Chapter 15 14
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Transport of
CO in Unsaturated Glacial and Eolian Sediments 2
Robert G. Striegl and Richard W. Healy U.S. Geological Survey, Box 25046, Mail Stop 413, Federal Center, Denver, CO 80225 Measurements of losses ofCO2to unsaturated sediment-water mixtures indicate that diffusion of CO2 in the unsaturated zone may be substantially retarded by isotopic exchange of C to an adsorbed inorganic C phase. Two geochemical models for calculating CO2 retention in the unsaturated zone were compared. The first accounted only for CO2 retention caused by C dilution to dissolved inorganic carbon. The second accounted for additional C dilution to an adsorbed C phase predicted from CO2 -loss experiments. The geochemical models were separately coupled with a two-dimensional, finite-difference model for gas diffu sion to simulate the distribution of P CO2 in the unsaturated zone near a disposal trench at a low-level radioactive waste-disposal site near Sheffield, Illinois. Com parison of simulated P CO2 distribution with onsite data supported the presence of the adsorbed C phase. 14
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Carbon exchange among mobile gaseous or aqueous phases and less mobile adsorbed or solid phases can result in alteration of the carbon-isotope composition of CO2 in the unsaturated zone atmosphere and of dissolved inorganic carbon (DIC) in soil water. In locations where gas or water are enriched with C relative to immobile phases, incomplete accounting of the C-exchange reser voir could result in unrealistically large predictions of C transport from radioactive-waste dis posal sites, or in radiocarbon ages that overestimate actual ages of underlying ground water. In this paper, the transport of C 0 2 in the unsaturated zone at a low-level radioactive-waste disposal site is considered. Two geochemical models are used to calculate the loss of C(>2 to isotopically exchangeable phases. The first model uses DIC concentration calculated from calcite equilibria to quantify the exchange reservoir. The exchange reservoir in the second model also includes an adsorbed inorganic C phase determined from measured CO2 isotherms. The geochemical models are separately coupled with a model for gas diffusion in the unsaturated zone to simulate the spa tial distribution of C(>2 partial pressure (P CC>2 ) near a waste-disposal trench. Spatial dis tributions of P C 0 2 predicted by each model are compared to the distribution of mean P CC>2 measured at the site during 1984-1986. 1 4
1 4
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1 4
14
SITE STUDY 1 4
The primary gaseous carrier for transport of C from the low-level radioactive-waste disposal site (lat. 41°20' N , long. 89°47' W), near Sheffield, Bureau County, Illinois is C 0 (1). Production of the gas is caused by aerobic microbial decomposition of organic waste buried in waste-disposal trenches. This results in steep gradients in P C 0 2 in undisturbed glacial and eolian sediments adjacent to the site. To collect samples of unsaturated zone gases, nests of gas piezometers were installed along a cross section in boreholes located at distances of 12,29, and 46 m from the end wall 1 4
2
1 4
This chapter not subject to U.S. copyright Published 1990 American Chemical Society
Melchior and Bassett; Chemical Modeling of Aqueous Systems II ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
15.
STRIEGL & HEALY
Transport of
203
CO- in Sediments
of a waste-disposal trench. The piezometers were screened in four lithostratigraphic units at depths of 1.8 to 13.6 m below the land surface (Figure 1). The uppermost units, the Peoria Loess and the Roxana Silt, are postglacial eolian silts having similar textural composition and porosity. The silts are underlain by the Radnor Till Member of the Glasford Formation, a mottled gray, clayey-silt till that overlies a pebbly sand outwash deposit of the Toulon Member of the Glasford Formation (2). The Toulon Member overlies weathered Pennsylvanian shale of the Carbondale Formation of the Desmoinesian Series (1, 3). Particle-size distributions, porosity values, and surface areas of the sediments are listed in Table I. Surface area was not determined for the Roxana Silt, but was assumed to be similar to that of the Peoria Loess because of the textural similarity of the silts. The water table is generally