Towards precise prediction of transport properties from synthetic computer tomography of reconstructed porous media

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.

Deposition of general ellipsoidal particles

We present a systematic overview of granular deposits composed of ellipsoidal particles with different particle shapes and size polydispersities. We study the density and anisotropy of such deposits as functions of small to moderate size polydispersity and two shape parameters that fully describe the shape of a general ellipsoid. Our results show that, while shape influences significantly the macroscopic properties of the deposits, polydispersity in the studied range plays apparently a secondary role. The density attains a maximum for a particular family of nonsymmetrical ellipsoids, larger than the density observed for prolate or oblate ellipsoids. As for anisotropy measures, the contact forces are increasingly preferred along the vertical direction as the shape of the particles deviates from a sphere. The deposits are constructed by means of a molecular dynamics method, where the contact forces are efficiently and accurately computed. The main results are discussed in the light of applications for porous media models and sedimentation processes.

High-precision synthetic computed tomography of reconstructed porous media

Multiscale simulation of transport in disordered and porous media requires microstructures covering several decades in length scale. X-ray and synchrotron computed tomography are presently unable to resolve more than one decade of geometric detail. Recent advances in pore scale modeling [Biswal, Held, Khanna, Wang, and Hilfer, Phys. Rev. E 80, 041301 (2009)] provide strongly correlated microstructures with several decades in microstructural detail. A carefully calibrated microstructure model for Fontainebleau sandstone has been discretized into a suite of three-dimensional microstructures with resolutions from roughly 128 μm down to roughly 500 nm. At the highest resolution the three-dimensional image consists of 32768^{3}=35184372088832 discrete cubic volume elements with gray values between 0 and 216. To the best of our knowledge, this synthetic image is the largest computed tomogram of a porous medium available at present.