Numerical simulation of the Saffman-Taylor instability in the Hele-Show cell

Abstract

© 2019 IOP Publishing Ltd. The process of displacing one viscous liquid with a less viscous one in porous medium is accompanied by folds formation on the border of liquids division. These folds called 'viscous fingers' grow with not the same velocity. This phenomenon doesn't allow extracting all oil while displacing it with water. The process of formation and growth of viscous fingers has a critical sustainability which depends on a number of parameters. One of these parameters is characteristics of imposed oscillations. Practical field experiments demonstrate the impact that imposed oscillations have on the watercut of extracted oil. Two-dimensional analogue of displacing oil with water is displacing viscous liquid from Hele-Show cell. The impact of characteristics of initial oscillation on the 'viscous fingers' formation and development process is studied in this paper. Dependencies of relative growth velocities of 'viscous fingers' on amplitude and frequency of influence are presented below.