First Principles Based Development of Hybrid Models of Distillation Towers

In this work, we developed a simultaneous hybrid model with a novel error correction model for distillation columns that can be used in process monitoring, scheduling, and optimization. The proposed hybrid model consists of two parts a simplified first principles model (SFPM) and an error correction term. The SFPM is specific for distillation columns and consists of mass, energy, and equilibrium equations for all the trays of the column. For the error correction term, we used a traditional residual model that predicts the differences between the flow outputs of the SPFM and plant flow outputs, and we introduced a novel multiplicative correction model (MCM). The MCM corrects the output mass fractions predictions of the SFPM using a multiplicative factor. The advantage of using the MCM is that the predictions of the hybrid model are physically meaningful and more accurate than the residuals model when inputs are extrapolated beyond the training region. The proposed hybrid multiplicative model has a mean relative percentage error of less than 2% compared to rigorous simulations for interpolation and extrapolation inputs.