Pore-scale Transport in Rocks of Different Complexity Modeled by Random Walk Methods

We investigate pore-scale transport of a passive solute in three types of reservoir rocks of distinctly different heterogeneity characteristics, using both random walk particle tracking (RWPT), a Lagrangian method free of numerical dispersion, and time domain random walk (TDRW), a regular-lattice-based approximation of the advection-diffusion equation. The transport behavior is probed in terms of solute breakthrough curves for a large range of values of the Peclet number, and for both flux-weighted and uniform injection conditions. We compare the two numerical modeling approaches and thereby highlight the impact of the distribution of pore-scale flow velocities on the large-scale transport behavior. We discuss the properties of two numerical approaches and analyze the influence of the numerical resolution of the velocity field on the simulated transport behaviors. A main difference consists in the presence of numerical dispersion in the TDRW method in contrast to the RWPT method. We find that this feature does not affect the simulated large-scale transport compared to the RWPT method, because numerical dispersion is negligible compared to the impact of the broad spectra of velocity fluctuations, which leads to heavy-tailed breakthrough curves and broad peak behaviors determined by hydrodynamic dispersion. The two random walk methods can be equivalently used to simulate hydrodynamic transport at pore scale. The direct simulations provide breakthrough curves that cover up to ten orders of magnitude in time. The tailing behavior is directly related to the distribution of pore-scale flow velocities using a continuous time random walk approach. The comparison of breakthrough curves and velocity distributions for three different rock types indicates that the solute breakthrough behavior can be used to infer the pore-scale velocity distribution and the medium structure.