Application of Differential Evolution in Chemical Reaction Engineering
3.5 Application of DE Method for Optimization of Reactor Conditions and Kinetic Parameters
3.5.2 Objective function or performance criterion
In all optimization problems, performance criterion or objective function must be defined. As the name suggests, it is the goal of the research study, and should be either maximized or minimized. Therefore, in different studies, based on the physical features of the problem, it has different formulas. In reactor engineering, yield or productivity is often considered as the objective function. For kinetic modeling, summation of the error (absolute deviation or relative error of the model results and experimental data) is usually the objective function. One can categorize optimization problems based on number of objectives, which are discussed in the following sub-sections (Rosenthal, 1985; Deb, 2001, 2014).
Single-objective optimization
Single-objective optimization refers to problems in which only one function should be optimized. Sometimes, there are different targets for a problem; instead of using multi-objective optimization, researchers use weighted sum of the objectives (Gennert and Yuille, 1988). There has been a great effort to use single-objective DE for optimizing reactor operating conditions and for estimating kinetic parameters. Wang et al.
(2001) used hybrid DE to estimate the kinetic parameters for the batch
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reactor of ethanol fermentation process. They had a min-max estimation problem in which the maximum error of all experiments was minimized.
Vakili et al. (2012) optimized the operating conditions of a thermally coupled membrane reactor in which DME (dimethyl ether) and benzene were produced simultaneously. The aim of their study was to use basic DE, and find the maximum values of DME and benzene production as well as hydrogen recovery. Thus, they considered a weighted sum of carbon monoxide (feed for the DME synthesis side) conversion, cyclohexane (feed for benzene production side) conversion and hydrogen mole fraction on the membrane side as the objective function. Hydrogen mole fraction on the membrane side was multiplied by 10, in order to make it comparable to other terms in the objective function.
Amirabadi et al. (2013) proposed an optimal thermally coupled membrane reactor for simultaneous methanol and hydrogen production.
They considered the summation of methanol, toluene, and hydrogen yields to be the objective function; the inlet temperatures of water permeation, exothermic side, endothermic side and hydrogen permeation side, as well as the initial molar flow rate of exothermic and endothermic sides were the six decision variables. Mirvakili et al. (2013) proposed two cascading fixed-bed and fluidized-bed dual reactors for the process of ammonium nitrate decomposition. Their study focused on applying DE to reduce the amount of NOx emissions and simultaneously enhance the conversion of ammonium nitrate. Therefore, they defined the objective function to be the summation of NOX and ammonium nitrate concentration in the outlet stream, which was minimized in the optimization. The fluidized bed temperature, gas velocity and fixed bed temperature were the three decision variables in their study.
Multi-objective optimization
In most of the cases, there is a need to optimize two or more objective functions simultaneously (e.g., maximizing the production and minimizing the cost). The multi-objective optimization results in a set of alternate solutions, which are equally good mathematically. In other words, those solutions do not necessarily lead to the best optimized value of each individual function; however, the net result is relatively the best one. The set of solutions found in multi-objective optimization is called Pareto-optimal solutions (Rangaiah, 2009), which provides tradeoffs among conflicting objective functions. The corner solutions on the
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Pareto-optimal front are the best optimal solutions for different objective functions.
There are some studies using multi-objective DE for the optimization
of reactors. Babu et al. (2005) proposed a DE based algorithm for multi-objective problems, and then they applied it to optimization of the
industrial reactor for styrene production. Productivity, selectivity and yield of the reactor were considered as the main objective functions, and ethyl benzene feed temperature, pressure, steam to reactant ratio and initial ethyl benzene flow rate were considered as decision variables.
Their research gave a Pareto-optimal front, providing a wide-range of optimal operating conditions, one of which should be chosen as per requirements of the decision maker. Moreover, they compared their results with an earlier study, which used non-dominated sorting genetic algorithm. They indicated that all objectives, except the profit, were improved by using multi-objective DE. Subsequently, Babu et al. (2007) proposed two new strategies for multi-objective optimization based on DE, named as MODE-1 and MODE-2. Then, they applied them to optimize the industrial styrene reactor, with productivity and selectivity as the objective functions. The results showed that MODE-2 leads to a wide range of optimal solutions, whereas MODE-1 is much faster.
