Analytical solution of a heat transfer model for a tubular co-current diluted moving bed reactor with indirect heating and intraparticle gradients

The understanding of the multiphase flow and the thermal behavior in moving beds is important for design and process optimization. Thus, in the present work, the heat transfer in a tubular moving bed reactor indirect heated by a flue gas is modeled, considering the thermal interactions: “conveyor fluid-flue gas”, “conveyor fluid-particle”, as well as the intraparticle heat transfer. The model is solved analytically by the powerful Self-Adjoint Operators Method (SAO), which allows the maximum maintenance of the physical characteristics of the problem. The consistency of this novel solution is shown through limiting solutions and comparison with simpler models: a lumped capacity model (LP), whose solution is independently obtained through the Laplace Transform Method, and an existing isothermal wall moving bed heat exchanger (MBHE) solution. For low particle Biot numbers systems, the LP and SAO solutions showed a very good agreement. The results also showed good validation of the solutions by comparing with experimental data. A numerical hybrid solution, through a combination of the Finite Difference Method (FD) and the Finite Analytical Method (FA), is also given and the comparison with the analytical solution shows excellent agreement. Finally, a scale analysis is proposed and performed. The scale analysis made it possible to assign a physical meaning to the model's parameters, to infer about the thermal behavior of the system, to evaluate the use of simpler models and to present semi-theoretical expressions for the maximum temperature difference into the particle and between particle surface and conveyor fluid, for systems with low Bip.