Using the Sequential Self-calibration Method and Genetic Algorithm Method to Optimally Design Tracer Test to Estimate Conductivity Distribution

Abstract

A gradient-based inverse method – the sequential self-calibrated method – is combined with a genetic algorithm method to search the optimal design scheme for a tracer test. The sequential self-calibrated method is developed for estimating conductivity distribution in a study domain conditioning on tracer test data. To improve the calculation efficiency, a fast streamline-based approach is used to compute the derivative of concentration with respect to the changes of hydraulic conductivity. Performance of the sequential self-calibrated method has been studied using a synthetic aquifer having a sandwich-like geologic structure where hypothetical tracer tests are conducted. The study results indicate that the locations and number of sampling wells will significantly affect accuracy in the estimates. To maximize estimating accuracy in the sequential self-calibrated method for a fixed number of sampling wells, a genetic algorithm method is applied to search the optimal locations for sampling wells. The results indicate that the optimal sampling well locations depend on the apparent geologic structure and the difference in conductivity values for the various regions. For the sandwich-like structure, when the difference between conductivity values in the two separate regions is large enough, the optimal locations for the sampling wells will be fixed, regardless of conductivity values. The study results also show that based on the optimal sampling-well scheme, estimating accuracy will increase as the number of sampling wells increases, even though the rate of increasing accuracy slows as the number of wells increases.