Quantitative determination of molecular propagator distributions for solute transport in homogeneous and heterogeneous porous media using lattice Boltzmann simulations

Abstract

We simulate flow and solute transport directly on pore space images of rock cores with increasing degree of heterogeneity: a bead pack, Bentheimer sandstone, and Portland carbonate. A novel scheme is proposed to predict probability distributions for molecular displacements using the lattice Boltzmann (LB) method to calculate both the flow field and solute dispersion. We observe that for homogeneous rock samples, such as bead packs, the displacement distribution remains Gaussian with time increasing. In the more heterogeneous rocks, the displacement distribution separates into a moving and a stagnant part. In this case, we observe that the magnitude of the moving distribution decreases whereas a stagnant peak at the initial position (ζ50) increases with increasing heterogeneity of the porous medium. We compare our results directly with NMR experimental data for molecular displacements and find excellent agreement. To quantify the degree of heterogeneity, we calculate the fraction of solute particles trapped by integrating over the stagnant peak. We observe that the fraction of trapped solute increases from the bead pack (0 %) to Bentheimer sandstone (1.488%) to Portland carbonate (8.131%). Our analysis shows that the LB-based propagator simulation is able to predict the transport in porous media efficiently and accurately. © 2013. American Geophysical Union. All Rights Reserved.