Improving heat exchanger fouling detection for phosphoric acid concentration units: A hybrid inverse approach integrating genetic algorithms and the Levenberg-Marquardt technique

This study aims to estimate the asymptotic fouling resistance and the time constant using an industrial database and the mathematical fouling model developed by Kern and Seaton. The results obtained with the Kern and Seaton model show an asymptotic evolution of the fouling resistance as a function of time, consistent with that observed in the experimental data. Subsequently, the influence of asymptotic resistance ( Rf *) and characteristic time (τ) on this model was examined. This inverse problem is formulated as the minimization of the sum of the quadratic differences between the measured thermal resistance and that calculated by the Kern and Seaton model. Different optimization methods, such as the genetic algorithm (GA) and the hybridization of the genetic algorithm with the Levenberg-Marquardt (LM) method, are employed. The GA method converges to the global minimum more slowly compared to the deterministic method. On the other hand, the hybridization between GA and LM shows a rapid convergence toward the global minimum with high precision, reaching a maximum relative error as low as 0.15%, 0.10%, and 0.12% for the three studied heat exchangers. The asymptotic fouling resistance was estimated to be 8.60×10 -6 m 2 .K/W for the stainless-steel tubular heat exchanger (HEx1), 5.42×10 -6 m 2 .K/W for the graphite polyblock exchanger “Supplier A” (HEx2), and 1. 54×10 -5 m 2 .K/W for “Supplier B” (HEx3), confirming the method’s reliability. This approach combines the genetic algorithm's global search capabilities with the Levenberg-Marquardt method's local refinement, demonstrating both robustness and efficiency in parameter estimation.