Pore-scale flow and transport processes are generally difficult to simulate using conventional models. Two state-of-the-art approaches are adopted in this study of solute transport in porous media. The first approach is a lattice Boltzmann model with the Bhatnagar, Gross, and Krook simplification (BGK) to determine both the advection and diffusion components of the transport process, while the second approach uses the BGK model to calculate the velocity field in conjunction with a random walk (RW) model to characterize diffusion (BGK/RW). Both approaches yield similar results. The BGK/RW model is an attractive alternative to the BGK model when it is necessary to simulate small values of the diffusion coefficient so as to avoid instabilities in the numerical solution. Nevertheless, the BGK/RW model is less accurate than the BGK model alone when compared with the analytic solution of the well-known Taylor–Aris dispersion model.