Geochemical Modeling of an Aquifer Storage Recovery Experiment, Charleston, South Carolina

By David L. Parkhurst¹ and Matthew D. Petkewich^2
1U.S. Geological Survey, P.O. Box 25046, MS 413, Denver Federal Center, Lakewood, Colorado 80225
²U.S. Geological Survey, 720 Gracern Road, Columbia, South Carolina, 29210

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Introduction

Geochemical modeling tools are well suited for analyzing aquifer storage recovery experiments. The types of modeling available include speciation modeling, solute-transport modeling, mole-balance modeling, batch-reaction modeling, and one-, two-, and three-dimensional reactive-transport modeling. These modeling techniques range from relatively simple speciation modeling to complex reactive-transport modeling, with corresponding simple to complex requirements of time, data needs, and computer resources. Geochemical modeling should be part of every aquifer storage recovery project, but the extent of modeling must be appropriate for the scale of the project.

In this report, example calculations of several types of geochemical modeling are applied to an aquifer storage recovery experiment in Charleston, South Carolina. The purpose of the aquifer storage operation is to store potable drinking water in a sand and limestone aquifer underlying the city of Charleston. Application of geochemical modeling approaches have been useful in this study in understanding the induced flow in the aquifer, deducing the important chemical reactions, building hypotheses, and identifying unanswered questions related to full-scale operations.

To date, three pilot injection-storage-recovery experiments have been completed. This report is limited to a preliminary analysis of the flow, solute transport, and chemical reactions in the third experiment, which was undertaken between September 11, 2000 and April 2, 2001. During this period, water was injected at approximately 0.042 m³/min (11 gpm) for 43 days, stored for 99 days, and extracted by pumping the injection well at a rate of 0.45 m³/min (120 gpm) for 61 days. Water was injected and recovered through well CHN-812 (fig. 1); water samples were taken from observation well CHN-809 throughout the experiment and from well CHN-812 during recovery. Both wells were screened over 70 percent of the 22-m-thick aquifer.

Figure 1. Aquifer storage recovery site and well locations, Charleston, South Carolina.

Solute Transport

Figure 2 shows the chloride concentration at observation well CHN-809 through the injection, storage, and recovery experiment. Given the relatively low injection rate, the rapid breakthrough of low-chloride water at the observation well (approximately 23 m from the injection well) indicates that the injected water must flow through a small volume of aquifer. If the breakthrough were representative of the entire aquifer, porosity of 2 percent or less would be required, which is not plausible for a predominantly sand aquifer. Alternatively, the flow must occur predominantly through a thin transmissive zone of the aquifer. A limestone layer of 3-m thickness or less occurs near the top of the aquifer. Electrical conductivity logs of observation wells during injection show that this layer has the lowest specific conductance within the aquifer, which indicates that it is the most transmissive zone. It is hypothesized that preferential flow through this layer is the cause of the rapid breakthrough of low-chloride water at the observation well.

Figure 2. Chloride concentration in observation well CHN-809 during injection, storage, and recovery; shaded area is period of storage with injection preceding and extraction following this period.

In the breakthrough of low-chloride water, the lowest concentrations of chloride are in the range of 170 to 230 mg/L, in contrast to the injection concentration of approximately 40 mg/L. Thus, it is apparent that although a large proportion of the water is moving through the more hydraulically conductive limestone, some water with large chloride concentration is moving from the rest of the aquifer into the observation well, which causes minimum chloride concentrations to be greater than the injected concentration. A solute-transport model was developed that included a 2-m zone of greater hydraulic conductivity than the rest of the aquifer. By trial and error, it was determined that a horizontal hydraulic conductivity ratio of 120:1, for the two model zones of the aquifer, produced concentrations of approximately 200 mg/L chloride in the observation well following initial breakthrough of low-chloride water. It was assumed that both zones of the aquifer contributed water to the observation well according to the corresponding thickness and hydraulic conductivity.

Geochemical Reactions

Speciation and inverse modeling were used to deduce chemical reactions that occurred during the experiment. Speciation modeling indicates that calcite should dissolve into the water that is injected into the aquifer.

Mole-balance models were developed for waters from the observation well by assuming the mixing of the injection and background waters. It was determined that mixing plus chemical reaction-dissolution of calcite and cation exchange-could adequately account for the water compositions in the observation well during the experiment. The exchange reaction removes calcium, magnesium, and potassium from solution to the exchanger, and removes sodium from the exchanger to the solution. The combination of removal of calcium and dissolution of calcite is consistent with the high pH and high alkalinity observed in the observation well after breakthrough of low-chloride water.

One-dimensional reactive-transport modeling with PHREEQC (Parkhurst and Appelo, 1999) was used to test whether equilibrium reactions were consistent with the observations. Whereas inverse modeling showed that calcite and cation-exchange mole transfers could account for the water compositions, mole-balance modeling takes no account of thermodynamic driving forces or kinetics of reactions. The one-dimensional modeling assumed equilibrium for calcite and cation-exchange reactions and used the default exchange constants of the database phreeqc.dat (Parkhurst and Appelo, 1999). The number of exchange sites could not be determined from the available data, except that a minimum number of sites were needed to match the observations; a value of 0.1 eq/L was assumed. The results of the one-dimensional reactive-transport modeling indicated that equilibrium calcite and cation-exchange reactions-plus mixing of water in the observation well-were consistent with the composition of water from the observation well.

