Energy approach to the analysis of partially-saturated flow

When fluid passes into or out of an aquifer, work is done at the boundaries which is partly used 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 described 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. The energy approach gives better insight into the dynamic behavior of aquifers and, also, becomes a rational basis to model aquifers. In particular, the energy associated with the wetting process in an unsaturated aquifer is used to adapt the time step in a transient unsaturated flow model. It is shown that the time step control procedure is particularly effective in modeling relatively dry porous media. The energy method is illustrated in a two- dimensional flow domain.