Afterwards, Gujarathi and Babu (2010) presented the hybrid multi-objective DE (H-MODE). They used this algorithm to optimize the operating conditions of an industrial wiped film polyethylene terephthalate reactor. Results of MODE and H-MODE were slightly different; however, H-MODE was much faster.
3.6 Conclusions
In many process, a significant incentive to enhance the reactor efficiency leads to the use of different optimization approaches. One of the most useful optimization methods is the differential evolution which is an efficient, relatively simple and robust technique. Since, the DE optimization technique has been extensively applied in chemical reaction engineering, this chapter reviews the most important facts about these applications. In fact, this chapter gives the readers a detailed insight about different aspects of reactor optimization using DE. At first, some general facts about the reactor design and kinetic modeling are discussed.
Afterwards, two important parts of optimization namely decision variables and objective functions are explained. Then, major decision
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variables for reactors including temperature, pressure, flow rate, membrane thickness, reactor size, feed concentration and kinetic parameters, are explained. Finally, two types of optimization problems (single and multi-objective) and their applications are discussed.
References
Abashar M.E., Alhabdan F.M., Elnashaie S.S., (2007). Staging distribution of oxygen in circulating fast fluidized-bed membrane reactors for the production of hydrogen, Industrial and Engineering Chemistry Research, 46, pp. 5493-5502.
Al-Mubaiyedh U., Ali S., Al-Khattaf S., (2012). Kinetic modeling of heavy reformate conversion into xylenes over mordenite-ZSM5 based catalysts, Chemical Engineering Research and Design, 90, pp. 1943-1955.
Amirabadi S., Kabiri S., Vakili R., Iranshahi D., Rahimpour M.R., (2013). Differential evolution strategy for optimization of hydrogen production via coupling of methylcyclohexane dehydrogenation reaction and methanol synthesis process in a thermally coupled double membrane reactor, Industrial and Engineering Chemistry Research, 52, pp. 1508-1522.
Anand P., Venkateswarlu C., Bhagvanth Rao M., (2013). Multistage dynamic optimization of a copolymerization reactor using differential evolution, Asia-Pacific Journal of Chemical Engineering, 8, pp. 687-698.
Andrigo P., Bagatin R., Pagani G., (1999). Fixed bed reactors, Catalysis Today, 52, pp. 197-221.
Angira R., Babu B., (2006a). Optimization of process synthesis and design problems: A modified differential evolution approach, Chemical Engineering Science, 61, pp. 4707-4721.
Angira R., Babu B., (2006b). Performance of modified differential evolution for optimal design of complex and non-linear chemical processes, Journal of Experimental and Theoretical Artificial Intelligence, 18, pp. 501-512.
Aris R., (2000). The Optimal Design of Chemical Reactors: A Study in Dynamic Programming, Elsevier.
Babu B., Angira R., (2006). Modified differential evolution (MDE) for optimization of
non-linear chemical processes, Computers and chemical engineering, 30, pp. 989-1002.
Babu B., Chakole P.G., Mubeen J.S., (2005). Multiobjective differential evolution (MODE) for optimization of adiabatic styrene reactor, Chemical Engineering Science, 60, pp. 4822-4837.
Babu B., Gujarathi A.M., Katla P., Laxmi V., (2007). Strategies of multi-objective differential evolution (MODE) for optimization of adiabatic styrene reactor, Proceedings of the international conference on emerging mechanical technology:
macro to nano (EMTMN-2007). Citeseer, p. 243.
Babu B., Munawar S., (2007). Differential evolution strategies for optimal design of shell-and-tube heat exchangers, Chemical Engineering Science, 62, pp. 3720-3739.
Bayat M., Hamidi M., Dehghani Z., Rahimpour M., Shariati A., (2014).
Hydrogen/methanol production in a novel multifunctional reactor with in situ adsorption: modeling and optimization, International Journal of Energy Research, 38, pp. 978-994.
Differential Evolution in Chemical Engineering Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 06/03/17. For personal use only.
Bayat M., Rahimpour M., (2013). Production of hydrogen and methanol enhancement via a novel optimized thermally coupled two-membrane reactor, International Journal of Energy Research, 37, pp. 105-120.
Deb K., (2001). Multi-objective Optimization Using Evolutionary Algorithms, John Wiley & Sons.