located at a depth of about 15 m in the Carbondale Formation, near the contact with the Toulon Member. More detailed explanations of the hydrogeology and the water balance at the site are presented in (3) and (4). Gas samples were collected from the piezometers on 10 occasions during 1984-86. A detailed description of the gas-piezometer installation; gas collection and analytical procedures; and listings of N2, O2 + A r , CO2 , C02 , CH4 and R n partial pressures for specific collection locations and dates are presented in (1). Partial pressures are products of the total barometric pressure and gas mole fractions. On days when samples were collected, barometric pressures ranged from 97,600 to 99,200 Pa; the average barometric pressure for the period of study was 98,600 Pa. Pressure transducer measurements indicated that differences between barometric pressure at the land surface and barometric pressure at the depths of the piezometer screens were not substantial. Consequently, P C O 2 and P C02 were calculated using the average barometric pressure as the total pressure. Mole fractions of CO2 were measured directly by gas chromatography, whereas C U 2 mole frac tions were a product of the CO2 mole fraction and the measured ratio of CC>2 to CO2 (1). CO2 sam ples were collected from the Peoria Loess, the Roxana Silt, the Radnor Till Member, and the Toulon Member; CC>2 samples were collected from the Roxana Silt, the Radnor Till Member, and the Toulon Member. There was little difference in mean P C O 2 between boreholes at each depth. Therefore, a single mean P C O 2 value was calculated for each lithostratigraphic unit (Table II). Steep horizontal gradients in P C 0 were observed within lithostratigraphic units, therefore a mean P C02 value was calculated for each piezometer sampled (Table III, column B). Variance in mean P C O 2 and P C 0 2 was greatest at locations nearest to the gas sources. The source for C O 2 was root and microbial respiration. This resulted in annual peaks of increased P C O 2 near the land surface dur ing the warm growing season; the amplitudes of annual cycles decreased with depth as CO2 dif fused downward (1). The predominant source of C U 2 was microbial decomposition of buried organic waste; greatest variance in P C02 occurred in the Toulon Member at the piezometer that was closest to the disposal trench. Releases of C02 did not exhibit temporal cycles and were apparently determined by the availability of substrate for decomposition. 14
2 2 2
14
1 4
14
14
1 4
14
2
14
1 4
14
14
GEOCHEMICAL AND TRANSPORT MODELING Coupling of a geochemical model of the phase distribution of carbon isotopes with a model of gas transport in unsaturated porous media is required for prediction of the spatial distribution of P C02 in the unsaturated zone. Because P C02 is very small relative to PCO2, seemingly large increases in P C02 caused by decomposition of low-level radioactive waste have negligible effect on the total concentration of inorganic carbon. Retardation of C02 transport is therefore con trolled chiefly by isotopic exchange of gaseous C to less mobile phases. Quantification of isotope exchange requires knowledge of the initial isotopic ratio and the concentration of C in all exchange able phases. Assuming that isotopic equilibrium is attained, equilibrium concentrations can then be calculated. Two geochemical models were used to quantify the exchangeable C reservoir: (1) a theoretical model based on calcite equilibrium control (calcite equilibrium model), and (2) an empirical model based on measured losses of CO2 from a surrogate unsaturated zone atmosphere to unsaturated water-sediment mixtures (CO2 retention model). 14
14
14
14
1 4
Melchior and Bassett; Chemical Modeling of Aqueous Systems II ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
0.30
Η P5 3 , M S .
0.43
^
(volume fraction)
P CO
3
ClCG
3
Φ
volume fraction)
.
S3
Η ο
ο
> Ο
2 3
δ'
ο
Ρ
Φ
S"
ce Φ ο-
Airfilled porosity (6)
;
to
ο
ο
26.40 2.14
to
00 to
00
9.82
00 απ
σι
00
Cn
Clay 4 μπι
to
3
^
to &
"Ρ
00 00 en 00
ο
to 00
W
adnor 11 )ulon ember
00
Η
S3
-r*
2? W £Γ
φ ο Ο Φ Ρ co 3 Ρ 3 Ρ
Sand >62 μηπ
α-
CO CO Φ
ο ο Η 3 Ρ
co
Ο
3
i
r 1
S a
φ
Ο Ο
Φ
co
ΝΗ
η
cr ο ο*
cV
3
Φ
§' o' Ρ,
3*
co
Ρ
Φ"
cr
Particle size (5) (weight percent)
Total rosity (6)
Melchior and Bassett; Chemical Modeling of Aqueous Systems II ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
15.
