CO2 transport through the capillary fringe in sand

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

Pergamon 0956-053X(94)00034-4

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 experimental 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.

14CO2 is transferred to g r o u n d w a t e r s or incorporated into plants). The 14C c a n be ingested as carbonate 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 pathw a y is m o r e critical b e c a u s e of the risk consequences associated with ingestion. The scenario described here applies to a waste disposal site built near the ground surface in an unf r a c t u r e d p o r o u s m e d i u m (sand) w i t h a s e m i p e r m e a b l e b o t t o m , which is located a b o v e and near the w a t e r table. The gaseous species 14CO 2 c a n escape f r o m the b o t t o m of the repository to the envir o n m e n t by two main pathways: gas-phase migration, 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 g r o u n d w a t e r and the transportation of it by aqueous migration. G a s e o u s migration of C02 is the dominant mechanism in dry and unsaturated soils b e c a u s e of the high gas diffusivity (7). T h e r e is a fast CO 2 gaseous exchange with the small a m o u n t of liquid w a t e r in the pores, and equilibrium is usually r e a c h e d within minutes. This e x c h a n g e , or retardation, is m o r e p r o n o u n c e d at higher w a t e r saturation and low CO 2 partial pressure (8). If a near-surface disposal site is

INTRODUCTION The C A N D U ® nuclear reactors produce 14C wastes originating p r e d o m i n a n t l y f r o m the neutron activation o f 170 p r e s e n t in the h e a v y - w a t e r m o d e r a t o r (I). T h e disposal o f low-level radioactive wastes containing 14C creates the potential for radioactive gas production and subsequent release to the biosphere. Various chemical f o r m s and p a t h w a y s are k n o w n for 14C migration f r o m radioactive waste disposal sites, and the major f o r m is C02 gas (2-4), f o r m e d b y microbial d e c o m p o s i t i o n , chemical degradation of the wastes, and volatilization. Methane production is not e x p e c t e d to b e important (3-5) as s o m e o f it would be c o n s u m e d b y m e t h a n o t r o p h s in soils, resulting in CO 2 (6). The emphasis of this work, therefore, is o n 14CO 2 gas migration. The risks associated with this c o n t a m i n a n t are inhalation (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. Financial contribution from COG (CANDU ®Owners Group) working party #49 is gratefully acknowledged. ® CANDU: CANada Deuterium Uranium. Registered trademark. 421

422 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 complex, and it is important to understand what happens in moist soils. In relatively dry soils, well above the water table, gas is a continuous phase and its migration is dominated by gas-phase diffusion (7). At lower elevations 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 occupied by gas and liquid in approximately equal amounts, forming a transition zone made of separate pockets of liquid. Neither phase is continuous, and water flow is minimal because of the phase discontinuity. This may become a barrier to liquid flow, and the hydraulic conductivity is so low that long periods of time are required for any appreciable water flow to occur (9). The gaseous diffusion process is also expected to be inhibited in this region because C02 has to transfer across several gasliquid and liquid-gas interfaces until the pores are predominantly filled with liquid. Below the transition zone, in a fully saturated medium (i.e., the tension-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 effective barrier to diffusion into groundwaters. It is important to quantify the contribution of this diffusion barrier to mass transfer in safety assessment calculations of radioactive waste disposal facilities, since the a m o u n t of 14CO2t r a ns f e r r e d to the groundwaters is not known at the present time. In static groundwater conditions, molecular diffusion can be the dominant migration mechanism, and it should be constant with time and space, provided 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 silica 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+ , M g 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 C 0 2 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-surface repository. In the present experiment, sand columns were used to determine the influence of the transition

F. CARON ET AL. 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 minimize advection, porewater migration and hydrodynamic dispersion, so molecular diffusion was expected to be the dominant migration mechanism for dissolved C02. The top of the columns were connected to a supply of C02 maintained at a constant partial pressure. The C02 concentration was expected to remain constant because the COz-water exchange is almost instantaneous, and the diffusivity in the gas phase is three to five orders of magnitude 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 hydrostatically 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 developed 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 (advection, etc.) controlled the mass transfer to the columns 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 surface, across which exchange can occur. Both regions 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 experimental apparatus, conditions at the top and bottom of the sand column are considered. As mentioned earlier, the CO 2 concentration in the soil gas is assumed to be the same as that in the flushing gas. Therefore, the " d r y " region (i.e., pores predominantly filled with gas) is modelled as one of constant concentration.

