The Invasion Percolation in a Gradient (IPG) model is capable of incorporating all forces -viscous (in both the wetting and nonwetting fluids), buoyancy, and capillary forces -relevant to geologic problems of two-phase flow in a porous medium. Calibration of the IPG model to a pre-existing data set of two-phase flow experiments on glass bead packs shows that the characteristic throat radius Rt is about 10% of the site radius Rs, assuming Rs-P?, the grain size. Two-dimensional model results of the fractal dimension D and the invasion probability of a throat on the interface are in excellent agreement with predictions for limiting cases of Capillary number Ca and Bond number Bo. In moving from twoto three-dimensional media, trapped wetting clusters do not scale with the extent of the invading cluster, remaining under 5 to 8 pores in size.
Two-phase flow in a porous medium has been an active area of research for more than five decades. Representative Elementary Volume (REV) assumptions, coupled with continuum concepts (Bear 1972), have provided the fundamental basis for most largescale models of two-phase flow. Recent experimental and theoretical work (Lenormand 1989, Baveye & Sposito 1984), however, show that such models fail to represent accurately both very slow and buoyancy dominated processes. This results in their inability to incorporate appropriately the influence of pore-scale mechanics on the geometry of the nonwetting fluid cluster at a macroscopic scale.
Percolation theory has received increasing attention for providing both a quantitative and conceptual framework for describing all types of two-phase flow phenomena (Yortsos et al. 1997, Xu et al. 1998, Hirsch & Thompson 1995). Although Ordinary Percolation (OP) theory was initially used to describe the final fluid configuration observed following (slow) immiscible displacement processes, it was the introduction of the Invasion Percolation (IP) model by Wilkinson & Willemsen, 1983 that allowed for a more complete investigation of the entire displacement process. Numerous experimental studies validate the use of IP to describe very slow immiscible displacement, yet it is not an appropriate model when spatial gradients in the capillary pressure Pc are present. Such gradients include not only viscous and buoyancy related gradients in the nonwetting fluid, but also gradients associated with viscous forces in the wetting fluid and with spatial variations in the permeability k (Chaouche et al. 1994, Meakin et al. 1992). The Invasion Percolation in a Gradient (IPG) model is capable of including all of these factors.
