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Show This chapter presents an optimization model that attempts to determine the maximum steady state or perennial yield from an aquifer under the above constraints. Our particular interest was in developing estimates of perennial yield for the principal aquifer in Salt Lake County, Utah. The general framework for developing the optimization model is next presented, followed by a presentation and discussion of the results for the Salt Lake County application. The system description and criteria for well selection delineated in Chapter 3 for the Salt Lake County applications were used for the applications and model development in this chapter as well. 4.1 Model Formulation A distributed parameter, hydraulic management, optimization model is presented in this chapter. The representation of the ground water system is limited to a regional mass balance over time in lumped parameter models. A unit response formulation was adopted for the optimization model developed in this chapter. The applications for Salt Lake County were performed for the principal aquifer only. This aquifer is largely confined, and hence the dependent or state variable used was the piezometric head. For a stratified aquifer system, the response matrix formulation could still be used through the Girinski potential as described in Chapter 2. Most of the groundwater management models presented in the literature with economic or hydraulic management objectives, consider drawdown, demand and sometimes water quality constraints. The determination of optimal aquifer yield subject to the above constraints as well as water rights considerations was performed in this study. Figures 3.5 and 3.4 show the general situation modeled, where there may be a number of independent water supply agencies that share common boundaries across the aquifer, leading to water rights concerns, there may be known areas of contamination in the aquifer, where water quality is of concern and in addition localized drawdown is of concern. The optimization model for steady state yield determination is formally presented in terms of its objective function and constraints. Objective Function: The objective of the model is to maximize the total steady state yield from the aquifer, defined as the sum of the annual pumpages Q^ a at the k* h well belonging to the a^ 1 water agency. A na MaxOBJ = XZQka < 41) a= l k= l where A is the total number of water agencies, and na is the number of wells operated by the am water agency. The total number of pumpage variables ( i. e. the number of pumping nodes considered) for the Salt Lake County applications was 46. 93 |