The continuous search for improving and optimizing MBRs motivates research in modeling and simulation. This work contributes to this area by presenting a semi-analytical solution for a lumped parameter kinetic and heat transfer model of a tubular MBR, where a first-order chemical reaction occurs uniformly within the particles. The local analytical solution was implemented within the FAM framework, resulting in a simple numerical programming scheme that is consistent, unconditionally stable, can fast integrate very stiff systems (SR = 10 !"# ), and requires a minimum of computational resources. These capabilities demonstrate the effectiveness of SAS as a methodology suitable for both academic research and industrial applications. Consequently, it signifies a substantial advancement for the modeling and optimization of moving bed reactors. For the sake of completeness, the other primary contributions of this work are itemized below: