Differential porosimetry and permeametry for random porous media

Accurate determination of geometrical and physical properties of natural porous materials is notoriously difficult. Continuum multiscale modeling has provided carefully calibrated realistic microstructure models of reservoir rocks with floating point accuracy. Previous measurements using synthetic microcomputed tomography (μ-CT) were based on extrapolation of resolution-dependent properties for discrete digitized approximations of the continuum microstructure. This paper reports continuum measurements of volume and specific surface with full floating point precision. It also corrects an incomplete description of rotations in earlier publications. More importantly, the methods of differential permeametry and differential porosimetry are introduced as precision tools. The continuum microstructure chosen to exemplify the methods is a homogeneous, carefully calibrated and characterized model for Fontainebleau sandstone. The sample has been publicly available since 2010 on the worldwide web as a benchmark for methodical studies of correlated random media. High-precision porosimetry gives the volume and internal surface area of the sample with floating point accuracy. Continuum results with floating point precision are compared to discrete approximations. Differential porosities and differential surface area densities allow geometrical fluctuations to be discriminated from discretization effects and numerical noise. Differential porosimetry and Fourier analysis reveal subtle periodic correlations. The findings uncover small oscillatory correlations with a period of roughly 850μm, thus implying that the sample is not strictly stationary. The correlations are attributed to the deposition algorithm that was used to ensure the grain overlap constraint. Differential permeabilities are introduced and studied. Differential porosities and permeabilities provide scale-dependent information on geometry fluctuations, thereby allowing quantitative error estimates.