Electric Analog Computers and Hydrogeologic System Analysis in Illinoisa
Authors: Walton W. C. 
Published: July 2006

Electric analog computers are playing an important role in the forecast of consequences of developing nonhomogeneous aquifers in Illinois having highly irregular shapes and boundaries and a wide variety of head and discharge controls. Analog computers are versatile and simple equipment, of low to moderate cost, with which ground‐water development schemes can be rapidly and accurately tested and the relative merits of alternate choices of development can be appraised.

The electric analog computer used by the Illinois State Water Survey consists of an analog model and excitation‐response apparatus, i.e., waveform generator, pulse generator and oscilloscope. Analog models are regular arrays of resistors and capacitors and are scaled‐down versions of aquifers and confining beds where present. Resistors are inversely proportional to the coefficients of transmissibility and vertical permeability aquifers and the coefficients of leakage of confining beds. Capacitors store electrostatic energy in a manner analogous to the storage of water in the aquifer. The behavior of the electrical network is described by an equation which has the same form as the finite‐difference equation for nonsteady state two or three‐dimensional flow of ground water. Electrical units (voltage, coulombs, amperes and seconds) and corresponding hydraulic units (feet, gallons, gallons per day and days) are connected by 4 scale factors.

Excitation‐response equipment force electrical energy in the proper time phase into the analog model and measure energy levels within the energy‐dissipative resistor‐capacitor network. Oscilloscope traces, i.e., time‐voltage graphs, are analogous to time‐drawdown or time‐recovery graphs and describe drawdown or recovery conditions after a step function‐type change in discharge. A catalog of time‐voltage graphs provides data for construction of a series of water‐level change maps. Close agreement of water‐level declines determined with an analog computer and analytical methods for 3 selected idealized aquifer situations is noted with satisfaction.

An electric analog model for the East St. Louis area was assembled. The sand and gravel aquifer in the East St. Louis area has an average thickness of 120 feet, an average width of 7 miles and an average length of 30 miles. The analog model for the aquifer consists of a regular array of 2800 resistors and 1350 capacitors. The scale of the model is 1 inch equals 2000 feet. Values of resistors range in magnitude from 2.2 megohms to 33,000 ohms; capacitors are 2500 micromicrofarads. The effects of the Mississippi River were simulated by terminating the portion of the electrical network along the river in an open circuit. Resistors large in magnitude were connected to terminals along the edge of the aquifer and to ground to simulate small amounts of sub‐surface flow through bluffs. The accuracy and reliability of the electric analog computer was established by comparing past records of water‐level declines and values of water‐level declines determined with the analog computer. The electric analog computer was used to evaluate the practical sustained yields of existing pumping centers, to predict the effects of a selected scheme of development and to deter‐mine the potential yield of the aquifer under assumed pump‐ing conditions.

An electric analog model for the Champaign‐Urbana area was assembled. The sand and gravel aquifers in the Champaign‐Urbana area are contained in the Mahomet buried bedrock valley which extends across the central part of Illinois from the Indiana border to the Illinois River Valley. The Mahomet buried bedrock valley averages about 12 miles wide in the Champaign‐Urbana area and is largely filled with glacial drift ranging in thickness from 50 to 440 feet. Sand and gravel are encountered within the glac‐ial drift at depths between 60 and 120 feet (upper aquifer), 140 and 170 feet (middle aquifer) and below a depth of 200 feet (lower aquifer). The upper aquifer is thin and discontinuous; the middle aquifer has an average thickness of 43 feet; and the lower aquifer often exceeds 100 feet thick. Till averaging 120 feet thick (upper confining bed) overlies the middle aquifer; about 30 feet of till (lower confining bed) separates the middle and lower aquifers. The analog model for the complex aquifer system consists of a regular array of 7500 resistors and capacitors. The scale of the model is 1 inch equals 1 mile. Values of resistors range from 1 to 68,000 ohms; values of capacitors range from 10e6 to lo‐' farads. The analog model consists of 2 horizontal arrays of resis‐tors and capacitors (lower and middle aquifers) and 1 hori‐zontal ground wire array (water table) interconnected by two vertical arrays of resistors (lower and upper confining beds). The accuracy and reliability of the electric analog computer are being assessed. The computer will be used to predict the effects of future ground‐water development and the practical sustained yields of existing pumping centers in the Champaign‐Urbana area.