U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2006-5052
By John B. Czarnecki
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The Mississippi River Valley alluvial aquifer is a water-bearing assemblage of gravels and sands that underlies most of eastern Arkansas and several adjacent States. Ground-water withdrawals have caused cones of depression to develop in the aquifer’s water-level surface, some as much as 100 feet deep. Rivers, such as the Arkansas, White, St. Francis, and Mississippi
Rivers, are in hydraulic connection with the alluvial aquifer.
Recharge to the alluvial aquifer from these rivers becomes induced as ground-water level declines. Long-term water-level measurements in the alluvial aquifer show an average annual decline of 1 foot per year in some areas. The expansion of the cones of depression and the consistent water-level declines indicate that ground-water withdrawals are occurring at a rate that is greater than the sustainable yield of the aquifer.
Ground-water flow models of two areas of the alluvial aquifer (north alluvial and south alluvial--divided by the Arkansas River) previously were developed for eastern Arkansas
and parts of northern Louisiana, southeastern Missouri, and adjacent States. The flow models showed that continued ground-water withdrawals at 1997 rates for the alluvial aquifer could not be sustained indefinitely without causing water levels to decline below half of the original saturated thickness of the alluvial aquifer.
To develop estimates of withdrawal rates that could be sustained
relative to the constraints of critical ground-water area designation, conjunctive-use optimization modeling previously was applied to the flow models. Optimization modeling was used to calculate the maximum sustainable yield from wells and rivers, while maintaining simulated water levels and streamflows
at or above minimum specified limits.
Modifications to the optimization models were made to evaluate the effects of varying ground-water level constraints and surface-water withdrawals from rivers on the model-calculated
sustainable yield of the aquifer and rivers. As ground-water-level constraints are relaxed, optimized sustainable yields from rivers decrease because more ground water is available for withdrawal, which would otherwise discharge to the rivers. In addition, sustainable yield of ground water was compared for four different management scenarios involving different water-level constraints and river withdrawal specifications. Scenario 1 is the baseline scenario in which river withdrawals were allowed from all river cells from 11 rivers specified in the north alluvial model, while maintaining ground-water levels at or greater than half the saturated thickness of the aquifer. Scenario 1 includes withdrawals from two irrigation project areas that would remove water from either the Arkansas or White Rivers. Scenario 2 differs from Scenario 1 in that the water-level constraints
were relaxed so that the aquifer must have at least 30 feet of saturated thickness everywhere. In Scenario 3, optimized surface-water withdrawal is removed from the model specification
in all 11 rivers; however, surface-water withdrawals are fixed at 2000 rates at select points, and no additional withdrawals
are permitted. In addition, no withdrawals from either of two irrigation project areas that would remove water from either the Arkansas or White Rivers are specified in Scenario 3, as in Scenarios 1 and 2. Water-level constraints in the aquifer are set to half the saturated aquifer thickness. For Scenario 4, the same conditions as for Scenario 3 were specified, but water-level constraints
were relaxed to have at least 30 feet of saturated aquifer thickness. Average differences in sustainable yield of ground water between baseline Scenario 1 and Scenarios 2, 3, and 4 show an increase of 6.74, 6.82, and 13.24 percent, respectively.
A large paper mill in Pine Bluff, Arkansas, currently pumps 30 million gallons per day from the Sparta aquifer, which underlies the alluvial aquifer. The alluvial aquifer has been considered by the mill operators as an alternative source of water, particularly if water were to be withdrawn from a well or wells constructed near the Arkansas River. One potential well site was simulated using an extant model of the south alluvial aquifer by adding it to the existing wells in the model beginning in 1998, and specifying it to pump at 30 million gallons per day for a period of 50 years. Pumping at that rate causes a cone of depression to occur in the alluvial aquifer with a maximum change in water level in the pumped cell of about 40 ft; no dry cells occur after 50 years. Saturated thickness in the pumped cell at 50 years is about 70 ft which is larger than half the original
aquifer saturated thickness of 58 ft. Running the model to steady-state conditions with a pumping rate of 30 Mgal/d resulted in water levels dropping an additional 0.1 ft near the pumped well, indicating that conditions were near steady state at 50 years, and that pumping at that rate could be sustained without causing water levels to go below half the aquifer saturated thickness, although this rate was near the maximum rate of about 38.9 million gallons per day, above which model cells would go dry.
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