Compatibility Between Boundary Conditions and Flow Assumptions in the Storative Semiconfining Layers of a Leaky Aquifer

Boundary conditions and flow assumptions used in the Hantush theory of a leaky aquifer with storative semiconfining layers were analyzed for compatibility. Boundary conditions considered were either a constant- head or a no-flow boundary at the top of the upper semiconfining layer and at the bottom of the lower semiconfining layer. A finite-difference radial, axisymmetric model based on MODFLOW was used to numerically compute the drawdown in the aquifer and semiconfining layers. Numerical results indicate that when a no-flow boundary condition at the bottom of the lower semiconfining layer is imposed, flow in this layer becomes two dimensional, inconsistent with the strictly one-dimensional, vertical flow in a semi¬confining layer that is generally assumed by analytical solutions. Analytical solutions were developed for two- dimensional flow in the semiconfining layers and one-dimensional in the aquifer. Drawdowns from the analytical solution were compared with the numerical solution for hypothetical but realistic aquifer tests. For isotropic conditions in the semiconfining layers, the numerical solution converges to the derived analytical solution in the aquifer and semiconfining layers as grid resolution increases; whereas for anisotropic conditions, no additional reduction in the differences between the solutions is gained after reaching a certain grid resolution. The Levenberg-Marquardt optimization method was used to minimize the sum-of-square errors between numerical and analytical drawdowns for two hypothetical tests and one real aquifer test. The analytically- computed optimal vertical hydraulic conductivities of the semiconfining layers had higher relative sensitivities than the optimal values computed numerically.