| Abstract: | ![]()
An exact solution is obtained for the problem of steady-state filtration of a heavy dense incompressible fluid in a thin, infinitely deep, inclined reservoir having a crack of given depth along the reservoir rise. The region of filtration of the lighter liquid (oil) has an impermeable upper boundary in the form of a horizontal fault line. Below the filtration region there is a free boundary, below which lies the region of stationary fluid (bottom water). The interface of the fluids, the fissure profile, and the reservoir fluid flow rate are determined from the solution of the problem on the basis of the given parameters (permeability of the reservoir and of the material filling the fissure, viscosity of the filtering fluid, specific weight of the upper and lower fluids, depth of the fissure, pressure differential between a point at the fissure and a point at the interface of the fluids). In the case when the thin reservoir is a vertical filtering layer, the considered flow is interpreted as the motion of the reservoir fluid through a vertical fissure of a thick reservoir (half-space) in the presence of an underlying fluid interface. The problem is solved in finite form with the aid of known analytic functions using integrals of the Cauchy type. The fundamental solution is first found of the special problem of flow with a point singularity. The fundamental solution is also of independent importance as an extension of the solution of certain known problems [1–4]. |
