Author(s)

Y.C. Yortsos

Abstract

A phase diagram of fully developed drainage in porous media is developed using concepts of Invasion Percolation in a Gradient. We show that the transition between stabilized displacement (where the conventional continuum description applies) and fingering is controlled by the change of the sign of the gradient of the percolation probability (from stabilizing to destabilizing). The transition boundary is described by scaling laws. 1 Introduction The displacement (drainage) of a wetting (w) fluid in a porous medium by a non-wetting (nw) fluid has been analysed in detail in the past. For drainage in an L X L pore-network at velocity g, Lenormand* identified three limiting patterns, Invasion Percolation^ (IP), Piston- like or Compact and Viscous Fingering^ (VF), and delineated their validity. As the displacemen

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