The fate of radionuclides in the subsurface is of critical importance to the planning, siting, and evaluation of repositories for radioactive wastes. Mathematical models are an integral component of this process. An accurate understanding of radionuclide transport is required to successfully formulate and use these models. It is well-known that the subsurface is both physically and chemically heterogeneous. Recent research has shown that the resultant spatial variability of hydraulic conductivity and of sorption capacity can significantly affect solute transport in the subsurface. The impact of hydraulic conductivity variability and sorption capacity variability on the transport of radionuclides is, therefore, of great interest. Very few well-controlled, experimentally based laboratory investigations of the transport of radionuclides in physically and chemically heterogeneous porous media have been reported in the literature. The purpose of this paper is to report the preliminary results of such an investigation. We present results obtained for transport of Co2+ in a column packed with two media of differing hydraulic conductivities and sorption capacities. In addition to being influenced by these heterogeneities, transport of the Co2+ is also influenced by rate-limited diffusive mass transfer and non-equilibrium sorption

Brusseau, Mark L.

Zachara, John M.

English

UNL | Libraries

University of Nebraska - Lincoln 
DigitalCommons@University of Nebraska - Lincoln 
US Department of Energy Publications U.S. Department of Energy 
1993 
Transport of Co2+ in a Physically and Chemically Heterogeneous 
Porous Medium 
Mark L. Brusseau 
University of Arizona 
John M. Zachara 
Pacific Northwest National Laboratory, john.zachara@pnl.gov 
Follow this and additional works at: https://digitalcommons.unl.edu/usdoepub 
 Part of the Bioresource and Agricultural Engineering Commons 
Brusseau, Mark L. and Zachara, John M., "Transport of Co2+ in a Physically and Chemically 
Heterogeneous Porous Medium" (1993). US Department of Energy Publications. 210. 
https://digitalcommons.unl.edu/usdoepub/210 
This Article is brought to you for free and open access by the U.S. Department of Energy at 
DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in US Department of Energy 
Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 
Environ. Sci, Technol. 1993, 27, 1937-1939 
Transport of Co2+ in a Physically and Chemically Heterogeneous Porous Medium 
Mark L. Brusseau' 
Soil and Water Science Department and Hydrology and Water Resources Department, University of Arizona, 
Tucson, Arizona 85721 
John M. Zachara 
Geosciences Department, Pacific Northwest Laboratory, Richland. 
Introduction 
The fate of radionuclides in the subsurface is of critical 
importance to the planning, siting, and evaluation of 
repositories for radioactive wastes. Mathematical models 
are an integral component of this process. An accurate 
understanding of radionuclide transport is required to 
successfully formulate and use these models. It is well- 
known that the subsurface is both physically and chem- 
ically heterogeneous. Recent research has shown that the 
resultant spatial variability of hydraulic conductivity and 
of sorption capacity can significantly affect solute transport 
in the subsurface. The impact of hydraulic conductivity 
variability and sorption capacity variability on the trans- 
port of radionuclides is, therefore, of great interest. Very 
few well-controlled, experimentally based laboratory in- 
vestigations of the transport of radionuclides in physically 
and chemically heterogeneous porous media have been 
reported in the literature. The purpose of this paper is 
to report the preliminary results of such an investigation. 
We present results obtained for transport of Co2+ in a 
column packed with two media of differing hydraulic 
conductivities and sorption capacities. In addition to being 
influenced by these heterogeneities, transport of the Co2+ 
is also influenced by rate-limited diffusive mass transfer 
and nonequilibrium sorption. 
Experimental Section 
The miscible displacement technique was used to obtain 
breakthrough curves for the transport of a nonreactive 
tracer (3H20) and Co2+ in a column packed with two media 
of differing hydraulic conductivities and sorption capac- 
ities. A stainless steel column (7.6 cm diameter, 30.5 cm 
length) was packed sequentially with the two media. First, 
a central core of no. 70-mesh fine sand, coated with poorly 
crystalline iron oxide (1.2% by mass), was emplaced; the 
diameter of the core was 4.1 cm. Second, the volume 
between the core and the column wall was filled with a no. 
20-mesh uncoated sand. The mass of no. 20 sand 
represented 74 5% of the total mass of solids packed in the 
column. The gravimetrically measured bulk density and 
porosity of the packed column were 1.44 g cm-3 and 0.49, 
respectively. The pore volume of the column was 680 cm3, 
and the dead volume was less than 2 cm3. 
