The mechanism of fluid migration in porous networks continues to attract great interest. Darcy's law (phenomenological continuum theory), which is often used to describe macroscopically fluid flow through a porous material, is thought to fail in nano-channels. Transport through heterogeneous and anisotropic systems, characterized by a broad distribution of pores, occurs via a contribution of different transport mechanisms, all of which need to be accounted for. The situation is likely more complicated when immiscible fluid mixtures are present. To generalize the study of fluid transport through a porous network, we developed a stochastic kinetic Monte Carlo (KMC) model. In our lattice model, the pore network is represented as a set of connected finite volumes (voxels), and transport is simulated as a random walk of molecules, which "hop" from voxel to voxel. We simulated fluid transport along an effectively 1D pore and we compared the results to those expected by solving analytically the diffusion equation. The KMC model was then implemented to quantify the transport of methane through hydrated micropores, in which case atomistic molecular dynamic simulation results were reproduced. The model was then used to study flow through pore networks, where it was able to quantify the effect of the pore length and the effect of the network's connectivity. The results are consistent with experiments but also provide additional physical insights. Extension of the model will be useful to better understand fluid transport in shale rocks.
Apostolopoulou, M., Day, R., Hull, R., Stamatakis, M., & Striolo, A. (2017). A kinetic Monte Carlo approach to study fluid transport in pore networks. Journal of Chemical Physics, 147(13). https://doi.org/10.1063/1.4985885