CO 2 TRANSPORT

THROUGH

THE CAPILLARY FRINGE IN SAND

The bottom of the column consists of a porous ceramic disk to hold the sand, yet water and dissolved species are allowed to flow and diffuse through. The porous disk is located a few centimetres 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 mathematical model, based on Fick's law, which is applicable over the semi-infinite region on the aqueous side of the air-water interface:

OC Ot

--=

D

02C

forx>0,

t>0;

[1]

with a far-field boundary condition given by

C ~ Ci as x --" +~', where C: t:

D:

Ci:

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 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 Cg

H = -Cl where H:

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 unionized carbonic acid in solution, eto, 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 negatives 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 chemistry-dependent flux F across the air-water interface (13) given by

[21

(cm2/s),

x:

423

[31

Henry's law coefficient (dimensionless), 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).

F=-D~x

=KL

- C atx=0,

[6]

where KL, expressed in velocity units (cm/s), represents 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] x erfc

+KL

[71

,x>~O.

This expression is strictly valid for unreactive gases. However, C02 dissociates into bicarbonate and c a r b o n a t e ions, and this r e a c t i o n is pHdependent. The partition between CO2(g ) and the

To make Eq. 7 applicable to a porous medium, the parameters must be adjusted for the current situation: C refers to the DIC concentrations in porewater, and KL represents a transport coefficient across the capillary fringe instead of across an open airwater 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 includes 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 ,

HzCO3(aq) and dissolved C02 since both are undistinguishable

C032 .

analytically.

Cx:

Cd

2 H2CO3*(aq) is defined as the sum of the " t r u e " carbonic acid

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

424

DO D - T2 ,

[8]

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., equilibrium) was reached. The values of Co, pH, and H c (from Eqs. 4 and 5) thus obtained are shown in Table la, along with the main characteristics of the columns. Calculations using the Gibbs free energy (AG °) o f the reaction of C02 dissolution in phosphate buffers and water produce values of p H and Co (total DIC) in agreement with these numbers. The b a c k g r o u n d aqueous concentrations C,- in Table 2 are averages of DIC measurements taken before the experiment began. These concentrations are essentially due to water being initially in equilibrium with normal atmospheric C02 concentrations. 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. M e a s u r e m e n t s of moisture content in the sand column show a transition zone of approximately 5 cm in thickness over which pore air is gradually displaced by porewater. The exact location of the air-water interface (where x = 0) is difficult to define and it is not important for modelling. The model does not reflect the details of the capillary fringe structure as this zone is treated as a planar interface. The C02 mass transfer coefficient KL

thus obtained reflects only the bulk b e h a v i o u r across the air-water interface of the capillary fringe.

MATERIALS AND EXPERIMENTAL P R O C E D U R E

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 p o l y c a r b o n a t e tube filled with sand. The column had a double jacketed wall to permit the circulation of water from a constant temperature bath held at 25°C (-+I.0°C). The bottom assembly consisted of a ceramic pressure plate (Soilmoisture Corp., 0.5 bar) supporting the sand and was connected to a reservoir of aqueous phosphate buffer (pH 6 or 7). The reservoir was maintained at a set elevation to fix the zero potentiomettic level for each experiment. Each column was equipped with a set of 10 collinear sampling probes set 3 cm apart. The probes were made of a porous ceramic tip (0.65 cm diameter × 3.2 cm long, rated 1 bar, supplied by Soilmoisture Corp.) glued to a threaded (1A"N P T fitting) polycarbonate tube. The volume inside each probe assembly was approximately 1 mL. The probes were screwed into the column and c h e c k e d 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 e x p e r i m e n t was started after the w a t e 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 # and Type*

Mean Grain Size (mm)t

pH Buffer

Pco 2 (atm)

Diffusion Boundary pH

Hc

Cg

Ci

1, w 2, w 3, w 5, w 6, w la, d 2a, d 3a, d 5a, d

0.248 0.248 0.248 0.248 0.152 0.248 0.248 0.248 0.248

6 6 7 7 7 6 6 7 7

0.2 0.2 0.2 0.2 0.04 0.04 0.04 0.04 0.04

5.88 5.88 6.66 6.66 6.75

0.869 0.869 0.364 0.364 0.314

101.6 101.6 101.6 101.6 20.3

0.353 0.353 1.107 1.107 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.

