Application of Energy Concepts to Groundwater Flow: Time Step Control and Integrated Sensitivity Analysis

Abstract

When fluid passes into or out of an aquifer, work is done at the boundaries which is used partly to change the internal energy of the system and partly to overcome resistance to flow. For a saturated medium, the change in internal energy is further partitioned into two terms, the strain energy stored in the elastic soil matrix and the strain energy stored in the pore water due to compression. A technique is developed in this paper which interprets the dynamic behavior of an aquifer in terms of its energy transformations. The central feature of this approach is the quantification of the physical processes into individual energy and work parameters which together characterize the response of an entire aquifer to a given set of excitations. By this means, the rate of change of strain energy is shown to be a natural index of the unsteadiness of a system, an insight which leads to an adaptive algorithm for adjusting the time step of a transient groundwater flow model. Further, the energy approach is used to assess differential compaction in a heterogeneous aquifer, thereby providing a basis for efficient computation and for rational acquisition of compressibility data.