Fluid Flow in Porous Media with the Lattice-boltzmann Method

Aaltosalmi, Urpo Fluid flow in porous media with the lattice-Boltzmann method Jyväskylä: University of Jyväskylä, 2005, 158 p. (Research report/Department of Physics, University of Jyväskylä, ISSN 0075-465X; 3/2005) ISBN 951-39-2222-7 Diss. The lattice-Boltzmann method has recently become a useful approach for computational fluid dynamics. Simple implementation of boundary conditions together with inherent grid generation makes the method geometrically very versatile, and it is thus convenient for simulating complex systems such as fluid flow in porous media. Solving realistic flow problems has become feasible because of increased computing capabilities and parallel processing, for which the spatially local updating rules of the lattice-Boltzmann method are particularly suitable. In this thesis, fluid dynamics in porous media and the basic principles of the lattice-Boltzmann method are first introduced. Application of the method to flow simulations is then discussed in terms of some practical problems, such as boundary conditions, discretization errors and numerical stability, and benchmark studies are carried out to validate the method. Finally, several single-fluid flow problems in irregular 3D geometries are analyzed numerically. The lattice-Boltzmann simulations are used to find out the quality of tomographic imaging techniques and numerical models of porous media. Dependence of permeability on porosity and other structural properties such as specific surface area, tortuosity, and shape and orientation of particles in the medium, are demonstrated and compared to those given by other methods, theory and experiment. The effects of size and resolution of tomographic images of several paper grades are examined by simulating fluid flow through the images and by image analysis. The lattice-Boltzmann, image analysis and experimental results for the permeability of tomographic images of hand sheets with different refining levels are reported. Models and a tomographic image of sandstone are analyzed by comparing the lattice-Boltzmann and finite-difference results also with experiment. The effect of specific surface area, via fines content and shape of fibres, is demonstrated by the lattice-Boltzman flow simulations through fibre-web-model samples.