CO 2

425

TRANSPORT THROUGH THE CAPILLARY FRINGE IN SAND TABLE 2 Other Secondary Parameters

Parameter Dliq Dga~ T H Pco2~ C* Co

K/. (open air)

Value 1.33 x 105 0.144 298 1.2 0.00035 0.60 1.07 105 21.5 250 59.5 1.31 x 10 4

Units

Remarks

cm2/s cm//s K atm mg/L mg/L mg/L mg/L mg/L mg/L cm/s

(as (as (as (as (as (as

C) C) C) C) C) C)

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 t o 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 dissolved CO 2 (8,16). The sand was t h o r o u g h l y 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 unlikely to have affected the particle-size distribution 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 assembled, including the probes and the bottom assembly, 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 vibration. Once the column was filled, a porous geotextile 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 intensity of the gamma rays varies as a function of the pore structure (detection of cavities and heterogeneities in the packing procedure) and water content. Each column was scanned at 0.5 cm intervals. The sand also settles following successive wetting 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 column was obtained by subtracting the wet profile from the dry one. Column Wetting Procedure A water circulation unit held at 25 -+ I°C was connected 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 piezometric 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 reservoir 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.

F. C A R O N E T AL.

426

CO2 gas mixh --IP,

3eramic tip 1 bar)

Water bubbler

~Polycarbonate rod (drilled and milled)

Geotext materi~

1" (2.5cm)

Inert Silica sa

mpling probe

Jacket for thermostated~ water "

Pressure plate (0.5 bar)

~

Hydraulic reference level h=0

.....

[~ 0

Buffer reservoir 1' (2.5crn)

I I

F I G U R E 1. S c h e m a t i c representation of the sand column and the a t t a c h m e n t s (Note: s o m e details were omitted for clarity).

The hydrostatic profiles of the columns had stabilized 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 repository, with no infiltration from above. The draining mode is intended to simulate a soil retaining water after an infiltration episode or a receding 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 consecutive 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. T w o C02 concentration levels were used: 20% and 4% (volume per-

cent). Initially, the gas mixture, 20% C02, 10% 02, and the balance nitrogen, was prepared by Matheson 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 pressure 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 columns 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 D o h r m a n n DC80 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 e x p e r i m e n t were pH 6 and 7 phosphate buffers (22) adjusted to 0.1 M ionic strength. The buffers were left open to

CO 2

TRANSPORT THROUGH THE CAPILLARY FRINGE IN SAND

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 withdrawn. 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 sampling each probe. For the columns in the draining mode, the volume withdrawn from the probes was replaced with the same volume of buffer to replenish the sand with the volume of water lost. The sampling conditions were also tested separately 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 capillary fringe in low moisture content sand needed a higher vacuum in order to collect a sufficient volume of solution. Most of the probes of the columns held in the draining mode also showed this problem because of the high water tension. These DIC results showed inconsistent values and low recoveries. In summary, the DIC measurements taken in saturated sand are believed to be reliable, whereas those in the unsaturated sand have a limited significance because of the sampling problems.

RESULTS

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

427

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 artifacts. As expected, the DIC levels decrease with distance from the diffusion boundary, and the concentration pattern appears consistent with a diffusion-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 difference between the columns whose interstitial water 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% (HCO3-) at pH 7. Aqueous speciation of the DIC involving a negatively charged species, therefore, does not affect D. This is added evidence that dissolved 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

5.0 ! | /

l / --

0.1

0.2

.

.

. . . . . . . IVlOlStUte p r o f i l e

0.3

0.4

/ ,

.

