A Laboratory Investigation of the Pseudo Relative Permeability Characteristics of Unstable Immiscible Displacements
Authors: Sarma H.K. , Maini B.B. , Purves R.W. , Jha K.N. N. 
Published: March 2010

Abstract
Enhanced oil recovery operations often involve immiscible displacement of the more viscous oil by a less viscous fluid. This often leads to an unstable and inefficient displacement process because of fingering of the more mobile displacing fluid through the more viscous oil. Although, with application of reported stability theories, it is possible to roughly predict whether or not a field displacement is likely to be unstable, rigorous mathematical models to predict the recovery performance of such unstable displacements are not available. The usual practice has been to employ a Buckley-Leverett type analysis, which is based on the assumption of a stable and stabilized displacement, and to account for the presence of instabilities by using empirical sweep efficiency corrections. The relative permeabilities used in this type of analysis are usually obtained from laboratory tests which pay little or no attention to possible viscous instabilities.
A more direct approach to account for the presence of viscous instabilities in immiscible displacements would be to use pseudo-relative permeabilities which are modified true relative permeability curves (modified to account for the instabilities). However, before development of such an approach is attempted, one needs to examine whether or not the conventional Buckley-Leverett model, with modified relative permeability curves, can be used to describe the recovery and pressure drop performance of unstable displacements. This was the main objective of this study.
Several unstable immiscible displacement experiments were carried out in a rectangular model. The effects of different parameters on the oil recovery were examined and pseudo-relative permeability curves were generated for each set of conditions. The dependence of these pseudo-relative permeability curves on displacement rate, viscosity ratio, gravity, and the presence or absence of initial water saturation were examined.
The performance of current stability theories in predicting the breakthrough recovery was tested against the results of these displacements. It was found that the "wettability number" proposed by Peters and Flock was not a constant for a given rock fluid system but rather a function of the flood velocity.

Introduction
Recovery of oil by waterflooding is an efficient process, provided the water advances as a stable front and sweeps the reservoir uniformly. This occurs when the oil is more mobile than the displacing water and the reservoir is not too heterogeneous. However, when the oil mobility is low as would be the case in medium gravity and heavy oils, the displacing water has a tendency to finger through the oil and this leads to poor recovery efficiency. The factors which control this type of flow instability include the displacement velocity, oil/water viscosity ratio, relative permeability characteristics and the interfacial tension between oil and water. Although, with application of reported stability theories, it is possible to roughly predict whether or not a field displacement is likely to be unstable, rigorous mathematical models to predict the recovery performance of such unstable displacements are not available. The usual practice has been to employ a Buckley-Leverett type analysis(1,2).
The Buckley-Leverett theory applies to a linear displacement process involving two immiscible fluids with no mass transfer taking place between them.