This chapter covers general models for simulating complex fluid flow, including lattice Boltzmann algorithms and applications. "Complex" means having more than one fluid present in a porous media, and having a variety of boundary conditions between the fluids and between the fluids and the solid backbone.
This section discusses modelling of electrical conductivity and fluid flow in two dimensions. The relationship between the electrical conductivity, fluid permeability, and various length scales, including lambda, the Katz-Thompson parameter, and the hydraulic radius, is studied.
This section presents a study of the polarizability (intrinsic conductivity) and the intrinsic viscosity for a very wide range of shapes. It is found that for a very wide range of shapes, the intrinsic conductivity, in the conducting limit, is proportional to the intrinsic viscosity in the vanishing shear limit.
This section presents various studies using the Lattice Boltzmann fluid flow algorithm. Developmental work on this algorithm is presented as well.
This section presents computations of the diffusivity through partially saturated porous media. These partially saturated media were formed using the Lattice Boltzmann fluid flow algorithm.
This section presents a derivation of how to build in energy conservation into the discrete Boltzmann nist-equation in non-ideal systems.
This section presents how basic equilibrium properties of lattice Boltzmann fluid mixtures are calculated to characterize the critical phenomena occurring in these model liquids and to establish a reduced variable description allowing a comparison with real fluid mixtures.
Results from large scale simulations of single and multi-component fluid flow through digitized Fontainebleau sandstone, generated by X-Ray microtomography, are given. Reasonably good agreement was found when compared to experimentally determined values of permeability for similar rocks. Modification of the lattice Boltzmann nist-equations, to describe flow in microporous materials, is described. The potential for modeling flows in other microstructures of interest to concrete technology will be discussed.
We show that accurate numerical micropermeametry can be performed on three- dimensional (3D) digitized images of sedimentary rock. The sample size can be very small, making it possible to predict properties from core material not suited for laboratory testing (e.g., drill cuttings, sidewall core and damaged core plugs). Simulation of fluid permeability on microtomographic images of Fontainbleau sandstone on sample sizes of less than 1 mm3 are in good agreement with experimental measurements over a wide range of porosities.
We investigate the stability of a polymer thread imbedded in a matrix that is confined between two parallel plates. Utilizing a combination of experiments, numerical simulations (lattice-Boltzmann), and surface area calculations, we find substantial deviations from the classical results when the diameter of the thread (D0 is comparable to the height (H) of the matrix.
A thermodynamic model is developed of the free energy of gas-filled voids formed within cavities on solid surfaces covered by a liquid. Capillary effects are assumed to be the only important contributions to the free energy, and expressions are derived for the free energy of the system as a function of the void size, the relative surface free energy densities involved, and the geometry of the cavity.
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