Mathematical and Neuro-Fuzzy Modeling of a Hollow Fiber Membrane System for a Petrochemical Process

This work presents a hybrid model that integrates a mechanistic multicomponent transport scheme in hollow-fiber membranes with an Adaptive Neuro-Fuzzy Inference System (ANFIS). The physical model incorporates pressure drops on the feed and permeate sides (Hagen–Poiseuille), non-ideal gas behavior (Peng–Robinson equation of state), and temperature-dependent viscosity; species permeances are treated as constant for model validation. After validation, a post-validation parametric exploration of permeance variability is carried out by perturbing the methane (CH4) permeance by one decade up and down. From an initial set of 18 variables, 4 key parameters were selected through rigorous statistical analysis (Pearson correlation, variance inflation factor (VIF), and mean absolute error (MAE)); likewise, other physical criteria have been considered: permeance, retentate volume, retentate pressure, and retentate viscosity. Trained with 70% of the simulated data and validated with the remaining 30%, the model achieves a coefficient of determination (R2) close to 0.999 and a root mean square error (RMSE) below 8 × 10−8 m3/h in predicting the methane volume in the retentate, effectively responding to both steady and dynamic fluctuations. The combination of first-principles modeling and adaptive learning captures both steady-state and dynamic behavior, positioning the approach as a viable tool for real-time analysis and supervisory control in petrochemical membrane operations.