(543e) Simultaneous Hybrid Modeling of Distillation Towers with a Linear Correction Model for Different Tower Operations

Modeling process equipment using rigorous first-principles models FPM has been one of the most important developments in chemical engineering. However, significant expertise is required to tune the FPM to monitor actual equipment accurately. Although data-driven models have been proven successful for monitoring distillation columns [1], these models do not extrapolate correctly and require a significant amount of data to train them. Hybrid models address the problems of these modeling approaches by combining FPM and data-driven models [2].

In this work, we present a simultaneous hybrid model for monitoring distillation towers. The model predicts product compositions given the operating variables: reflux ratio, reboiler duty, and temperature measurements, and the model consists of a simplified first principles model (SFPM) and an error correction model. The SFPM includes mass and energy balances and simplified vapor-liquid equilibrium equations. Due to the characteristics of the model and the inclusion of selected tray temperatures, it is possible to predict the parameters of SFPM using partial least squared instead of the non-linear empirical model presented in previous similar works [3][4]. Moreover, our model estimates the internal vapor and liquid flows of the distillation columns, which can be used to determine flooding regions. Furthermore, we introduce a multiplicative correction model that avoids the problem of negative predictions of mass fractions.

Rigorous simulations of a butane splitter were used to substitute actual equipment data. The butane splitter was selected due to the narrow boiling point of the mixture. This modeling approach is expected to be used for wide boiling point mixtures since they are less sensitive to errors in tray temperature measurements. In addition to generating data for a base operation (Murphree efficiency 100%), the efficiency of the distillation column was modified to illustrate equipment performance changes. The hybrid models were evaluated using traditional metrics (e.g., mean relative error %MeanRE) and sensitivity analysis.

The results show that the proposed hybrid multiplicative model is able to predict the mass fractions of the products (%MeanRE of 1.44% of nC4 in the distillate and %MeanRE of 1.24% iC4 in the bottoms) accurately. As opposed to traditional residuals models, the MCM is able to reduce the error of the SFPM even for extrapolation cases. The results also displayed that the hybrid multiplicative model can be corrected using a linear correction model without estimating the SFPM parameters for tower efficiencies changes up to 10%, as shown in the figure. The sensitivity analysis shows that the hybrid multiplicative model accurately estimates the signs of the derivatives and values, even for changes of 15% in efficiency.

Due to the advantages of our proposed model: (i) physically meaningful predictions, (ii) high accuracy comparable to tray-tray simulations, (iii) facility to maintain (i.e., a linear model is able to account different efficiencies), (iv) estimation of internal flows and (v) accurate estimation of sensitivity, it is expected that the introduced hybrid model could be used in process monitoring or real-time optimization applications

[1] L. Fortuna, S. Graziani, and M. G. Xibilia, “Soft sensors for product quality monitoring in debutanizer distillation columns,” Control Eng. Pract., vol. 13, no. 4, pp. 499–508, 2005.

[2] M. von Stosch, R. Oliveira, J. Peres, and S. Feyo de Azevedo, “Hybrid semi-parametric modeling in process systems engineering: Past, present and future,” Comput. Chem. Eng., vol. 60, pp. 86–101, 2014, doi: 10.1016/j.compchemeng.2013.08.008.

[3] A. A. Safavi, A. Nooraii, and J. A. Romagnoli, “A hybrid model formulation for a distillation column and the on-line optimisation study,” J. Process Control, vol. 9, no. 2, pp. 125–134, 1999.

[4] F. Zapf and T. Wallek, “Gray-box surrogate models for flash, distillation and compression units of chemical processes,” Comput. Chem. Eng., vol. 155, p. 107510, 2021, doi: 10.1016/j.compchemeng.2021.107510.