By Paul W. McKee, Brian R. Clark, and John B. Czarnecki
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Conjunctive-use optimization modeling was done to assist water managers and planners by estimating
the maximum amount of ground water that hypothetically could be withdrawn from wells within the Sparta aquifer indefinitely without violating
hydraulic-head or stream-discharge constraints.
The Sparta aquifer is largely a confined aquifer of regional importance that comprises a sequence of unconsolidated sand units that are contained within the Sparta Sand. In 2000, more than 35.4 million cubic feet per day (Mft3/d) of water were withdrawn from the aquifer by more than 900 wells, primarily for industry, municipal supply, and crop irrigation in Arkansas. Continued,
heavy withdrawals from the aquifer have caused several large cones of depression, lowering hydraulic heads below the top of the Sparta Sand in parts of Union and Columbia Counties and several
areas in north-central Louisiana. Problems related to overdraft in the Sparta aquifer can result in increased drilling and pumping costs, reduced well yields, and degraded water quality in areas of large drawdown.
A finite-difference ground-water flow model was developed for the Sparta aquifer using MODFLOW, primarily in eastern and southeastern Arkansas and north-central Louisiana. Observed aquifer conditions in 1997 supported by numerical simulations of ground-water flow show that continued pumping at withdrawal rates representative of 1990 - 1997 rates cannot be sustained indefinitely without causing hydraulic heads to drop substantially below the top of the Sparta Sand in southern Arkansas and north-central Louisiana. Areas of ground-water levels below the top of the Sparta Sand have been designated as Critical Ground-Water Areas by the State of Arkansas. A steady-state conjunctive-use optimization model was developed to simulate optimized surface-water and ground-water withdrawals while maintaining hydraulic-head and streamflow constraints, thus determining the "sustainable yield" for the aquifer.
Initial attempts to estimate sustainable yield using simulated 1997 hydraulic heads as initial heads in Scenario 1 and 100 percent of the baseline 1990-1997 withdrawal rate as the lower specified limit in Scenario 2 led to infeasible results. Sustainable yield was estimated successfully for scenario 3 with three variations on the upper limit of withdrawal rates. Additionally, ground-water withdrawals in Union County were fixed at 35.6 percent of the baseline 1990-1997 withdrawal rate in Scenario 3. These fixed withdrawals are recognized by the Arkansas Soil and Water Conservation Commission to be sustainable as determined in a previous study. The optimized solutions maintained hydraulic heads at or above the top of the Sparta Sand (except in the outcrop areas where unconfined conditions occur) and streamflow within the outcrop areas was maintained at or above minimum levels. Scenario 3 used limits of 100, 150, and 200 percent of baseline 1990-1997 withdrawal rates for the upper specified limit on 1,119 withdrawal decision variables (managed wells) resulting in estimated sustainable yields ranging from 11.6 to 13.2 Mft3/d in Arkansas and 0.3 to 0.5 Mft3/d in Louisiana. Assuming the total 2 Conjunctive-Use Optimization Model and Sustainable-Yield Estimation for the Sparta Aquifer of Southeastern Arkansas and North-Central Louisiana water demand is equal to the baseline 1990-1997 withdrawal rates, the sustainable yields estimated from the three scenarios only provide 52 to 59 percent of the total ground-water demand for Arkansas; the remainder is defined as unmet demand that could be obtained from large, sustainable surface-water withdrawals.
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