservoir was main- tained at a set elevation to fix the zero potentiomet- tic level for each experiment.

Each column was equipped with a set of 10 col- linear sampling probes set 3 cm apart. The probes were made of a porous ceramic tip (0.65 cm diam- eter × 3.2 cm long, rated 1 bar, supplied by Soil- moisture Corp.) glued to a threaded (1A" NPT fitting) polycarbonate tube. The volume inside each probe assembly was approximate ly 1 mL. The probes were screwed into the column and checked for leaks between the sand and the recirculating water. The C02 mixture was saturated with water vapour by bubbling through a water trap prior to reaching the column. The outlet was open, allowing gases to flow through the column without pressure build-up.

The expe r imen t was s tar ted af ter the wa te r reached hydrostatic equilibrium in the sand column (see method section for details). Usually the column was saturated to about 75% of its height. Then the gas mixture was allowed to flow in the dry sand, and the subsequent analysis of pore water samples provided several DIC profiles at various points in time.

TABLE 1 Principal Characteristics and Main Parameters of the Columns in this Study

Column # Mean Grain pH Pco 2 Diffusion and Type* Size (mm)t Buffer (atm) Boundary pH H c Cg Ci

1, w 0.248 6 0.2 2, w 0.248 6 0.2 3, w 0.248 7 0.2 5, w 0.248 7 0.2 6, w 0.152 7 0.04 la, d 0.248 6 0.04 2a, d 0.248 6 0.04 3a, d 0.248 7 0.04 5a, d 0.248 7 0.04

5.88 0.869 101.6 0.353 5.88 0.869 101.6 0.353 6.66 0.364 101.6 1.107 6.66 0.364 101.6 1.107 6.75 0.314 20.3 2.225

*Type: w: wetting mode, d: draining mode. tParticle size distribution determined with series of sieves.The graphical standard deviation is 0.26 phi units for both sands. Suppliers: Columns 1-5 and la-5a: Fisher Scientific; Column 6: Wedron Co., Wedron, IL.

Page 5: CO2 transport through the capillary fringe in sand

C O 2 TRANSPORT THROUGH THE CAPILLARY FRINGE IN SAND

TABLE 2 Other Secondary Parameters

425

Parameter Value Units Remarks

Dli q 1.33 x 105 cm2/s Dga~ 0.144 cm//s T 298 K H 1.2 Pco2~ 0.00035 atm C* 0.60 mg/L (as C)

1.07 mg/L (as C) Co 105 mg/L (as C)

21.5 mg/L (as C) 250 mg/L (as C) 59.5 mg/L (as C)

K/. (open air) 1.31 x 10 4 cm/s

CO 2 in water, tortuous medium CO2 in air (at 276 K) (11) Maintained with circulator bath (14) Atmospheric COz pressure pH 6 buffer, equilibrated with the atmosphere Same, but for pH 7 buffer pH 6 buffer at the interface (Pco2 = 0.2 atm) Same as above, but Pco2 = 0.04 atm pH 7 buffer at the interface (Pco2 = 0.2 atm) Same as above, but Pco2 = 0.04 arm Determined in our laboratory

*To be compared to C i of Table 1. The value from Table 1 is used in the model.

Sand and Column Preparation Silica sand (two sizes from different suppliers, see Table 1) was chosen because it is inert with dis- solved CO 2 (8,16). The sand was thoroughly cleaned to remove carbonates and major soluble ions (modified from (17,18)) with a 0.5 M sodium acetate solution adjusted to pH 4. Two volumes of this solution were mixed with one bulk volume of sand in a large beaker and then vigorously stirred with a mechanical stirrer for 1-2 h. After settling, the supernatant was discarded and replaced with deionized water. The sand was rinsed and stirred four times for 15 min with fresh deionized water each time until the pH of the rinsing water was near neutral. The wet sand was dried in an oven at 85°C for at least 3 days. The cleaning procedure is un- likely to have affected the particle-size distribu- tion because the unsettled fine particles (<200 mesh) constituted less than 0.3% per weight of these sands.

The probes were wetted and tested for leaks at 1 atm pressure (14 psi) to ensure their integrity. The probes and the porous ceramic plates were soaked overnight in 1 M HCI and rinsed several times with deionized water until the pH was neutral (19).

Packing the column with sand had to be done carefully to approach maximum packing density. For this operation, the column was nearly fully as- sembled, including the probes and the bottom as- sembly, but the top was left open. The assembly was then attached to a modified vibratory feeder. Pre-treated sand was poured in small increments, leaving some time for the particles to settle by vi- bration. Once the column was filled, a porous geo- textile was laid on top of the sand to avoid spillage during column manipulation. The top cap was then installed, firmly attached, and tightened.

A custom-made gamma scanner (20) provided an axial attenuation profile for the column, from which the water content and the packing homogeneity of

the sand columns were determined (21). The inten- sity of the gamma rays varies as a function of the pore structure (detection of cavities and heteroge- neities in the packing procedure) and water content. Each column was scanned at 0.5 cm intervals.

The sand also settles following successive wet- ting and drying cycles. Each column was wetted, then dried overnight (85°C) and scanned again until the profile of the dry column was reproducible. Usually, only one to two wet/dry cycles were needed. The water profile in the equilibrated col- umn was obtained by subtracting the wet profile from the dry one.

