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Show the spatial distribution of demand deviates from the implicit water rights specification of the historical record. The optimization model was solved on a GOULD 9080 superminicomputer ( approximately 4 times faster than a VAX 11/ 780 computer for floating point arithmetic). Solutions typically required 1276 Kilobytes of memory, from 10 to 50 SLP iterations, with the pumping rates for existing conditions supplied as the initial solution, and required 3 to 5 hours of CPU time. No significant convergence problems were experienced with any of the solutions. 3.3.2 Uniform Demand Over Time A total of seven parametric optimization runs were made for the uniform demand condition. These are run numbers 2 through 8 identified in Table 3.6. Two sets of base demand ( Qi0) patterns were considered to define the spatial distribution of demand. Run numbers 2,3 and 4 correspond to uniform demands over time, that are 100%, 110%, 120% and 150% respectively of the average annual 1973- 1982 pumping record for each water supply agency. Summary results for these runs are presented in Tables 3.7 through 3.10. Run numbers 5 through 8 correspond to uniform demands over time, that are 100%, 110%, 120% and 150% respectively of the 1982 pumping for each water supply agency. Results for these runs are presented in Tables 3.7, 3.8 and 3.10. Only the general trends apparent from these results are discussed in this section with respect to spatial demand pattern, demand level, total and unit costs, drawdown and influence of boundary and contaminant flow constraints on the solution. A general trend obvious from Table 3.6 is that the number of pumping wells at the optimal solution decreases as the demand level increases. This is to be expected, since as the general areal drawdown ( and hence lift) increases, the wells that have higher pumping lifts are screened out. This reduction in the number of pumping wells is constrained by the feasibility requirements of maintaining the water rights structure and contaminant flow control. As expected, the total pumping cost, as wefi as the average ( unit) pumping cost increase with the demand level ( Tables 3.7, and 3.8). The optimal, total pumping cost for run 2 ( 100% of historical average annual pumping) is significantly reduced over the corresponding actual, total pumping cost ( run 1) for the same period ( from $ 4,907 million to $ 2,123 million). While this might suggest that the actual pumping strategy used by the water agencies in the county is far from being economically optimal, a cautionary note is in order. Since distribution system costs are ignored in the model presented in this system, it is to be expected that fewer wells will pump and that the optimal, total pumping costs will be lower than the actual total pumping costs. Of note, however is the sharp decrease in the average pumping cost ( from $ 11.83/ Acre- foot to $ 3.81/ Acre- foot) for the optimal solution ( run 2). A perusal of Table 3.8 shows that while the model was unable to effect significant reductions in the average pumping costs for areas 6, 7 and 8 ( Riverton, Granger and White City), the average costs for the other agencies are drastically reduced. This observation does tend to support the hypothesis that reductions in pumping costs are possible through optimization. A more realistic application of the model would consider the distribution costs incurred for water supply from each well to the demand points within each agency. It should also be possible to model the distribution constraints, by specifying lower bounds on the aggregate pumping from subsets of wells within each agency to represent service areas within each agency and their demand distribution. 58 |