Clays are the most important minerals providing exchange sites, and previous work has shown that clays with significant exchangeable sodium are subject to expansion accompanied by decreased hydraulic conductivity when exchangeable sodium or dilute water is injected (McNeal and Coleman, 1966; Brown and Silvey, 1977). The need for cation exchange to account for chemical compositions and the presence of clays in the aquifer implies that the aquifer may be subject to permeability changes caused by clay expansion. A significant decrease in breakthrough of low-chloride concentrations from the first experiment (approximately 30 days) to the third experiment (approximately 8 days) may be the result of expansion of clay in the less transmissive zone of the aquifer, forcing more water through the limestone zone.

Three-Dimensional Reactive-Transport Model

A three-dimensional model of the injection, storage, and recovery experiment used the hydraulic properties derived from the solute-transport analysis of chloride and the reactions deduced by speciation, inverse, and one-dimensional reactive-transport modeling. The calculations used the simulator PHAST (Parkhurst, and others, 1995, Kipp and Parkhurst, in press). Figure 3 presents the results of the simulations for observation well CHN-809. An additional simulation was run by assuming that only conservative transport occurred, with no calcite or cation-exchange reactions. The simulation that included equilibrium reactions more closely matches the alkalinity, calcium, and pH observations, and, in fact, closely matches the observed concentrations for all major ions.

Figure 3. Observed concentrations in well CHN-809 during injection, storage, and recovery compared to concentrations modeled by assuming equilibrium reactions and conservative transport.

Figure 4 compares observed and simulated values for the extraction well during the recovery part of the experiment. The withdrawal of low-chloride water requires less time in the simulation than in the experiment. The difference in recovery duration must result from an inconsistency in the nominal injection and pumping rate, such that the actual recovery appears to produce more low-chloride water than can be accounted for by the injection. However, there is no reason to suspect errors in either the pumping- or injection-rate estimates.

Figure 4. Observed concentrations in extraction well 810 compared to concentrations modeled by assuming equilibrium reactions.

The simulation of the nonconservative constituents for the extraction well was found to be sensitive to the time step used in the numerical modeling. The converging flow at the extraction well generates large velocities (up to 150 m/d at the central model cell boundaries) and a sufficiently small time step is needed to obtain an accurate solution. With 5-m model cells, a time step of 0.01 days produced a stable numerical solution during the extraction part of the simulation. With the refined numerical solution, the comparison between calculated and observed concentrations is adequate. However, delayed breakthrough of all constituents is evident, which is related to the discrepancy noted for chloride breakthrough. Equilibrium reactions appear to be applicable, but details may be difficult to match in the dynamic environment of the pumping well. The large velocities may result in incomplete cation-exchange or calcite equilibration, and the appropriate simulation of dispersivity in this environment is not clear.

Conclusions

The predominant flow in the aquifer storage recovery experiment appears to be in a limestone layer near the top of the aquifer that is approximately 2 m thick. A hydraulic conductivity ratio of 120:1 for this zone relative to the rest of the aquifer accounts for the timing of the breakthrough of low-chloride water and the minimum chloride concentrations in the observation well, which exceed injection concentrations. By including calcite and cation-exchange equilibrium reactions, results of a three-dimensional reactive transport model are in agreement with the time sequence of major-ion concentrations in the observation and extraction wells. However, several questions can be raised as a result of the geochemical modeling:

1. Why is the modeled extraction of low-chloride water less than that observed?
2. Will water injected in the limestone remain extractable for a long period of time? Or will regional gradients cause the pool of fresh water to migrate?
3. If the water is injected primarily into a thin transmissive zone, will the large surface area of the interfaces between the transmissive layer and adjacent high-chloride layers cause water-quality degradation by leakage across the interfaces?
4. Does injection of low-concentration water affect clay particles and decrease permeability in parts of the aquifer?

References

Brown, D.L., and Silvey, W.D., 1977, Artificial recharge to a freshwater-sensitive brackish-water sand aquifer, Norfolk, Virginia: U.S. Geological Survey Professional Paper 939, 53 p.

Kipp, K.L., and Parkhurst, D.L., in press, Parallel processing for PHAST-A 3D reactive-transport simulator: XIV International Conference on Computational Methods in Water Resources, Delft, The Netherlands, 2002, Proceedings.

McNeal, B.L., and Coleman, N.T., 1966, Effect of solution composition on soil hydraulic conductivity and effect of solution composition on the swelling of extracted soil clays: Soil Science Society of America Proceedings, Vol. 30, No. 3, pp. 308-317.

Parkhurst, D.L., and Appelo, C.A.J., 1999, User's guide to PHREEQC (Version 2)-A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations: U.S. Geological Survey Water-Resources Investigations Report 99-4259, 312 p.

Parkhurst, D. L., Engesgaard, Peter, and Kipp, K. L., 1995 Coupling the geochemical model PHREEQC with a 3D multi-component solute-transport model: V.M. Goldschmidt Conference, 1995, State College, Pa., Program and Abstracts, pp. 77-78.

In George R. Aiken and Eve L. Kuniansky, editors, 2002, U.S. Geological Survey Artificial Recharge Workshop Proceedings, Sacramento, California, April 2-4, 2002: USGS Open-File Report 02-89

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