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 $\mu$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

Lattice Boltzmann simulations of soft matter systems

This article concerns numerical simulations of the dynamics of particles immersed in a continuum solvent. As prototypical systems, we consider colloidal dispersions of spherical particles and solutions of uncharged polymers. After a brief explanation of the concept of hydrodynamic interactions, we give a general overview over the various simulation methods that have been developed to cope with the resulting computational problems. We then focus on the approach we have developed, which couples a system of particles to a lattice Boltzmann model representing the solvent degrees of freedom. The standard D3Q19 lattice Boltzmann model is derived and explained in depth, followed by a detailed discussion of complementary methods for the coupling of solvent and solute. Colloidal dispersions are best described in terms of extended particles with appropriate boundary conditions at the surfaces, while particles with internal degrees of freedom are easier to simulate as an arrangement of mass points with frictional coupling to the solvent. In both cases, particular care has been taken to simulate thermal fluctuations in a consistent way. The usefulness of this methodology is illustrated by studies from our own research, where the dynamics of colloidal and polymeric systems has been investigated in both equilibrium and nonequilibrium situations.Comment: Review article, submitted to Advances in Polymer Science. 16 figures, 76 page

Comparison of multiphase SPH and LBM approaches for the simulation of intermittent flows

Smoothed Particle Hydrodynamics (SPH) and Lattice Boltzmann Method (LBM) are increasingly popular and attractive methods that propose efficient multiphase formulations, each one with its own strengths and weaknesses. In this context, when it comes to study a given multi-fluid problem, it is helpful to rely on a quantitative comparison to decide which approach should be used and in which context. In particular, the simulation of intermittent two-phase flows in pipes such as slug flows is a complex problem involving moving and intersecting interfaces for which both SPH and LBM could be considered. It is a problem of interest in petroleum applications since the formation of slug flows that can occur in submarine pipelines connecting the wells to the production facility can cause undesired behaviors with hazardous consequences. In this work, we compare SPH and LBM multiphase formulations where surface tension effects are modeled respectively using the continuum surface force and the color gradient approaches on a collection of standard test cases, and on the simulation of intermittent flows in 2D. This paper aims to highlight the contributions and limitations of SPH and LBM when applied to these problems. First, we compare our implementations on static bubble problems with different density and viscosity ratios. Then, we focus on gravity driven simulations of slug flows in pipes for several Reynolds numbers. Finally, we conclude with simulations of slug flows with inlet/outlet boundary conditions. According to the results presented in this study, we confirm that the SPH approach is more robust and versatile whereas the LBM formulation is more accurate and faster

Catalytic flow with a coupled Finite Difference -- Lattice Boltzmann scheme

Many catalyst devices employ flow through porous structures, which leads to a complex macroscopic mass and heat transport. To unravel the detailed dynamics of the reactive gas flow, we present an all-encompassing model, consisting of thermal lattice Boltzmann model by Kang et al., used to solve the heat and mass transport in the gas domain, coupled to a finite differences solver for the heat equation in the solid via thermal reactive boundary conditions for a consistent treatment of the reaction enthalpy. The chemical surface reactions are incorporated in a flexible fashion through flux boundary conditions at the gas-solid interface. We scrutinize the thermal FD-LBM by benchmarking the macroscopic transport in the gas domain as well as conservation of the enthalpy across the solid-gas interface. We exemplify the applicability of our model by simulating the reactive gas flow through a microporous material catalysing the so-called water-gas-shift reaction

Link-wise Artificial Compressibility Method

The Artificial Compressibility Method (ACM) for the incompressible Navier-Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the Lattice Boltzmann Method (LBM). The main advantage is the possibility of exploiting well established technologies originally developed for LBM and classical computational fluid dynamics, with special emphasis on finite differences (at least in the present paper), at the cost of minor changes. For instance, wall boundaries not aligned with the background Cartesian mesh can be taken into account by tracing the intersections of each link with the wall (analogously to LBM technology). LW-ACM requires no high-order moments beyond hydrodynamics (often referred to as ghost moments) and no kinetic expansion. Like finite difference schemes, only standard Taylor expansion is needed for analyzing consistency. Preliminary efforts towards optimal implementations have shown that LW-ACM is capable of similar computational speed as optimized (BGK-) LBM. In addition, the memory demand is significantly smaller than (BGK-) LBM. Importantly, with an efficient implementation, this algorithm may be one of the few which is compute-bound and not memory-bound. Two- and three-dimensional benchmarks are investigated, and an extensive comparative study between the present approach and state of the art methods from the literature is carried out. Numerical evidences suggest that LW-ACM represents an excellent alternative in terms of simplicity, stability and accuracy.Comment: 62 pages, 20 figure

Improved three-dimensional color-gradient lattice Boltzmann model for immiscible multiphase flows

In this paper, an improved three-dimensional color-gradient lattice Boltzmann (LB) model is proposed for simulating immiscible multiphase flows. Compared with the previous three-dimensional color-gradient LB models, which suffer from the lack of Galilean invariance and considerable numerical errors in many cases owing to the error terms in the recovered macroscopic equations, the present model eliminates the error terms and therefore improves the numerical accuracy and enhances the Galilean invariance. To validate the proposed model, numerical simulation are performed. First, the test of a moving droplet in a uniform flow field is employed to verify the Galilean invariance of the improved model. Subsequently, numerical simulations are carried out for the layered two-phase flow and three-dimensional Rayleigh-Taylor instability. It is shown that, using the improved model, the numerical accuracy can be significantly improved in comparison with the color-gradient LB model without the improvements. Finally, the capability of the improved color-gradient LB model for simulating dynamic multiphase flows at a relatively large density ratio is demonstrated via the simulation of droplet impact on a solid surface.Comment: 9 Figure