Saturated water tent

I

~10.0

e ~0 15.0

'~20.0

~ O_

25.0 [

=

3o.o I 0

!

........ 20

40

.Hi 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).

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 saturation - 0 . 3 mL/mL near the bottom. This gradual decrease occurs in the top -20-25 cm of the column, 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 coincide where the water content is high, which is consistent 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. Models 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 decrease the DIC content in samples taken in unsaturated sand. Other models (8,25), however, could not explain these results.

Watercontent,mL/mL 0

0.1

0.0

0.2

Moisture'profiles:

,i~ y

E t--

0.3

I -

'(,-

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 characteristics and the conditions under which the data were obtained. Even before the model is developed, examination 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. Examination 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 mentioned earlier, the water content was so low that sampling was difficult, and a systematic error was introduced. Domain II measurements appear to behave linearly with a decreasing slope (as indicated

0.4 0.0

I ~

- - -480 h after start I

!ill`

o

MATHEMATICAL TREATMENT OF THE DATA

500 h her°re start

5.0

_0_

Based on this ambiguity, it is not possible to determine 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 dominates at lower water content. The error associated with this location is minimal because the water content 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 capillary fringe in the wetting mode.

Saturated water

rE

5.0

'6 CL

content 0.290 mL/mL

O

'~ 10.0

o 10.0 Q..

o E15.0

;

...............................

..

~

~

Domain I

E15.o mg CIL

~O20.0

oE20.0

. J ' J ' ~ J m

Domain II

t-O .:'~_--2 5 . 0

tO

~.~_~25.0 0

"qDo,c -. J

T

30.0 ................................................ 0

5

10

15

o 13.. 30.0

20

25

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

I Domain III

2'o

40 ....

6o

80'

100

120

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

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

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 p o r o u s c e r a m i c plate, so that " b a c k diffusion" may be raising background DIC measurements 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 Domain II are considered. Values for KL were found by fitting model predictions to experimental data so that the error between predictions and measurements is minimized. The error is defined as the discrete-valued L2-norm (26) of the difference between simulated and experimental c o n c e n t r a t i o n s of each profile, and is given by

E = ~[ where C(xi, t):

Cx(xi, t):

N:

i

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

,

TABLE 3 Parameters of the Columns Calculated With the Fitting Routine Column

Time (h)

Pin

KL

1

6.6 45.6 69.6 141.5 237.4 357.4 501.6 719.5 839.1 1031.3 1178.1 27.6 47.5 70.9 143.3 239.2 359.2 503.0 720.1 839.7 1033.8 1178.8 2.8 22.0 46.2 167.8 238.3 359.9 554.8 674.5 867.1 1056.3 3.8 23.6 47.7 171.0 239.8 362.4 555.4 675,2 867.8 1058.8 74.8 218.8 387.7 554.4 722.5 1226.3

15.0 21.0 18.0 18.0 18.0 15.0 18.0 15.0 12.9 12.9 12.0 12.0 15.0 15.0 15.0 15.0 15.0 12.0 12.0 12.0 8.6 12.0 15.0 15.0 15.0 18.0 18.0 18.0 15.0 15.0 12.0 12.0 9.0 9.0 9.0 9.0 15.0 15.0 15.0 14.0 13.5 9.5 9.0 8.5 9.0 9.0 6.0 9.0

2.9e-6 2.7e-6 3.5e-6 2.0e-6 2.1e-6 2.0e-6 2.0e-6 2.0e-6 3.6e-6 2.3e-6 1.2e-6 2.4e-6 3.2e-6 5.9e-6 2.4e-6 3.5e-6 2.5e-6 2.9e-6 1.3e-6 1.4e-6 1.8e-6 6.0e-7 1.0e-5 1.2e-5 9.1e-6 3.9e-6 4.3e-6 3.8e-6 3.9e-6 3.6e-6 2.9e-6 2.2e-6 1.8e-5 1.2e-5 1.2e-5 9.0e-6 4.8e-6 4.4e-6 2.8e-6 4.4e-6 1.9e-6 4.7e-6 4.0e-6 5.3e-6 3.9e-6 2.9e-6 6.3e-6 1.4e-6

2

[9]

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 implementations of Eqs. 4, 5, 7, and 9 and from numerical algorithms for finding the minimum values of functions (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 estimates thus consisted of measured or averaged interface positions and KL-values estimated from c o n c e n t r a t i o n gradients near the interface for each profile.

