GEOCHEMICAL MODELING OF AN AQUIFER STORAGE RECOVERY experiment,
charlEston, south carolina

*By* David L. Parkhurst and Matthew D. Petkewich

( <dlpark@usgs.gov> and <mdpetkew@usgs.gov> )

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.

![](media/image1.png){width="5.0137795275590555in"
height="3.09251968503937in"}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 m^3^/min (11 gpm) for 43 days, stored
for 99 days, and extracted by pumping the injection well at a rate of
0.45 m^3^/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.

# 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.

![](media/image2.jpeg){width="3.3188976377952755in"
height="2.2708661417322835in"}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

![](media/image3.jpeg){width="3.0in"
height="3.5in"}![](media/image4.jpeg){width="3.0in"
height="3.6251968503937007in"}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 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.

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.