The effects of viscous crossflow on sharp front displacements in two-layered porous media

Abstract

The effects of viscous crossflow may play an important role in the overall displacement of oil by water. This work seeks not only to determine when viscous crossflow is important but also to calculate its effects on vertical sweep efficiency. This thesis analyzes viscous crossflow by comparing the existing solutions of Dykstra-Parsons and Hearn to computer simulation results. The solution by Dykstra-Parsons, which assumes no vertical permeability, agreed well with the numerical solution. However, the Hearn solution, which assumes infinite vertical permeability, required modifications when it was applied to displacements with mobility ratios greater than one. The computer simulator was a two-phase, two-dimensional, finite difference model written by Dr. R. C. MacDonald. The simulator was modified in certain areas, such as the solution technique, injection scheme, and the coordinate system, as well as other areas in order to handle our particular objectives. Perhaps the most significant result presented in this thesis is that the infinite vertical permeability analytic solution may be attained without excessively large vertical permeabilities, if the length-to-thickness ratio is large. A correlation presented in this thesis in graphical form indicates when a reservoir may be described assuming no crossflow or when it may be described assuming infinite vertical permeability. Finally, modifications are made to the Hearn analytic solution which makes the solution more general and allows it to correctly handle sharp front displacements where the mobility ratio is greater than one.