DISCUSSION Table 3 shows the fitted parameter values for the interface position ( " P i n " ) and the transfer coefficient (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.

429

3

5

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 column 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 factor R is defined, therefore, as the ratio of KL for the open air-water surface (Table 2) over the KL obtained in the sand column. It is a measure of resistance enhancement provided by the capillary fringe.

430

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

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

TABLE 4 Column Mass Transfer Coefficients and Resistances K e (cm/s) Column

Mean

SD

Mean Resistance Factor

I 2 i & 2 3 5 3& 5 6 (3 & 5) & 6

2.4e-6 2.5e-6 2.5e-6 5.7e-6 7.4e-6 6.5e-6 4.0e-6 5.9e-6

6.8e-7 1.3e-6 1.1e-6 3.4e-6 4.9e-6 4.3e-6 1.6e-6 4.0e-6

55 52 53 23 18 20 33 22

0.0

5.0

E "-a 0 10.0 0 15.0

E 20.0

E

Fitted Experimental

c- 25.0 0

[10]

where 1 - a : test significance (i.e., confidence level), v = n x + n v - 2 : degrees of freedom, t~/2.~ : a statistic of the Students t-distribution; and the test statistic t is given by

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 experimental 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 C 0 2 partial pressure. In the case of Column 6, the lower C 0 2 partial pressure causes a smaller shift in pH, but essentially the solution properties 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 population 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-

o

[tl > ta/2,v

•

t = (IXx - Ixr)/ [V((nx

- 1)~2 + ( n r - 1)%z)(1/nx + 1 / n r ) / v ] ,

[11] where ~;: (r~: ni:

mean of population i, variance of population i, and 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 presents details of the testing. Differences in K L between 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 columns 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 significantly different from Column 6. This seems to indicate that KL increases with increasing p H and is unaffected by grain size. The grain size differences are probably not discriminating enough to affect the mass transfer coefficient KL. A smaller particle size would affect the capillary rise and the transition zone would be thicker, and the interface more broken up into bubbles, thus adding a longer region of phase discontinuity. The gases would transfer across more airwater 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

30,0

Column

35.0 0

20

40

60

80

100

120

t

t~/2. ~

v

Ho

-0.378 -0.917 -4.315 1.410

1.725 1.734 1.684 1.711

20 18 38 23

accepted accepted rejected accepted

140

DIC concentration (mg C/L) F I G U R E 5. E x a m p l e of model fitting of the DIC concentrations for C o l u m n 2 (t = 360 h).

1 3 (I & 2) (3 &

& 2 & 5 & (3 & 5) 5) & 6

CO2 TRANSPORT THROUGH THE CAPILLARY FRINGE IN SAND 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 surprising. 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 unionized H2C03", whereas bicarbonate HCO 3 predominates at pH 7 (the actual boundary pH is 6.7). The kinetics of ionization H2C03 ~ H C 0 3 - are fast (14), and the proportion of bicarbonate may be high enough at pH 6.7-7 to consider a kinetic enhancement 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 (increase 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 nature 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 i n t e r f a c e m i c r o l a y e r , which t r a ns l at es into a HCO 3- gradient and the CO 2 concentration gradient 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 enhancement 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 expected 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

431

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 interface condition (electroneutrality) but suggests no need for kinetic enhancement at pH 7. This point is still unresolved, but our results suggest that a pHdependent model may need to be developed.

SUMMARY AND CONCLUSION The concentration profile of the Dissolved Inorganic 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 columns used in this work were probably too short to reach this diffusion boundary, and the DIC results likely reflected solely equilibration with gaseous C02. We were able to extract mass transfer coefficients (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 particle size had an influence on KL. We conclude that the two sizes of sand used in this study were probably not discriminating enough to create a difference 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 ionization 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 designed 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

F. CARON ET AL.

432 is needed to d e v e l o p a full-scale model of around a near-surface repository.

