Simulation of Tracer Dispersion in Porous Media Using Lattice Boltzmann and Random Walk Models

of a simplification of the relaxation time as suggested by Bhatnagar, Gross, and Krook (Bhatnagar et al., 1954). Pore-scale flow and transport processes are generally difficult to Among many other applications, BGK models have simulate using conventional models. Two state-of-the-art approaches are adopted in this study of solute transport in porous media. The been adopted in the analysis of dispersion phenomena first approach is a lattice Boltzmann model with the Bhatnagar, Gross, (Flekkoy, 1993; Flekkoy et al., 1995; Zhang et al., 2002). and Krook simplification (BGK) to determine both the advection Application of the BGK model to solute transport in and diffusion components of the transport process, while the second porous media allows a more accurate description of the approach uses the BGK model to calculate the velocity field in con- two main processes, advection and dispersion. junction with a random walk (RW) model to characterize diffusion Nevertheless, the use of the BGK model in solute (BGK/RW). Both approaches yield similar results. The BGK/RW dispersion problemsis limited by thedifficult simulation model is an attractive alternative to the BGK model when it is neces- of prescribed values of kinematic viscosity and diffusion sary to simulate small values of the diffusion coefficient so as to avoid coefficient, especially when the values of these paraminstabilities in the numerical solution. Nevertheless, the BGK/RW eters imply relaxation times near 0.5 that produce numodelislessaccuratethantheBGKmodelalonewhencomparedwith the analytic solution of the well-known Taylor–Aris dispersion model. mericalinstabilities,aswillbe explainedintheMaterials and Methods section. For problems of solute transport in porous media, simulations of kinematic viscosities do not pose any problem since the corresponding relaxO ne of the most important challenges in the soil ation times are 0.5. However, the simulated diffusion