ON THE STABILITY OF DISPLACEMENT FRONTS IN POROUS MEDIA: A DISCUSSION OF THE MUSKAT–ARONOFSKY MODEL

It is well known that, during the displacement of a fluid contained in a porous medium by another less viscous one, the displacement front may become unstable: Fingers occur which proceed rapidly through the system.The Muskat–Aronofsky model of displacement in porous media, in which it is assumed that a sharp front exists with maximum saturation by the respective fluid being present on either side of the front, is analyzed in the light of the phenomenon of fingering. It is shown that the Muskat–Aronofsky model, in fact, demands that fingering occurs for mobility ratios (displaced/displacing fluid) smaller than one. This model should, therefore, not be used for the calculation of the steady progress of a front for such mobility ratios. The Muskat–Aronofsky model also yields some conditions regarding the geometry of fingers; the latter are deduced. It does not, however, describe the fingering process completely. In this connection, one would have to take recourse to the statistical geometry of porous media. This will be done in a separate paper.