A Theoretical Analysis of Viscous Crossflow

Abstract

ABSTRACT A theory predicting fluid flow in a stratified reservoir considering the affects of viscous crossflow is presented. The development of equations accounts only for crossflow due to pressure gradients formed by the displacing (injected) and displaced (initial) fluids having unequal mobilities; all other forces initiating flow (vertical or horizontal) are considered negligible. The primary simplifying assumption requires the transfer of material between two or more layers to be instantaneous; the assumption is usually referred to as vertical equilibrium (VE). In theory, the equations describing flow are applicable to an arbitrary number of layers, arbitrary initial and injection conditions, arbitrary phase properties affecting flow, and encompasses fractional flow theory applied to water-oil displacements as well as enhanced oil recovery processes. At present the development is restricted to two phases and two components in the injected phase with no partitioning of material between phases.