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Show polluted site. This was achieved by specifying constraints that restrict flow rates out of each contaminated area to prescribed levels. The restriction on flow rates may be achieved by restricting the hydraulic gradient in the neighborhood of the contaminated area. A number of pairs of nodes ( ij) and ( I J ) is identified around each contaminated site, for the purpose of defining hydraulic gradients in different directions from the site. A typical constraint for head gradient control is then stated as V H " < pG ( 4.9) d- " P° y where PG^ is the permissible gradient for the p^ 1 pair of nodes for the c m contaminated area. One such constraint is specified for each pair of nodes considered for head gradient control for each contaminated area. For the Salt Lake County application, 16 such constraints were specified for 3 major contaminated areas. The three contaminated areas considered were Vitro tailings, located in the north central part of Salt Lake County, and two Kennecott Copper tailings ponds, one in the northwestern corner, and the other in the southwestern corner of Salt Lake County. For the Salt Lake County application, the permissible gradients PGpc were specified by computing the existing ( 1982) gradients across each pair of nodes. Other choices for these that are more restrictive can also be adopted. In particular, if artificial recharge in the neighborhood of the contaminated area, or pumping water out of the contaminated area is considered, values of PG^ that lead to no flow out of the contaminated area may be specified. ( 6) Bounds on pumping rates The pumping rate at each candidate well node in the model is restricted to an upper limit, Qk l , that recognizes the maximum permissible pumping rate of all possible wells in the area associated with the node. One such constraint is specified for each well node. This constraint is stated as : 0 * Qk. * <& ( 4 9) 4.2 Salt Lake County Applications The optimization model described in the previous section, resulted in 225 decision variables ( 44 pumping rates and 181 heads) and 252 constraints ( 181 head computation, 47 water rights, 10 demand and 16 water quality) for the Salt Lake County application. The drawdown constraints were translated into lower bounds for heads at each point of interest, resulting in some savings in the number of constraints. This constitutes a linear programming problem of moderate size. Parametric solutions of the model by varying demands, and bounds on pumping and drawdown were obtained. The 1982 spatial demand pattern ( Table 4.1) across the 10 agencies was considered as the base demand. Results for a run where the upper bound on pumpages was set to 3 times the 1982 value for each well, a maximum point drawdown of 15 feet over 1982 levels was permitted, and all flow gradient constraints were set to 1982 values are first 97 |