Ground water flux distribution between matrix, fractures, and conduits: constraints on modeling

Calculations are presented to show the relative contribution of the matrix, fracture, and conduit permeability to the overall flow of ground water through a karst aquifer. The conceptual model is a cross-section spanning the full width and thickness of the aquifer. A constant, but adjustable head is assumed. The rock matrix is characterized by an adjustable hydraulic conductivity. Varying proportions of fractures and conduits of adjustable fracture apertures and conduit diameters were the calculational parameters. Calculations used Darcy’s law for matrix flow, the cube law for fracture flow, and the Darcy-Weisbach equation for conduit flow. The results show a surprising dominance of fracture flow in the early stages of aquifer development. A focusing mechanism is needed to localize the flow into a relatively small number of conduits.