Published in Vadose Zone Journal 3:867-874 (2004)
© 2004 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SPECIAL SECTION: RESEARCH ADVANCES IN VADOSE ZONE HYDROLOGY THROUGH SIMULATIONS WITH THE TOUGH CODES
Coupled Processes of Fluid Flow, Solute Transport, and Geochemical Reactions in Reactive Barriers
Jeongkon Kima,d,*,
Franklin W. Schwartzb,
Tianfu Xuc,
Heechul Choid and
In S. Kima,d
a Korea Institute of Water and Environment, Korea Water Resources Corporation, Daejon, Korea
b Department of Geological Sciences, The Ohio State University, Columbus, OH 43210
c Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
d Department of Environmental Science and Engineering, Kwangju Institute of Science and Technology, Gwangju, Korea
* Corresponding author (jkkim{at}kowaco.or.kr)
Received 29 August 2003.
 |
ABSTRACT
|
|---|
A complex pattern of coupling between fluid flow and mass transport develops when heterogeneous reactions occur. For instance, dissolution and precipitation reactions can change a porous medium's physical properties, such as pore geometry and thus permeability. These changes influence fluid flow, which in turn impacts the composition of dissolved constituents and the solid phases, and the rate and direction of advective transport. Two-dimensional modeling studies using TOUGHREACT were conducted to investigate the coupling between flow and transport developed as a consequence of differences in density, dissolution–precipitation, and medium heterogeneity. The model includes equilibrium reactions for aqueous species, kinetic reactions between the solid phases and aqueous constituents, and full coupling of porosity and permeability changes resulting from precipitation and dissolution reactions in porous media. In addition, a new permeability relationship is implemented in TOUGHREACT to examine the effects of geochemical reactions and density difference on plume migration in porous media. Generally, the evolutions in the concentrations of the aqueous phase are intimately related to the reaction-front dynamics. Plugging of the medium contributed to significant transients in patterns of flow and mass transport.
|
INTRODUCTION
|
|---|
OFTEN WATERS FROM LANDFILLS or mining operations contain elevated concentrations of Fe and other metals at low pH. A promising approach to minimize groundwater contamination by acidic metallic compounds is the use of calcareous reactive barriers. For example, in a ferric-calcareous barrier, hydrolysis of Fe3+ generates H+, which is neutralized by reaction with calcite, causing the formation of ferric oxyhydroxide. Because iron oxyhydroxides form hydrous aggregates capable of reducing porosity and permeability, their precipitation along the front of a contaminant plume is potentially useful in slowing the spread of the contaminant (Fryar and Schwartz, 1994). The essence of this technology is the combination of containment, in which low-permeability barriers are installed around the contaminant plume, with in situ treatment, in which reactions are induced to immobilize contaminants.
The main objective of this study was to evaluate the impact of dissolution–precipitation and heterogeneity on mass transport and reaction zone development in a two-dimensional reactive barrier system.
|
PROBLEM DESCRIPTION
|
|---|
In this study, chemical evolution within a ferric-calcareous barrier was examined using a two-dimensional model. Specifically, we demonstrated the coupled effects of variable density fluid flow and heterogeneous reactive mass transport and their influence on the reaction front development. The aqueous species involved in the reaction are H+, OH–, Cl–, Na+, Fe3+, ClO–4, Ca2+, H2CO03, HCO–3, and CO–3, and the mineral phases are calcite and Fe(OH)3(s).
Shi (2000) conducted a series of experiments using a flow tank measuring 1.82 m long, 0.62 m high, and 0.10 m deep, providing a total volume and inflow area of 0.1133 m3 and 0.062 m2, respectively. The tank was evenly filled with coarse-grained glass beads (0.75 mm) mixed with 0.3% (w/w) calcite. The inflow rate was fixed at a linear flow velocity of 2.56 cm h–1. An acidic (pH 
2.5) contaminant solution consisting of 2000 mg L–1 NaCl (conservative tracer) and 300 mg L–1 Fe(ClO4)3 (reactive tracer) was injected at 65.0 mL min–1 at an injection point (x = 0.2 m and z = –0.2 m). The experiments were conducted at about 20°C.
The numerical simulations were conducted employing the same conditions as used in the experiment. A computational mesh was created for the model domain using 3552 elements (74 columns x 48 rows). Modeling parameters are summarized in Table 1. Assuming that the effects of calcite on the porosity and hydraulic conductivity were negligible, the hydraulic conductivity values for the 0.75-mm glass beads was estimated to be 4.20 x 10–2 cm s–1, which is approximately 4.20 x 10–10 m2. Total concentrations for the resident, inlet, and injection fluids are listed in Table 2. Boundary conditions for flow included, depending on the application, constant pressures or constant fluxes assigned at the left boundary, whereas a hydrostatic pressure profile was specified at the right outflow boundary. For transport, constant concentrations were assigned at the left inlet boundary, and a free-exit boundary was specified at the right boundary. Initial dissolved concentrations were values that were in equilibrium with calcite throughout the domain. The fluid densities in the tank, inlet, and injection source were estimated to be 998.2, 998.2, and 999.7 kg m–3, respectively, at 20°C. The concentrations of the inlet fluid were different from those of the resident fluid because only in the resident solution were the dissolved species in equilibrium with calcite.
