Influence of stagnant zones on solute transport in heterogeneous porous media at the pore scale

Solute transport in porous media is sensitive to heterogeneity at all scales. However, the pore-scale solute transport behavior may considerably affect the behavior at larger scales. Here, a multi-relaxation-time lattice Boltzmann method with Flekkøy's mass transfer scheme is employed for simulating the fluid flow and solute transport in three-dimensional porous media obtained from high-resolution micro focus x-ray computed tomography, namely, randomly packed glass beads and four consolidated sandstones with an increasing level of heterogeneity, i.e., Fontainebleau, Berea, Takoh, and Shirahama. The flow field heterogeneity is carefully resolved for each porous media in terms of streamlines, Eulerian velocity fields, and the ratio of stagnant zones, which is consistent with the sequence of coordination numbers. Dispersion results show that Fick's law is satisfied well for glass beads, whereas early arrivals and late-time tailings are observed for heterogeneous rocks from the residence time distribution. Then, the dispersion coefficient is calculated using the time moment method, indicating that more heterogeneous porous media exhibit larger dispersion coefficients. The scalar dissipation rate (SDR) is resolved to characterize the mixing state. Two distinctive time regimes are recognized for heterogeneous rocks, separating at around 10 convective time scales. At a later time, a universal power-law scaling of SDR with time is observed, with the power-law γ being approximately 1.5 for glass beads (indicative of Fickian dispersion) and 2–3 for heterogeneous rocks. Finally, the significance of the mass transfer rate between the mobile and stagnant zones on the mechanical dispersion is evaluated in terms of the Damhöhler (Da) number.