A new model for groundwater flow in fractured rock based on the analytic element method

Otto Strack
Civil, Environmental, and Geo- Engineering
University of Minnesota

ABSTRACT
The motivation for this work is the critical importance of efficient recovery of groundwater from all kinds of aquifers, including fractured rock, in today's environment of widespread water shortage.

This presentation concerns flow of groundwater through fractured rock as in karst in Minnesota and Germany, and in granite in Sweden. Such flow is poorly understood; information from wells is difficult to interpret because we do not know from which fractures the sampled water is collected.

An attractive alternative is to construct an accurate mathematical/numerical model capable of dealing with very large numbers of fractures of vastly different sizes. The advantage of a computer model is access to all data such as pressures and velocities. The idea of numerical tests is inspired by that pioneered by Peter Cundall and Otto Strack in the nineteen seventies for numerical testing of granular media on the scale of particles.

Otto Strack and his co-author Erik Toller approximate the medium, usually rock, as impermeable and the fractures as thin aquifers. The flow in the fractures is governed by Darcy's law and mass balance. They formulate the problem in terms of complex variables and introduce a complex potential in each fracture, defined inside a circular impermeable boundary. Some of the fractures are connected to stream- or riverbeds and wells may be drilled through the system. The fractures may have intersections that connect some of them; the flow is from one fracture to another via the intersections. The complex potential in each fracture is the sum of analytic elements; some represent sources of water, mostly head-specified sources, others are sinks. Each intersection is modeled with a special analytic element. Conditions along the intersections are that the flow out of one fracture enters the connected one and that the heads in connected fractures match.