https://cyberleninka.org/article/n/22310.pdf

Pore-scale imaging and modelling

Network models that represent the void space of a rock by a lattice of pores connected by throats can predict relative permeability once the pore geometry and wettability are known. Micro-computerized-tomography scanning provides a three-dimensional image of the pore space. However, these images cannot be directly input into network models. In this paper a modified maximal ball algorithm, extending the work of Silin and Patzek [D. Silin and T. Patzek, Physica A 371, 336 (2006)], is developed to extract simplified networks of pores and throats with parametrized geometry and interconnectivity from images of the pore space. The parameters of the pore networks, such as coordination number, and pore and throat size distributions are computed and compared to benchmark data from networks extracted by other methods, experimental data, and direct computation of permeability and formation factor on the underlying images. Good agreement is reached in most cases allowing networks derived from a wide variety of rock types to be used for predictive modeling.

Pore-network extraction from micro-computerized-tomography images

Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow.

We present a process based method for reconstructing the full three-dimensional microstructure of sandstones. The method utilizes petrographical information obtained from two-dimensional thin sections to stochastically model the results of the main sandstone forming processes – sedimentation, compaction, and diagenesis. We apply the method to generate Fontainebleau sandstone and compare quantitatively the reconstructed microstructure with microtomographic images of the actual sandstone. The comparison shows that the process based reconstruction reproduces adequately important intrinsic properties of the actual sandstone, such as the degree of connectivity, the specific internal surface, and the two-point correlation function. A statistical reconstruction of Fontainebleau sandstone that matches the porosity and two-point correlation function of the microtomography data differs strongly from the actual sandstone in its connectivity properties. Transport properties of the samples are determined by solving numerically the local equations governing the transport. Computed permeabilities and formation factors of process based reconstructions of Fontainebleau sandstone compare well with experimental measurements over a wide range of porosity.

http://webtools.klapp.no/data/numerical/vedlegg/32_TiPM_2002-2.pdf

Process based reconstruction of sandstones and prediction of transport properties

Reconstruction of Berea sandstone and pore-scale modelling of wettability effects

Numerical micropermeametry is performed on three-dimensional porous samples having a linear size of approximately 3 mm and a resolution of 75 microm One of the samples is a microtomographic image of Fontainebleau sandstone Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample The fourth sample is a physical model that mimics the processes of sedimentation, compaction, and diagenesis of Fontainebleau sandstone The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples The physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately, while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude This finding confirms earlier qualitative predictions based on local porosity theory Two numerical algorithms were used in these simulations One is based on the lattice-Boltzmann method, and the other on conventional finite-difference techniques The accuracy of these two methods is discussed and compared, also with experiment

Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media.

A simulated annealing algorithm is employed to generate a stochastic model for a Berea sandstone and a Fontainebleau sandstone, with each a prescribed two-point probability function, lineal-path function, and ''pore size'' distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandstones. Also, the mean survival time of a random walker in the pore space is reproduced with good accuracy. However, a more detailed investigation by means of local porosity theory shows that there may be significant differences of the geometrical connectivity between the reconstructed and the experimental samples. (c) 2000 The American Physical Society.

Stochastic reconstruction of sandstones

A quantitative comparison between the experimental microstructure of a sedimentary rock and three theoretical models for the same rock is presented. The microstructure of the rock sample (Fontainebleau sandstone) was obtained by microtomography. Two of the models are stochastic models based on correlation function reconstruction, and one model is based on sedimentation, compaction and diagenesis combined with input from petrographic analysis. The porosity of all models closely match that of the experimental sample and two models have also the same two point correlation function as the experimental sample. We compute quantitative dierences and similarities between the various microstructures by a method based on local porosity theory. Dierences are found in the degree of anisotropy, and in uctuations of porosity and connectivity. The stochastic models dier strongly from the real sandstone in their connectivity properties, and hence need further renement when used to model transport. c 1999 Elsevier Science B.V. All rights reserved.

Quantitative analysis of experimental and synthetic microstructures for sedimentary rock

A quantitative comparison of the pore space geometry for three natural sandstones is presented. The comparison is based on local porosity theory which provides a geometric characterization of stochastic microstructures. The characterization focusses on porosity and connectivity fluctuations. Porosity fluctuations are measured using local porosity distributions while connectivity fluctuations are measured using local percolation probabilities. We report the first measurement of local percolation probability functions for experimentally obtained three-dimensional pore space reconstructions. Our results suggest the use of local porosity distributions and percolation probabilities as a quantitative method to compare microstructures of models and experiment.

Three-dimensional local porosity analysis of porous media

A simulated annealing algorithm is applied to the reconstruction of two-dimensional porous media with prescribed correlation functions. The experimental correlation function of an isotropic sample of Fontainebleau sandstone and a synthetic correlation function with damped oscillations are used in the reconstructions. To reduce the numerical effort we follow a proposal suggesting the evaluation of the correlation functions only along certain directions. The results show that this simplification yields significantly different microstructures as compared to a full evaluation of the correlation function. In particular, we find that the simplified reconstruction method introduces an artificial anisotropy that is originally not present.

C. Manwart

Papers

Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media.

Stochastic reconstruction of sandstones

Quantitative analysis of experimental and synthetic microstructures for sedimentary rock

Three-dimensional local porosity analysis of porous media

Reconstruction of random media using Monte Carlo methods.