After packing and prior to the transport experiment, 
the column was flushed with approximately 10 pore 
volumes of an electrolyte solution M Ca(C104)21 of 
pH 6.5. A piston-driven high-performance liquid chro- 
matography pump (SSI Model 300) was used to generate 
constant flow. The transport experiment was performed 
by injecting into the column a step input of solution 
containing the solutes a t  constant concentration, CO [3H20, 
* Corresponding author. 
0013-9363(/93/0927- 1937$04.00/0 0 1993 American Chemical Society 
Washington 99352 
31 000 CPM cm-3; Co2+, 0.59 mg L-' with 30 000 CPM 
cm-3 as 57Col. The effluent was directed to a fraction 
collector (ISCO Retriever), and selected fractions were 
analyzed by liquid scintillation (Packard Tricarb). The 
flow rate a t  which the experiment was performed was 
equivalent to an average linear porewater velocity ( u )  of 
approximately 8 cm h-I. 
Models based on the dual-porosity concept were used 
to analyze the breakthrough curves. With the dual- 
porosity approach, the porous medium is assumed to 
consist of two domains: one with a relatively large hydraulic 
conductivity such that advective-dispersive transport 
occurs and another with a relatively low hydraulic con- 
ductivity such that there is minimal advective-dispersive 
transport. Exchange of solute mass between the two 
domains is represented by the use of a first-order mass 
transfer equation. A model developed for nonsorbing 
solutes (1) was used to analyze the 3H20 breakthrough 
curve. This model has the following four parameters: P, 
the Peclet Number; $, the fraction of porosity that is 
associated with the advective domain; w ,  the ratio of 
hydraulic residence time to mass transfer time; and the 
input pulse, T. For the stratified-media column, the no. 
20-mesh sand will be assumed to comprise the advective 
domain, whereas the no. 70-mesh sand will be assumed to 
comprise the nonadvective domain. With the mass of the 
no. 20 sand representing 74 % of the total mass of solids, 
the foregoing assumption results in a value of 0.74 for 4. 
The input pulse is known from the experiment. A value 
for P (100) was obtained from an experiment performed 
with a homogeneously packed column. This leaves w as 
the only unknown. The optimized value was found by use 
of a nonlinear least-squares optimization program (2). 
A model that accounts for spatially variable hydraulic 
conductivity, spatially variable sorption capacity (dual- 
porosity approach), rate-limited mass transfer, and rate- 
limited sorption/desorption (two-compartment approach) 
(3)  was used to analyze the breakthrough curve obtained 
for Co2+. In addition to P, 9, and w, values for which were 
reported above, this model has the following parameters: 
f ,  mass fraction of sorbent comprising the advective 
domain; K, and K,, the equilibrium sorption constants 
for the advective (a) and nonadvective (n) domains; R,  the 
global retardation factor; F, the fraction of sorbent for 
which sorption is instantaneous; and k2, the reverse 
sorption rate coefficient. With the assumption that the 
no. 20-mesh sand comprises the advective domain, f is 
calculated to be 0.74. Values for K,  and K,  were obtained 
from batch sorption experiments. Isotherms were mea- 
sured for both media following the typical batch procedure, 
with each isotherm consisting of five different initial 
concentrations and with four replicates for each concen- 
tration. A value for R was calculated by using the measured 
1837 Environ. Sci. Technol., Vol. 27, No. 9, 1993 
0 Data I 
- Slmulatlon 
~ 
phy.ICU h.t.ros.n.lly 
.o,Dtlon h.l.,og.".lIY 
r.l.-llmlt.d mai. traniimr 
r.t.-llmlt.d .wpllon 
- - Slmulatlon 
P R Y l l S l l  h.t.rw.n.lfy 
nomos.n.0u. .wpllo" 
r.t.-llmll.d m... IIl"ll.l 
r.I.-llm,l.d 10,210" , 
rll.-llmll.d ma.. 1r.n.l.r 
in.1.nI.n.o". ."pflon 
0 5 10 15 20 25 30 
PORE VOLUMES 
Figure 1. Experimental and simulated breakthrough curves for transport 
of Co2+ through a column packed with two porous media of differing 
hydraulic conductivities and sorption capacities. 
