Modelagem matemática e estimativa de parâmetros para extração em sistemas multicomponentes utilizando fluido supercrítico

Abstract

Several studies have addressed the mathematical modeling of supercritical fluid extraction, highlighting significant advances in simulation techniques and mass transfer mechanisms; however, most of these approaches are limited to single-component extraction. In this thesis, a mathematical model was developed to simulate multicomponent supercritical extraction, based on differential mass balances applied to both the extraction bed and solid particles, while accounting for macropore and micropore dynamics through an equilibrium function. To simplify the radial coordinate, the Classical Analysis of Lumped Systems and the Coupled Integral Equations Approach were employed, with the numerical solution obtained using the Method of Lines. The simulated results demonstrated high accuracy and good agreement with experimental data from the literature. Model validation was performed using the relative root mean square error (rRMSE), which revealed that most values remained within the 10–20% range, supporting the reliability of the proposed model. Kinetic parameter estimation was carried out through the Markov Chain Monte Carlo method with the Metropolis-Hastings algorithm, enabling the model to be fitted to experimental measurements. The results confirmed the potential of the proposed approach as a tool for simulating and optimizing supercritical extraction processes in multicomponent systems. Statistical analysis, based on the relative root mean square error, demonstrated satisfactory results and good performance after parameter calibration of the developed model.