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Show from 1969 to 1982 as a background condition for optimization. ( 3) Develop response matrices for drawdown for unit pumping at each candidate well node. The response matrices were evaluated by performing transient simulations with unit pumping at each well using the GW3D program, referred to in section 3.1. Background conditions were first identified by simulating the aquifer system over the time period of interest with no pumping in the aquifer. Another simulation was used to determine the change in heads and flow rates at all nodes and sections of interest with all wells not considered for optimization pumping at specified rates ( 1982 pumping for one set, historical pumping from 1969 to 1982 for another set). Forty seven additional simulations were then performed, one for each candidate well, with only unit pumping specified at the candidate well node. The relative drawdown between the simulation with no pumping, and the simulation with unit pumping was recorded in each case. An influence distance for each well was identified as the distance at which the relative drawdown was less than 5 % of maximum relative drawdown even after 20 years of pumping. Relative drawdowns to unit pumping at each candidate well were stored as its response matrix, for all nodes of interest that lie within the influence distance. Some savings in computer memory requirements were thereby effected. Actually instead of using unit pumping, a larger pumping rate ( e. g., 10 cfs) was used for the simulations, and the resulting response matrices were scaled accordingly. This was done to ensure a conservative specification of the influence distance of the well. It was also noted that 10 years was usually long enough to reach steady - state. The response matrix may then be reinitialized after every 10 year period, and there is no need to store response matrix terms beyond 10 years. Based on this observation, a 10 year operation period for groundwater pumping was selected. ( 4) Estimate response matrices for flow across agency boundaries and contaminated areas. The simulations employed in the previous set were used to first compute the background flows across each boundary of interest for each year. The relative flow across each boundary due to unit pumping at each candidate well site was then estimated using the response matrices for drawdown developed in the previous step. ( 5) Define objective function and constraints. The objective function presented in section 3.2.5 considered capital and operation and maintenance costs. These costs included costs for water treatment and distribution. It was found that groundwater from Salt Lake County does not undergo any substantial treatment ( some supplies are chlorinated, and this cost is not significant). Data indicated that the two major costs for well operation were power cost and energy cost. A power cost is assessed as a function of capacity whenever a pump of a particular electrical capacity comes on line. Energy costs are charged in terms of actual energy usage. For an annual operation it was considered that a measure of the total operating cost may be provided by the energy cost. The base assumption here is that for long term well operation the power cost is incurred approximately in proportion to the energy cost across all well sites. If this assumption is questionable, a mechanism to directly consider power capacity costs would need to be developed. Song ( 1986) presents some regression equations for monthly pumping cost that could possibly be adapted for the purpose. The energy cost was calculated by determining the energy used in providing the average head lift for a given year and the well discharge for the year. The lift was determined using the surface elevations and the end of year piezometric head at each node. A unit energy cost of 9 cents per kilowatt hour was applied to all wells. While this may not be representative of individual water supply agencies, it was felt that a uniform cost criterion should be adopted 55 |