Semi-Analytical Solution for a Lumped Model of a Co-Current Moving Bed Reactor

Several industrial processes are carried out on moving bed reactors (MBRs), and the development of mathematical models plays a fundamental role in designing, optimizing, and controlling these processes. Thus, this work initially develops a local solution for a linearized vertical MBR model to lumped parameters in the solid and fluid phases. Then, a semi-analytical solution (SAS) of the original nonlinear problem is obtained from the local solution. The SAS is easy to implement, stable, accurate, and performs fast, making it an efficient tool for MBR simulations. Excellent agreement was found comparing the SAS results with those of traditional numerical methods. SAS is capable of fast integration of model equations for systems with stiffness ratio SR=10^33. A numerical analysis was also carried out, indicating optimal refining parameters in relation to linearization error and machine error. The developments carried out can be easily extended to systems with multiple first-order reactions.