Model Description
The simulations were performed using the nonisothermal reactive geochemical transport code TOUGHREACT (Xu and Pruess, 1998). This code was developed by introducing reactive chemistry into the framework of the existing multiphase fluid and heat flow code TOUGH2 (Pruess, 1991), which uses integral finite differences (Narasimhan and Witherspoon, 1976) for space discretization. An implicit time-weighting scheme is used for the individual components of the model consisting of flow, transport, and kinetic geochemical reaction. TOUGHREACT employs a sequential iteration approach, which solves the transport and the reaction equations separately. After solution of the flow equations, the fluid velocities and phase saturations provide the basis for the chemical transport simulation, which is solved on a component basis. The resulting concentrations are substituted into the chemical reaction model. The system of chemical reaction equations is then solved on a grid-block basis by means of Newton–Raphson iterations, similar to Parkhurst et al. (1980) and Wolery (1992). The chemical transport and reactions are iteratively solved until convergence is achieved. Full details on the numerical methods are given in Xu and Pruess (1998). The model can be applied to one-, two-, or three-dimensional porous and fractured media with physical and chemical heterogeneity, accommodating any number of chemical species present in the liquid, gas, and solid phases. A wide range of subsurface thermo-physical-chemical processes can be considered, including:- fluid flow in both liquid and gas phases under pressure and gravity forces
- capillary pressure effects for the liquid phase
- heat flow by conduction, convection, and diffusion
- transport of aqueous and gaseous species by advection and molecular diffusion in both liquid and gas phases
- aqueous chemical complexation and gas dissolution–exsolution under local equilibrium
- mineral dissolution and precipitation under local equilibrium or kinetic conditions
Permeability–Porosity Relationship
TOUGHREACT accounts for porosity and permeability changes that occur as a result of chemical reactions in porous medium by employing the Carman–Kozeny model (Bear, 1972), a macroscopic model that considers the porous medium as a bundle of cylindrical pores. However, the conditions we deal with are far more complicated in many aspects because:
- Calcite grains mixed with glass beads are not physically connected among themselves in the porous medium because of the small mass fraction of calcite (0.3% [w/w]). Thus, dissolution of calcite grains is unlikely to affect the permeability of the porous medium.
- Iron commonly exists in two oxidation states: Fe(II) and Fe(III). Ferrous Fe in a spent acid will precipitate as gelatinous ferric hydroxide when the pH of the acid rises above 2 (Crowe, 1986), which will result in plugging when only small quantities of solids have precipitated.
- Carbon dioxide gas exsolution due to the dissolution of calcite was found to reduce hydraulic conductivity by 2 or more orders of magnitude, causing the plume to decelerate (Fryar and Schwartz, 1998).
There was no information available on how the calcite grains existing unconnected affects changes in permeability and hydraulic conductivity. In addition, the current version of TOUGHREACT did not account for direct coupling of gas exsolution and phase change in the density-dependent flow module. The porous medium used in this study (e.g., 0.75-mm glass beads) is very uniform, with a simple geometry, which excluded the use of microscopic models based on a "cut-and-random-rejoin" approach assuming that pores of different radii are randomly distributed within the porous medium and hydraulic conductivity is determined by the interconnectivity of the pores.
Accordingly, a new permeability-porosity relationship was developed and implemented in TOUGHREACT to approximate changes in permeability and hydraulic conductivity by employing lumped parameters as a function of Fe(OH)3(s). It was assumed that the contribution of calcite dissolution to permeability change was negligible under the conditions of this study. The new permeability–porosity function is in the following form:
 | [1] |
where k is the permeability, ki is the intrinsic permeability, 
i and Fe
3 are the initial porosity and the volume fraction of Fe(OH)3(s), and 
and ß are fitting constants. Taylor and Jaffé (1990) used a similar function to describe permeability reduction due to biomass growth in porous media.
|
RESULTS AND DISCUSSION
|
|---|
Permeability–Porosity Relationship Comparison
Simulation results obtained using the Carman–Kozeny model, as implemented in TOUGHREACT, were compared with one of many trial simulation results conducted using Eq. [1] to determine a set of and ß that reasonably describes development of reaction zone and dissolved plumes as shown by the experimental data of Shi (2000). Figure 1
shows the experimental result obtained under the same condition as with the numerical simulations. Figures 2a through 2e
show profiles for permeability, Fe(OH)3(s), Fe3+, pH, and Cl–, respectively, obtained using the Carman–Kozeny equation. Permeability of the porous medium did not change appreciably in most of the reaction zones (Fig. 2a). As a result, all profiles show a thin, elongate plume shape (Fig. 2b–2e). The advective flow carries the solute plume laterally across the domain without much vertical spreading because of the lack of permeability reduction.