K, and K, values. Values for F and k2 will be obtained 
by optimization of the Co2+ breakthrough curve. 
Results and Discussion 
The two sorption isotherms were well-fitted by the 
Freundlich equation [S = K@I, with Kf = 2.05, n = 0.71 
for the no. 20 sand and Kf = 6.86, n = 0.72 for the no. 
7O/FeOx sand. The sorption capacities of the two media, 
therefore, differ by about a factor of 3. Sorption was 
reversible for both sorbents, and neither material contained 
strong oxidants such as manganese oxides that may 
catalyze transformation of Co(I1) to Co(II1) (cf. refs 4 and 
5). The sorption of Co2+ was dominated by surface 
coordination reactions with iron-oxides and silica, with a 
small contribution of selective ion exchange to the 
micaceous mineral fraction. 
The breakthrough curve for 3Hz0 (not shown) was 
asymmetrical and exhibited a delayed approach to relative 
concentrations of 1 and 0 (i.e., tailing). The optimized 
(one parameter) simulation produced with the dual- 
porosity model matched the data quite well. The retar- 
dation factor was 1, demonstrating the absence of sorptive 
interactions. The asymmetrical and tailed breakthrough 
curve for 3H20, a nonreactive and nonsorbing solute, 
indicates the effect of hydraulic conductivity variability 
on solute transport. It is expected that the hydraulic 
conductivity variability will also influence the transport 
of Co2+. Based on the results of the 3H20 transport 
experiment and the sorption isotherm experiment, it  is 
evident that the column does indeed consist of two media 
with differing hydraulic conductivities and sorption ca- 
pacities. 
The breakthrough curve obtained for the transport of 
Co2+ through the column is presented in Figure 1. A 
simulated curve produced for the case of a homogeneous 
porous medium and instantaneous sorption is also pre- 
sented in Figure 1. The Co2+ breakthrough curve is shifted 
to the left of the curve obtained for ideal conditions. In 
addition, the Co2+ breakthrough curve exhibits a delayed 
approach to relative concentration of 0. The comparison 
reveals that transport of Co2+ through the heterogeneous 
porous medium is significantly nonideal. 
The result obtained from analyzing the 3H20 break- 
through curve with a dual-porosity-based model is used 
to provide a value for (J (0.02), the parameter that 
1838 Envlron. Scl. Technol., VoI. 27, No. 9, 1993 
represents the effect of physical heterogeneity on the 
transport of Co2+. Note that thew value obtained for 3H20 
is modified to account for the difference in diffusivities 
between 3H20 and 57C0 (3). The results from the sorption 
isotherm experiments are linearized [K1= K&o"-~I (6)  to 
provide values for K, (2.38) and K, (7.92). Using these 
data, the global retardation factor [R = 1 + (p/t9)(fKa + 
(1 - f)Kn)l is calculated to be 12.2. 
The optimized curve obtained for the case of hydraulic 
conductivity variability, sorption capacity variability, rate- 
limited mass transfer between the two layers, and rate- 
limited sorption/desorption is shown in Figure l. This 
curve matches the experimental data quite well. The 
values obtained for the two optimized parameters were k2 
= 0.14 h-l and F = 0.68. These values are within the range 
of values obtained from batch sorption experiments 
performed with Co2+ and other radionuclides (7-9). A 
simulated curve produced for the case of hydraulic 
conductivity variability, sorption capacity variability, rate- 
limited mass transfer between the two layers, and instan- 
taneous sorption/desorption is shown in Figure 1. This 
simulation does not describe the experimental data very 
well. The fact that nonequilibrium sorption terms are 
required to fully describe the experimental data and that 
the values of the nonequilibrium parameters are similar 
to published kinetic data supports the contention that 
the transport of Co2+ in our porous-media system was 
influenced by rate-limited sorption/desorption. 
A simulated curve for the case of homogeneous sorption, 
hydraulic conductivity variability, and rate-limited mass 
transfer and sorption is also presented in Figure 1. Clearly, 
the influence of sorption variability must be considered 
to accurately simulate the transport of Co2+. Based on 
the preceding results, it appears that the transport of Co2+ 
was influenced by several factors, including hydraulic 
conductivity variability, sorption capacity variability, rate- 
limited mass transfer between the two layers, and rate- 
limited sorption/desorption. 
