However, these applications require high equipment efficiency levels, making it essential to model the phenomena involved for scaling up and process optimization. Therefore, several studies in MBR modeling with analytical and/or numerical solutions have been carried out, such as: , , , , , , Among these studies, the works of and are directly related to this investigation. The authors developed a semi-analytical solution of a lumped parameter model ; to the butane pyrolysis process, with the assumed conditions: first-order chemical reaction in gas phase, reactor with adiabatic walls, particles considered as spheres and inert. The model solution was developed using the concepts of the Finite-Analytic Method (FAM) with the difference that first, using integrating factors, an integral representation of the model equations is developed; then, by linearization and discretization of the resulting coupled system of integral equations, the interval solution is obtained.