### Design of Reactive Distillation Processes Using Simulated Annealing

J. K. Cheng1, Hao-Yeh Lee2, Hsiao-Ping Huang1, and Cheng-Ching Yu1. (1) Chemical Engineering, National Taiwan University, Taipei, 107-16, Taiwan, (2) Department of Chemical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan

Reactive distillation (RD) offers an attractive alternative for the production of many important industrial chemicals. As pointed out by Hung et al. [1], the multifunctional nature leads to input multiplicity which makes the simulation and convergence of the RD flowsheet difficult. Unlike conventional separation units, there are much more design variables, e.g., number of separation trays, number of reactive trays, feed tray location etc., associated with the RD column. The design of the RD column becomes a combinatorial optimization problem where the objective function is the total annual cost (TAC). Conventionally, a sequential design approach is taken where the variable is changed one at a time to minimize the design objective [2-3]. However, as the dimensionality of design variables increases, the sequential method approach imposes heavy computing load, especially for the coupled reactive distillation/separation columns processes [3]. Mathematical optimization algorithms provide an attractive alternative to improve the computational efficiency. As we known, the derivative-based mathematical programming cannot guarantee the global solution for the non-convex problem. Unfortunately, the optimization problems of the RD design are non-convex, and derivative-free algorithms, e.g., Simulated Annealing (SA), Genetic Algorithm (GA), Tabu search (TS) etc, are preferred. Among all of them, SA has the advantage that it is simple to program. The concept of SA was originally proposed by Metropolis et al. [4]. It uses Monte Carlo simulation to calculate the energy distribution of molecules and simulate the cooling of material in a heat bath. Kirkpatrick et al. [5] is among the first to apply this idea to optimization and a traveling salesman problem was solved successfully using SA. After that, many applications of this method were proposed for the optimization of chemical processes.

In recent years, process simulators have been used extensively for the simulation of chemical processes. Because of the “black box” nature of these simulators, derivative-free algorithms can easily be implemented for optimization problems. In this work, we investigate the application of a SA algorithm to obtain the optimal design of two reactive distillation systems. The SA algorithm is implemented in the Visual Basic Application (VBA) which interfaces with the process simulator, Aspen Plus. In performing optimization, parameters associated with the annealing system, such as the initial temperature, temperature decrement factor and quasi-equilibrium detection and the space of design variables, should be defined.

Two reactive distillation systems, methyl acetate and butyl acetate production, are used to illustrated the design using the SA algorithm. The results indicate that improved design can be achieved with relatively efficient computing. The SA approach is recommended for highly nonlinear processes with non-monotonic characteristics such as reactive distillation systems.

Reference

1. Hung, S. B.; Lee, M. J.; Tang, Y. T.; Chen, Y. W.; Lai, I. K.; Huang, H. P.; Yu, C. C. “Control of different reactive distillation configurations” AIChE Journal, 2006, 52, 4, 11423-1440.

2. Tang, Y. T.; Chen, Y. W.; Huang, H. P.; Yu, C. C.; Hung, S. B. ; Lee, M. J., “Design of reactive distillations for acetic acid esterification” AIChE Journal, 2005, 51, 6, 1683-1699.

3. Lin, Y. D., Cheng, J. H.; Cheng, J. K.; Huang, H. P.; Yu, C. C. “Process alternatives for methyl acetate conversion using reactive distillation. 1. Hydrolysis,” Chem. Res. Sci., 2008, 63, 1668-1682.

4. Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E.; “Equation of state calculations by fast computing machines,” J. Chem. Phys., 1953, 21, 1087-1092.

5. Kirkpatrick, S., Gelatt, C. D.; Vecchi, M. P.; “Optimization by simulated annealing,” Science, 1983, 220, 671-680.

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