Column Wetting Procedure A water circulation unit held at 25 -+ I°C was con- nected to the jackets of the packed columns. Flasks containing phosphate buffers (pH 6 and 7) were connected to each column from the bottom (Fig. 1). The experiments were performed in the wetting and drying modes. In both modes, the columns were wetted from the bottom. For columns 1, 2, 3, 5, and 6, (in the wetting mode; see Table la), the buffer reservoir was set at a level such that the zero pie- zometric line was near the bottom of the column, allowing the water to rise by capillary action. The top of the capillary fringe was 20-25 cm above the zero piezometric line. Columns la, 2a, and 3a (held in the drying mode; see Table la) were flooded with water fed from the bottom by raising the buffer res- ervoir above the top of the column. Then, the buffer reservoir (hence the zero piezometric level) was lowered below the column, resulting in partial drainage. The water content was variable between these columns, and, as expected, the gradients were more gradual than for the wetting mode. Typically, the pore water saturation ranged from 30-100% (-0.12-0.35 mL/mL).

The evolution of the water content profile was monitored periodically with the gamma scanner.

Page 6: CO2 transport through the capillary fringe in sand

426 F. C A R O N ET AL.

CO 2 gas mixh - - I P ,

Water bubbler

Geotext materi~

Inert Silica sa

Jacket for thermostated~

water "

Pressure plate (0.5 bar)

1' (2.5 crn)

3eramic tip ~Polycarbonate rod 1 bar) (drilled and milled)

1" (2.5 cm)

mpling probe

~ Hydraulic [ ~ reference

. . . . . level h=0

I I

0

Buffer reservoir

FIGURE 1. Schemat ic representa t ion of the sand column and the a t tachments (Note: some details were omit ted for clarity).

The hydrostat ic profiles of the columns had stabi- lized about 48 h for the columns in the wetting mode, and up to 1 week for those in the draining mode. The wetting mode is intended to simulate water rising from a rising or stable water table under a dry reposi tory, with no infiltration from above. The draining mode is intended to simulate a soil retaining water after an infiltration episode or a re- ceding water table. These are the two extremes that can be met in the field, and reality lies between the two.

The conditions were satisfactory when consecu- tive gamma scans revealed no change of the water profiles in the columns. Only then was the C02 gas mixture turned on, and this marked the time t = 0 of the experiment.

Other Preparation and Analyses The gas was supplied to the top of each column with the outlet open to the atmosphere, so the columns were at ambient pressure at all times. The gas flow rate was about 20-30 mL/min. Two C02 concentra- tion levels were used: 20% and 4% (volume per-

cent). Initially, the gas mixture, 20% C02, 10% 02, and the balance nitrogen, was prepared by Mathe- son Gas. After 1 month of operation, this mixture had to be replaced with C02 and nitrogen gases (20-80% volume basis, respectively) prepared in our laboratory by in-line mixing. The partial pres- sure of C02 in the mixture was monitored using a gas chromatograph (GC). This change did not affect the results. The 4% C02 gas mixture used for col- umns 6, la, 2a, and 3a was also prepared in the laboratory with nitrogen and checked periodically using a GC.

The DIC was determined using a Dohrmann DC- 80 total carbon analyzer. The detection limit was approximately 0. l mg C/L for a 200 ~L sample. The accuracy of the calibration was checked several times every sampling day using a fresh carbonate standard. The precision was approximately -+0.3% (400 mg/L range), -+0.5-1% (40 mg/L range), and -+5-10% (1-2 mg/L range).

The soil pore waters used in this exper iment were pH 6 and 7 phosphate buffers (22) adjusted to 0.1 M ionic strength. The buffers were left open to

Page 7: CO2 transport through the capillary fringe in sand

CO 2 TRANSPORT THROUGH THE CAPILLARY FRINGE IN SAND 427

the air for at least 2-3 months to allow equilibration with atmospheric C02 (partial pressure 0.00035 atm). This constitutes the background value for DIC used in Eqs. 2 and 7. In addition, the buffers were equilibrated with sand in the columns for at least 48 h before sampling for background DIC. The results (Tables 1 & 2) suggest that the Fisher sand is neither a source nor a sink of DIC, whereas the Wedron sand shows a higher DIC concentration.

Porewater samples were collected by applying a partial vacuum (up to 0.75 bar) on each of the probes until approximately 1 mL of liquid was with- drawn. In the early sampling episodes (first -300 h), all the probes were sampled on the column, the pH was measured and the samples analyzed for DIC within 30 min. The procedure was changed thereafter to take the pH and DIC immediately after sampling each probe because DIC loss over the waiting period was identified as a potential problem.

For columns 6, la, 2a, and 3a, the samples were analyzed for pH and DIC immediately after sam- pling each probe. For the columns in the draining mode, the volume withdrawn from the probes was replaced with the same volume of buffer to replen- ish the sand with the volume of water lost.

