Pressure changes during diffusion with chemical reaction in a porous pellet

Chemical Reactor Modeling

2014

It is convenient to introduce the notion of collisional invariants (or summational invariants) (e.g., [55], p. 460; [90], p. 150). The validity of (2.211) is commonly justified by the following arguments: Due to the symmetry properties of the collision term expression, interchanging variables gives the following equalities:These symmetry properties can be combined to give the following relationship:The linearity of the J operator allows the latter result to be manipulated as:In conclusion, a function ψ(c) is a summation invariant if:

Section: Relevance and Previous Investigationsmentioning

confidence: 98%

Section: Lagrangian Mechanicsmentioning

confidence: 99%

Section: Lagrangian Mechanicsmentioning

confidence: 99%

Section: Application Of the Maxwell-stefan Model To Dense Gases And Lmentioning

confidence: 99%

“…For non-ideal mixtures, the Fick first law binary diffusivity, D 12 , can thus be expressed in terms of the Maxwell-Stefan diffusivity,D 12 , by:…”

Section: Maxwell-stefan Model Consistency With Fick's First Lawmentioning

confidence: 99%

See 3 more Smart Citations

Elementary Kinetic Theory of Gases

Chemical Reactor Modeling

2014

Simulation of pellet model with multicomponent mass diffusion closure using least squares spectral element solution method

Rout

2013

Can J Chem Eng

Mass‐ and mole‐based pellet models have been solved using least‐squares formulation to describe the evolution of species composition, pressure, velocity, total concentration and mass diffusion fluxes in porous pellets for the steam methane reforming (SMR) process. The objective of this work has been to compare the mass‐ and mole‐based diffusion flux models, convection and fluid velocity for the SMR process using the least‐squares spectral element method (LS‐SEM). The diffusion–reaction problems are computationally intensive, requiring efficient numerical methods for dealing with them. This paper presents formulation and algorithm of LS‐SEM for solving multicomponent mass diffusion pellet models. The mass diffusion flux is described according to the rigorous Maxwell Stefan model. This flux may be defined either with molar‐ or mass‐averaged velocities. The effectiveness factors have been calculated for the SMR process and compared with the literature data. The model evaluations revealed that: ‐ The least‐squares method is well‐suited for solving the multicomponent mass diffusion pellet models for the SMR process, achieving exponential convergence. ‐ Molar‐ and mass‐based pellet models do not give fully identical results for the SMR process, since the pellet model is not completely consistent.

A numerical study of fixed bed reactor modelling for steam methane reforming process

Rout

2015

Can J Chem Eng

A numerical comparison of the pseudo-homogeneous, conventional heterogeneous, and simplified heterogeneous reactor models is performed for the steam methane reforming process. The pseudo-homogeneous reactor model consists of a set of partial differential equations, where the diffusional limitations are accounted for by considering the effectiveness factor. The heterogeneous model is divided into two categories: conventional and simplified heterogeneous models. In the conventional heterogeneous model, there are separate equations for the fluid phase species mass balance, the fluid inside the catalyst pores. This is type of reactor model is needed when there is a considerable amount of interphase mass transfer resistance present in the process. However, in the simplified heterogeneous reactor model the mass transport phenomenon is accounted for by accounting the efficiency factors. The model is validated against literature data. Several closures for the intra-particle mass diffusion fluxes, the Maxwell-Stefan, Wilke, dusty gas, and Wilke-Bosanquet models, have been compared on the level of the catalyst pellet and the impacts of the different particle flux closures on the reactor performance are investigated.The simulations show that the conventional heterogeneous reactor model is necessary for the SMR process, because the effectiveness factor values of different reactions of the SMR process vary along the reactor axis. The maximum deviation between the pseudo-homogeneous and the conventional heterogeneous reactor model is less than 38 %, whereas between the conventional and simplified heterogeneous reactor models it is less than 21 %. A parametric study of the transport phenomena on the pellet level is recommended prior to any large-scale reactor simulation to determine what the rate-determining transport mechanisms are.