Microsoft Word - 211.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 61, 2017 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří JKlemeš Copyright © 2017, AIDIC ServiziS.r.l. ISBN978-88-95608-51-8; ISSN 2283-9216 Global Optimization of Reactive Distillation Processes Using Bat Algorithm Jiawei Lua, Jihai Tanga,b,c, Xian Chena, Mifen Cuia, Zhaoyang Feia,b, Zhuxiu Zhanga, Xu Qiaoa,b,c,* a College of Chemical Engineering, Nanjing Tech University, China b State Key Laboratory of Materials-Oriented Chemical Engineering, Nanjing Tech University, China c Jiangsu National Synergetic Innovation Center for Advanced Materials (SICAM), China qct@njtech.edu.cn Reactive distillation (RD) is an important process intensification approach with several advantages. It can improve the reaction selectivity and yield, overcome the thermodynamic restrictions, and reduce the cost/energy. However, the optimal design of RD relies on highly nonlinear and multivariable optimization including continuous and integer design variables. The objective function is generally non-convex with several constraints. For this problem, the conventional derivative-based optimization algorithms are faced with convergence problems and fail to guarantee the global optimal solution. Stochastic optimization algorithms appear to be a better alternative for the optimal design of RD because of the high robustness and efficiency. Bat algorithm (BA), which combines advantages of other existing algorithms, is a potential stochastic optimization algorithm. In this work, the BA was used to optimize the RD for the production of methyl acetate (MeAc). The link between Matlab and Aspen Plus was also created to ensure that each solution was provided from rigorous simulations. The total annual cost (TAC) was set as the objective function. Product purity constraints were achieved through Aspen plus instead of algorithms to simplify the process. BA can find the global optimal solution within less computation time than other stochastic algorithms or sequential optimization. 1. Introduction Process intensification (PI) is an effect strategy to save resources and energy. The purpose of the PI is to decrease the back mixing, reduce the mass and heat transfer resistances and accelerate the reaction rate in chemical process. (Moulijn et al., 2008) One of the most common process intensification approaches is the reactive distillation (RD), which combines chemical reaction and distillation separation in a device, where the reaction process and the distillation process promote each other. Because of this, it can effectively improve the reaction selectivity and yield, overcome the thermodynamic restrictions and increase the reaction heat efficiency. However, the optimal design of RD is a more complex and difficult problem, which is different from the traditional distillation process. Ciric and Gu (1994) were first to present a rigorous model based on the reaction kinetic rate equations and the MESH. The optimization problem of RD was transformed into a MINLP problem, which was solved with Generalized Benders Decomposition (GBD). But this formulation exhibited poor numerical behaviour. Zondervan et al. (2011) have developed a MINLP model to optimize the design of RD. The results indicated that DICOPT could find a solution near to global optimality. Harwardt et al. (2011) argued that the MINLP problem of the RD process is challenging and reformulated the MINLP problem as a continuous NLP problem to achieve better convergence. In recent years, several deterministic algorithms are used for the optimization of RD. However, the objective function is generally non-convex with several constraints. Therefore, the optimization process is always faced with convergence problems, and easy to fall into the local optimum. Stochastic optimization algorithms appear to be a better alternative for the optimal design of RD because of the high robustness and efficiency. A new simulated annealing-based algorithm, which combined the simplex DOI: 10.3303/CET1761211 Please cite this article as: Lu J., Tang J., Chen X., Cui M., Fei Z., Zhang Z., Qiao X., 2017, Global optimization of reactive distillation processes using bat algorithm, Chemical Engineering Transactions, 61, 1279-1284 DOI:10.3303/CET1761211 1279 method of Nelder and Mead, was applied to the MINLP problem. (Cardoso et al., 2000) But this method still cannot guarantee the global optimum. Cheng et al. (2009) studied the simulated annealing for the optimization of RD. This method could find a better design than the