The sampling conditions were also tested sepa- rately with solutions saturated in C02 (g) to verify whether our sampling procedure introduced a bias. The probes located in the saturated sand did not show sampling problems. The tests indicated that DIC recoveries (at C02 saturation in water) were reproducible and they were ~85% (at pH 6) and ~93% (pH 7). Tests suggested that DIC losses are minimal in solutions below DIC saturation. For the columns in the wetting mode, the probes located well above the water table, at the top of the capil- lary fringe in low moisture content sand needed a higher vacuum in order to collect a sufficient vol- ume of solution. Most of the probes of the col- umns held in the draining mode also showed this problem because of the high water tension. These DIC results showed inconsistent values and low re- coveries.

In summary, the DIC measurements taken in sat- urated sand are believed to be reliable, whereas those in the unsaturated sand have a limited signif- icance because of the sampling problems.

RESULTS

Columns in the Wetting Mode The experimental results are the DIC concentra- tions as a function of the axial position in the col- umn. These profiles are obtained at various times. As time advances, more C02 dissolves into the wa-

ter and migrates further down into the column. A typical DIC concentration profile, superimposed on the water content profile, is shown in Fig. 2. The maximum DIC value corresponds to the top of the saturated sand, but its value is still lower than the expected Co (105 and 250 mg C/L for pH 6 and 7 buffers, respectively). The DIC value above this point (12 cm) is invalidated because of sampling ar- tifacts. As expected, the DIC levels decrease with distance from the diffusion boundary, and the con- centration pattern appears consistent with a diffu- sion-dominated system.

A crude model was used to verify the value of the diffusion coefficient (D) and to determine whether the dissolved C02 was migrating by diffusion (16). The experimental value of D was within 10% of the theoretical value, and there was no significant dif- ference between the columns whose interstitial wa- ter was at pH 6 or 7. This is important because the distribution of the carbonate species is different at these pHs. It is 67% as HzC03* and 33% as HC03 at pH 6, whereas it is 17% (H2C03") and 83% (HCO 3-) at pH 7. Aqueous speciation of the DIC involving a negatively charged species, therefore, does not affect D. This is added evidence that dis- solved carbonates do not interact with silica sand, whether the mechanism is surface sorption or ion exchange. This may not be the case in true soils because carbonates, iron (oxy)hydroxides or other reacting substrates may be present.

Columns in the Draining Mode A DIC concentration profile and a moisture profile are shown in Fig. 3 for column la. Both DIC and

Water content (mL/mL) 0 0.1 0.2 0.3 0.4

. . / ,

5.0 ! Saturated water I | l . . . . . . . . tent / / - - IVlOlStUte p r o f i l e

~10.0

e ~0 15.0

' ~ 2 0 . 0

~ 25.0

O_ [ = !

3o.o I . . . . . . . . .Hi 0 20 40 60 80 1 O0 120

DIC concentration (mg C/L)

FIGURE 2. DIC profile (t = 360 h) and moisture profile for Column 2 (wetting mode).

Page 8: CO2 transport through the capillary fringe in sand

428 F. CARON ET AL.

water profiles are not reproducible with the other two columns (2a and 3a, not shown), although they behave similar to column la. The water content profile shows a more gradual increase with depth than for the columns in the wetting mode, going from -0.1 mL/mL near the top to approximate sat- uration -0 .3 mL/mL near the bottom. This gradual decrease occurs in the top -20-25 cm of the col- umn, as opposed to - 5 cm in the wetting mode. The water content profile suggests that there is always a significant proportion of the sand pores filled with gas, thus probably allowing gas-phase diffusion to dominate.

The DIC results do not show the expected trend with depth, and the values are always about half the saturation value (7-12 mg C/L), thus significantly above background. High DIC values seem to coin- cide where the water content is high, which is con- sistent with sampling artifacts as explained earlier. The DIC value of 8.5 mg C/L located at 30 cm is of special interest, especially at the early stage of the experiment (t = 70 h). This DIC content is too high to be explained by a diffusional mass transfer to porewaters in a saturated aqueous phase. Only the dominance of gas-phase diffusion at these water contents could explain the absence of a definite DIC gradient with distance from the top and the high DIC value close to the bottom of the column. Mod- els by Lai et al. (23) and Simunek and Suarez (24) could explain the value of -8 .5 mg C/L observed at this time and location. Note that this value should be higher because sampling artifacts tend to de- crease the DIC content in samples taken in unsatu- rated sand. Other models (8,25), however, could not explain these results.

Water content, mL/mL 0 0.1 0.2 0.3 0.4

0.0 , i ~ Moisture'profiles: I ~ y I - 500 h her°re start

t-- '(,- - - -480 h after start E 5 .0 I Saturated water

_ _ !ill ̀ content 0 0.290 mL/mL o

o 10.0 Q.. o ; ~ ~ E 15.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

mg CIL

oE20.0

t - O

~.~_~ 25.0

0

"qDo,c - . J T 30.0 ................................................

0 5 10 15 20 25

DIC concentration (mg C/L) FIGURE 3. DIC profile (t = 70 h) and column moisture profile for Column la (draining mode).

Based on this ambiguity, it is not possible to de- termine the exact position of the diffusion interface. As a first approximation, the diffusion interface is set at the location of the 75% water-filled porosity for modelling the columns in the wetting mode. There is sufficient evidence that gas diffusion dom- inates at lower water content. The error associated with this location is minimal because the water con- tent gradient is steep in the wetting hydraulic mode. Hence, the rest of the discussion will deal only with the modelling of the mass transfer through the cap- illary fringe in the wetting mode.