View larger version (35K):
[in this window]
[in a new window]
|
Fig. 2. Profiles using the Carman–Kozeny model at 38 d for (a) permeability, (b) Fe(OH)3(s), (c) Fe3+, (d) pH, and (e) Cl–.
|
|
Figures 3a through 3e
show results of the same simulations using the new permeability–porosity relationship, with = 50.0 and ß = 0.5. This set of and ß values were found to best describe experimental data. Unlike the profiles in Fig. 2, profiles for permeability, Fe(OH)3(s), Fe3+, pH, and Cl– in Fig. 3 indicate a significant vertical spreading resulting from permeability reduction in the reaction front as the acid plume migrates. In both cases, there are similar degrees of precipitation and dissolution, as shown in Fig. 2b and 3b. Precipitation in Fig. 2, however, occurs along a narrow, long strip because of the lack of permeability reduction calculated using the Carman–Kozeny model. However, in Fig. 3 permeability reduction as calculated using Eq. [1] is much greater, resulting in a wide, short precipitation zone. The effect of density on vertical plume migration is more obvious in Fig. 3 than in Fig. 2 because of reduced horizontal flow velocity caused by stronger permeability reduction in Fig. 3.
Reaction Zone Development
Figure 4
presents the evolution of Fe(OH)3(s) precipitation and redissolution dynamics as the heterogeneous reaction taking place between solid and liquid phases progresses. The development of the reaction zones is a continuous process in which the heterogeneous reactions (dissolution and precipitation) evolve sequentially or simultaneously as calcite comes into contact with the introduced contaminants. One of the primary concerns in a reactive barrier, such as a calcareous wall, is the effective hydraulic behavior of the reactive barrier. Figure 4 clearly shows that a complex pattern of coupling between fluid flow and mass transport develops when heterogeneous reactions occur.
The coupling between geochemical reactions caused by the injection of Fe(ClO4)3 solution and the density-dependent flow influence the reactions and dissolved plume migration in a complicated manner. Although the main migration direction of the dissolved plume is controlled by the ambient flow of water, density-driven flow related to the large concentration of dissolved ions in the injected source water caused significant vertical movement to develop in both the dissolved plume and the reaction zone. In this study, there was a difference in density of approximately 0.15% between the ambient and injection waters, based on the density of water estimated at 2000 mg L–1 NaCl at 20°C. Note that the current version of TOUGHREACT could not account for multiple species in calculating density changes. Thus, it was assumed that solute density could be calculated based on NaCl concentration only, neglecting contributions from other species, which was justified by the fact that the NaCl concentration was much greater than that of other species.
The reaction zones propagated much more slowly than the dissolved plume. While the nonreactive species (Cl–, Na+, ClO–4, Ca2+) spread beyond the reaction zone (Fig. 4), the reactive species (Fe3+) is effectively retained in the reaction zone and moves much more slowly (Fig. 4). The final shape of the reaction zone was significantly influenced by the geochemical reactions in addition to the density gradients.
Effect of Heterogeneity
Chemical heterogeneity of a porous medium influences the pattern of reactions in a highly complex and nonlinear manner. Heterogeneity in permeability is another factor that influences the pathway of reactive plumes. For instance, local heterogeneity can perturb the interface and promote the formation of fingering in dense plumes (Schincariol, 1998).
Previous simulations discussed here assume that the porous medium is both chemically (calcite content) and physically (permeability) homogeneous. However, it was inevitable to completely avoid some sort of heterogeneity created even under well-designed experimental conditions. In this section, simulation results from a chemically and physically heterogeneous porous medium are presented.
Spatially variable random fields for calcite content and for permeability were generated using the Fourier spectral technique of Robin et al. (1993) with correlation lengths of 2.54 and 1.27 cm in the x and z directions, respectively. Figures 5a and 5b show the random fields for calcite content and permeability, respectively. The mean and variance of the calcite content random field are 0.302% (w/w) and 0.088, respectively, and those of the permeability (ln k) are –21.55 and 0.695, respectively. Note that the field is spatially unrelated.