14CO2

REFERENCES l. Liepins, L. Z. and T h o m a s , K. W. S u r v e y of ~4C literature relevant to a geologic nuclear waste repository. Rad. Waste Manag. Nucl. Fuel Cycle 10:357 (1988). 2. Striegl, R. G. Fate of g a s e o u s tritium and Carbon-14 released from buried low-level radioactive waste, lOth annual DOE low-level waste management conference. Aug. 30Sept. 1, 1988, 29-34 (1989). 3. Striegl, R. G. Distribution of g a s e s in the u n s a t u r a t e d zone at a low-level radioactive waste disposal site near Sheffield, IL. W a t e r R e s o u r c e s Investigation Report 88-4025, United States Geological Survey, U r b a n a , IL (1988). 4. Killey, R. W. D. and Mattie, J. F. Carbon-14 in the vicinity of W a s t e M a n a g e m e n t Area C: Results of a scoping study. A E C L 10795, A t o m i c E n e r g y of C a n a d a , Ltd., Chalk River, Ontario, C a n a d a (in preparation). 5. Torok, J. and H a a s , M. K. Gas generation by compacted waste. Proceedings o f a workshop on gas generation and release from radioactive waste repositories. Sept. 23-26, 1991, A i x - e n - P r o v e n c e , France. N E A , O E C D , Paris, 175 (1992). 6. Striegl, R. G. and Ishii, A. L. Diffusion and 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 IL. J. ttydrol. 111:133 (1989). 7. T h o r s t e n s o n , D. C., W e e k s , E. P., H a a s , H. and Fisher, D. W. Distribution of g a s e o u s ~2C02, ~3C02, and 14C02 in the sub-soil u n s a t u r a t e d zone of the w e s t e r n U.S. Great Plains. Radiocarbon 2 5 : 3 1 5 - 3 4 6 (1983). 8. J o h n s t o n , H. M. Laboratory studies o f the transport o f Carbon-14 in unsaturated geologic materials. Ph.D. thesis, Univ. of Waterloo, Waterloo, Ontario (1990). 9. Hillel, D. Fundamentals o f soil physics. A c a d e m i c Press, Orlando (1980). 10. Striegl, R. G. and A r m s t r o n g , D. E. Carbon dioxide retention and carbon e x c h a n g e on u n s a t u r a t e d quaternary sedim e n t s . Geochim. Cosmochim. Acta 54:2277 (1990). II. Reid, R. C., Prausnitz, M. J. and Poling, E. B. The properties o f gases and liquids (4th ed). M c G r a w Hill, N e w 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 t u m m , W. and Morgan, J. J. Aquatic chemistry (2nd ed.). J. Wiley & Sons, N e w York (1981).

