Effect of Layer Ordering on Viscous Crossflow in Stratified Systems

An analytical treatment of viscous crossflow in unordered layered systems is performed under the assumption of viscous dominated vertical equilibrium (VVE) and piston-like displacement. The method developed is essentially a generalization of earlier approaches (Hearn, 1971) to unordered systems. It is shown that the fluid interface is influenced by a non-monotonic fluid front profile, leading to formation of “extra zones” of oil or water between the layer fronts. The internal ordering of layers in a system may have a significant effect on fluid crossflow and interfaces, and thereby on the reservoir performance. The procedure of ordering layers before calculating reservoir performance or VVE pseudo fliinctions (Ream 1971, El-Khatib 1985) may therefore lead to significant errors.