chemical engineering research and design 9 1 ( 2 0 1 3 ) 296–317 Contents lists available at SciVerse ScienceDirect Chemical Engineering Research and Design journa l h o me pa ge: www.elsevier.com/locate/cherd 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 K.R. Rout * , M. Hillestad, H.A. Jakobsen Department of Chemical Engineering, Norwegian University of Science and Technology, NTNU, N-7491 Trondheim, Norway a b s t r a c t 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: - 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. - The parallel pore model is deviating from the random pore model for the methanol synthesis process. The results of both the parallel- and random pore models have been compared with experimental data available in the literature. It is found that the result of the parallel pore model is well agreement with experimental data. - A small but significant differences in the mole fraction profiles of methanol along the reactor axis where the diffusion fluxes are described according to the Wilke-, Maxwell–Stefan- and dusty gas models. - The consistent models are about 20 and 60% more computationally expensive than the simplified and not always consistent Wilke model. It is recommended to use the consistent models instead of Wilke approach. © 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Multicomponent diffusion; Methanol synthesis; Wilke model; Maxwell–Stefan model; Dusty gas model; Heterogeneous reactor model ∗ Corresponding author. Tel.: +47 73594146; fax: +47 73594080. E-mail addresses: kumar.rout@chemeng.ntnu.no, ranjan8109@gmail.com (K.R. Rout). Received 8 December 2011; Received in revised form 15 July 2012; Accepted 8 September 2012 0263-8762/$ – see front matter © 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cherd.2012.09.003