MATHEMATICAL TREATMENT OF THE DATA

For a good fit between a mathematical model and experimental data, one must be concerned not only with the model, but also with the data characteris- tics and the conditions under which the data were obtained. Even before the model is developed, ex- amination of the data can yield information as to the level of detail required in the modelling and can suggest the procedure by which model parameters are fitted. Data characteristics include random noise in measurements and systematic error. Examina- tion of the data can help in identifying the sources and domains over which the errors dominate.

Concentration profiles consist of three features, marked as Domain I, II, and III in Fig. 4. Domain I measurements do not show a consistent behavior with respect to the vertical profile because, as men- tioned earlier, the water content was so low that sampling was difficult, and a systematic error was introduced. Domain II measurements appear to be- have linearly with a decreasing slope (as indicated

0.0

r -

E 5.0 '6 O '~ 10.0 CL E15.o

~O20.0

t-- O

.:'~_-- 2 5 . 0

o 13..

30.0

Domain I

. J ' J ' ~ J m Domain II

I Domain III

'o . . . . o ' 2 40 6 80 100

DIC concentration (mg C/L)

120

FIGURE 4. DIC concentration profile for column 2 (t = 360 h) showing the different domains for modelling applications.

Page 9: CO2 transport through the capillary fringe in sand

C O 2 T R A N S P O R T T H R O U G H T H E C A P I L L A R Y F R I N G E IN SA N D 429

by the heavy line). In Domain III, measurements reflect background concentrations at early times. At later times, C 0 2 diffusion is probably hindered by the porous ceramic plate, so that "back - diffusion" may be raising background DIC mea- surements in this domain. The above models (Eqs. 1, 6 and 7) do not account for this process. In the following analyses, only the measurements of Do- main II are considered.

Values for KL were found by fitting model pre- dictions to experimental data so that the error be- tween predictions and measurements is minimized. The error is defined as the discrete-valued L2-norm (26) of the difference between simulated and exper- imental concentra t ions of each profile, and is given by

i E = ~[ IC(xi, t) - Cx(xi, t)l 2 , i=1

[9]

where C(xi, t):

Cx(xi, t):

N :

Simulated concentrations (mg C/L) from Eq. 7 at position xi and time t, Experimental concentration (mg C/L) at the same position and time, and Number of points in the profile at time t.

If E is considered as a function of the parameters being fitted (i.e., the interface position x = 0, and the coefficient KL), then optimum parameter values can be computed by finding the minimum error. Computer routines were developed from implemen- tations of Eqs. 4, 5, 7, and 9 and from numerical algorithms for finding the minimum values of func- tions (27). To begin the algorithm, initial estimates of the interface position and KL were needed for each profile. Measurements of the water content with position were made for a few profiles on each column, and an interface position was defined as the position with 75% water content. Initial esti- mates thus consisted of measured or averaged in- terface positions and KL-values estimated from concent ra t ion gradients near the interface for each profile.

DISCUSSION

Table 3 shows the fitted parameter values for the interface position ("Pin") and the transfer coeffi- cient (KL) obtained for each column, at various points in time. Except for some initial variation in Columns 3 and 5, no trends in K L with time were noted.

TABLE 3 Parameters of the Columns Calculated With the Fitting Routine

Column Time (h) Pin K L

1 6.6 15.0 2.9e-6 45.6 21.0 2.7e-6 69.6 18.0 3.5e-6

141.5 18.0 2.0e-6 237.4 18.0 2.1e-6 357.4 15.0 2.0e-6 501.6 18.0 2.0e-6 719.5 15.0 2.0e-6 839.1 12.9 3.6e-6

1031.3 12.9 2.3e-6 1178.1 12.0 1.2e-6

2 27.6 12.0 2.4e-6 47.5 15.0 3.2e-6 70.9 15.0 5.9e-6

143.3 15.0 2.4e-6 239.2 15.0 3.5e-6 359.2 15.0 2.5e-6 503.0 12.0 2.9e-6 720.1 12.0 1.3e-6 839.7 12.0 1.4e-6

1033.8 8.6 1.8e-6 1178.8 12.0 6.0e-7

3 2.8 15.0 1.0e-5 22.0 15.0 1.2e-5 46.2 15.0 9.1e-6

167.8 18.0 3.9e-6 238.3 18.0 4.3e-6 359.9 18.0 3.8e-6 554.8 15.0 3.9e-6 674.5 15.0 3.6e-6 867.1 12.0 2.9e-6

1056.3 12.0 2.2e-6 5 3.8 9.0 1.8e-5

23.6 9.0 1.2e-5 47.7 9.0 1.2e-5

171.0 9.0 9.0e-6 239.8 15.0 4.8e-6 362.4 15.0 4.4e-6 555.4 15.0 2.8e-6 675,2 14.0 4.4e-6 867.8 13.5 1.9e-6

1058.8 9.5 4.7e-6 6 74.8 9.0 4.0e-6

218.8 8.5 5.3e-6 387.7 9.0 3.9e-6 554.4 9.0 2.9e-6 722.5 6.0 6.3e-6

1226.3 9.0 1.4e-6

The column means and standard deviations of KL, and mean resistances to mass transfer across the interface, are presented in Table 4 for each col- umn and for selected groups of columns. If K L is a measure of mass conductance across an air-water interface, then its inverse is a measure of resistance to mass transfer. The dimensionless resistance fac- tor R is defined, therefore, as the ratio of KL for the open air-water surface (Table 2) over the KL ob- tained in the sand column. It is a measure of resis- tance enhancement provided by the capillary fringe.