sequential design approach and save more computation time. Domingues et al. (2014) studied the particle swarm optimization and genetic algorithm for the ETBE synthesis reaction distillation optimization. The results show that these two algorithms can get the similar structure of the column. Although the stochastic algorithms have the ability to escape the local optimum, it often need to cost great amount computation time. Therefore, how to improve the efficiency of the stochastic algorithm or find a better algorithm has become the focus of the research. (Segovia-Hernández et al., 2015) This work studied a new stochastic algorithm, bat algorithm (BA). Compared to other existing stochastic algorithm, BA can automatically switch from global search to local search when the conditions are met to reduce the search time. Because of this, the BA, which was implemented in the Matlab, was applied to optimize the reactive distillation for the production of methyl acetate (MeAc). The process simulator, Aspen Plus, was also used for the simulation of RD to ensure the reliability of the calculation. 2. Bat algorithm The bat algorithm is a new nature-inspired stochastic optimization algorithm, which is based on the echolocation behaviour of bats. (Saji et al., 2016) The points in the search space are considered as the bats in nature. The whole process can be simplified as that the bats fly with velocity vi, varying frequency fi and loudness Ai at position xi to search for prey. They can automatically adjust the frequency and the rate of pulse emission ri according to the distance between the target and their own. 2.1 Velocity and position vectors of virtual bats In simulations, the rules have to be defined how the positions xi and velocities vi are updated. Because of the particularity of the BA, it has local search and global search in the search process. In a d-dimensional search space, for the global search part, the new positions xt i and velocities v t i at time step t are given by: i min max minf = f + (f - f )β (1) t t-1 t * i i i iv = v + (X - X )f (2) t t-1 t i i iX = X + v (3) Where β ∈ [0, 1] is a random vector drawn from a uniform distribution. Here x* is the current global optimal position, which is located after all the bat positions are sorted. In the simulation, the values of the fmin and fmax depend on the size of the search space. Initially, the frequency of the bat is achieved by randomization. For the local search part, once the optimal solution is selected from the current solution, a new local solution for each bat is generated around the optimal solution by random walk: t new oldX = X +εA (4) Where ε ∈ [-1, 1] is a random number, and At is the average loudness of all the virtual bats at time step t. It can be seen that the update of the position of the BA has some similarity to the formula in the standard particle swarm optimization (PSO) and harmony search (HS). The reason is that PSO and HS are the special cases of BA after appropriate simplifications. 2.2 Variations of loudness and pulse emission Furthermore, the loudness Ai and the rate of pulse emission ri have to be updated as the iterations proceed. As the iteration increases, the loudness of the virtual bats will gradually decrease, and finally reach the minimum while the rate of pulse emission will increase. t+1 t i iA = αA (5) [ ]t+1 0i ir = r 1- exp(-γt) (6) Where α and γ are constants. For any 0 ＜ α ＜ 1, γ ＞ 0, we have t 0i i0, r r , as t→ → → ∞ t iA (7) 1280 In generally, the choice of parameters requires some experiments. But in our simulations, for simplicity, the values of α and γ are chosen in the range of [0.80, 95]. Initially, the loudness and the rate of pulse emission of each virtual bat are achieved by randomization. For example, the initial loudness A0 i can typically be [1, 2], while the rate of pulse emission r0 i can be any value in the range of [0, 1]. 2.3 Iteration process The Pseudo-code of bat algorithm is described in following steps: 1. Parameter initialization: population size N, loudness attenuation coefficient α, pulse emission rate increasing coefficient γ, Maximum loudness A0 i , Maximum pulse emission rate r 0 i and the maximum number of iteration iterMax. 2. Initialize the position xi and velocity vi, calculate fitness, find the current optimal bat and its location x *. 3. Adjust the frequency to generate a new solution and change the velocity and position, calculate its fitness. 4. If rand > ri, then walk randomly around the best solution and generate a local solution. 5. If rand < Ai and f (xnew)