Monte-Carlo simulations of surface and gas phase diffusion in complex porous structures

Abstract

A new procedure for estimating surface di usivities and tortuosities within realistic models of complex porous structures is reported. Our approach uses Monte-Carlo tracer methods to monitor mean-square displacements for molecules restricted to wander on pore walls within model random mesoporous solids typical of those used as adsorbents, heterogeneous catalysts, and porous membranes. We consider model porous solids formed from initial packings of spheres with unimodal, Gaussian, or bimodal distributions of size; changes in pellet porosity are achieved by increasing microsphere radii and by randomly removing spheres from highly densiÿed packings in order to simulate densiÿcation and coarsening, respectively. Geometric tortuosities for the surface phase reached large values at void fractions near 0.04 and 0.42 for densiÿed solids; the surface tortuosity gave a minimum value of 1.9 at a void fraction of ∼0.26. These high tortuosities correspond to percolation thresholds for the void and solid phases, which in turn re ect packing densities at which each phase becomes discontinuous. Surface tortuosities for coarsened solids at low void fractions were similar to those in densiÿed solids; however, at void fractions above ∼0.3, surface tortuosities of coarsened solids increased only gradually with void fraction, because coarsening retains signiÿcant overlap among spheres at void fractions above those giving disconnected solids in densiÿed structures. Simulations of bulk di usion within voids were used to compare the transport properties and connectivity of the void space with those of surfaces that deÿne this void space. Surface and void tortuosities were similar, except for void fractions near the solid percolation threshold, because unconnected solid particles interrupt surface connectivity but not gas phase di usion paths. Surface and void tortuosities were also similar for channels within linear chains of overlapping hollow spheres as both tortuosities increased with decreasing extent of sphere overlap. These simulations provide a basis for estimates of surface and void tortuosities, which are essential in the interpretation and extrapolation of di usion rates in complex porous media. Surface and void di usivity estimates di ered signiÿcantly from those obtained from lattice and capillary models of complex porous structures. ?

Effective Transport Coefficients for Porous Microstructures in Solid Oxide Fuel Cells

“…The principles of our MC simulation were similar to previous MC methods performed in various porous media (3,24,29). First the initial position of a molecule was set in the desired phase (pore, electron-conducting or ion-conducting phases).…”

“…In recent years, various numerical methods have been widely applied to evaluate effective coefficients. Repeated sampling techniques (such as the Monte-Carlo simulation) evaluate effective transport quantities on disordered random-resistor networks (23,24), random packing of spheres (2,3), clusters of hollow spheres and cylinders (29), and 3-D pixelized structures (30). On the other hand, continuum-scale methods (such as finite element method) have been applied for randomdistributed pore structures (17,18).…”

Tortuosity based on Anisotropic Diffusion Process in Structured Plate-like Obstacles by Monte Carlo Simulation

“…Of the several methods of computer simulation, Monte Carlo approach has been a favorable choice for elucidating migration cased by random walk in porous media T. Ohkubo (B) Japan Atomic Energy Agency (JAEA), 4-33 Muramatsu, Tokai-mura, Naka-gun, Ibaraki-ken 319-1194, Japan e-mail: ohkubo.takahiro@jaea.go.jp with meso-scopic space (Sandry and Stevenson 1970;Riley et al 1995;Pandey et al 1984). For example, the Monte Carlo simulation has been utilized to simulate the diffusion of gas molecules in zeolite (Theodorou and Wei 1983) and complex porous media (Zalc et al 2003) Trinh et al have also indicated that the diffusion coefficient calculated by the Monte Carlo method agreed reasonably well with experimental results (Trinh et al 2000).…”

An alternative procedure for modeling of Knudsen flow and surface diffusion

“…Achieving such an understanding not only involves the gas-phase diffusion but also the adsorptive properties of the material and the surface diffusion [1]. Experimental studies have shown that surface diffusion contributes significantly to the total diffusive flux in both mesoporous and microporous systems [2,3]. There are examples where the surface diffusion accounts for more than 50% of the total mass flow rate [4,5].…”

“…Fick's law approach is the most widespread in use [4,6] and assumes that the gaseous and the surface fluxes are independent of each other [6]. Usually the connection between the gas phase concentration profile and the surface concentration profile is achieved via an adsorption equilibrium assumption [1,2,4,[8][9][10][11][12][13][14].…”