15. Dullien, F. A. L. Porous media: Fluid transport and pore structure. A c a d e m i c Press, N e w York (1979). 16. Caron, F., Haas, M. K. and Torok, J. T r a n s f e r of C02 to groundwaters through the capillary fringe in porous medium: 1. L a b o r a t o r y s t u d y . COG-92-118 ( R e s t r i c t e d R e p o r t ) , Atomic Energy of C a n a d a Ltd., (1993). 17. K u n z e , G. W. and Dixon, J. B. P r e t r e a t m e n t for mineralogical analysis. In: Methods o f Soil Analysis. Part 1: Physical and Mineralogical Methods (2nd ed.), Klute, A. (Ed.). A m . Soc. Agron., Soil Sci. Soc. A m . , 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 Mineralogical Methods (2rid ed.), Klute, A. (Ed.). A m . Soc. Agron., Soil Sci. Soc. A m . , Madison, WI 9 : 3 8 3 (1986). 19. Creasey, C. L. and Dreiss, S. J. Soil water samples: Do they significantly bias concentrations in water s a m p l e s ? Proceedings o f N W W A Conference, Denver, CO, 173 (1985). 20. Burton, G. R., Keller, N. A., Torok, J. and W o o d s , B. L. Scanning g a m m a spectrometer: U s e r s manual. Atomic Energy of Canada, Ltd., Chalk River, Ontario, C a n a d a (Unpublished report). 21. Gardner, W. H. W a t e r content. In: Methods o f Soil Analysis. Part 1: Physical and Mineralogical Methods (2nd ed.), Klute, A. (Ed.). A m . Soc. Agron., Soil Sci. Soc. A m . , Madison, W l 9 : 4 9 3 (1986). 22. Weast, R. C. (Ed.). CRC Handbook o f Chemistry and Physics. (60th ed.) C R C Press, B o c a Raton (1980). 23. Lai, S. H., Teidje, J. M. and Erickson, A. E. In situ meas u r e m e n t of gas diffusion coefficient in soils. Soil Sci. Soc. Am. J. 4 0 : 3 (1976). 24. Simunek, J. and Suarez, D. L. Modeling of carbon dioxide transport and production in soil. 1. Model d e v e l o p m e n t . Water Resour. Res. 29:487 (1993). 25. Currie, J. A. M o v e m e n t of g a s e s 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. A d d i s o n Wesley, Reading, MA (1964). 27. Press, W. H., Flannery, B. P., T e u k o l s k y , S. A. and Vetterling. W. T. Numerical Recipes--The Art o f Scientific Computing. Cambridge University Press, N e w York (1986). 28. Beyer, W. H. (Ed.). Handbook o f Probability and Statistics (2nd ed.). C R C Press, Cleveland (1968). 29. Hoover, T. E. and Berkshire, D. C. Effects of hydration on carbon dioxide e x c h a n g e across an air-water interface. J. Geophys. Res. 7 4 : 4 5 6 (1969). 30. Quinn, J. A. and Otto, N. C. C a r b o n dioxide e x c h a n g e at the air-sea interface: Flux a u g m e n t a t i o n by chemical reaction. 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. cm 3 6 9 12 15 18 21 24 27 30

Time (h) 26.6 N.A. N.A. N.A. 23.0 25.8 18.9 15.7 8.2 0.5 0.5

45.6 N.A. N.A. N.A. N.A. 26.6 26.7 29.2 16.8 1.1 0.9

69.6 N.A. N.A. N.A. 25.7 24.6 38.2 33.9 26.7 2.6 1.3

141.5 N.A. N.A. 16.9 22.9 22.0 32.0 24.5 15.1 4.2 1.8

237.4 N.A. N.A. 15.0 22.9 32.5 39.(I 32.8 13.5 8.0 4.5

357.4 N.A. N.A. 21.2 30.2 40.7 36.5 23.2 26.1 7.2 5.0

501.6 N.A. N.A. 27.6 41.1 47.3 54.7 32.3 21.4 13.1 8.1

719.5 N.A. N.A. 44.7 51.5 59.9 46.8 19.9 20.9 13.6 12.0 ,

839. I N.A. N.A. 64.8 68.9 62.2 48.0 20.9 19.0 12.4 8.2

1031.3 N.A. N.A. 56.6 62.6 57.4 40.9 24.7 14.4 11.0 6.7

1178.1 N.A. N.A. 43.6 47.2 42.6 32.6 20.5 14.4 9.0 6.0

(continued)

CO2 TRANSPORT THROUGH THE CAPILLARY FRINGE IN SAND APPENDIX

433

Continued

Column 2: Fisher sand, pH buffer 6, wetting mode. Pos. cm 3 6 9 12 15 18 21 24 27 30

