A six-State area in the northern Midwest of the United States has become increasingly dependent on ground water from the Cambrian-Ordovician aquifer system, which consists of a sequence of sandstones, carbonate rocks, and shales. Ground-water withdrawals from the aquifer system began in the late 1800's and increased to approximately 684 million gallons per day (1,058 cubic feet per second) by 1980. This withdrawal has caused more than 900 feet of decline in the potentiometric surface of the aquifer system in parts of the Chicago, Ill., area. Pumping in Minneapolis-St. Paul, Minn., Milwaukee, Wis., and central Iowa has produced a few hundreds of feet of water-level decline.

A quasi-three-dimensional ground-water flow model was developed to improve understanding of the regional ground-water flow system by simulating the aquifer system under the conditions that existed before and during ground-water development. The Cambrian-Ordovician aquifer system and the overlying rocks were incorporated in the conceptual model as five aquifer layers with four intervening confining layers. The aquifer layers, from top to bottom, are as follows: Quaternary deposits and Cretaceous rocks (aquifer layer 5); basal Devonian carbonate rocks and underlying Silurian carbonate rocks (aquifer layer 4); Middle Ordovician St. Peter Sandstone, Lower Ordovician Prairie du Chien Group, and Upper Cambrian Jordan Sandstone (aquifer layer 3); Upper Cambrian Ironton and Galesville Sandstones (aquifer layer 2); and Upper Cambrian Mount Simon Sandstone and Precambrian Hinckley Sandstone (aquifer layer 1).

The effects on the flow system of ground water having variable density and the individual aquifer layer contribution of flow to wells open to several aquifer layers were simulated by incorporating appropriate terms in the ground-water flow equation and corresponding modifications in the ground-water flow model.

Results of steady-state simulations are shown as maps of freshwater head and as flow-rate vectors. A comparison was made of available predevelopment head data and simulated predevelopment heads for the Mount Simon, St. Peter-Prairie du Chien-Jordan, and Silurian-Devonian aquifers. The root mean square of the differences between observed and simulated heads for these aquifers was 53, 36, and 44 feet, respectively.

Steady-state model simulation indicates that regional recharge areas are located in northwestern Iowa, southeastern Minnesota, much of Wisconsin, northern Illinois, and central Missouri. Regional discharge areas are located near the Mississippi River and its tributaries, the Missouri River, Lake Michigan, and the Illinois basin.

Results of a transient simulation of the period 1861 to 1980 are shown as maps of freshwater head and freshwater-head decline. The root mean square of the differences between observed and simulated heads for the St. Peter-Prairie du Chien-Jordan aquifer was 63 feet. In addition, hydrographs of simulated hydraulic head were compared with hydrographs of observed head in wells open to various combinations of aquifers. The numerous head measurements within a model node display a wide range in magnitude; however, their historical trend generally follows the trend of the simulated heads.

The simulated recharge from the glacial drift to the immediately underlying bedrock aquifers averages 0.03, 0.06, 0.24, and 0.02 inch per year, respectively, to the Mount Simon, Ironton-Galesville, St. Peter- Prairie du Chien-Jordan, and Silurian-Devonian aquifers for predevelopment conditions and 0.03, 0.07, 0.45, and 0.07 inch per year, respectively, to the same aquifers for 1976-80. These recharge rates are less than 1.5 percent of average annual precipitation of about 30 inches per year. Most of the recharge from precipitation discharges to streams as base flow through local and intermediate ground-water flow systems. Only a small fraction of the precipitation recharges the deeper, regional flow system. The simulated predevelopment recharge of 571 cubic feet per second is balanced by an equivalent discharge. For the period 1976-80, simulated recharge increased to 1,398 cubic feet per second. Total discharge, including pumpage from the four bedrock aquifers, increased to 1,619 cubic feet per second. The difference in recharge and discharge during this period is from aquifer storage.

Results of variable-density simulations indicate that the rate of ground-water movement is small in areas where ground water is highly mineralized. The rates and directions are controlled by the intrinsic permeability of the rock, freshwater head gradients, and gravitational force.