A Theoretical Description of Water-Drive Processes Involving Viscous Fingering

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Abstract
Published in Petroleum Transactions, AIME, Vol. 213, 1958, pages 103–112.Paper presented at 32nd Annual Fall Meeting of SPE in Dallas, Texas, Oct. 6–9, 1957. Abstract From observations of the linear displacement of oil by water from a porous medium as visualized in transparent models, new insight into the mechanism of viscous fingering, as occurring in the case of unfavorable oil-water viscosity ratios, has been obtained. A mathematical description of the observed phenomena leads to formulas expressing both oil production and pressure drop across the formation as a function of cumulative water injection with the oil-water viscosity ratio as a parameter. Theoretical results are compared with those obtained from scaled laboratory experiments in sand-filled tubes in which water was injected at the one end and production was obtained from the other end. In the second part of the paper the same principles are used to calculate a more realistic production scheme in which production of oil and water is obtained from wells regularly distributed over the field. Results show satisfactory agreement with production data of an actual oil field. Application of the theory is extremely simple as only a limited number of readily available parameters have to be known and results are presented in an analytical form. Introduction When oil is displaced from a porous medium by water having a viscosity lower than the oil, the oil-water interface is essentially unstable and has the tendency to break up into what are called "fingers" or "streamers". This viscous fingering has been noted before by Engelberts and Klinkenberg and has recently been demonstrated in transparent models by van Meurs. It is highly questionable whether it is at all possible to perform relative permeability measurements in the laboratory reproducing the same distribution of water and oil in the cores as present in practice. Therefore, we based our descriptive theory on an idealized model which was "tailored" to the fingering mechanism as observed in transparent models under scaled conditions. This approach was the more attractive, as a highly simplified model had already yielded an adequate description of the process. Though we are aware our theoretical approach can be extended in several ways, it is given here in its simplest form to explain the fundamental principles and to avoid complicated formulas.

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