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Show V t - r S w ^ t n ^ ^ m t m - l . . . . M , t - 2 . . . . T ( 2.23) n Points where drawdown is of interest in the dewatering problem will depend on the finite difference grid used in the aquifer simulation program, which in turn is related to the geometry of the excavated area. The optimization model for dewatering management has N* T bands, M* T constraints, and ( N+ M) T decision variable; where N the total number of well points, M the total number of drawdown points, and T the total number of time periods. The decision variables are QPtn ^ d gmt. The constraint set is linear in these decision variables. The solution algorithm chosen will depend upon the choice of objective function. The following section presents applications of the dewatering problem. A single period optimization is carried out. All 3 objective function formulations are considered. 2.3 Applications of dewatering model: The dewatering model was applied to a rectangular area with pumps located on the perimeter. Drawdown control points are located along the edges of the area and along the centerline ( Figure 2.3). This configuration is similar to the one used by Yeh ( 1982) a stratified aquifer system and Aguado and Remson ( 1974, 1980) in aquifer management studies. The area contains 22 possible well points and 45 drawdown control points. O Well Location x Dravdovn Control Point Figure 2.3 Site plan for dewatering applications ( not to scale) Equation 2.23 can be rewritten as n Only one time period is being considered for this application, and the right hand side of this equation represents the change in Girinski potential with pumping. This change must be greater than a minimum value to achieve the desired state. This constraint may then be written for one time period as 19 |