The retardation factor calculated by using data obtained 
from batch-isotherm experiments was very representative 
of the observed transport of Co2+ in the column. In 
addition, the mass transfer of Co2+ between the two layers 
appears to have been represented well by using the results 
obtained from analysis of the 3Hz0 breakthrough curve. 
This consistency between different experiments supports 
the contention that the nonideal transport exhibited by 
Co2+ was indeed caused by acombination of several discrete 
factors. 
Conclusion 
The impact of hydraulic conductivity variability and 
sorption capacity variability on the transport of radio- 
nuclides in porous media is critically important to an 
accurate understanding of the fate of radionuclides in the 
subsurface. The results of a well-controlled, experimen- 
tally based investigation of the transport of Co2+ in a 
physically and chemically heterogeneous porous medium 
have demonstrated that transport in heterogeneous porous 
media can be significantly nonideal. As such, transport 
of radionuclides in heterogeneous porous media should 
receive further attention. For the present case, rate-limited 
sorption of Co2+ by the porous media appeared to be 
important. I t  must be remembered, however, that other 
processes, such as oxidation by manganese oxides [Co(II) 
- Co(III)] with subsequent surface precipitation, may 
also be important for the transport of Co2+ in subsurface 
environments. (3) 
Acknowledgments  
(4) 
(5) 
This work was supported by the U.S. Department of 
Energy: partly by the Subsurface Science Program of the 
by the NORCUS/DOE Program (Grant DE-FG06-89ER- 
Szecsody for their assistance. 
Literature C i t ed  
(6) 
Office of Health and Environmental Research and partly (7) 
75522). The authors thank Jerry Phillips and Jim (8) 
(9) 
search Report 119; U S .  Salinity Laboratory, U.S. Depart- 
ment of Agriculture: Washington, DC, 1981. 
Brusseau, M. L.; Jessup, R. E.; Rao, P. S. C. Water Resour. 
Res. 1989,25, 1971. 
Hem, J. D. Chem. Geol. 1978, 21, 199.. 
Hem, J. D.; Roberson, C. E.; Lund, C. J. Geochim. 
Cosmochim. Acta 1985,49, 801. 
Brusseau, M. L.; Rao, P. S. C. CRC Crit. Rev. Environ. 
Control 1989, 19, 33. 
Bencala, K. E.; Jackman, A. P.; Kennedy, V. C.; Avanzino, 
R. J.; Zellweger, G. W. Water Resour. Res. 1983, 19, 725. 
Lyon, K. E.; Patterson, R. J. Water Pollut. Res. J. Can. 
1984, 19, 23. 
Fuentes, H. R.; Polzer, W. L.; Essington, E. H.; Roensch, 
F. R. In Proceedings of Waste Management '85, Waste 
Management Association: Tucson, AZ, Mar 24-28, 1985. 
(1) Coats, K. H.; Smith, B. D. J. SOC. Pet .  Eng. 1964, 4 ,  73.  
(2) van Genuchten, M. Th. Non-equilibrium transport p a -  
rameters from miscible displacement experiments; Re- 
Received for review March 3, 1993. Revised manuscript re- 
ceived May 3, 1993. Accepted May 6, 1993. 
