Transient Reservoir-Aquifer Interaction

The moving boundary problem of the interaction of a reservoir-aquifer system is studied. The nonlinear PDE of Boussinesq is used to describe the transient flow conditions in the semi-infinite, unconfined aquifer. The method of solution involves discretization of only the time derivative to obtain an ODE in space. The resulting ODE is integrated analytically once and the remaining initial value problem is solved numerically. The solution developed is of the similarity type. The cases of sudden drawdown and buildup are considered, and computed dimensionless profiles vs. dimensionless similarity parameter are compared with experimental data, exact-analytical, linear-analytical and numerical solutions for different boundary values. Also analytical relationships for the exchange flows and flow volumes have been derived.