An analytic element model for flow in fractured impermeable rock

We present an analytic element model for three-dimensional flow in fractured impermeable rock. The flow in each fracture is governed by both Darcy’s law and mass balance. We 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, others 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.