Simulation of Miscible Viscous Fingering Using a Modified Method of Characteristics: Effects of Gravity and Heterogeneity

Abstract

ABSTRACT The effects of gravity and of the structure of the porous medium on unstable miscible displacement are studied by means of numerical simulation. The numerical method combines a modified method of characteristics with a mixed finite element method. The permeability fields used in the simulations are generated by a statistical method so that they have a given coefficient of variation and a given correlation length. Results indicate that a displacement may be dominated by gravity override or by viscous fingering or both mechanisms may be important. When gravity tonguing is dominant, the results are early breakthrough and little oil recovery after breakthrough. Finger generation is governed by the permeability distribution near the inflow end. Shielding and merging during the displacement reduce the initial number of fingers to a smaller number of "active fingers", which dominate the displacement. The number of active fingers is a decreasing function of the correlation length, the coefficient of permeability variation and the viscosity ratio, but, with these parameters fixed, it is largely independent of the specific permeability distribution. The root mean square growth rate of the fingers stays approximately constant throughout the displacement; its value is an increasing function of the viscosity ratio and coefficient of variation, while its dependence on the correlation length is of a more complex character.