Chemical Reactor Investigations; Modeling, Implementation and Simulation

Abstract

Applied to chemical reactor problems, this work involves mathematical modeling, analyzes of numerical methods, and simulation studies. The simulation results presented are based on in-house codes.

The first part deals with the modeling and numerical analysis of the pellet equations. The pellet model has been applied to methanol dehydration, methanol synthesis, and steam–methane reforming with and without CO2-capture. The effects of modeling assumptions on the behavior of the mass and mole based pellet model equations are investigated revealing limitation of the Wilke and Wilke–Bosanquet models. The Maxwell– Stefan and dusty gas closures are recommended as identical simulation results can be obtained with the mass and mole based pellet equations where the average mixture velocities are used consistently. For a pellet with CO2-capture properties, the conventional pellet equations should be modified to include the effects of reduced void fraction, product layer diffusion resistance, and multiple carbonation/regeneration cycles as these effects significantly influence on the pellet performance.

The second part considers the modeling and numerical analysis of a transient onedimensional two-fluid model which has been applied to simulate cold flows and reactive flows in fluidized beds. The one-dimensional model predictions of the chemical process performance are in good agreement with the corresponding profiles predicted with a twodimensional model. The deviations are larger comparing the flow details but these do not owe significant impact on the chemical process which to a large extent is determined by the imposed temperature in the reactor.

The third part makes use of the population balance equation to model and simulate fluid particle size distributions. Parameter identifications to breakage model parameters are performed, review of breakage and coalescence modeling is carried out, and a combined multifluid-population balance model is implemented. By solving the fundamental population balance equation by a weighted residual method, the breakage and coalescence parameters gain more relevance as more details are resolved, and therefore clearer definition and better correlations for these are required.

The fourth part evaluates the performance of the solution techniques in the family of weighted residual methods. The numerical method analyzes base on the solution of differential and integro–differential equations such as the pellet equations and the population balance equation. Due to some favorable properties, recent publications in the chemical engineering community have considered the least-squares method as a good candidate for the solution of chemical reactor models. However, these authors did not compare the least-squares technique to other solution schemes in the weighted residual framework. The present work reveals that methods such as the Galerkin and orthogonal collocation can be superior to the least-squares approach with respect to the convergency properties of the methods. For example, the least-squares method suffers from poor convergency for problems with solutions having steep gradients such as arise in diffusion limited pellet processes. Though the least-squares method gives favorable simulation results for certain problems, its overall performance suffers compared to that of the more conventional weighted residual methods. The conclusions given here are based on a limited number of selected model equations subjected to a given analysis framework (nodal basis, Picard, etc.).