Improved LDF Model for Unsteady-State Diffusion and Reaction in Porous Catalysts - Szukiewicz, Mirosław K.; Chmiel-Szukiewicz, Elżbieta (Engineering Science & Technology, 2025)
Partial Differential Equations (PDEs) describe chemical or biochemical diffusion and reaction processes and result from the principles of conservation of mass and heat. They most often require numerical solutions due to non-linearity. Approximate Models (ApM) are transient models described by Ordinary Differential Equations (ODEs) that operate with an average concentration or temperature. Replacing PDEs with appropriate ODEs simplifies both the model solution and the analysis of results. Therefore, ApMs are applied as part of a more complex model, for example, to describe mass or heat balances for the gas phase in a heterogeneous reactor [1]. The ApMs are also a suitable tool for the analysis of a steady state; for example, the effectiveness factor for heterogeneous catalysis processes or biochemical processes that are realised in the real world can easily be found [2]. The work presents the idea of improving the Generalised Linear Driving Force approximation Model (GLDFM), previously presented in [3]. Its application is limited. For fast processes inside porous pellets or biofilms, sharp profiles of concentration, temperature, or both appear, in which cases the GLDFM fails. To improve the precision of GLDFM, we introduce an additional factor into the model and develop a robust way of determining its value. The appropriate relationship for that factor is presented based only on correction parameters, replacing the Thiele modulus by a modified value. An appropriate relationship is presented. To achieve this, we use computational experiments (simulations). The improvement extends the range of operating conditions for which the GLDFM model can be applied without loss of precision. This means that the error observed by the Modified Approximate Model referred to as ApMM the main text under the steady state of a = 2 and Φ ≤ 20 should be less than 5%. As presented in the main part, this restriction results from the nonlinearity of a generation term bounded by 0 ≤ DR ≤ 5. Various examples previously presented by various authors confirm the correctness of the idea applied. The results are discussed, and intentions for future research are presented.