Gravitational and Finite‐Size Effects On Pressure Saturation Curves During Drainage

Monem Ayaz,Gerhard Schäfer,Renaud Toussaint,Knut Jørgen Måløy

doi:10.1029/2019wr026279

Abstract

AbstractWe experimentally and numerically study the influence of gravity and finite‐size effects on the pressure‐saturation relationship in a given porous medium during slow drainage. The effect of gravity is systematically varied by tilting the system relative to the horizontal configuration. The use of a quasi two‐dimensional porous media allows for direct spatial monitoring of the saturation. Exploiting the fractal nature of the invasion structure, we obtain a relationship between the final saturation and the Bond number using percolation theory. Moreover, the saturation, pressure, and Bond number are functionally related, allowing for pressure‐saturation curves to collapse onto a single master curve, parameterized by the representative elementary volume size and by the Bond and capillary numbers. This allows to upscale the pressure‐saturation curves measured in a laboratory to large representative elementary volumes used in reservoir simulations. The large‐scale behavior of these curves follows a simple relationship, depending on Bond and capillary numbers, and on the flow direction. The size distribution of trapped defending fluid clusters is also shown to contain information on past fluid flow and can be used as a marker of past flow speed and direction.

Highlights

Displacement of one immiscible fluid by another in a porous medium is an important research topic both from a fundamental and an applied perspective
We see that by inserting pore-scale description of the system, and taking into account the gravity effect across the cell, we are able to collapse the PS curves onto a single master curve: This equation, Equation 14, captures properly the entrance pressure, the rise of the pressure drop with the drainage, and the final pressure buildup when the invader is limited by the semipermeable membrane
For a system unaffected by boundary effects, the PS relation during such drainage is entirely specified by a characteristic capillary pressure that can be obtained from percolation threshold pc for the occupancy probability and the cumulative distribution of capillary pressure thresholds f as f −1(pc), a straight line with a slope given byBoSnFw, and a final saturation, SnFw = Bo[(nu∕(1+nu))(D−Dc)]

Summary

Introduction

Displacement of one immiscible fluid by another in a porous medium is an important research topic both from a fundamental and an applied perspective. We study two phase flow in a quasi two-dimensional (2-D) porous confinement and look at the simple case of drainage at pore scale, where a nonwetting phase displaces a wetting one Such experiments have shown to generate displacement structures that depend on the density and viscosity contrast between the fluids, surface tension, and the flow rates at which the system is driven (Lenormand et al, 1983; Løvoll et al, 2004; Toussaint et al, 2005). The trapped islands are characterized by their power law distribution in size with an exponential cutoff directly related to the gravitational forces (Blunt & King, 1990) and the system's finite size

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Discussion

Conclusion