Well Hydraulics in Heterogeneous Porous Media

Abstract

Heterogeneous porous media consisting of components of markedly different properties are commonly encountered in under-ground engineering practice. In groundwater and petroleum reservoir engineering these are, for. example, the sedimentary deposits of clay interbedded with layers-of sand, fractured formations of tight matrix rock broken up by fissures of secondary origin, or multiporous carbonate sediments such as limestones and dolomites. The mechanism of fluid flow in such heterogeneous formations is governed by distinct diffusivities along the characteristic flow paths within each component. Intercomponent interaction is provided by fluid transfer from a component of low diffusivity (with a resulting slow response to pressure changes) to a component of high diffusivity (correspondingly rapid response to pressure changes). This crossflow enhances the flow through one component of the medium while depleting the other until the transient flow interaction achieves a quasi-steady state and the medium behaves as an equivalent uniform system with composite properties. In naturally fractured reservoirs, for example, fractures serve as high permeability conduits that transmit fluids to a well, while contributing very little to the original reservoir porosity (or storage.) Hence, the high diffusivity of a fracture results in a short, almost instantaneous, response along the fracture to any pressure change such as that due to well production. The rock matrix, on the contrary, has a low permeability but relatively high primary porosity that contains the fluid. The low matrix diffusivity results in a ‘delayed’ matrix response to pressure changes that occur in the surrounding fractures. Such nonconcurrent response causes an intercomponent pressure depletion that induces matrix-to-fracture crossflow. The flow to a well, now enhanced by a time-variant crossflow, is no longer radial. As time progresses, the matrix blocks near the well deplete to pressure equilibrium with the fractures.