Category: Precision Simulations

Differential porosimetry and permeametry for random porous media

Post author By R Hilfer
Post date January 5, 2015

R. Hilfer, A. Lemmer

Physical Review E 92, 013305 (2015)
https://doi.org/10.1103/PhysRevE.92.013305

submitted on
Monday, January 5, 2015

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 850 μm, 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.

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Porous Media Precision Simulations Simulations

Continuum-based rock model of a reservoir dolostone with four orders of magnitude in pore sizes

Post author By R Hilfer
Post date May 28, 2010

S. Roth, B. Biswal, G. Afshar, R. Held, P. Øren, L. Berge, R. Hilfer

AAPG Bulletin 95, 925 (2011)
DOI:10.1306/12031010092

submitted on
Friday, May 28, 2010

A continuum-based pore-scale representation of a dolomite reservoir rock is presented, containing several orders of magnitude in pore sizes within a single rock model. The macroscale rock fabric from a low-resolution x-ray microtomogram was combined with microscale information gathered from high- resolution two-dimensional electron microscope images. The low-resolution x-ray microtomogram was segmented into six separate rock phases in terms of mineralogy, matrix appearances, and open- versus crystal-filled molds. These large-scale rock phases were decorated (modeled) with geometric objects, such as different dolomite crystal types and anhydrite, according to the high-resolution information gathered from the electron microscope images. This procedure resulted in an approximate three-dimensional representation of the diage- netically transformed rock sample with respect to dolomite crystal sizes, porosity, appearance, and volume of different matrix phases and pore/matrix/cement ratio. The resulting rock model contains a pore-size distribution ranging from moldic macropores (several hundred micrometers in diameter) down to mudstone micropores ( less than 1 mm in diameter). This allows us to study the effect and contribution of different pore classes to the petrophysical properties of the rock. Higher resolution x-ray tomographs of the same rock were used as control volumes for the pore-size distribution of the model. The pore-size analysis and percolation tests performed in three dimensions at various discretization resolutions indicate pore-throat radii of 1.5 to 6 mm for the largest interconnected pore network. This also highlights the challenge to determine appropriate resolutions for x-ray imaging when the exact rock microstructure is not known.

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image analysis Porous Media Precision Simulations Simulations

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

Post author By R Hilfer
Post date April 4, 2009

B. Biswal, R.J. Held, V. Khanna, J. Wang, R. Hilfer

Physical Review E 80, 041301 (2009)
https://doi.org/10.1103/PhysRevE.80.041301

submitted on
Saturday, April 4, 2009

Transport properties of a multiscale carbonate rock are predicted from pore scale models, reconstructed using a continuum geometrical modeling technique. The method combines crystallite information from two-dimensional high-resolution images with sedimentary correlations from a three-dimensional low-resolution microcomputed tomography micro-CT-image to produce a rock sample with calibrated porosity, structural correlation, and transport properties at arbitrary resolutions. Synthetic micro-CT images of the reconstructed model match well with experimental micro-CT images at different resolutions, making it possible to predict physical transport parameters at higher resolutions.

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Porous Media Precision Simulations

Modeling of Multiscale Porous Media

Post author By R Hilfer
Post date January 30, 2009

B. Biswal, P.E. Øren, R.J. Held, S. Bakke, R. Hilfer

Image Analysis and Stereology 28, 23-34 (2009)
DOI: 10.5566/ias.v28.p23-34

submitted on
Friday, January 30, 2009

A stochastic geometrical modeling method for reconstructing three dimensional pore scale microstructures of multiscale porous media is presented. In this method the porous medium is represented by a random but spatially correlated structure of objects placed in the continuum. The model exhibits correlations with the sedimentary textures, scale dependent intergranular porosity over many decades, vuggy or dissolution porosity, a percolating pore space, a fully connected matrix space, strong resolution dependence and wide variability in the permeabilities and other properties. The continuum representation allows discretization at arbitrary resolutions providing synthetic micro-computertomographic images for resolution dependent fluid flow simulation. Model implementations for two different carbonate rocks are presented. The method can be used to generate pore scale models of a wide class of multiscale porous media.

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