THE STATISTICAL BEHAVIOR OF INSTABILITIES IN DISPLACEMENT PROCESSES IN POROUS MEDIA

Abstract

The problem of growth of instabilities (fingers) in displacement processes in porous media is analyzed from a statistical viewpoint. The relative area occupied by fingers is represented as a "saturation", and the equations of motion for this "saturation" are derived. It is shown that these equations are analogous to the Buckley–Leverett equations of immiscible displacement, with a fictitious "relative permeability" being introduced. The latter can be calculated and thus the statistical equations of motion of a fingered-out front can be written down explicitly. These equations of motion can then be solved by the well-known method of characteristics. It is shown that the statistical theory does not lead to any stabilization of the fingers.