Mean Transport Pore Model MTPM

The constitutive equations of transport in porous media comprise both physical properties of components and pairs of components and simplifying assumptions about the geometrical characteristics of the porous medium. Two advanced effective-scale (i.e., space-averaged) models are commonly applied for description of combined bulk diffusion, Knudsen diffusion and permeation transport of multicomponent gas mixtures—Mean Transport-Pore Model (MTPM)—and Dusty Gas Model (DGM) cf. Mason and Malinauskas (1983), Schneider and Gelbin (1984), and Krishna and Wesseling (1997). The molar flux intensity of the z th component A) is the sum of the diffusion Nc- and permeation N contributions,... 

At present two models are available for description of pore-transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[4,5] and the Dusty Gas Model (DGM)[6,7]. Both models permit combination of multicomponent transport steps with other rate processes, which proceed simultaneously (catalytic reaction, gas-solid reaction, adsorption, etc). These models are based on the modified Maxwell-Stefan constitutive equation for multicomponent diffusion in pores. One of the experimentally performed transport processes, which can be used for evaluation of transport parameters, is diffusion of simple gases through porous particles packed in a chromatographic column. 

The Mean Transport Pore Model (MTPM) described diffusion and permeation the model (represented as a boundary value problem for a set of ordinary differential equations) are based on Maxwell-Stefan diffusion equation and Weber permeation law. Parameters of MTPM are material constants of the porous solid and, thus, do not dependent on conditions under which the transport proeesses take place. 

Two standard methods (mercury porosimetry and helium pycnometry) together with liquid expulsion permporometry (that takes into account only flow-through pores) were used for determination of textural properties. Pore structure characteristics relevant to transport processes were evaluated fiom multicomponent gas counter-current difhision and gas permeation. For data analysis the Mean Transport-Pore Model (MTPM) based on Maxwell-Stefan diffusion equation and a simplified form of the Weber permeation equation was used. 

As a model we have used the Mean Transport-Pore Model (MTPM) [6] which assumes that the decisive part of the gas transport takes place in transport-pores that are visualized as cylindrical capillaries. The transport-pore radii are distributed around the mean value (first model parameter). The width of this distribution is characterized hy the mean value of the squared transport-pore radii, (second model parameter). The third model parameter is the ratio of porosity, y/i, and tortuosity of transport-pores, qt, q/= Pore diffusion is described by the Maxwell-Stefan diffusion equation extended to account for Knudsen transport [6]. For gas permeation the simplified form of Weber equation [8-10] is used. 

MTPM assumes that the decisive part of the gas transport takes place in transport-pores that are visualised as cylindrical capillaries with radii distributed around the mean value (first model parameter). The second model parameter can be looked upon as ratio of tortuosity, q, and porosity of transport-pores, S, = St t- The third transport parameter,... 

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