Page 10: CO2 transport through the capillary fringe in sand

430 F. C A R O N E T A L .

TABLE 4 Column Mass Transfer Coefficients and Resistances

K e (cm/s) Mean

Column Mean SD Res is tance Factor

I 2.4e-6 6.8e-7 55 2 2.5e-6 1.3e-6 52

i & 2 2.5e-6 1.1e-6 53 3 5.7e-6 3.4e-6 23 5 7.4e-6 4.9e-6 18

3 & 5 6.5e-6 4.3e-6 20 6 4.0e-6 1.6e-6 33

(3 & 5) & 6 5.9e-6 4.0e-6 22

The mean R is the dimensionless resistance factor calculated from the mean KL.

Table 4 shows that values of KL determined by the model range approximately 18-55 times higher than for an open air-water interface. Figure 5 shows the fitted profile compares will with the experimen- tal results.

Factors that could affect KL are the pH, which affects DIC solubility, and the sand particle size. Columns 1 and 2 differ from Columns 3 and 5 in pH, while column 6 differs from the others in pH, grain size, and C02 partial pressure. In the case of Col- umn 6, the lower C 0 2 partial pressure causes a smaller shift in pH, but essentially the solution propert ies are the same as for Columns 3 and 5.

If KL is independent of pH and grain size, then values of KL for all columns are from the same pop- ulation distribution. This hypothesis can be tested statistically (28). Formally, the hypothesis H o states that the means of two populations X and Y are equivalent assuming that both populations are nor-

0.0

5.0 E "-a

0 10.0

0

15.0

E o

20.0

E

c- 25.0 0

30,0

Fitted Experimental •

35.0 0 20 40 60 80 100 120 140

DIC concentration (mg C/L)

FIGURE 5. Example of model fitting of the DIC concentra t ions for Co lumn 2 (t = 360 h).

mally distributed and have the same variances. The hypothesis Ho is rejected when the means are not equivalent if

[tl > ta/2,v [10]

where 1 - a : test significance (i.e., confidence level), v = nx + nv - 2 : degrees of f reedom, t~/2.~ : a statistic of the Students t-distribu- tion;

and the test statistic t is given by

t = (IXx - Ixr)/

[ V ( ( n x - 1)~ 2 + (nr - 1)%z)(1/nx + 1 /nr ) / v ] , [11]

where ~;: mean of population i, (r~: variance of population i, and ni: sample size of population i.

A 90% confidence limit is chosen (a = 0.1) as the test significance to accept or reject Ho. Table 5 pre- sents details of the testing. Differences in K L be- tween Columns 1 and 2 (pH 6 buffer) and between Columns 3 and 5 (pH 7) are shown to be statistically significant. Profile data for these two sets of col- umns are therefore combined (boldface, Table 4). While Table 4 shows that there are differences in KL between the three sets of columns (i.e., Columns 1 and 2, Columns 3 and 5, and Column 6), it does not show KL values from Columns 3 and 5 to be signif- icantly different from Column 6. This seems to in- dicate that KL increases with increasing pH and is unaffected by grain size.

The grain size differences are probably not dis- criminating enough to affect the mass transfer co- efficient KL. A smaller particle size would affect the capillary rise and the transi t ion zone would be thicker, and the interface more broken up into bub- bles, thus adding a longer region of phase disconti- nuity. The gases would transfer across more air- water surfaces, and thus a higher resistance for the capillary fringe overall. R would therefore equal unity for an open-surface, close to unity for a very large grain size, greater than unity for a medium grain size, and much greater than unity for a small

TABLE 5 Testing of Hypothesis H o

Column t t~/2. ~ v H o

1 & 2 - 0 . 3 7 8 1.725 20 accepted 3 & 5 - 0 . 9 1 7 1.734 18 accepted

(I & 2) & (3 & 5) - 4 . 3 1 5 1.684 38 rejected (3 & 5) & 6 1.410 1.711 23 accepted

Page 11: CO2 transport through the capillary fringe in sand

CO 2 TRANSPORT THROUGH THE CAPILLARY FRINGE IN SAND 431

grain size. Stronger experimental evidence would be needed by using larger differences in particle size to demonstrate this point.

The difference in KL for pH 6 and 7 is not sur- prising. The model used in this work is valid only if the gas is not reactive, or if reactive, the model may still be valid if the kinetics of ionization are slow at the pH of interest. For carbonic acid, however, the first ionization constant is log K = -6 .3 , which means that, at pH 6, the dominating species is un- ionized H2C03", whereas bicarbonate HCO 3 pre- dominates at pH 7 (the actual boundary pH is 6.7). The kinetics of ionization H2C03 ~ HC03- are fast (14), and the proportion of bicarbonate may be high enough at pH 6.7-7 to consider a kinetic enhance- ment factor in modelling.

Two models involving a kinetic enhancement factor were considered: a) the refinement of Hoover and Berkshire (29) to the general model of Liss and Slater (13), and b) the Quinn and Otto model (30). Both these models were developed for the mass transfer across the microlayer on a liquid.

