A numerical study of pellet model consistency with respect to molar and mass average velocities,pressure gradients and porosity models for methanol synthesis process: Effects of flux models on reactor performance

The objective of this work is to compare mass- and mole based diffusion flux models, convection, fluid velocity and pore structure models for methanol synthesis process. Steady-state models have been derived and solved using least-squares spectral method (LSM) to describe the evolution of species composition, pressure, velocity, total concentration and diffusion fluxes in porous pellets for methanol synthesis. Mass diffusion fluxes are described according to the rigorous Maxwell Stefan model, dusty gas model and the more simple Wilke model. These fluxes are defined with respect to molar- and mass averaged velocities. The different effects of choosing the random- and parallel pore models have been investigated. The effects of Knudsen diffusion have been investigated. The result varies significantly in the dusty gas model. The effectiveness factors have been calculated for the methanol synthesis process for both mass- and mole based pellet models. The values of effectiveness factors for both mass- and mole based pellet models do not vary so much. The effect of Wilke-, Maxwell–Stefan- and dusty gas mass diffusion fluxes on the reactor performance have been studied. Steady-state heterogeneous fixed bed reactor model is derived where the intra-particle mass diffusion fluxes in the voids of the pellet are described by Wilke-, Maxwell–Stefan- and dusty gas models. Furthermore, the total computational efficiency of the heterogeneous fixed bed reactor model is calculated with several closures for the intra-particle mass diffusion fluxes. The model evaluations revealed that:

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The mass- and mole based pellet models are not completely consistent. However, the small deviation (less than 2%) between mass- and mole based pellet models is due to the model equations are not fully consistent. If one pellet model is to be chosen for the methanol synthesis process, the optimal diffusion flux model is the Maxwell–Stefan model.