Time (h) 27.6 N.A. N.A. N.A. 22.4 17.3 4.6 0.5 0.5 0.4 0.4

47.5 N.A. N.A. N.A. 36.2 34.7 14.7 2.5 0.9 0.6 0.8

70.9 N.A. N.A. N.A. 26.5 57.6 22.7 5.7 1.2 0.9 1.2

143.3 N.A. N.A. N.A. 19.2 39.4 22.9 9.9 1.5 0.9 1.0

239.2 N.A. N.A. N.A. 32.1 53.8 44.2 16.4 3.8 1.4 1.7

359.2 N.A. N.A. N.A. 36.2 58.0 29.5 21.4 4.7 1.4 1.7

503.0 N.A. N.A. N.A. 56.9 46.8 41.9 13.2 4.5 2.9 3.2

720.1 N.A. N.A. 65.0 44.0 32.6 23.1 12.9 8.5 4.5 4.5

839.7 N.A. N.A. 75.9 55.1 33.3 25.2 15.3 7.4 4.7 4.1

1033.8 N.A. N.A. 61.6 48.1 24.6 19.0 11.9 7.3 4.0 4.8

1178.8 N.A. N.A. 49.2 31.0 26.0 18.6 11.3 7.1 4.6 4.6

Column 3: Fisher sand, pH buffer 7, wetting mode. Pos. cm 3 6 9 12 15 18 21 24 27 30

Time (h) 2.8 N.A. 73.7 129.3 111.8 70.4 5.0 3.2 3.0 2.5 3.6

22.0 N.A. N.A. 161.7 132.0 153.0 116.4 15.5 2.8 2.9 4.2

46.2 N.A. N.A. 145.2 145.0 145.0 129.6 54.4 5.2 3.5 3.9

167.8 N.A. N.A. 118.5 140.2 158.4 129.6 87.0 32.2 7.6 4.7

238.3 N.A. N.A. 149.2 156.6 172.7 145.0 107.6 43.9 9.7 5.3

359.9 N.A. N.A. 195.3 179.0 178.9 158.6 107.0 56.4 17.7 6.0

554.8 N.A. N.A. 171.4 170.2 177.9 115.8 82.8 52.1 26.4 7.9

674.5 N.A. N.A. 186.8 172.0 183.4 127.3 85.0 46.7 27.6 8.2

867.1 N.A. 193.1 181.7 161.0 153.0 81.1 63.6 45.5 22.8 11.0

1056.3 N.A. 190.5 186.7 156.7 140.0 80.1 55.9 43.2 24.8 11.6

171.0 N.A. 121.0 159.5 136.3 115.5 92.5 39.3 7.5 4.9 6.3

239.8 N.A. 164.6 177.0 165.0 152.9 107.0 57.5 13.3 6.6 7.2

362.4 N.A. 180.1 195.7 175.3 154.9 136.0 62.3 22.7 10.1 9.0

555.4 N.A. 183.6 191.9 171.0 150.0 117.3 64.5 28.8 15.8 11.5

675.2 N.A. 177.6 185.3 177.4 169.5 136.8 62.5 20.3 15.8 11.2

867.8 185.7 175.3 174.6 149.2 123.7 86.2 48.8 25.3 14.2 10.9

1058.8 177.4 191.5 168.4 144.3 120.2 76. I 50.2 25.5 14.8 I 1.3

Column 5: Fisher sand, pH buffer 7, wetting mode. Pos. cm 3 6 9 12 15 18 21 24 27 30

Time (h) 3.8 159.9 164.6 115.9 73.6 2.5 2.6 3.0 2.6 2.6 4.7

23.6 N.A. 145.6 153.6 107.8 12.8 4.2 2.3 2.0 2.6 4.5

47.7 N.A. 145.7 167.4 110.5 74.9 17.5 4.6 2.6 3.7 6.2

Column 6: Wedron sand, pH buffer 7, wetting mode. Pos. cm 3 6 9 12 15 18 21 24 27 30

Time (h) 74.8 N.A. 42.0 26.9 6.3 3.3 3.0 4.0 4.9 4.9 11.0

218.8 N.A. 45.1 37.4 15.2 5.6 4.1 4.3 4.1 3.9 3.7

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

387.7 N.A. 46.5 38.5 27.9 8.6 6.0 5.2 14.2 3.7 4.1

554.4 N.A. 46.2 38.1 25.5 13.0 9.4 6.2 5.5 5.2 5.5

722.6 N.A. 46.7 40.9 23.8 14.3 10.2 8.2 5.9 5.7 6.3

1226.3 74.1 50.4 29.9 26.2 17.1 13.0 10.4 9.7 8.9 9.3