STRIEGL & HEALY
Transport of
C0
205
in Sediments
2
Table II. Mean PCO2 Values (in pascals ± 1 standard deviation) Depth (m)
Location
PC0 (Pa)
0 1.8
Atmosphere Peoria Loess Roxana Silt Radnor Till Member Toulon Member
33 ± 3% 2100 ± 48%
3.6 7.3 11.6, 13.6
2
2310 ± 31% 3420 ± 19% 3800 ±
5%
Table III. Simulated and Mean P C 0 2 Values For Locations Where C(>2 Samples Were Collected (in pascals) 14
14
Depth, (m)
A
3.6 7.3 11.6 13.6
* * * *
3.6 7.3 11.6
+ + +
3.6 7.3 11.6
++ ++ ++
A Β C * + ++
C
Β
Horizontal distance from trench = 12 meters. 5.79 χ 10" 5.80 χ ΙΟ^ ± 92% 1.69 χ ΙΟ" 1.19 χ ΙΟ" ± 97% 4.17 χ ΙΟ" 2.54 χ ΙΟ" ± 103% 1.54 χ ΙΟ" 2.03 χ ΙΟ" ± 120% Horizontal distance from trench = 29 meters. 8.04 χ ΙΟ" 3.54 χ ΙΟ" ± 98% 8.49 χ 10" 3.89 χ ΙΟ" ± 73% 2.21 χ ΙΟ" 7.88 χ ΙΟ" ± 85% Horizontal distance from trench = 46 meters. 4.76 χ ΙΟ" 5.90 χ ΙΟ" ± 70% 7.75 χ ΙΟ" 7.45 χ ΙΟ" ± 24% 1.58 χ ΙΟ" 7.48 χ ΙΟ" ± 28% 6
6
5
5
5
5
5
5
7
7
6
6
5
6
7
9
6
7
5
7
* * * *
14
1 4
2
1 4
5
5
6
* 9.50 χ ΙΟ" * 4.56 χ ΙΟ" + 1.12 χ 10"
2
2
6
6
14
1 4
10" ΙΟ" ΙΟ" 10"
7
14
1 4
χ χ χ χ
* 1.16 χ ΙΟ" * 1.83 χ 10" * 5.85 χ 10"
P C 0 2 simulated using calcite equilibrium model. Mean P C 0 ± 1 standard deviation (S.D.). P C 0 2 simulated using CO2 retention model. Modeled P C 0 is in the range of mean P C 0 ± 1 S.D. Modeled P C 0 is greater than mean P C 0 ± 1 S.D. Modeled P CC>2 is more than 10 times greater than mean P C 0 2 1 4
4.91 1.10 2.93 5.07
2
2
1 4
Melchior and Bassett; Chemical Modeling of Aqueous Systems II ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
6
9
7
6
206
CHEMICAL MODELING OF AQUEOUS SYSTEMS II
Calcite Equilibrium Model. 14
Estimates of CC>2 transport are simplified if concentrations of exchangeable inorganic C phases can be calculated from thermodynamic constants and a minimum of site-specific measurements. This is possible if calcite equilibrium control accurately quantifies the exchangeable C reservoir in the unsaturated zone; similar calcite equilibrium control in water-saturated systems is well documented (8, 9, JO). Because isotope exchange to mineral lattices is slow with respect to gas residence times (11, 12), DIC is regarded as the exchange reservoir for gaseous C . For moderately alkaline locations where the DIC concentration is approximately equal to the concentration of HCO3", the DIC reservoir can be quantified from the calcite equilibrium reaction: 14
C0
+
2
+ H 0 + CaC0 ) = 2 HC03(aq) + C a + 2
3(s
( a q )
.
(1)
In terms of HCO3 and P C O 2 , the equilibrium constant for equation 1 is: K
= [HCO3 ] /2 P C 0 , 3
e q
(2)
2
which re-arranges to [ H C O 3 ] = (2 Keq P C 0 )
1 / 3
(3)
2
Equation 3 was previously applied by Thorstenson et al. (13) to describe the relation between [HCO3 ] and P C 0 in an unsaturated zone in the Western Great Plains. It has direct application to the site near Sheffield where unsaturated zone pH is about 7.5 and calcite coatings on sediment particles are present (1). 2
Carbon Dioxide Retention Model. To simulate onsite conditions, batch experiments were conducted that measured losses of CO2 and C 0 from a surrogate atmosphere similar to the unsaturated zone atmosphere at the cross sec tion ( N , 0.752; 0 , 0.200; A , 0.009; C 0 , 0.039; and enriched with 48 dpm/mL of C 0 ) to unsaturated sediments (10 percent water content by mass) collected from the site. Measured CO2 losses were 8 to 17 times larger than losses predicted from Equation 3 (14). The majority of CO2 loss is thought to be dominated by adsorption of bicarbonate (15,16) or carbonate (16) anions on metal oxide surfaces. Ratios of the relative losses of CO2 and C 0 in the batch experiments indicate bicarbonate formation. The reactive surfaces of carbonate minerals are potentially an additional reservoir for C dilution (12, JL7,_18). Exchange of C to carbonate surfaces was estimated to represent 5 to 15 per cent of total C02 losses in several batch experiments (14). For the purpose of transport modeling, measured CO2 losses to unsaturated sediments were quantified by Freundlich isotherms for a P C O 2 range commonly present in unsaturated zones (400 to 4000 Pa). The isotherms define the moles of dissolved plus adsorbed CO2 / m of sediment surface (CO2) associated with the deposits in which onsite measurements were made: 1 4
2
14
2
2
r
2
2
1 4
2
1 4
14
14
2
eolian silts (Peoria Loess and Roxana Silt), C0
8
0
61
= 2[(1.514 χ 10" ) P o - ];
2
C
2
4a
glacial till (Radnor Till Member), 10
C0
2
0
80
= 2[(4.365 χ 10" ) Pco - ]; 2
4b
< )
and outwash sand (Toulon Member), C0
10
2
0
97
= 2[(1.698 χ 10" ) P o - ]C
2
4c
CONCENTRATIONS OF E X C H A N G E A B L E C P E R VOLUME OF UNSATURATED ZONE Coupling of geochemical and gas diffusion models requires common units of concentration for all
Melchior and Bassett; Chemical Modeling of Aqueous Systems II ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
15.