Figures 6 and 7
show the profiles for permeability, Fe(OH)3(s), Fe3+, pH, and Cl– for the chemical heterogeneous case and for the physical heterogeneous case, respectively. It is clear that both chemical and physical heterogeneities significantly impact the progress of heterogeneous reactions and dissolved plumes in the calcite reactive barrier. As shown in Fig. 6 and 7, both physical and chemical heterogeneities affected permeability changes in response to precipitation along the fast flowing paths. The two heterogeneous fields generated with different conditions have differing distributions of permeability or calcite content, although the mean values are very close. Therefore, it is quite difficult to directly compare the results obtained from the two cases and determine which effect is more significant in controlling the reaction front dynamics. However, one could tell that fingering is more pronounced in the chemically heterogeneous porous medium (Fig. 6) than in the physically heterogeneous porous medium (Fig. 7). Averaging within a grid block (and also in a homogeneous system) must have greatly reduced our ability to capture clogging effects in detail. That is, the results may change, depending on the grid size. For example, permeability reductions might be less evident if larger grid sizes were used due to the averaging effect.
View larger version (43K):
[in this window]
[in a new window]
|
Fig. 6. Profiles for (a) permeability, (b) Fe(OH)3(s), (c) Fe3+, (d) pH, and (e) Cl– in the chemically heterogeneous porous medium at 38 d.
|
|
View larger version (54K):
[in this window]
[in a new window]
|
Fig. 7. Profiles for (a) permeability, (b) Fe(OH)3(s), (c) Fe3+, (d) pH, and (e) Cl– in the physically heterogeneous porous medium at 38 d.
|
|
|
CONCLUSIONS
|
|---|
We have examined coupled and geochemically reactive systems in homogeneous and heterogeneous porous media using TOUGHREACT. A new permeability–porosity relationship model was developed and implemented in TOUGHREACT. We demonstrate the coupled effects of variable density fluid flow and heterogeneous reactive mass transport and their influence on developing a reaction front. Generally, the evolutions in the concentrations of the aqueous phase are clearly related to the reaction-front dynamics. Plugging of the medium contributed to significant transients in patterns of flow and mass transport. Although the new permeability model describes approximately the general trend of reactive plume migration under heterogeneous reactions, this approach is subject to further verification.
|
ACKNOWLEDGMENTS
|
|---|
Funding for this study was provided by the National Science Foundation, EAR-9814820. This research was also supported by a grant (4-1-1) from Sustainable Water Resources Research Center (SWRRC) of the 21st Century Frontier R&D program through the Water Reuse Technology Center (WRTC) at Kwangju Institute of Science & Technology (K-JIST).
|
REFERENCES
|
|---|
- Bear, J. 1972. Dynamics of fluids in porous media. American Elsevier, New York.
- Crowe, C.W. 1986. Precipitation of hydrated silica from spent hydrofluoric acid: How much of a problem is it? J. Pet. Technol., p. 1234–1240.
- Fryar, A.E., and F.W. Schwartz. 1994. Modeling the removal of metals from ground water by a reactive barrier: Experimental results. Water Resour. Res. 30:3455–3469.
- Fryar, A.E., and F.W. Schwartz. 1998. Hydraulic-conductivity reduction, reaction-front propagation, and preferential flow within a model reactive barrier. J. Contam. Hydrol. 32(3–4):333–351.
- Narasimhan, T.N., and P.A. Witherspoon. 1976. An integrated finite difference method for analyzing fluid flow in porous media. Water Resour. Res. 12:57–64.
- Parkhurst, D.L., D.C. Thorstenson, and L.N. Plummer. 1980. PHREEQE: A computer program for geochemical calculations. USGS Water Resources Investigation 80-96.
- Pruess, K. 1991. TOUGH2—A general-purpose numerical simulator for multiphase fluid and heat flow. Rep. LBL-29400. Lawrence Berkeley Natl. Lab., Berkeley, CA.
- Robin, M.J.L., A.L. Gutjahr, E.A. Sudicky, and J.L. Wilson. 1993. Cross-correlated random field generation with the direct Fourier transform method. Water Resour. Res. 29:2385–2397.
- Schincariol, R.A. 1998. Dispersive mixing dynamics of dense miscible plumes: Natural perturbation initiation by local-scale heterogeneities. J. Contam. Hydrol. 34:247–271.
- Shi, J. 2000. Conservative and reactive mass transport in homogenous and heterogeneous systems. pH.D. diss. The Ohio State University, Columbus.
- Taylor, S.W., and P.R. Jaffé. 1990. Biofilm growth and the related changes in the physical properties of a porous medium. 1. Experimental investigation. Water Resour. Res. 26:2153–2159.
- Wolery, T.J. 1992. EQ3/6: Software package for geochemical modeling of aqueous systems: Package overview and installation guide (version 8.0). Rep. UCRL-MA-110662 PT I. Lawrence Livermore Natl. Lab., Livermore, CA.
- Xu, T., and K. Pruess. 1998. Coupled modeling of non-isothermal multiphase flow, solute transport and reactive chemistry in porous and fractured media: 1. Model development and validation. Rep. LBNL-42050. Lawrence Berkeley Natl. Lab., Berkeley, CA.
TOP
ABSTRACT
INTRODUCTION
