Prediction of the effective diffusivity in pore networks close to a percolation threshold

A pore network model for diffusion in nanoporous carbons: Validation by molecular dynamics simulation

“…Sahimi et al (1983) combined the EMA with elements of renormalisation-group theory to give the renormalised effective medium approximation (REMA), which is accurate even near the percolation threshold. Zhang and Seaton (1992) further developed the REMA method to take into account a distribution of conductances (all bonds had the same conductance in the original method of Sahimi et al) and showed that the effective diffusion coefficients calculated using REMA are very close to those obtained by solving the mass-balance equations directly. The advantage of the REMA method is that it is very fast, only taking a few minutes on a single PC processor, compared with the many hours required for an accurate direct solution.…”

“…The advantage of the REMA method is that it is very fast, only taking a few minutes on a single PC processor, compared with the many hours required for an accurate direct solution. A detailed description of the REMA method can be found in the papers by Sahimi et al (1983) and Zhang and Seaton (1992).…”

“…While representing the porous carbon by a single, typical pore can give physical insights into diffusion in real carbons, for example giving a reasonable account of the effects of temperature and pressure, the predictive ability of models of this type is limited by the fact that they ignore the variation in pore size and the interconnectedness of the pores of real nanoporous carbons. A more realistic approach is to model the solid by using a pore network model (PNM) (Sahimi et al, 1983;Burganos and Sotirchos, 1987;Sahimi and Stauffer, 1991;Hollewand and Gladden, 1992;Zhang and Seaton, 1992), in which these structural features are taken into account. In this model, the pore space of a carbon is represented by a network of pores of distributed size---quantified in terms of the pore size distribution (PSD)---with a mean coordination number, Z, which is defined as the average number of pores meeting at a junction, as shown in Fig.…”

The effective diffusivities in porous media with and without nonlinear reactions

“…Here, = R M /r, where R M is the molecular radius of the reactants which may, in general, be comparable with the pore radius r. This gives rise to the phenomenon of hindered diffusion (Deen, 1987), whereby molecular diffusion in a porous medium is restricted by the relatively large molecules being excluded from parts of the pore space, a phenomenon that has also been studied by the pore network models (Sahimi and Jue, 1989;Sahimi, 1992;Zhang and Seaton, 1992). Therefore, the -dependence of D p must be taken into account.…”

Continuum random walk simulations of diffusion and reaction in catalyst particles

“…Sahimi et al (1990) and Reyes and Iglesia (1993) have reviewed the applications of lattice models, as well as other aspects of modeling diffusion and reaction in porous solids. Recent applications of lattice models include the articles by Beyne and Froment (19901, Arbabi and Sahimi (1991a,b), Sahimi (1992), Zhang and Seaton (1992), McGreavy et al (1992), Hollewand and Gladden (19921, and Zhdanov (1993). Lattice models are extremely tractable; a number of approximate solutions exist and direct simulation of diffusion and reaction is within the reach of current computers.…”