Environ. Sci. Technol., Vol. 27, No. 9, 1993 1839 


Transport of Co2+ in a Physically and Chemically Heterogeneous Porous Medium

DigitalCommons@University of Nebraska

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln US Department of Energy Publications U.S. Department of Energy 1993 Transport of Co2+ in a Physically and Chemically Heterogeneous Porous Medium Mark L. Brusseau University of Arizona John M. Zachara Pacific Northwest National Laboratory, john.zachara@pnl.gov Follow this and additional works at: https://digitalcommons.unl.edu/usdoepub  Part of the Bioresource and Agricultural Engineering Commons Brusseau, Mark L. and Zachara, John M., "Transport of Co2+ in a Physically and Chemically Heterogeneous Porous Medium" (1993). US Department of Energy Publications. 210. https://digitalcommons.unl.edu/usdoepub/210 This Article is brought to you for free and open access by the U.S. Department of Energy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in US Department of Energy Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Environ. Sci, Technol. 1993, 27, 1937-1939 Transport of Co2+ in a Physically and Chemically Heterogeneous Porous Medium Mark L. Brusseau' Soil and Water Science Department and Hydrology and Water Resources Department, University of Arizona, Tucson, Arizona 85721 John M. Zachara Geosciences Department, Pacific Northwest Laboratory, Richland. Introduction The fate of radionuclides in the subsurface is of critical importance to the planning, siting, and evaluation of repositories for radioactive wastes. Mathematical models are an integral component of this process. An accurate understanding of radionuclide transport is required to successfully formulate and use these models. It is well- known that the subsurface is both physically and chem- ically heterogeneous. Recent research has shown that the resultant spatial variability of hydraulic conductivity and of sorption capacity can significantly affect solute transport in the subsurface. The impact of hydraulic conductivity variability and sorption capacity variability on the trans- port of radionuclides is, therefore, of great interest. Very few well-controlled, experimentally based laboratory in- vestigations of the transport of radionuclides in physically and chemically heterogeneous porous media have been reported in the literature. The purpose of this paper is to report the preliminary results of such an investigation. We present results obtained for transport of Co2+ in a column packed with two media of differing hydraulic conductivities and sorption capacities. In addition to being influenced by these heterogeneities, transport of the Co2+ is also influenced by rate-limited diffusive mass transfer and nonequilibrium sorption. Experimental Section The miscible displacement technique was used to obtain breakthrough curves for the transport of a nonreactive tracer (3H20) and Co2+ in a column packed with two media of differing hydraulic conductivities and sorption capac- ities. A stainless steel column (7.6 cm diameter, 30.5 cm length) was packed sequentially with the two media. First, a central core of no. 70-mesh fine sand, coated with poorly crystalline iron oxide (1.2% by mass), was emplaced; the diameter of the core was 4.1 cm. Second, the volume between the core and the column wall was filled with a no. 20-mesh uncoated sand. The mass of no. 20 sand represented 74 5% of the total mass of solids packed in the column. The gravimetrically measured bulk density and porosity of the packed column were 1.44 g cm-3 and 0.49, respectively. The pore volume of the column was 680 cm3, and the dead volume was less than 2 cm3. After packing and prior to the transport experiment, the column was flushed with approximately 10 pore volumes of an electrolyte solution M Ca(C104)21 of pH 6.5. A piston-driven high-performance liquid chro- matography pump (SSI Model 300) was used to generate constant flow. The transport experiment was performed by injecting into the column a step input of solution containing the solutes a t  constant concentration, CO [3H20, * Corresponding author. 0013-9363(/93/0927- 1937$04.00/0 0 1993 American Chemical Society Washington 99352 31 000 CPM cm-3; Co2+, 0.59 mg L-' with 30 000 CPM cm-3 as 57Col. The effluent was directed to a fraction collector (ISCO Retriever), and selected fractions were analyzed by liquid scintillation (Packard Tricarb). The flow rate a t  which the experiment was performed was equivalent to an average linear porewater velocity ( u )  of approximately 8 cm h-I. Models based on the dual-porosity concept were used to analyze the breakthrough curves. With the dual- porosity approach, the porous medium is assumed to consist of two domains: one with a relatively large hydraulic conductivity such that advective-dispersive transport occurs and another with a relatively low hydraulic con- ductivity such that there is minimal advective-dispersive transport. Exchange of solute mass between the two domains is represented by the use of a first-order mass