Biomedical subjects

R Hilfer

Publications and source records attributed to R Hilfer.

18 recordsLinked to original sources

PubMed2002

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

Numerical micropermeametry is performed on three-dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5 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.

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PubMed2002

H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems.

Analytical expressions in the time and frequency domains are derived for non-Debye relaxation processes. The complex frequency-dependent susceptibility function for the stretched exponential relaxation function is given for general values of the stretching exponent in terms of H-functions. The relaxation functions corresponding to the complex frequency-dependent Cole-Cole, Cole-Davidson, and Havriliak-Negami susceptibilities are given in the time domain in terms of H-functions. It is found that a commonly used correspondence between the stretching exponent of Kohlrausch functions and the stretching parameters of Havriliak-Negami susceptibilities are not generally valid.

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PubMed2001

Permeability and conductivity for reconstruction models of porous media.

The purpose of this paper is to examine representative examples of realistic three-dimensional models for porous media by comparing their geometrical and transport properties with those of the original experimental specimen. The comparison is based on numerically exact evaluations of permeability, formation factor, porosity, specific internal surface, mean curvature, Euler number, local porosity distributions, and local percolation probabilities. The experimental specimen is a three-dimensional computer tomographic image of Fontainebleau sandstone. The three models are examples of physical and stochastic reconstructions for which many of the geometrical characteristics coincide with those of the experimental specimen. We find that in spite of the similarity in the geometrical properties the permeability and formation factor can differ greatly between models and experiment. Our results seem to indicate that the truncation of correlations is responsible for some of these observed discrepancies. A physical reconstruction model by Bakke and Øren [SPEJ 2, 136 (1997)] based on sedimentation, compaction and diagenesis of sandstones yields surprisingly accurate predictions for permeability and conductivity. These findings imply that many of the presently used geometric descriptors of porous media are insufficient for the prediction of transport.

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PubMed2001

On the analysis of spatial binary images.

This paper deals with the analysis of spatial images taken from microscopically heterogeneous but macroscopically homogeneous microstructures. A new method is presented, which is strictly based on integral-geometric formulae such as Crofton's intersection formulae and Hadwiger's recursive definition of the Euler number. By means of this approach the quermassdensities can be expressed as the inner products of two vectors where the first vector carries the 'integrated local knowledge' about the microstructure and the second vector depends on the lateral resolution of the image as well as the quadrature rules used in the discretization of the integral-geometric formulae. As an example of application we consider the analysis of spatial microtomographic images obtained from natural sandstones.

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PubMed2000

Stochastic reconstruction of sandstones

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.

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PubMed1999

Reconstruction of random media using Monte Carlo methods.

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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PubMed1999

Trapping and mobilization of residual fluid during capillary desaturation in porous media.

We discuss the problem of trapping and mobilization of nonwetting fluids during immiscible two-phase displacement processes in porous media. Capillary desaturation curves give residual saturations as a function of capillary number. Interpreting capillary numbers as the ratio of viscous to capillary forces the breakpoint in experimental curves contradicts the theoretically predicted force balance. We show that replotting the data against a novel macroscopic capillary number resolves the problem for discontinuous mode displacement.

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PubMed1995