Capillary displacement and percolation in porous media

Abstract

We consider capillary displacement of immiscible fluids in porous media in the limit of vanishing flow rate. The motion is represented as a stepwise Monte Carlo process on a finite two-dimensional random lattice, where at each step the fluid interface moves through the lattice link where the displacing force is largest. The displacement process exhibits considerable fingering and trapping of displaced phase at all length scales, leading to high residual retention of the displaced phase. Many features of our results are well described by percolation-theory concepts. In particular, we find a residual volume fraction of displaced phase which depends strongly on the sample size, but weakly or not at all on the co-ordination number and microscopic-size distribution of the lattice elements.

Influence of Viscous Fingering on Dynamic Saturation–Pressure Curves in Porous Media

“…If the flow rate is sufficiently low (Ca 1), one reaches the capillary fingering regime (Lenormand et al 1983;Lenormand and Zarcone 1985), for which the displacement structure is controlled solely by the fluctuations in the capillary threshold pressures. This regime is shown to have strong analogies to invasion percolation (Lenormand and Zarcone 1985;Chandler et al 1982;Wilkinson and Willemsen 1983), and the invasion structure is fractal Mandelbrot (1982) ;Feder (1988) with a fractal dimension D c = 1.83 ± 0.01 (Lenormand andZarcone 1985, 1989). If the invasion rate is high, the displacement is either stable or unstable depending on the viscosity contrast M. If a fluid with high viscosity is invading a fluid with low viscosity (M ≥ 1), the resulting pressure field due to the viscous dominated displacement will act against the growth of the invasion front, leading to stabilization of the displacement front at a finite width (Saffman and Taylor 1958;Lenormand et al 1988;Lenormand 1989;Frette et al 1997;Xu et al 1998).…”

Structure and conductivity of clusters generated by variable-range hopping percolation

“…However, in this study we have mainly grown clusters with a so-called invasion percolation ͑IP͒ algorithm, which was originally developed to study multiphase flow problems in porous media. [16][17][18] We will use the abbreviation VRH-IP for this approach.…”

An overview of instability and fingering during immiscible fluid flow in porous and fractured media

“…This case is amenable to analysis by a technique known as invasion percolation which is computationally much more efficient than the standard approach though it has traditionally disregarded gravity (Lenormand and Bories, 1980;Chandler et al, 1982;Wilkinson and Willemsen, 1983;Wilkinson, 1986). In this method, each site and bond at the interface is ranked according to its level of participation in movement: During invasion of a nonwetting fluid, the highest rank is associated with the highest threshold pressure and, during invasion of a wetting fluid, with the lowest threshold pressure.…”