In the work of Hoover and Berkshire (29), the authors argue that the pH across the diffusion boundary is assumed to remain constant because the liquid diffusion coefficient for H + is - 8 times faster than for other ions. They report a significant flux enhancement between pH 6.375 and 6.742 (in- crease of I0-76%), which translates into a higher value of KL. In our experiment, the thickness of the diffusion boundary is unknown because of the na- ture of the transition zone. In addition, the DIC controls the pH, and there is a DIC gradient; thus it is difficult to assume that the pH is constant in the diffusion layer.

The model of Quinn and Otto (30) uses the pH differences between the top and the bottom of the interface micro layer , which t ranslates into a HCO 3- gradient and the CO 2 concentration gradi- ent between the gas and the bulk solution. They mention that electroneutrality, not the pH, must be constant. This model would partly explain the high fluxes early in the experiment (Columns 1, 2, 3 and 5; (16)). This model shows a significant flux en- hancement at pH 8.3 for oceanic waters, but it does not show any significant enhancement at pH 7 or below. In addition, in the transition zone on top of the capillary fringe, the diffusion interface is ex- pected to be broken up by the phase discontinuity: CO 2 gas transfers to liquid, then gas, then liquid, etc., until the liquid phase is continuous. The C02 gradient at each interface, therefore, is expected to be fairly small, especially after a few days to weeks.

The difference in KL obtained at different pHs seems to indicate that the pH 7 columns are at the limit for justifying the use of kinetic enhancement

factor. One model (29) suggests that such correction is required, but it is doubtful that it fully applies to our situation. The other model (30) has a better in- terface condition (electroneutrality) but suggests no need for kinetic enhancement at pH 7. This point is still unresolved, but our results suggest that a pH- dependent model may need to be developed.

SUMMARY AND CONCLUSION

The concentration profile of the Dissolved Inor- ganic Carbon (DIC) in the column in the wetting mode are in good agreement with the solution of the diffusion equation derived from Fick's law but only in the saturated zone.

The results from the columns in the draining mode were inconclusive. The water content profile had a gentle gradient, allowing gas exchange to take place over almost the whole length of the column. Gases diffusing in such columns would eventually reach a diffusion boundary, which would delineate between gas- and liquid-phase diffusion. The col- umns used in this work were probably too short to reach this diffusion boundary, and the DIC re- sults likely reflected solely equilibration with gas- eous C02.

We were able to extract mass transfer coeffi- cients (K/) using a data-fitting computer routine, which predicts values for both the interface position and KL. The key assumption in this model is that the thickness of the air-water interface has a minor effect on mass transfer and that its position can be represented by a specific value.

No statistical evidence was found that the parti- cle size had an influence on KL. We conclude that the two sizes of sand used in this study were prob- ably not discriminating enough to create a differ- ence in KL.

The value of K L was shown to be influenced by the pH of the interstitial water (pH values of 6 to 7). Evidence suggests that the kinetics of the first ion- ization of carbonic acid are fast enough to augment the flux of C02 gas to the aqueous phase. Existing models give ambiguous indications as to what is the lowest pH that would affect the mass transfer of a reactive species.

Future experiments, already under way, are de- signed to obtain the mass transfer coefficient KL through the capillary fringe above a moving aquifer. The system is more complex because liquid-phase diffusion may no longer dominate. Factors such as hydrodynamic dispersion, advection, sorption, and maybe a pH-driven kinetic effect will need to be considered in a more sophisticated model. Other transport parameters are available, and only this KL

Page 12: CO2 transport through the capillary fringe in sand

432

is needed to develop a full-scale model of 14CO2 around a near-surface reposi tory.

R E F E R E N C E S

l. Liepins, L. Z. and T homas , K. W. Survey of ~4C literature re levant to a geologic nuclear waste repository. Rad. Waste Manag. Nucl. Fuel Cycle 10:357 (1988).

2. Striegl, R. G. Fate of gaseous trit ium and Carbon-14 re- leased from buried low-level radioactive waste , lOth annual DOE low-level waste management conference. Aug. 30- Sept. 1, 1988, 29-34 (1989).

3. Striegl, R. G. Distr ibution of gases in the unsa tura ted zone at a low-level radioact ive waste disposal site near Sheffield, IL. Wate r Resou rces Invest igat ion Report 88-4025, United States Geological Survey, Urbana , IL (1988).

4. Killey, R. W. D. and Mattie, J. F. Carbon-14 in the vicinity of Was te M a n a g e m e n t Area C: Resul ts of a scoping study. A E C L 10795, Atomic Energy of Canada , Ltd. , Chalk River, Ontario, Canada (in preparation).

5. Torok, J. and Haas , M. K. Gas generat ion by compacted waste . Proceedings o f a workshop on gas generation and release from radioactive waste repositories. Sept. 23-26, 1991, Aix-en-Provence , France . N E A , OECD, Paris, 175 (1992).

6. Striegl, R. G. and Ishii, A. L. Diffusion and consumpt ion of me thane in an unsa tu ra ted zone in North-Centra l IL. J. tty- drol. 111:133 (1989).

