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Show 3.2 Model Formulation A nonlinear optimization model is developed to address the objectives of groundwater management stated in the previous section. This section presents the formulation of the model developed. The general framework under which the model is developed is first discussed. Fundamental relationships for representing groundwater flow and piezometric head relationships are next developed. This is followed by a presentation of the model formulation, and a brief discussion of the solution technique employed. 3.2.1 General Framework The general situation addressed may be described with the aid of Figure 3.5. It is presumed that a number of water supply agencies serve the locale. These agencies develop surface and groundwater supplies to meet their demands. An ideal management strategy for water supply would be to conjunctively operate and develop the groundwater and surface resources. The intent of this study was to develop a groundwater management model that could be embedded in a model for conjunctive management of ground and surface waters, or used directly for groundwater management. Consequently it was assumed that the demands for groundwater for each agency may be exogenously specified. Demands for groundwater that vary in time are considered to examine issues related to increased demand due to population growth and drought conditions. The model formulation is general enough to consider any operational time scale, even though the applications performed to Salt Lake County considered annual demands over a 10 year time period. The decision variables of the model were the pumping rates at each candidate well location, for each time period. The factors considered important in the development of the management model were ( 1) controlled aquifer drawdown, ( 2) demand satisfaction, ( 3) maintenance of water rights, and ( 4) preservation of groundwater quality. The maximum point drawdowns in the aquifer usually occur at the well sites. The prediction of piezometric head at each well location as a response to pumping is thus of interest. The issue of water rights is rather complex, since uniform laws governing and defining groundwater rights are not usually available. Water rights infringements may be defined in terms of adverse effects in terms of drawdown or available flow at the site affected. A priority structure for groundwater use may also exist. The perspective adopted in this study was to constrain the groundwater flow rates across the boundaries of water supply agencies to prescribed values, as a mechanism for preservation of the water rights structure. It was felt that this constraint together with constraints limiting drawdown at well sites in the aquifer, would lend some measure of equity to groundwater use in the region. There are often localized areas of poor groundwater quality in the aquifer. A groundwater use strategy that precludes the spread of contaminated water, particularly into water supply wells is desirable. Artificial recharge of groundwater may be used to reverse the flow of contaminated water from zones of poor water quality. Removal of contaminated water, or in situ treatment of poor quality water are other management possibilities. A passive management alternative is to develop a pumping strategy that restricts flow out of the contaminated areas, and thereby preserves the quality of water in supply wells. For all these options, the central mechanism is the control of outflow from the contaminated area. The strategy used in developing the optimization model was to constrain the outflows from the contaminated area to prescribed values. A unit response formulation was used to develop a distributed parameter optimization model for groundwater management. The response of the aquifer to unit pumping at candidate well locations is first estimated using a groundwater simulation 42 |
