(253bt) Fluid Transport through Nano-Pores: A Stochastic Approach

Fluid transport through nano-pores: a stochastic approach

Maria Apostolopoulou ^a, Alberto Striolo ^aâ? , Michail Stamatakis ^aâ? , Richard Day ^b

^a University College London, Department of Chemical Engineering, Torrington Place, London WC1E 7JE, United Kingdom.

^b Halliburton, Building 4 Chiswick Park 566, Chiswick High Road, London W4 5YE, United Kingdom.

â? Corresponding authors: a.striolo@ucl.ac.uk, m.stamatakis@ucl.ac.uk

Keywords: computational molecular engineering, fluid mechanics, shale gas

Abstract

The mechanism of fluid migration in porous networks continues to attract great interest. Although single and two-phase flow systems have been successfully studied in macroscale and microscale channels, the transport of fluids through networks of nanochannels is yet to be fully understood. The Darcyâ??s law (phenomenological continuum theory) is often used to describe macroscopically fluid flow through a porous material and can efficiently describe the fluid transport through micro pores, in which the dominant regime is viscous flow. However, it appears that Darcyâ??s formalism fails to describe flow in nano-channels, in which some studies have suggested that water and air exhibit several orders of magnitude higher flowrate than that predicted by continuum theory. This observation, first reported by Klinkenberg in 1941, was attributed to the slip-flow effect.

Fluid transport can be studied by using several computational techniques, such as Molecular Dynamics or Lattice-Boltzmann, each with its own limitations. Molecular Dynamics simulations are used to describe the trajectories of individual atoms and allow us to follow the dynamics of molecular processes in great detail. However, they are incapable of probing large systems for long times, due to computational limitations. Lattice-Boltzmann simulations can provide larger time scale analysis, while accounting the slip boundary condition, at the expense of molecular-level phenomena that might become important in nanopores.

To overcome the current limitations, we implement a stochastic approach to describe fluid transport through porous networks. This method is based on the multi-variate master equation, by which the space is represented as set of connected finite volumes (voxels), and transport is simulated as a random walk of molecules, which hop from voxel to voxel with a given propensity. We validated the approach using a 1D model consisting of two neighbouring voxels. The results were compared against deterministic equations that describe the system at equilibrium. The key parameters for the stochastic approach were the energy barrier between the two states (voxel occupancies) and the diffusion coefficients. We examined the equilibrium occupancies of voxels and the error between the stochastic and the deterministic approach for different populations of molecules (100, 1000, 10000 and 100000) while changing the initial configuration. While the stochastic approach yields errors of less than 1%, the lack of limitations on occupancies could be a source of uncertainty in other scenarios. Overall, these results indicate that the model can be extended to accurately describe fluid transport in 1D or 2D networked systems, in which single phase or multiphase flow takes place. We will present here results obtained for models representing simplified versions of shale rocks.