Deb K., (2014). Multi-objective Optimization: Search Methodologies, Springer, pp. 403-449.
Dragoi E.N., Curteanu S., (2016). The use of differential evolution algorithm for solving chemical engineering problems, Reviews in Chemical Engineering, 32, pp. 149-180.
Farsi M., Jahanmiri A., (2011). Mathematical simulation and optimization of methanol dehydration and cyclohexane dehydrogenation in a thermally coupled dual-membrane reactor, International Journal of Hydrogen Energy, 36, pp. 14416-14427.
Farsi M., Jahanmiri A., Rahimpour M., (2013). Optimal operating conditions of radial flow moving-bed reactors for isobutane dehydrogenation, Journal of Energy Chemistry, 22, pp. 633-638.
Farsi M., Asemani M., Rahimpour M., (2014). Mathematical modeling and optimization of multi-stage spherical reactor configurations for large scale dimethyl ether production, Fuel Processing Technology, 126, pp. 207-214.
Gennert M.A., Yuille A.L., (1988). Determining the optimal weights in multiple objective function optimization, International Conference Computer Vision, pp. 87-89.
Ghodasara K., Hwang S., Smith R., (2015). Catalytic propane dehydrogenation:
Advanced strategies for the analysis and design of moving bed reactors, Korean Journal of Chemical Engineering, 32, pp. 2169-2180.
Goldberg D.E., (1989). Genetic Algorithms in Search Optimization and Machine Learning, Addison-wesley Reading Menlo Park.
Gujarathi A.M., Babu B., (2009). Improved multiobjective differential evolution (MODE) approach for purified terephthalic acid (PTA) oxidation process, Materials and Manufacturing Processes, 24, pp. 303-319.
Gujarathi A.M., Babu B., (2010). Hybrid multi-objective differential evolution (H-MODE) for optimisation of polyethylene terephthalate (PET) reactor,
International Journal of Bio-Inspired Computation, 2, pp. 213-221.
Gujarathi A.M., Motagamwala A.H., Babu B., (2013). Multiobjective optimization of industrial naphtha cracker for production of ethylene and propylene, Materials and Manufacturing Processes, 28, pp. 803-810.
Hamedi N., Iranshahi D., Rahimpour M., Raeissi S., Rajaei H., (2015a). Development of a detailed reaction network for industrial upgrading of heavy reformates to xylenes using differential evolution technique, Journal of the Taiwan Institute of Chemical Engineers, 48, pp. 56-72.
Hamedi N., Tohidian T., Rahimpour M., Iranshahi D., Raeissi S., (2015b). Conversion enhancement of heavy reformates into xylenes by optimal design of a novel radial flow packed bed reactor, applying a detailed kinetic model, Chemical Engineering Research and Design, 95, pp. 317-336.
Hill C.G., (1977). An Introduction to Chemical Engineering Kinetics and Reactor Design, John Wiley & Sons, New York.
Hoomans B., Kuipers J., Briels W., Van Swaaij W., (1996). Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: a hard-sphere approach, Chemical Engineering Science, 51, pp. 99-118.
Differential Evolution in Chemical Engineering Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 06/03/17. For personal use only.
88 M.R. Rahimpour and N. Hamedi
Differential Evolution in Chemical Engineering 9in x 6in b2817-ch03
Iranshahi D., Bahmanpour A.M., Pourazadi E., Rahimpour M.R., (2012). A comparative study on optimised and non-optimised axial flow, spherical reactors in naphtha reforming process, The Canadian Journal of Chemical Engineering, 90, pp. 1102-1111.
Iranshahi D., Jafari M., Rafiei R., Karimi M., Amiri S., Rahimpour M.R., (2013a).
Optimal design of a radial-flow membrane reactor as a novel configuration for continuous catalytic regenerative naphtha reforming process considering a detailed kinetic model, International Journal of Hydrogen Energy, 38, pp. 8384-8399.
Iranshahi, D., Karimi M., Amiri S., Jafari M., Rafiei R., Rahimpour M.R., (2014).
Modeling of naphtha reforming unit applying detailed description of kinetic in continuous catalytic regeneration process, Chemical Engineering Research and Design, 92, pp. 1704-1727.