7. Thors t enson , D. C., Weeks , E. P., Haas , H. and Fisher, D. W. Distr ibution of gaseous ~2C02, ~3C02, and 14C02 in the sub-soil unsa tu ra ted zone of the wes tern U.S. Great Plains. Radiocarbon 25:315-346 (1983).

8. Johns ton , H. M. Laboratory studies o f the transport o f Car- bon-14 in unsaturated geologic materials. Ph.D. thes is , Univ. of Water loo, Water loo, Ontario (1990).

9. Hillel, D. Fundamentals o f soil physics. Academic Press, Orlando (1980).

10. Striegl, R. G. and Armst rong , D. E. Carbon dioxide reten- tion and carbon exchange on unsa tura ted quaternary sedi- ments . Geochim. Cosmochim. Acta 54:2277 (1990).

II . Reid, R. C., Prausni tz , M. J. and Poling, E. B. The proper- ties o f gases and liquids (4th ed). McGraw Hill, New York (1987).

12. Crank, J. The mathematics o f diffusion (2nd ed.). Clarendon Press , Oxford (1986).

13. Liss , P. S. and Slater, P. G. Flux of gases across the air-sea interface. Nature 247:181 (1974).

14. S tumm, W. and Morgan, J. J. Aquatic chemistry (2nd ed.). J. Wiley & Sons , New York (1981).

F. CARON ET AL.

15. Dullien, F. A. L. Porous media: Fluid transport and pore structure. Academic Press , New York (1979).

16. Caron, F., Haas , M. K. and Torok, J. Transfer of C02 to groundwaters through the capillary fringe in porous medium: 1. L a b o r a t o r y s tudy . COG-92-118 (Res t r i c t ed Repor t ) , Atomic Energy of Canada Ltd. , (1993).

17. Kunze , G. W. and Dixon, J. B. Pre t rea tment for mineralog- ical analysis . In: Methods o f Soil Analysis. Part 1: Physical and Mineralogical Methods (2nd ed.), Klute, A. (Ed.). Am. Soc. Agron. , Soil Sci. Soc. Am. , Madison, WI 9 :91 (1986).

18. Gee, G. W. and Bauder, J. W. Particle-size analysis . In: Methods o f Soil Analysis. Part 1: Physical and Mineralogi- cal Methods (2rid ed.), Klute, A. (Ed.). Am. Soc. Agron. , Soil Sci. Soc. Am. , Madison, WI 9 :383 (1986).

19. Creasey, C. L. and Dreiss, S. J. Soil water samples: Do they significantly bias concent ra t ions in water samples? Proceed- ings o f N W W A Conference, Denver , CO, 173 (1985).

20. Burton, G. R., Keller, N. A. , Torok, J. and Woods , B. L. Scanning g a m m a spectrometer : Use r s manual . Atomic En- ergy of Canada, Ltd. , Chalk River, Ontario, Canada (Un- published report).

21. Gardner , W. H. Water content . In: Methods o f Soil Analy- sis. Part 1: Physical and Mineralogical Methods (2nd ed.), Klute, A. (Ed.). Am. Soc. Agron. , Soil Sci. Soc. Am. , Mad- ison, Wl 9 :493 (1986).

22. Weast , R. C. (Ed.). CRC Handbook o f Chemistry and Phys- ics. (60th ed.) CRC Press, Boca Raton (1980).

23. Lai, S. H. , Teidje, J. M. and Erickson, A. E. In situ mea- su rement of gas diffusion coefficient in soils. Soil Sci. Soc. Am. J. 40 :3 (1976).

24. Simunek, J. and Suarez, D. L. Modeling of carbon dioxide t ransport and production in soil. 1. Model deve lopment . Wa- ter Resour. Res. 29:487 (1993).

25. Currie, J. A. Movemen t of gases in soil respiration. In: Sorp- tion and Transport Processes in Soils. Monograph Soc. Chem. Ind. 152 (1970).

26. Rice, J. R. The Approximation o f Functions. Addi son- Wesley, Reading, MA (1964).

27. Press , W. H., Flannery, B. P., Teukolsky , S. A. and Vet- terling. W. T. Numerical Recipes--The Art o f Scientific Computing. Cambridge Univers i ty Press , New York (1986).

28. Beyer, W. H. (Ed.). Handbook o f Probability and Statistics (2nd ed.). CRC Press, Cleveland (1968).

29. Hoover , T. E. and Berkshire , D. C. Effects of hydrat ion on carbon dioxide exchange across an air-water interface. J. Geophys. Res. 74:456 (1969).

30. Quinn, J. A. and Otto, N. C. Carbon dioxide exchange at the air-sea interface: Flux augmenta t ion by chemical reac- tion. J. Geophys. Res. 76:1539 (1971).

APPENDIX: DIC Results on Columns 1, 2, 3, 5 and 6

Column 1: Fisher sand, pH buffer 6, wetting mode.

