Transient boundary layer effect in underground oil and gas reservoir depletion processes (Q1081483)

Modern methods of exploiting underground deposits of oil and gas are characterized by conditions that vary slowly with time, which makes it possible to treat them over an extended period as near-equilibrium processes and use for their analysis the effective methods of perturbation theory. At the same time, during a brief initial period these systems display essentially nonequilibrium behavior leading to a transient boundary layer effect. For closed reservoir depletion problems a measure of the degree of nonequilibrium of the reservior system is introduced and for real deposits shown to be small, the existence of a boundary layer is established, and the exterior and interior problems are formulated, together with the matching conditions. The general form of the exterior asymptotic behavior, in which the space variables and time are separated, is established and the initial parabolic system is reduced to a linear Poisson equation. Examples of problem solving are given.