Iranshahi D., Pourazadi E., Paymooni K., Bahmanpour A., Rahimpour M., Shariati A., (2010). Modeling of an axial flow, spherical packed-bed reactor for naphtha reforming process in the presence of the catalyst deactivation, International Journal of Hydrogen Energy, 35, pp. 12784-12799.
Iranshahi D., Rahimpour M., Paymooni K., Pourazadi E., (2013b). Utilizing DE optimization approach to boost hydrogen and octane number, through a combination of radial-flow spherical and tubular membrane reactors in catalytic naphtha reformers, Fuel, 111, pp. 1-11.
Jakobsen H.A., (2008). Fluidized Bed Reactors, in: Jakobsen, H.A. (editor), Chemical Reactor Modeling, Springer-Verlag, Berlin Heidelberg.
Karimi M., Rahimpour M.R., Rafiei R., Shariati A., Iranshahi D., (2016). Improving thermal efficiency and increasing production rate in the double moving beds thermally coupled reactors by using differential evolution (DE) technique, Applied Thermal Engineering, 94, pp. 543-558.
Khademi M., Setoodeh P., Rahimpour M., Jahanmiri A., (2009). Optimization of methanol synthesis and cyclohexane dehydrogenation in a thermally coupled reactor using differential evolution (DE) method, International Journal of Hydrogen Energy, 34, pp. 6930-6944.
Khajeh S., Aboosadi Z.A., Honarvar B., (2015). Optimizing the fluidized-bed reactor for synthesis gas production by tri-reforming, Chemical Engineering Research and Design, 94, pp. 407-416.
Kirkpatrick S., Vecchi M.P., (1983). Optimization by simulated annealing, Science, 220, pp 671-680.
Kordnejad M., Shokroo E.J., Shahcheraghi M., (2013). Real time optimization of shell and tube methanol reactor using evolutionary and genetic algorithms, Petroleum and Coal, 55, pp. 322-329.
Lee M.H., Han C., Chang K.S., (1999). Dynamic optimization of a continuous polymer reactor using a modified differential evolution algorithm, Industrial and Engineering Chemistry Research, 38, pp. 4825-4831.
Lin M. H., Tsai J. F., Yu C. S., (2012). A review of deterministic optimization methods in engineering and management, Mathematical Problems in Engineering, 2012, pp. 1-15.
Mirvakili A., Bahrani S., Jahanmiri A., (2013). An environmentally friendly configuration for ammonium nitrate decomposition, Industrial and Engineering Chemistry Research, 52, pp. 13276-13287.
Olah G. A., Molnar A., (2003). Hydrocarbon Chemistry, Wiley; New York.
Differential Evolution in Chemical Engineering Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 06/03/17. For personal use only.
Parvasi P., Mostafazadeh A.K., Rahimpour M., (2009). Dynamic modeling and optimization of a novel methanol synthesis loop with hydrogen-permselective membrane reactor, International Journal of Hydrogen Energy, 34, pp. 3717-3733.
Price K., Storn R., (1997). Differential evolution: a simple evolution strategy for fast optimization, Dr. Dobb’s Journal, 22, pp. 18-24.
Rahimpour M., (2008). A two-stage catalyst bed concept for conversion of carbon dioxide into methanol, Fuel Processing Technology, 89, pp. 556-566.
Rahimpour M., Asgari A., (2008). Modeling and simulation of ammonia removal from purge gases of ammonia plants using a catalytic Pd–Ag membrane reactor, Journal of Hazardous Materials, 153, pp. 557-565.
Rahimpour M., Khademi M., Bahmanpour A., (2010). A comparison of conventional and optimized thermally coupled reactors for Fischer–Tropsch synthesis in GTL technology, Chemical Engineering Science, 65, pp. 6206-6214.
Rahimpour M.R., Aboosadi Z.A., Jahanmiri A.H., (2013). Differential evolution (DE) strategy for optimization of methane steam reforming and hydrogenation of nitrobenzene in a hydrogen perm-selective membrane thermally coupled reactor, International Journal of Energy Research, 37, pp. 868-878.
Rahimpour M.R., Iranshahi D., Paymooni K., Pourazadi E., (2011a). Enhancement in research octane number and hydrogen production via dynamic optimization of a novel spherical axial-flow membrane naphtha reformer, Industrial and Engineering Chemistry Research, 51, pp. 398-409.
