Numerical simulation of the displacement of oil by water

Abstract

If the mobility of a displacing fluid is greater than the mobility of the displaced fluid, the displacement is unstable (see, for example, [1–3]), and the originally plane displacement front is broken up into irregular tongues. It follows from the linear analysis of stability that initially the amplitude of the perturbation increases exponentially, and according to [1] the extended tongues that are formed move with constant velocity relative to the displaced fluid. The intermediate stages in the development of the instability, like questions relating to a more precise formulation of the problem (which involves giving up the piston displacement approximation) remain unstudied. A natural approach to their study is through numerical simulation, which was realized for the first time in [4, 5]. Some of the results of such an investigation are presented in the present paper. In contrast to [4], the main attention is devoted to the development of regular perturbations. It is shown that for the investigated mobility ratios the development of the perturbations follows the linear theory unexpectedly long, and then arrives at a stationary asymptotic regime. We also investigate the influence of the loss of displacement stability on waterless oil extraction in the case of displacement in homogeneous and inhomogeneous strata.