14
Transport of CO
STRIEGL & HEALY
in Sediments
2
207
3
interacting phases. For the modeled example, the units are moles per m of unsaturated zone (gaswater-solid matrix) at in-situ conditions. Gas Phase. 1 4
Regarding CO2 and C 0 as ideal gases at in-situ temperatures and pressures, their concen trations in the unsaturated zone can be calculated by: 2
C
A
= (0D) (PA) / R T
(5) 3
where
C A = concentration of gas A in the unsaturated zone, mol/m ; #D air-filled porosity, dimensionless; PA partial pressure of gas A, Pa; R = gas constant, 8.314 Pa m / K mol; and Τ = mean in-situ temperature, 283 K. =
=
3
Aqueous Phase (Calcite Equilibrium Model) 3
For in-situ conditions, the concentration of HCO3" per m of unsaturated zone (HCO3") is: H C O 3 = (0
where
T
- 0D) (2 K
PC0 )
e q
1 / 3
(6)
2
#τ = total porosity, dimensionless.
Assuming that isotopic equilibrium is attained between the gaseous and aqueous phases, the concentration of H CC>3 per m of unsaturated zone (H C03 ) is: 14
3
14
H C03
14
1/s
14
= (0 - 0D) (2 K ^ PC0 ) T
(P C0 /PC0 ).
2
2
(7)
2
Aqueous plus Adsorbed Phases (C0 Retention Model) 2
According to the C 0 retention model the total concentration of aqueous plus adsorbed C 0 per m of unsaturated zone ( C 0 ) is: 2
2
3
2
-
C Ô 2 = (1-0T) (C0 ) (SA ) ( ) 2
where
S
(8)
Ps
1—θ γ = volume fraction of solids, unitless; SA = surface area of sediment, m /g; and ρs = average density of solids, g/m . 2
S
3
Assuming that isotopic equilibrium is attained between the gaseous and aqueous plus adsorbed phases, the concentration of aqueous plus adsorbed C 0 per m of unsaturated zone ( 1 C0 ) is: 1 4
3
2
4
2
4
1 C0 = ( C 2
14c02
) (C0
2
/C o ). C
2
(9)
GAS TRANSPORT Ordinary molecular diffusion is generally recognized as the primary mechanism for gas transport in the unsaturated zone (19,20,21). Fundamental theory for ordinary diffusion according to Fick's first and second laws is presented in (22); more extensive theoretical discussions of gas transport in porous media are presented in (23, 24, 25). Transient one-dimensional diffusion of gas A into gas Β is given by Fick's second law:
Melchior and Bassett; Chemical Modeling of Aqueous Systems II ACS Symposium Series; American Chemical Society: Washington, DC, 1990.
208
CHEMICAL MODELING OF AQUEOUS SYSTEMS II
a 2
DAB
c
d
_
A
c
A
=
a χ2
(10)
at
=
where
2
DAB molecular diffusion constant for diffusion of gas A into gas B, m /s; C = concentration of gas A in the gas mixture, mol/m of gas; χ == dimension in the direction of diffusion, m; and t = time, s. 3
A
1 4
Development of C 0 Transport Equations 2
According to the calcite equilibrium model, Fick's second law for unsaturated zone can be generalized as: 2
a c
dc
1 4 c o
P - =
A B
dw*m
1 4 c 0 2
2
rD
^S- +
2
dx
+ λ
dt
/ (C
dt
1 4
C0
2
diffusion in the
_ — χ + H"COs)
1 4 c 0 9 Δ
(ID
where r = tortuosity factor for resistance to diffusion caused by the physical structure of the porous medium, dimensionless; and λ = radioactive decay constant, t For the C 0 retention model, the transport equation is generalized as: _1
2
r
D
A
B
f ^ L d x
-
'J** dt
2
^
+
χ (c
+
1 4 c 0 2
+
C ^ ) -
(12)
dt
1 4
-4
1
Because the C decay constant (1.21 χ 10 yr- ) is very small, it was possible to disregard the last term on the right side of Equations 11 and 12 for the waste site example. Substitution of Equations 5 and 7 into Equation 11 gives:
2
t
D
a
14
a [fl (P co )/RT] d x
b
D
2
2
14
aifl (P co )/RT] dt D
2
1/3
+
14
a[(^T-
