Simplified modeling of butane dehydrogenation: deeper understanding of the system’s dynamics

The dehydrogenation of butane is a catalytic process that involves the separation of hydrogen atoms from an organic molecule, and it relies on the presence of a catalyst Z, such as Ni, Pt, Pd, Fe, ZnO, Cr 2 O 3, or Fe 2 O 3. In this paper, we introduce two highly effective mathematical techniques known as Lumping Compartments (LC) and Intrinsic Low Dimensional Manifold (ILDM) to simplify the complexity of the dehydrogenation of butane. Initially, the model consists of seven nonlinear differential equations with eight parameters. To streamline the model, we applied LC to ten different cases, considering various initial states and parameters. As a result, the number of compartments significantly decreased from seven to three. The obtained computational results and total differences reveal a remarkable agreement between the complete model and the simplified version, demonstrating a high degree of predictive accuracy. Additionally, ILDM is employed to enhance the initial estimation of the slow invariant manifold. This enables us to easily distinguish between the fast and slow variations at each point, with the variations acting as chemical kinetics attractors. Fast chemical reactions are drawn towards these attractors, while slow chemical reactions occur within the manifolds.