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465615 Optimal Design and Control of a Catalytic Distillation Column. Case Study: Ethyl *Tert*-Butyl Ether (ETBE) Synthesis Column

*Tert*-Butyl Ether (ETBE) Synthesis Column

**Optimal design and control of a catalytic distillation column. Case study: Ethyl**

*tert*-butyl ether (ETBE) synthesis column.**David E. Bernal and Jorge M. Gómez**

Most of the chemical processes include two of the most important operations, chemical reaction and thermodynamic separation. These two operations are used to be carried out in different equipment. The reactions take place in different equipment, called reactors (continuously stirred tank reactors -CSTR-, tubular reactors or batch reactors, among others), and are operated under different conditions. On the other hand, the separation is usually made by different unitary operations (distillation, extractions, crystallization, absorption, among others) being the distillation by far the most common one [1]. Distillation is the most popular liquid mixture separation technique in the chemical and in the oil industry. The energy requirement of this operation can represent up to 40% of the whole plant’s energy requirement [2], [3].

Recycle streams are used between the reaction and separation sections to increase the yield and conversion, minimize the undesired products synthesis, improve the energetic efficiency and guarantee the controllability of these processes. Instead of carrying the reaction and separation in independent units, these operations can be carried out in a single equipment [1]. The implementation of these combined processes represents one of the most promising methodologies of process intensification. Economic and environmental considerations have led the industry to develop this kind of processes [4], which offer considerable benefits compared to the traditional multi-unit scheme.

Integrating reaction and product purification in a single multifunctional unit leads to considerable improvements compared to the traditional sequential approach such as: overcoming of the chemical equilibrium limitations, increment in product selectivity and the use of the reaction heat for the separation [5]. A limitation of this integration is that the “operational window” is reduced considerably as the conditions of the reaction and the separation must be satisfied simultaneously [1]. The general concept this process intensification is referred as Reactive Distillation (RD) and when a heterogeneous catalyst is involved it is referred as Catalytic Distillation (CD).

The operation of the distillation with a chemical reaction is important in the process, becoming into a critical unit and in certain cases a limiting unit, therefore its stable behavior must be guaranteed. This unit is very sensitive to perturbations, which means that a change in the operational conditions may affect the process dynamics compromising significantly the steady state operation, affecting the product purity, the energy consumption or the produced quantity [6].

Traditionally, the design of a process has been made in a sequential manner. First, a stationary analysis determines the process design and then a dynamic analysis determines its control law. Ziegler and Nichols [7] identified a direct relationship between the design of a process and its dynamic response under uncertainty, which compels to consider the process controllability in the first stages of the design [8], [9]. From this fact, the optimal control arises as a field where mathematical optimization tools are used to find the optimal profiles of operational variables for a certain process guaranteeing the product quality and the process profitability and security facing a periodic change or a perturbation to the system. Coupling the optimal design and optimal control results in a process that maximizes its profitability, assuring the specifications of its product even when the system is subjected to dynamic disturbances.

Taking into account these facts, the optimal design and control of a CD column becomes important. This kind of problems have a considerable mathematical complexity because of the interactions that exist between the coupled processes of separation and reaction. The modeling of these phenomena is highly nonlinear, which generates complications while solving it and the possibility of multiple solutions [10]. The mathematical complexity of this type of problems is mainly that the set of equations that describe the dynamic behavior of the system is a differential algebraic system of equations (DAE), which requires certain mathematical reformulations for solving it. The DAE problems are reformulated into large-scale NonLinear Programming (NLP) problems using orthogonal collocation.

The optimal design and control of a CD column designed for the production of Ethyl *tert*-butyl ether (ETBE) has been proposed as the case study of this work. The ETBE is a chemical compound used as oxygenate for fuels and it is classified as semi-renewable, as it can be synthetized from the etherification of bioethanol and isobutene in the presence of an acid catalyst [11]. The optimal control problem had included tracking objectives and an economic objective, for instance a weighted sum of the objectives was used as objective function. A methodology for determining the weighting parameters of each objective was proposed, based on an offline multi-objective utopia tracking optimization [12].

A comparison is made between the sequential and the simultaneous approach in the optimal design and control for this equipment. The results show that both approaches result in different design parameters that affect the economic profit of the process, its controllability and the satisfaction of the operational constraints of the system.

Several formulations of the dynamic model were proposed based on the description level and the assumptions that support them and resulted in different index DAE problems. This models were compared in terms of resulting NLP problem size (e.g. number of equations and variables) and results by solving and OCP problem. Finally, a first approach to an advanced control strategy called Economic-Oriented Nonlinear Model Predictive Control (EO-NMPC) was implemented and compared to a PI (Proportional and Integral) controller, showing advantages of the EO-NMPC in terms of economic profit.

**References**

[1] W. L. Luyben and C.-C. Yu, *Reactive Distillation Design and Control*. 2005.

[2] D. C. White, “Optimize Energy Use in Distilation,” *Am. Inst. Chem. Prog.*, no. March, p. 7, 2014.

[3] P. Fact, “Distillation Column Modelling Tools,” *Chem. Proj. Fact Sheet*, 2001.

[4] T. Keller, B. Dreisewerd, and A. Görak, “Reactive distillation for multiple-reaction systems: Optimisation study using an evolutionary algorithm,” *Chem. Process Eng. - Inz. Chem. i Proces.*, vol. 34, no. 1, pp. 17–38, 2013.

[5] K. Sundmacher and A. Kienle, *Reactive distillation: status and future directions*, vol. 3. 2006.

[6] R. Ross, J. D. Perkins, E. N. Pistikopoulos, G. L. M. Koot, and J. M. G. Van Schijndel, “Optimal design and control of a high-purity industrial distillation system,” in *Computers and Chemical Engineering*, 2001, vol. 25, no. 1, pp. 141–150.

[7] J. G. Ziegler and N. B. Nichols, “Optimum settings for automatic controllers,” *InTech*, vol. 42, no. 6, pp. 94–100, 1995.

[8] V. Bansal, J. D. Perkins, E. N. Pistikopoulos, R. Ross, and J. M. G. Van Schijndel, “Simultaneous design and control optimisation under uncertainty,” *Comput. Chem. Eng.*, vol. 24, no. 2–7, pp. 261–266, 2000.

[9] R. L.-N. de la Fuente and A. 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.

[10] M. G. Sneesby, M. O. Tadé, and T. N. Smith, “Multiplicity and Pseudo-Multiplicity in MTBE and ETBE Reactive Distillation,” *Chem. Eng. Res. Des.*, vol. 76, no. 4, pp. 525–531, 1998.

[11] H. E. P. and its Offices, “Bio-ETBE: The Right Road to High Quality 21st Century Motor Fuels,” Washington, 2012.

[12] V. M. Zavala and A. Flores-Tlacuahuac, “Stability of multiobjective predictive control: A utopia-tracking approach,” *Automatica*, vol. 48, no. 10, pp. 2627–2632, 2012.

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