Pos. Time (h) cm 26.6 45.6 69.6 141.5 237.4

3 N.A. N.A. N.A. N.A. N.A. 6 N.A. N.A. N.A. N.A. N.A. 9 N.A. N.A. N.A. 16.9 15.0

12 23.0 N.A. 25.7 22.9 22.9 15 25.8 26.6 24.6 22.0 32.5 18 18.9 26.7 38.2 32.0 39.(I 21 15.7 29.2 33.9 24.5 32.8 24 8.2 16.8 26.7 15.1 13.5 27 0.5 1.1 2.6 4.2 8.0 30 0.5 0.9 1.3 1.8 4.5

357.4 501.6 719.5 839. I 1031.3 1178.1 N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. 21.2 27.6 44.7 64.8 56.6 43.6 30.2 41.1 51.5 68.9 62.6 47.2 40.7 47.3 59.9 62.2 57.4 42.6 36.5 54.7 46.8 48.0 40.9 32.6 23.2 32.3 19.9 20.9 24.7 20.5 26.1 21.4 20.9 19.0 14.4 14.4 7.2 13.1 13.6 12.4 11.0 9.0 5.0 8.1 12.0 , 8.2 6.7 6.0

(continued)

Page 13: CO2 transport through the capillary fringe in sand

CO2 TRANSPORT THROUGH THE CAPILLARY FRINGE IN SAND

APPENDIX Continued

433

Column 2: Fisher sand, pH buffer 6, wetting mode.

Pos. Time (h) cm 27.6 47.5 70.9 143.3 239.2 359.2 503.0 720.1 839.7 1033.8 1178.8

3 N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. 6 N .A . N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. 9 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 65.0 75.9 61.6 49.2

12 22.4 36.2 26.5 19.2 32.1 36.2 56.9 44.0 55.1 48.1 31.0 15 17.3 34.7 57.6 39.4 53.8 58.0 46.8 32.6 33.3 24.6 26.0 18 4.6 14.7 22.7 22.9 44.2 29.5 41.9 23.1 25.2 19.0 18.6 21 0.5 2.5 5.7 9.9 16.4 21.4 13.2 12.9 15.3 11.9 11.3 24 0.5 0.9 1.2 1.5 3.8 4.7 4.5 8.5 7.4 7.3 7.1 27 0.4 0.6 0.9 0.9 1.4 1.4 2.9 4.5 4.7 4.0 4.6 30 0.4 0.8 1.2 1.0 1.7 1.7 3.2 4.5 4.1 4.8 4.6

Column 3: Fisher sand, pH buffer 7, wetting mode.

Pos. Time (h) cm 2.8 22.0 46.2 167.8 238.3 359.9 554.8 674.5 867.1 1056.3

3 N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. N.A. 6 73.7 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 193.1 190.5 9 129.3 161.7 145.2 118.5 149.2 195.3 171.4 186.8 181.7 186.7

12 111.8 132.0 145.0 140.2 156.6 179.0 170.2 172.0 161.0 156.7 15 70.4 153.0 145.0 158.4 172.7 178.9 177.9 183.4 153.0 140.0 18 5.0 116.4 129.6 129.6 145.0 158.6 115.8 127.3 81.1 80.1 21 3.2 15.5 54.4 87.0 107.6 107.0 82.8 85.0 63.6 55.9 24 3.0 2.8 5.2 32.2 43.9 56.4 52.1 46.7 45.5 43.2 27 2.5 2.9 3.5 7.6 9.7 17.7 26.4 27.6 22.8 24.8 30 3.6 4.2 3.9 4.7 5.3 6.0 7.9 8.2 11.0 11.6

Column 5: Fisher sand, pH buffer 7, wetting mode.

Pos. Time (h) cm 3.8 23.6 47.7 171.0 239.8 362.4 555.4 675.2 867.8 1058.8

3 159.9 N.A. N.A. N.A. N.A. N.A. N.A. N.A. 185.7 177.4 6 164.6 145.6 145.7 121.0 164.6 180.1 183.6 177.6 175.3 191.5 9 115.9 153.6 167.4 159.5 177.0 195.7 191.9 185.3 174.6 168.4

12 73.6 107.8 110.5 136.3 165.0 175.3 171.0 177.4 149.2 144.3 15 2.5 12.8 74.9 115.5 152.9 154.9 150.0 169.5 123.7 120.2 18 2.6 4.2 17.5 92.5 107.0 136.0 117.3 136.8 86.2 76. I 21 3.0 2.3 4.6 39.3 57.5 62.3 64.5 62.5 48.8 50.2 24 2.6 2.0 2.6 7.5 13.3 22.7 28.8 20.3 25.3 25.5 27 2.6 2.6 3.7 4.9 6.6 10.1 15.8 15.8 14.2 14.8 30 4.7 4.5 6.2 6.3 7.2 9.0 11.5 11.2 10.9 I 1.3

Column 6: Wedron sand, pH buffer 7, wetting mode.

Pos. Time (h) cm 74.8 218.8 387.7 554.4 722.6 1226.3

3 N.A. N.A. N.A. N.A. N.A. 74.1 6 42.0 45.1 46.5 46.2 46.7 50.4 9 26.9 37.4 38.5 38.1 40.9 29.9

12 6.3 15.2 27.9 25.5 23.8 26.2 15 3.3 5.6 8.6 13.0 14.3 17.1 18 3.0 4.1 6.0 9.4 10.2 13.0 21 4.0 4.3 5.2 6.2 8.2 10.4 24 4.9 4.1 14.2 5.5 5.9 9.7 27 4.9 3.9 3.7 5.2 5.7 8.9 30 11.0 3.7 4.1 5.5 6.3 9.3

N.A.: measurement not available (no water present). Note: results not corrected for background.