General Dusty Gas Model for porous media with a specified pore size distribution

Significance 

Diffusion processes occur in systems with different concentrations, which are not in equilibrium, and lead to their equalization. Chemical engineers have had a close familiarity with this process for a long time. Diffusion modeling has thus become a vital aspect in the design of various systems such as reactors, distillation columns, electrolyte systems etc. When dealing with a porous medium, Maxwell Stefan diffusion model comes in handy and has led to the so called Dusty Gas Model (DGM). In porous structures, diffusion takes place through three mechanisms: Bulk diffusion, Knudsen diffusion and Surface diffusion.

Recent years have witnessed a spurt in the application of DGM, which is well suited to handle Bulk and Knudsen diffusion. As such, refining DGM has become a lifelong commitment for various researchers, particularly in matters of modeling theory. Unfortunately, a deficiency within the standard DGM attributable to a long-standing assumption in its derivation limits its efficiency when modeling in porous medium. The standard DGM for multicomponent diffusion in a porous medium assumes a single pore size in the domain whereas it would be more appropriate to consider a distribution of pore sizes.

It is becoming increasingly clear that the DGM should be adequately equipped to handle a general pore-size distribution. This has prompted various researchers to look into the matter, however, the DGM was not tackled on this aspect in any of the reviewed literature. In this context, Dr. Sandipan Kumar Das from the Process Technology Department at ExxonMobil Research and Engineering proposed to address the aforementioned issues by developing a general DGM that could handle any given pore size distribution of the porous medium. For him to realize such, he followed a fundamentally different approach in that he incorporated the effects of the pore size distribution. His work is currently published in the research journal, Chemical Engineering Science.

With the focus being to explicitly explore in detail the different effects of the pore size distribution on the diffusive process in a single-phase environment, Dr. Das started by carrying out theoretical derivations of the proposed new model. He then shifted his focus to numerical applications of the model following which he ran model simulations with different pore-size distributions to better understand their influence on the diffusion fluxes.

Dr. Das observed that the pore-size distribution plays a dominant role in the Knudsen diffusion regime. In fact, he established that the bimodal distribution suppressed the molar fluxes as compared to a monomodal distribution with the same overall mean pore size. Further inspection revealed that the bimodal nature rather than the actual distribution parameters played a bigger role in determining the molar fluxes in the Knudsen regime. Unsurprisingly, he noted that the pore size distribution had no role in the bulk diffusion regime.

In summary, the study derived a general form of the DGM that accounted for any pore-size distribution. Dr. Das was able to reduce his general model to the standard model by assuming a single pore size given by a Delta Dirac function at constant tortuosity. He also established that accounting for the variation of the tortuosity with the pore size may lead to significantly different results. Lastly, the study further elucidated on the effects of the temperature and the pore size dependent variable tortuosity and also recognized the need for new targeted experiments for further validation.

Reference

S. K. Das. General Dusty Gas Model for porous media with a specified pore size distribution. Chemical Engineering Science, volume 203 (2019) page 293–301.

Go To Chemical Engineering Science

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