Tag: sediments

Categories
dielectric relaxation electrical conductivity Heterogeneous Materials

Macroscopic Dielectric Constant for Microstructures of Sedimentary Rocks

R. Hilfer, J. Widjajakusuma, B. Biswal

Granular Matter 2, 137 (1999)
https://doi.org/10.1007/s100359900035

submitted on
Friday, May 21, 1999

An approximate method to calculate dielectric response and relaxation functions for water saturated sedimentary rocks is tested for realistic three-dimensional pore space images. The test is performed by comparing the prediction from the approximate method against the exact solution. The approximate method is based on image analysis and local porosity theory. An empirical rule for the specification of the length scale in local porosity theory is advanced. The results from the exact solution are compared to those obtained using local porosity theory and various other approximate mixing laws. The calculation based on local porosity theory is found to yield improved quantitative agreement with the exact result.



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Categories
image analysis Porous Media

Quantitative Analysis of Experimental and Synthetic Microstructures for Sedimentary Rock

B. Biswal, C. Manwart, R. Hilfer, S. Bakke, P.E. Øren

Physica A 273, 452 (1999)
https://doi.org/10.1016/S0378-4371(99)00248-4

submitted on
Monday, May 17, 1999

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 differences and similarities between the various microstructures by a method based on local porosity theory. Differences are found in the degree of anisotropy, and in fluctuations of porosity and connectivity. The stochastic models differ strongly from the real sandstone in their connectivity properties, and hence need further refinement when used to model transport.



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Categories
dielectric relaxation electrical conductivity fluid flow Porous Media

Exact and Approximate Calculations for Conductivity of Sandstones

J. Widjajakusuma, C. Manwart, B. Biswal, R. Hilfer

Physica A 270, 325 (1999)
https://doi.org/10.1016/S0378-4371(99)00141-7

submitted on
Tuesday, January 5, 1999

We analyze a three-dimensional pore space reconstruction of Fontainebleau sandstone and calculate from it the effective conductivity using local porosity theory. We compare this result with an exact calculation of the effective conductivity that solves directly the disordered Laplace equation. The prediction of local porosity theory is in good quantitative agreement with the exact result.



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Categories
Porous Media Simulations

Reconstruction of Random Media Using Monte Carlo Methods

C. Manwart, R. Hilfer

Physical Review E 59, 5596 (1999)
https://doi.org/10.1103/PhysRevE.59.5596

submitted on
Tuesday, September 8, 1998

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.



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