87 research outputs found
Stochastic reconstruction of sandstones
A simulated annealing algorithm is employed to generate a stochastic model
for a Berea and a Fontainebleau sandstone with 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.Comment: 12 pages, 5 figure
Quantitative analysis of numerical estimates for the permeability of porous media from lattice-Boltzmann simulations
During the last decade, lattice-Boltzmann (LB) simulations have been improved
to become an efficient tool for determining the permeability of porous media
samples. However, well known improvements of the original algorithm are often
not implemented. These include for example multirelaxation time schemes or
improved boundary conditions, as well as different possibilities to impose a
pressure gradient. This paper shows that a significant difference of the
calculated permeabilities can be found unless one uses a carefully selected
setup. We present a detailed discussion of possible simulation setups and
quantitative studies of the influence of simulation parameters. We illustrate
our results by applying the algorithm to a Fontainebleau sandstone and by
comparing our benchmark studies to other numerical permeability measurements in
the literature.Comment: 14 pages, 11 figure
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 m. 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 which 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.Comment: to appear in: Phys.Rev.E (2002), 32 pages, Latex, 1 Figur
Finite difference calculations of permeability in large domains in a wide porosity range.
Determining effective hydraulic, thermal, mechanical and electrical properties of porous materials by means of classical physical experiments is often time-consuming and expensive. Thus, accurate numerical calculations of material properties are of increasing interest in geophysical, manufacturing, bio-mechanical and environmental applications, among other fields. Characteristic material properties (e.g. intrinsic permeability, thermal conductivity and elastic moduli) depend on morphological details on the porescale such as shape and size of pores and pore throats or cracks. To obtain reliable predictions of these properties it is necessary to perform numerical analyses of sufficiently large unit cells. Such representative volume elements require optimized numerical simulation techniques. Current state-of-the-art simulation tools to calculate effective permeabilities of porous materials are based on various methods, e.g. lattice Boltzmann, finite volumes or explicit jump Stokes methods. All approaches still have limitations in the maximum size of the simulation domain. In response to these deficits of the well-established methods we propose an efficient and reliable numerical method which allows to calculate intrinsic permeabilities directly from voxel-based data obtained from 3D imaging techniques like X-ray microtomography. We present a modelling framework based on a parallel finite differences solver, allowing the calculation of large domains with relative low computing requirements (i.e. desktop computers). The presented method is validated in a diverse selection of materials, obtaining accurate results for a large range of porosities, wider than the ranges previously reported. Ongoing work includes the estimation of other effective properties of porous media
Reconstruction of three-dimensional anisotropic microstructures from two-dimensional micrographs imaged on orthogonal planes
Response Analysis for the Early Stages of Sedimentation Processes
We study correlations between the velocity and the density distribution in non-Brownian particle suspensions at small particle Reynolds numbers Re Ăź 1 under the influence of gravity. If the system is initially at rest, the velocity distribution will soon organize itself into different regions of flow mainly moving in and against the direction of gravity. A specific width is associated with the emerging fingers or "streets" both in bulk suspensions and in unstably stratified systems, where particle laden fluid is placed above pure fluid. Whereas for the case of unstable stratification classical Rayleigh-Taylor theory predicts exponential growth of the arising initial velocity fluctuations, we find that the system is driven by the initial density inhomogeneities that necessarily exist in a particulate suspension. The corresponding velocity modes saturate exponentially. The spatial correlation length of the emerging fingers grows in time until it reaches a limit, which depends either on t..
Parallel domain decomposition method with non-blocking communication for flow through porous media
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