Rahimpour M.R., Iranshahi D., Pourazadi E., Bahmanpour A.M., (2012). Boosting the gasoline octane number in thermally coupled naphtha reforming heat exchanger reactor using de optimization technique, Fuel, 97, pp. 109-118.
Rahimpour M.R., Iranshahi D., Pourazadi E., Paymooni K., (2011b). Evaluation of optimum design parameters and operating conditions of axial-and radial-flow tubular naphtha reforming reactors, using the differential evolution method, considering catalyst deactivation, Energy and Fuels, 25, pp. 762-772.
Rangaiah G.P., (2009). Multi-objective Optimization: Techniques and Applications in Chemical Engineering, World Scientific.
Rosenthal R.E., (1985). Concepts, theory, and techniques principles of multiobjective optimization, Decision Sciences, 16, pp. 133-152.
Schuurman P.J., (1985). Moving Bed Reactor, Google Patents.
Schwefel H.P., (1981). Numerical Optimization of Computer Models, John Wiley &
Sons, Inc.
Sharma R., Sheth P.N., Gujrathi A.M., (2016). Kinetic modeling and simulation:
Pyrolysis of Jatropha residue de-oiled cake, Renewable Energy, 86, pp. 554-562.
Storn R., Price K.V., (1996). Minimizing the real functions of the ICEC'96 Contest by differential evolution, International Conference on Evolutionary Computation, pp.
842-844.
Storn R., Price K., (1997). Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, 11, pp.
341-359.
Tsai T.C., Chen W.H., Lai C.S., Liu S. B., Wang I., Ku C.S., (2004). Kinetics of toluene disproportionation over fresh and coked H-mordenite, Catalysis Today, 97, pp. 297-302.
Differential Evolution in Chemical Engineering Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 06/03/17. For personal use only.
90 M.R. Rahimpour and N. Hamedi
Differential Evolution in Chemical Engineering 9in x 6in b2817-ch03
Vakili R., Eslamloueyan R., (2013). Design and optimization of a fixed bed reactor for direct dimethyl ether production from syngas using differential evolution algorithm, International Journal of Chemical Reactor Engineering, 11, pp. 147-158.
Vakili R., Rahimpour M., Eslamloueyan R., (2012). Incorporating differential evolution (DE) optimization strategy to boost hydrogen and DME production rate through a membrane assisted single-step DME heat exchanger reactor, Journal of Natural Gas Science and Engineering, 9, pp. 28-38.
Vakili R., Setoodeh P., Pourazadi E., Iranshahi D., Rahimpour M., (2011). Utilizing differential evolution (DE) technique to optimize operating conditions of an integrated thermally coupled direct DME synthesis reactor, Chemical Engineering Journal, 168, pp. 321-332.
Wang C., Zhu J., (2015). Developments in the understanding of gas–solid contact efficiency in the circulating fluidized bed riser reactor: A review, Chinese Journal of Chemical Engineering, 24, pp. 53-62.
Wang F.S., Su T. L., Jang H. J., (2001). Hybrid differential evolution for problems of kinetic parameter estimation and dynamic optimization of an ethanol fermentation process, Industrial and Engineering Chemistry Research, 40, pp. 2876-2885.
Worstell J., (2014). Adiabatic Fixed-Bed Reactors: Practical Guides in Chemical Engineering, Butterworth-Heinemann.
Yeoh J.X., Chong C.K., Choon Y.W., Chai L.E., Deris S., Illias R.M., Mohamad M.S., (2013). Parameter estimation using improved differential evolution (IDE) and bacterial foraging algorithm to model tyrosine production in mus musculus (Mouse), Pacific-Asia Conference on Knowledge Discovery and Data Mining, Springer, pp.
179-190.
Yerushalmi J., Cankurt N., (1979). Further studies of the regimes of fluidization, Powder Technology, 24, pp. 187-205.
Zhao Y., Li H., Ye M., Liu Z., (2013). 3D numerical simulation of a large scale MTO
fluidized bed reactor, Industrial and Engineering Chemistry Research, 52, pp. 11354-11364.
Differential Evolution in Chemical Engineering Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 06/03/17. For personal use only.
Chapter 4