The Instability of Slow, Immiscible, Viscous Liquid-Liquid Displacements in Permeable Media

Abstract

Published in Petroleum Transactions, AIME, Volume 216, 1959, pages 188–194. Introduction The purposes of this paper are to present theoretical and experimental evidence for occurrence of macroscopic instabilities in displacement of one viscous fluid by another immiscible with it through a uniform porous medium and to compare available experimental data with some predictions of a theory of instability developed by the first author. The instabilities are referred to as macroscopic in the sense that spatially quasi-sinusoidal, growing fingers of the displacing liquid are formed, the width and peak-to-peak separation (wavelength) of which is large relative to a characteristic length of the particular permeable medium such as grain size. Visual models of two kinds have been used to obtain observations: displacement of oil by water-glycerine solutions through the flow channel formed by closely spaced parallel plates and displacement of oil by water with and without initial interstitial water through unconsolidated glass powder packs, employing the technique of matching indices of refraction. In all cases we have observed macroscopic instabilities or fingers under conditions predicted by the theory to be favorable for their occurrence. The phenomenon discussed here is not the production of streamers due to gross inhomogeneities such as permeability stratification of the porous medium.It is our object to show, on the contrary, that a quantitative prediction of finger spacing is possible in a porous medium known to be macroscopically homogeneous and isotropic throughout. The importance of the phenomenon in its influence on the configuration of oil and water with respect to oil production behavior was noted earlier by Engelberts and Klinkenberg who coined the term "viscous fingering". Theory Necessary and Sufficient Conditions for Instability and Initial Kinematics There are several levels of increasing complexity in the theoretical description of instability of fluid displacements in permeable media. Of these, the simplest description, adapted to low permeability systems, is selected for presentation. More inclusive descriptions are reserved for separate publication.