A kinetic Monte Carlo approach to study fluid transport in pore networks

Abstract

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.

Methane transport through hierarchical silica micro-mesoporous materials: From non-equilibrium atomistic simulations to phenomenological correlations

“…Monte Carlo simulations [19,80] have been attempted, each with both promising features and drawbacks, to access longer length and time scales while accounting for fluid-rock interactions and the wide range of confined fluid states.…”

“…For example, Bhandari et al [13] reported permeability as low as 2 nanodarcy, and anisotropy of 40 (ratio between permeability measured in two directions) for their samples, which consisted of 4% total organic content and contained large amounts of quartz, calcite, and clay. Measured shale permeability ranges from 0.1 to 1000 nanodarcy [12,14], and anisotropy from as little as 5 to 10000 or more [12,15], Starting from these experimental data, research has focussed on reconstructing three-dimensional volumes to map the pore space distribution and simulate permeability using, e.g., the Lattice Boltzmann Method [3,[16][17][18], stochastic modelling [19], or a combination of the Metropolis-Hastings and genetic algorithms [20].…”

Clathrate hydrates: recent advances on CH4 and CO2 hydrates, and possible new frontiers

“…KMC has been successfully applied to catalysis, where a number of chemical reactions can occur simultaneously to transform reactants and intermediates into a variety of products, to describe transport in porous networks, as well as in many other applications. [187][188][189][190] Experimental validation. It is necessary to validate the quantitative understanding achieved via fundamental research.…”

Estimating permeability in shales and other heterogeneous porous media: Deterministic vs. stochastic investigations

“…The coordination number z is kept constant and equal to 4, 3 3 as we consider rectangular twodimensional (2D) networks. Building on previous work on KMC, 29 the term "voxel" refers here to a single cell of a matrix representing a pore network. For Eq.…”

“…28 Alternatively, KMC can follow molecular trajectories and yield permeability calculations with satisfactory accuracy and orders of magnitude lower computational cost compared to Molecular Dynamics (MD) simulations. 29,30,31 The promise of fast and straightforward estimates makes deterministic approaches appealing to practitioners. However, considering the nature of shale formations (high heterogeneity and a significantly large percent of micro-porosity due to the contribution of small pores 32 ) the deterministic approaches considered here may be inapplicable.…”