Lattice-Boltzmann simulation of solvent diffusion into oil-saturated porous media

We simulated the diffusion process into oil-saturated porous media using the modified diffusion-limited aggregation and the lattice Boltzmann method algorithms. The results were matched to visual experiments for cocurrent (two sides of the model open to flow) and countercurrent (only one side of the model open to flow) diffusion for horizontally and vertically positioned samples. The model saturated with oil was exposed to pentane in order for a miscible interaction to take place. These experiments mimic the transfer between the rock matrix and fracture during gas or liquid solvent injection for enhanced oil recovery, underground waste disposal, groundwater contamination, and $\mathrm{C}{\mathrm{O}}_{2}$ sequestration in naturally fractured reservoirs. Finger development at the early stages of the process was controlled by oil viscosity and the interaction type dictated by the boundary conditions. The convective transport driven by the buoyancy that was experimentally observed on vertically oriented samples and transfer driven by diffusion on the horizontal ones were captured in the LBM simulation of the process.