MODELING GROUNDWATER FLOW IN LAYERED, ANISOTROPIC, AND HETEROGENEOUS AQUIFER SYSTEMS USING DISCRETE ANALYTIC DOMAINS

This new analytic modeling technique allows modeling of flow in layered aquifer systems with complex heterogeneity and anisotropy. It has the accuracy, geometric flexibility, and simple input of previous analytic element methods (AEM), but greater versatility with heterogeneity, anisotropy, and efficient implementation of multiple layers.

The flow field is divided into discrete polygonal domains, each with its own definition of isotropic or anisotropic aquifer parameters and each with its own flow model defined with analytic elements. Unlike previous AEM techniques, the anisotropy orientation and ratio can differ from one domain to another. With this approach, the potential and discharge vector functions are the sum of contributions from elements within or on the boundary of the domain; elements beyond the domain boundary don't contribute to these functions, which saves computation. Models for anisotropic domains are written in transformed coordinates as suggested by Muskat (1937).

Each domain model is the sum of contributions from basic elements: point sinks, high-order line elements, and multi-quadric area sinks. Point sinks represent pumping wells that may be either discharge- or head-specified. Line elements represent inter-domain boundaries, head-specified boundaries, river boundaries, normal-flux specified boundaries, or flux-specified boundaries. Multi-quadric area sinks represent spatially-variable distributed sources such as recharge, vertical leakage between layers, and storage fluxes in transient models. Boundary condition equations are written so that the number of equations equals the number of unknown element strength parameters. The sparse system of equations is solved with an iterative solver, allowing non-linear boundary conditions.

This technique has the novel ability to have multiple layers with vertical leakage in the main area of interest, tapering to fewer layers or just one layer in distant areas, efficiently concentrating detail just where it is needed and warranted by data.

The method is demonstrated in an example model with 7 domains and in another model that compares to a MODFLOW simulation of the same problem.