Some Computational Experiences Using Embedding Technique for Ground-Water Management

ABSTRACT A distributed parameter ground‐water management model was developed using finite‐difference approximations of the governing partial differential equation for ground‐water flow in a confined aquifer. The resulting system of simultaneous equations was embedded in an optimization model, which used hydraulic heads and pumpages as unknown state variables and decision variables, respectively. The model was applied to several hypothetical examples of varying size and complexity and to one real‐world example, the Las Vegas Valley aquifer. The grid spacing, time increment, bounds placed on pumpage, and the number of constraints were found to affect not only the execution time, but also whether the model would execute at all. In order to accommodate long‐term management goals, a lumped transient model should be used which incorporates all time periods the model encompasses. Some objective functions, such as the maximization of the head, can be executed in a stepwise manner in which the final heads from the current period are used as the initial heads for the next period. The embedding technique proved useful for small management problems, but had numerical difficulties with the large real‐world problems of considerable heterogeneity. Unless the embedding technique can become computationally efficient and stable, it should be bypassed in favor of the response matrix approach.