Chemical Engineering Diffusion-Reaction Analysis via Helmholtz Equation and Radial Basis Function Methods

Analyzing steady-state concentration profiles in diffusion-reaction systems is crucial for designing and optimizing many chemical engineering processes, including catalytic reactors and separation units. These phenomena are frequently described by Helmholtz or modified Helmholtz equations. This study investigates the practical application of a meshless numerical technique, the radial basis function-method of approximate particular solutions (RBF-MAPS), for simulating such systems. The inherent meshless nature of RBF-MAPS offers significant advantages for handling the complex geometries often encountered in chemical engineering equipment. We apply the method to model two representative scenarios: reactant diffusion and first-order reaction within a square catalytic plate reactor incorporating an internal source term, and within a circular catalyst pellet with surface boundary conditions. The RBF-MAPS approach effectively discretizes the governing Helmholtz-type equations, and the resulting algebraic systems are robustly solved using singular value decomposition. To establish the reliability of the simulations for engineering analysis, the method’s implementation is rigorously verified using the method of manufactured solutions, demonstrating high-order convergence. Furthermore, convergence studies on specific application problems confirm the stability of the computed concentration profiles. This work validates RBF-MAPS as a flexible and accurate computational tool for chemical engineers needing to analyze diffusion-reaction behavior governed by Helmholtz equations in diverse reactor geometries.