transfer equation. A model developed for nonsorbing solutes (1) was used to analyze the 3H20 breakthrough curve. This model has the following four parameters: P, the Peclet Number; $, the fraction of porosity that is associated with the advective domain; w ,  the ratio of hydraulic residence time to mass transfer time; and the input pulse, T. For the stratified-media column, the no. 20-mesh sand will be assumed to comprise the advective domain, whereas the no. 70-mesh sand will be assumed to comprise the nonadvective domain. With the mass of the no. 20 sand representing 74 % of the total mass of solids, the foregoing assumption results in a value of 0.74 for 4. The input pulse is known from the experiment. A value for P (100) was obtained from an experiment performed with a homogeneously packed column. This leaves w as the only unknown. The optimized value was found by use of a nonlinear least-squares optimization program (2). A model that accounts for spatially variable hydraulic conductivity, spatially variable sorption capacity (dual- porosity approach), rate-limited mass transfer, and rate- limited sorption/desorption (two-compartment approach) (3)  was used to analyze the breakthrough curve obtained for Co2+. In addition to P, 9, and w, values for which were reported above, this model has the following parameters: f ,  mass fraction of sorbent comprising the advective domain; K, and K,, the equilibrium sorption constants for the advective (a) and nonadvective (n) domains; R,  the global retardation factor; F, the fraction of sorbent for which sorption is instantaneous; and k2, the reverse sorption rate coefficient. With the assumption that the no. 20-mesh sand comprises the advective domain, f is calculated to be 0.74. Values for K,  and K,  were obtained from batch sorption experiments. Isotherms were mea- sured for both media following the typical batch procedure, with each isotherm consisting of five different initial concentrations and with four replicates for each concen- tration. A value for R was calculated by using the measured 1837 Environ. Sci. Technol., Vol. 27, No. 9, 1993 0 Data I - Slmulatlon ~ phy.ICU h.t.ros.n.lly .o,Dtlon h.l.,og.".lIY r.l.-llmlt.d mai. traniimr r.t.-llmlt.d .wpllon - - Slmulatlon P R Y l l S l l  h.t.rw.n.lfy nomos.n.0u. .wpllo" r.t.-llmll.d m... IIl"ll.l r.I.-llm,l.d 10,210" , rll.-llmll.d ma.. 1r.n.l.r in.1.nI.n.o". ."pflon 0 5 10 15 20 25 30 PORE VOLUMES Figure 1. Experimental and simulated breakthrough curves for transport of Co2+ through a column packed with two porous media of differing hydraulic conductivities and sorption capacities. K, and K, values. Values for F and k2 will be obtained by optimization of the Co2+ breakthrough curve. Results and Discussion The two sorption isotherms were well-fitted by the Freundlich equation [S = K@I, with Kf = 2.05, n = 0.71 for the no. 20 sand and Kf = 6.86, n = 0.72 for the no. 7O/FeOx sand. The sorption capacities of the two media, therefore, differ by about a factor of 3. Sorption was reversible for both sorbents, and neither material contained strong oxidants such as manganese oxides that may catalyze transformation of Co(I1) to Co(II1) (cf. refs 4 and 5). The sorption of Co2+ was dominated by surface coordination reactions with iron-oxides and silica, with a small contribution of selective ion exchange to the micaceous mineral fraction. The breakthrough curve for 3Hz0 (not shown) was asymmetrical and exhibited a delayed approach to relative concentrations of 1 and 0 (i.e., tailing). The optimized (one parameter) simulation produced with the dual- porosity model matched the data quite well. The retar- dation factor was 1, demonstrating the absence of sorptive interactions. The asymmetrical and tailed breakthrough curve for 3H20, a nonreactive and nonsorbing solute, indicates the effect of hydraulic conductivity variability on solute transport. It is expected that the hydraulic conductivity variability will also influence the transport of Co2+. Based on the results of the 3H20 transport experiment and the sorption isotherm experiment, it  is evident that the column does indeed consist of two media with differing hydraulic conductivities and sorption ca- pacities. The breakthrough curve obtained for the transport of Co2+ through the column is presented in Figure 1. A simulated curve produced for the case of a homogeneous porous medium and instantaneous sorption is also pre- sented in Figure 1. The Co2+ breakthrough curve is shifted to the left of the curve obtained for ideal conditions. In addition, the Co2+ breakthrough curve exhibits a delayed approach to relative concentration of 0. The comparison reveals that transport of Co2+ through the heterogeneous porous medium is significantly nonideal. The result obtained from analyzing the 3H20 break- through curve with a dual-porosity-based model is used to provide a value for (J (0.02), the parameter that 1838 Envlron. Scl. Technol., VoI. 27, No. 9, 1993 represents the effect of physical heterogeneity on the transport of Co2+. Note that thew value obtained for 3H20 is modified to account for the difference in diffusivities between 3H20 and 57C0 (3). The results from the sorption isotherm experiments are linearized [K1= K&o"-~I (6)  to provide values for K, (2.38) and K, (7.92). Using these data, the global retardation factor [R = 1 + (p/t9)(fKa + (1 - f)Kn)l is calculated to be 12.2. The optimized curve obtained for the case of hydraulic conductivity variability, sorption capacity variability, rate- limited mass transfer between the two layers, and rate- limited sorption/desorption is shown in Figure l. This curve matches the experimental data quite well. The values obtained for the two optimized parameters were k2 = 0.14 h-l and F = 0.68. These values are within the range of values obtained from batch sorption experiments performed with Co2+ and other radionuclides (7-9). A simulated curve produced for the case of hydraulic conductivity variability, sorption capacity variability, rate- limited mass transfer between the two layers, and instan- taneous sorption/desorption is shown in Figure 1. This simulation does not describe the experimental data very well. The fact that nonequilibrium sorption terms are required to fully describe the experimental data and that the values of the nonequilibrium parameters are similar to published kinetic data supports the contention that the transport of Co2+ in our porous-media system was influenced by rate-limited sorption/desorption. A simulated curve for the case of homogeneous sorption, hydraulic conductivity variability, and rate-limited mass transfer and sorption is also presented in Figure 1. Clearly, the influence of sorption variability must be considered to accurately simulate the transport of Co2+. Based on the preceding results, it appears that the transport of Co2+ was influenced by several factors, including hydraulic conductivity variability, sorption capacity variability, rate- limited mass transfer between the two layers, and rate- limited sorption/desorption. The retardation factor calculated by using data obtained from batch-isotherm experiments was very representative of the observed transport of Co2+ in the column. In addition, the mass transfer of Co2+ between the two layers appears to have been represented well by using the results obtained from analysis of the 3Hz0 breakthrough curve. This consistency between different experiments supports the contention that the nonideal transport exhibited by Co2+ was indeed caused by acombination of several discrete factors. Conclusion The impact of hydraulic conductivity variability and sorption capacity variability on the transport of radio- nuclides in porous media is critically important to an accurate understanding of the fate of radionuclides in the subsurface. The results of a well-controlled, experimen- tally based investigation of the transport of Co2+ in a physically and chemically heterogeneous porous medium have demonstrated that transport in heterogeneous porous media can be significantly nonideal. As such, transport of radionuclides in heterogeneous porous media should receive further attention. For the present case, rate-limited sorption of Co2+ by the porous media appeared to be important. I t  must be remembered, however, that other processes, such as oxidation by manganese oxides [Co(II) - Co(III)] with subsequent surface precipitation, may also be important for the transport of Co2+ in subsurface environments. (3) Acknowledgments  (4) (5) This work was supported by the U.S. Department of Energy: partly by the Subsurface Science Program of the by the NORCUS/DOE Program (Grant DE-FG06-89ER- Szecsody for their assistance. Literature C i t ed  (6) Office of Health and Environmental Research and partly (7) 75522). The authors thank Jerry Phillips and Jim (8) (9) search Report 119; U S .  Salinity Laboratory, U.S. Depart- ment of Agriculture: Washington, DC, 1981. Brusseau, M. L.; Jessup, R. E.; Rao, P. S. C. Water Resour. Res. 1989,25, 1971. Hem, J. D. Chem. Geol. 1978, 21, 199.. Hem, J. D.; Roberson, C. E.; Lund, C. J. Geochim. Cosmochim. Acta 1985,49, 801. Brusseau, M. L.; Rao, P. S. C. CRC Crit. Rev. Environ. Control 1989, 19, 33. Bencala, K. E.; Jackman, A. P.; Kennedy, V. C.; Avanzino, R. J.; Zellweger, G. W. Water Resour. Res. 1983, 19, 725. Lyon, K. E.; Patterson, R. J. Water Pollut. Res. J. Can. 1984, 19, 23. Fuentes, H. R.; Polzer, W. L.; Essington, E. H.; Roensch, F. R. In Proceedings of Waste Management '85, Waste Management Association: Tucson, AZ, Mar 24-28, 1985. (1) Coats, K. H.; Smith, B. D. J. SOC. Pet .  Eng. 1964, 4 ,  73.  (2) van Genuchten, M. Th. Non-equilibrium transport p a -  rameters from miscible displacement experiments; Re- Received for review March 3, 1993. Revised manuscript re- ceived May 3, 1993. Accepted May 6, 1993. Environ. Sci. Technol., Vol. 27, No. 9, 1993 1839 

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Transport of Co2+ in a Physically and Chemically Heterogeneous Porous Medium

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