Pressure saturation curves and the critical volume fraction for percolation: Accessibility function of percolation theory

Abstract

The pressure-saturation curves of porous media give fundamental information about the pore space. In equilibrium, ignoring effects due to hysteresis and pore accessibility, it should be possible to extract a pore-size distribution from h(?) data, asdescribed in Chap. 4. However, a number of percolation effects complicate the analysis and make such a simple inference impossible. The pressure-saturation relation is affected by both the lack of continuity of the air phase near saturation, and by a similar lack of continuity of the water phase near the dry end. Given that these effects are due to phase transitions (in the percolation sense), small changes in experimental conditions can produce major (and sometimes puzzling) changes in the results. Further, since the correlation length diverges near these transitions, numerical simulations under both wet and dry conditions are amenable to finite-size scaling analysis. Since the critical volume fractions for percolation of air and water are critical to the discussion, experimental evidence regarding these values is presented toward the end of this chapter. © 2014 Springer International Publishing Switzerland.