Mass diffusion Wilke model

Mass transport inside the catalyst has been usually described by applying the Fick equation, by means of an effective diffusivity Deff a Based on properties of the interface and neglecting the composition effect, composite diffusivity of the multi-component gas mixture is calculated through the simplified Wilke model [13], The effect of pore-radius distribution on Knudsen diffusivity is taken into account. The effective diffusivity DeffA is given by... 

Approximate mass based Wilke diffusion model... 

The corresponding mass based Wilke approximate formulation [161] is outlined next. In this model the diffusion of species i in a multicomponent mixture is written in the form of Pick s law with an effective diffusion coefficient instead of the conventional binary molecular diffusion coefficient. Following the ideas of Wilke [161] we postulate that an equation for the combined mass flux of species s in a multicomponent mixture can be written as ... 

More recently, Solsvik and Jakobsen [140] performed a numerical study comparing several closures for mass diffusion fluxes of multicomponent gas mixtures the Wilke, Maxwell-Stefan, dusty gas, and Wilke-Bosanquet models, on the level of the single catalyst pellet and the impacts of the mass diffusion flux closures employed for the pellet, on the reactor performance. For this investigation, the methanol synthesis operated in a fixed packed bed reactor was the chemical process adopted. In the mathematical modeling study of a novel combined catalyst/sorbent pellet. Rout et al. [121] investigated the performance of the sorption-enhanced steam methane reforming (SE-SMR) process at the level of a single pellet. Different closures... 

For multicomponent systems the diffusive flux terms may be written in accordance with the approximate Wilke bulk flux equation (2.450), the approximate Wilke-Bosanquet combined bulk and Knudsen flux for porous media (2.454), the rigorous Maxwell-Stefan bulk flux equations (2.421), and the consistent dusty gas combined bulk and Knudsen diffusion flux for porous media (2.504). The different mass based diffusion flux models are listed in Table 2.3. The corresponding molar based diffusion flux models are listed in Table 2.4. In most simulations, the catalyst pellet is approximated by a porous sphericai pellet with center point symmetry. For such spherical pellets a representative system of pellet model equations, constitutive laws and boundary conditions are listed in Tables 2.5,2.6 and 2.7, respectively. 

In order to solve the mathematical model for the emulsion hquid membrane, the model parameters, i. e., external mass transfer coefficient (Km), effective diffu-sivity (D ff), and rate constant of the forward reaction (kj) can be estimated by well known procedures reported in the Hterature [72 - 74]. The external phase mass transfer coefficient can be calculated by the correlation of Calderback and Moo-Young [72] with reasonable accuracy. The value of the solute diffusivity (Da) required in the correlation can be calculated by the well-known Wilke-Chang correlation [73]. The value of the diffusivity of the complex involved in the procedure can also be estimated by Wilke-Chang correlation [73] and the internal phase mass transfer co-efficient (surfactant resistance) by the method developed by Gu et al. [75]. 

Solving this flow model for the velocity the pressure is calculated from the ideal gas law. The temperature therein is obtained from the heat balance and the mixture density is estimated from the sum of the species densities. It is noted that if an inconsistent diffusive flux closure like the Wilke equation is adopted (i.e., the sum of the diffusive mass fluxes is not necessarily equal to zero) instead, the sum of the species mass balances does not exactly coincide with the mixture continuity equation. 

The experimental evidence, as summarized by Sherwood, Pigford, and Wilke, indicates that the mass transfer coefficients are more nearly proportional to the molecular diffusivity to the square root power. Nevertheless, the film theory is used in the development of the working equations in this chapter, since the physical picture it depicts is simple and adequate. Actually, it is irrelevant, from a pragmatic point of view, what model is used to develop a working equation based on empirical mass or heat transfer coefficients that must, ultimately, be obtained from experimental data. 

Effective diffusivities were used for the calculation of the mass-transfer coefficients. In contrast to the binary Maxwell-Stefan diffusivities, the effective diffusivities were calculated via available procedures in ASPEN Custom Modeler , whereas the Wilke-Chang model was used for the liquid phase and Chapman-Enskog-Wilke-Lee model for the vapor phase [94]. In the full model, computationally intensive matrix operations for the Maxwell-Stefan equations are necessary. The model has been further extended to consider the presence of liquid-liquid separation [110, 111]. 

To describe the combined bulk and Knudsen diffusion fluxes in the transition gas transport regime, the simple Wilke-Bosanquet model [11, 70, 151] and the more rigorous dusty gas model [62, 70, 71, 94] can be used either on the mass or molar forms. Knudsen diffusion refers to a gas transport regime where the mean free... 

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