| Solutions to many problems of flow in leaky aquifers are based on differential equations that include a leakage term in addition to the usual terms of the equation of groundwater motion. In general, solution for the response of a multi-aquifer system to pumping requires solving a three-dimensional flow equation which is computationally intensive. A quasi three-dimensional leaky aquifer theory is proposed as an alternative to the above method. In this theory, flows in aquifers are assumed horizontal and two-dimensional, while flows in aquitard are assumed vertical.; A major contribution to the quasi three-dimensional leaky aquifer theory was provided by Herrera and Figueroa. In their formulation, the need for directly obtaining the aquitard solution was eliminated by an analytical technique. The ensuing equation was an integrodifferential equation.; Laplace transformation is applied to the integrodifferential equations, which removes the time dependence and the integral expression in the equation system. The final equation is a set of partial differential equations which are non-transient, elliptic, linear, and in two spatial dimensions. The analytical solution to the above equations for pumping well problems in a multi-layer system is presented. The key to this solution is the ability to define a Green's function for the problem. Numerical solutions are also developed using the Boundary Element Method (BEM) and Finite Difference Method (FDM) techniques. The effective computational dimension of a given problem is reduced by one because only the boundary of the region is discretized in the BEM formulation. The reduction in computation makes the BEM a less expensive technique to use over the other numerical methods such as the FDM, or the Finite Element Method (FEM). BEM and FDM models are developed for up to three-aquifer system, while the analytical solution is developed for up to six-layer system. The accuracy of the solutions obtained is verified by comparing these solutions with one another, and by also comparing the two-aquifer system case with Neuman and Witherspoon's analytical solution. (Abstract shortened with permission of author.)... |
