OCR Text |
Show An optimization model to address these objectives was developed and applied to the Salt Lake County aquifer system. Optimization models presented in the literature for groundwater management have not explicitly addressed water rights and water quality. Most of them solve for optimal pumping for one agency with drawdown and demand constraints and often only for steady- state problems. Also field scale applications of these models have been very restricted because of the large mathematical size of the problem. The model developed in this chapter uses the Response Matrix Method for the computation of heads and flow rates. The U. S. Geological Survey three- dimensional finite difference flow model was used to simulate the responses of the piezometric head in the aquifer to unit pumping at each well location. Repeated simulations with unit pumping at each well ( one at a time) allow the establishment of a unit response matrix. This response matrix is then used by the optimization model to aid decisions on annual pumping rates. There are several ways to solve constrained nonlinear optimization problems. These include Successive Linear Programming ( SLP), Exterior and Interior Penalty methods, Reduced Gradient methods and Augmented Lagrangian methods. The Successive Linear Programming Algorithm was used for solving the largely linear optimization model formulated. This model was applied to Salt Lake County for ten water agencies ( Table 3.1) including Salt Lake County Water Conservancy District, City of Murray, Salt Lake City Department of Public Utilities, City of South Salt Lake, Holladay Water Co., City of Riverton, Granger- Hunter Improvement District, White City Water Co., City of Sandy, and Magna Water Co. and Improvement District. Their groundwater demands ( Table 3.1) range from 1409 acre- ft / yr to 8890 acre- ft / yr based on the average of annual pumpage records from 1970- 1982. Three major contaminated areas in Salt Lake County were considered. These include two areas near the Magna Tailings pond and Lark Tailings area, and the Vitro Tailings area in central Salt Lake City. The 1981 water use pattern by agency is shown by Table 3.2. The groundwater use as a percentage of total water use ranges from 12 % to 100 % for different agencies. The model developed was applied parametricaUy for several demand scenarios over a 10 year period. The first scenario considered uniform demands of 100 %, 120 % and 150 % of the average annual pumpage from 1970 to 1982. This scenario considers a situation where the groundwater use is uniform over the planning period, but the base use level is higher than the current levels. This may be due to population growth or to a prolonged drought. The second scenario considered linearly demand growth for each of the 10 years, starting from each of the base levels identified in the first scenario. The third scenario considered demand schedules that increased linearly for the first 5 years and then decreased linearly for the next 5 years for each demand base. This scenario considers a drought situation where the groundwater system is stressed during the drought. Each of these scenarios was applied uniformly to each of the ten water supply agencies. This is clearly not optimal, since the proportion of groundwater use relative to total water use ( ground and surface water) varies for each agency, and hence demand growth and drought response conditions would be different for each agency. The scale of the problem modeled, however, curtailed the degree of effort that could have been spent on modeling these factors directly. The model formulated, however, is capable of treating these , variations. 30 |