The Onset of Instability During Two-Phase Immiscible Displacement in Porous Media

This paper presents a dimensionless number and its critical value for predicting the onset of instability during immiscible displacement in porous media. The critical dimensionless number obtained from a stability theory for a cylindrical system successfully predicted the onset of instability in laboratory floods. Therefore, this number can be used to classify the stability of two-phase incompressible displacements in homogeneous porous media. Introduction When a fluid displaces a more viscous fluid, the displacement front may become unstable, resulting in viscous fingering. This phenomenon raises both practical and theoretical concerns. Apart from further reducing the displacement efficiency of an already inefficient displacement arrangement, instability may invalidate the usual method of simulating immiscible displacement performance based on relative permeability and capillary pressure concepts. Also, it introduces an additional scaling requirement for using model tests to forecast prototype displacement results. Therefore, it would be most beneficial to predict the onset of instability, so as to avoid viscous fingering, or, where it is unavoidable, to be able to recognize it as a factor in the displacement.The onset of instability call be predicted by a stability analysis of the displacement. The objective of such an analysis is to determine the conditions under which small disturbances or perturbations of the displacement front will grow to become viscous fingers. Ideally, the analysis should give a universal dimensionless scaling group together with its critical value above which instability will occur. The stability classification then would entail no more than the calculation of one dimensionless number in a manner analogous to the calculation of a Reynolds number to distinguish between laminar and turbulent flow.Several stability studies of immiscible displacement have been reported in the literature. Collectively, they show that these variables are pertinent to the stability problem:mobility (or viscosity) ratio,displacement velocity, system geometry and dimensions,capillary and gravitational forces, andsystem permeability and wettability. However, none of the previous studies have combined these variables into one dimensionless number that can be used to quantify the stability classification.The objective of this study was to obtain, by means of a stability analysis, a universal dimensionless scaling group and its critical value for predicting the onset of instability during immiscible displacement in porous media. This paper shows how the stability theory of Chuoke et al. was extended to achieve this objective and presents the results of laboratory floods that confirm the predicted onset of instability in cylindrical cores. Theory The pertinent dimensionless number for predicting the onset of instability was obtained by extending the stability theory of Chuoke et al. Their theory was based on a piston-like unperturbed displacement model in which the oil and water zones are separated by a planar interface. Details of the theory and our extension of it are presented in the following sections. SPEJ P. 249^