(627c) Derivation of the Optimal Control of an Extractive Distillation Unit in the Production Process of Fuel Grade Ethanol

The extractive distillation of ethanol using glycerol as entrainer is studied in order to find its optimal control profiles when the azeotropic feed is subjected to composition disturbances.

Recently, a research presented by Garcia-Herreros et al [1] proposed the design and operating conditions that maximizes a profit function for the extractive distillation of fuel grade ethanol using glycerol as entrainer. That process is aimed to offer the greatest economic benefit in stationary conditions. However, to maintain the optimal operating conditions of the process time invariant parameters are required. In practice, distillation processes are subjected to disturbances that cannot be avoided and adversely affect normal operation.

In order to establish the usefulness of the proposed process for the industrial production of fuel grade ethanol, it is necessary to analyze its dynamic behavior and its controllability. The dynamic stability of the extractive distillation might represent a forceful advantage over the azeotropic distillation with benzene [2], the traditional method for the production of fuel grade ethanol. The azeotropic distillation has proved to have high parametric sensitivity and the presence of multiple steady states [3–5], which often implies low ethanol recovery [6].

The use of dynamic optimization for analyzing the control possibilities allows identifying the optimal process behavior and selecting the best control strategy based on quantitative criteria. It implies finding the variables profiles that minimize an objective function in a system subjected to disturbances. The process is modeled by the Differential-Algebraic Equation (DAE) system that represents the dynamics of the equilibrium stages in the extraction column. Then, the optimal control problem is solved by discretizing the time domain through orthogonal collocation on finite elements [7–9], which converts it into a Non-Linear Programming (NLP) problem.

Initially, the effect of a step and sinusoidal disturbances on product flow and quality is analyzed. Subsequently, a profit objective function is formulated and the optimal profiles of the control variables (reflux ratio and reboiler duty) are found, subjected to quality constraints. The solution is obtained by solving the Non-Linear Programming (NLP) problem that results from the discretization. The problem was modeled and solved in GAMS using IPOPT as the nonlinear solver. It is also important to note that the efficiency of some of the linear solvers (two HSL subroutines, i.e MA57 and MA86 [10]) used by IPOPT is also addressed.

All problems were successfully solved, obtaining an optimal control policy which minimizes off specification product and maximizes the overall profit in a fixed time horizon. In order to analyze if there is an improvement on the overall profit with a composite objective function, an optimization was carried out with a control - only objective function.

The optimization was performed with three different initializations in order to increase the probability of finding local optima within variable bounds. The results obtained with the three different initializations were exactly the same. This is likely to confirm that at least the local optimum has been found. It is also remarkable that the controllability of the extractive distillation process was confirmed, showing that the designed process proposed by García – Herreros et al [1] is not only stable and operable in steady state operation but also subjected to dynamic disturbances.

1. References.
   

[1] Pablo García-Herreros, Jorge M. Gómez, Iván D. Gil, and Gerardo Rodríguez, “Optimization of the Design and Operation of an Extractive Distillation System for the Production of Fuel Grade Ethanol Using Glycerol as Entrainer,” Industrial & Engineering Chemistry Research, vol. 50, pp. 3977–3985, 2011.

[2] Yasuki Kansha, Naoki Tsuru, Chihiro Fushimi, and Atsushi Tsutsumi, “New Design Methodology Based on Self-Heat Recuperation for Production by Azeotropic Distillation,” Energy Fuels, vol. 24, no. 11, pp. 6099–6102, 2010.

[3] Rodrigo López-Negrete de la Fuente and Antonio Flores-Tlacuahuac, “Integrated Design and Control Using a Simultaneous Mixed-Integer Dynamic Optimization Approach,” Ind. Eng. Chem. Res., vol. 48, no. 4, pp. 1933–1943, 2009.

[4] Maurizio Rovaglio and Michael F. Doherty, “Dynamics of heterogeneous azeotropic distillation columns,” AIChE Journal, vol. 36, no. 1, pp. 39–52, Jan. 1990.

[5] Klavs Esbjerg, Torben Ravn Andersen, Dirk Müller, Wolfgang Marquardt, and Sten Bay Jørgensen, “Multiple Steady States in Heterogeneous Azeotropic Distillation Sequences,” Ind. Eng. Chem. Res., vol. 37, no. 11, pp. 4434–4452, 1998.

[6] G. J. Prokopakis and W. D. Seider, “Feasible specifications in azeotropic distillation,” AIChE Journal, vol. 29, no. 1, pp. 49–60, Jan. 1983.

[7] J. E. Cuthrell, L. T. Biegler, and Carnegie Mellon University. Engineering Design Research Center., “On the Optimization of Differential-Algebraic Process Systems.” Carnegie Mellon University], Engineering Design Research Center, 1986.

[8] James E. Cuthrell and Lorenz T. Biegler, “Simultaneous Optimization and Solution Methods for Batch Reactor Control Profiles.” Carnegie Mellon University], Engineering Design Research Center, 1987.

[9] J. E. Cuthrell and L. T. Biegler, Simultaneous Solution and Optimization of Process Flowsheets with Differential Equation Models. Pittsburgh, PA.: Design Research Center, Carnegie-Mellon University, 1984.

[10] HSL, “A Collection of Fortran Codes for Large Scale Scientific Computation.” 2011.