chemical engineering, until the year 2009. Recently, Dragoi and Curteanu (2016) reviewed DE applications for solving chemical engineering problems. In order to provide an overview of DE applications in chemical engineering in recent years, Scopus database was searched using the keyword ‘differential evolution’ in the article title and keywords. Other criteria for narrowing the Scopus search are as follows: fields — article or review article, date range — January 2008 to April 2016, subject area — chemical engineering, energy and environmental science, language — English. In total, 904 articles were found, and 216 articles were short-listed based on their relevance to DE and chemical engineering. From these short-listed articles, Fig. 1.4 shows the number of journal papers on DE applications in chemical engineering and related areas over the years 2008 to 2016, and Table 1.2 summarizes number of articles published in different journals. It can be seen that nearly 70 papers are in energy-related journals (Table 1.2).
DE applications in chemical engineering can be divided into two broad categories: (1) modeling or parameter estimation, and (2) process design and optimization. About 60% studies on DE applications in chemical engineering, energy and environmental science from the year
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2008 to April 2016 are on process design and optimization, and the remaining are on parameter estimation, mainly for estimating reaction kinetics. Most of the studies considered single objective function; only about 10% of studies considered two or more objective functions. Tables 1.3 and 1.4 summarize applications of DE in chemical engineering, and the commonly used objectives in these applications. Energy Conversion and Management journal has attracted the most number of DE studies (20 papers) followed by the Energy journal with 14 papers.
Fig. 1.4 Number of reported DE applications in chemical engineering and related areas in recent years; number for 2016 is until April only
Some recent studies on DE applications have also considered modifications in DE algorithm aspects. Important modifications in DE algorithm are summarized below. The modified DE algorithms have been used for optimization of chemical engineering related applications.
Adaptation of mutation factor, crossover probability and/or mutation strategy
Population initialization, different sub-populations with different mutation strategies
Termination criteria, equality and inequality constraints handling
DE with PSO, DE with free search, DE with group search, DE with tabu list, DE with chaotic search, DE with sequential simplex, DE with clustering, DE with conjugate gradient method
Permutation based DE, Discrete binary DE
0 5 10 15 20 25 30 35 40
2008 2009 2010 2011 2012 2013 2014 2015 2016
No. of Journal Papers
Year of Publication
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Introduction 15
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Table 1.2 Number of reported DE applications in different journals (N - number of journal papers): January 2008 to April 2016
Name of Journal (J) N
Adsorption Science and Technology AIChE J, Biochemical Engineering J, Bioprocess and Biosystems Engineering, Chemical Engineering Transactions, Energy and Fuels, International J of Heat and Mass Transfer, J of Environmental Chemical Engineering, J of Renewable and Sustainable Energy, Powder Technology, Water Science and Technology
1
Biotechnology and Bioprocess Engineering, Canadian J of Chemical Engineering, Chemical Industry and Chemical Engineering Quarterly, Computer Aided Chemical Engineering, Frontiers in Energy, J of Chemical and Engineering Data, J of Chemical Technology and Biotechnology, Korean J of Chemical Engineering, Petroleum Science and Technology, Renewable and Sustainable Energy Reviews, Separation and Purification Technology
2
Chemical Engineering and Technology, Chemical Engineering Communications, Chemical Engineering J, Ecological Modelling, Indian Chemical Engineer, International J of Energy Research, J of Petroleum Science and Engineering
3
Chemical Engineering Science, Chemical Product and Process Modeling, International J of Chemical Reactor Engineering, J of Chemical Engineering of Japan, J of Industrial and Engineering Chemistry, Renewable Energy
4
Asia-Pacific J of Chemical Engineering, Chemical Engineering Research
and Design, Water Resources Research 5
Applied Thermal Engineering, Chemical Engineering and Processing:
Process Intensification, J of the Taiwan Institute of Chemical Engineers
6
Computers and Chemical Engineering 8
Chinese J of Chemical Engineering, Fluid Phase Equilibria 9
Applied Energy 10
J of Natural Gas Science and Engineering 11
Industrial and Engineering Chemistry Research, International J of Hydrogen
Energy 12
Energy 14
Energy Conversion and Management 20
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Table 1.3 Recent applications of DE in process modeling or parameter estimation Reaction Engineering: Jet stirred reactor combustor, double moving beds coupled reactors, pyrolysis, industrial fluid catalytic cracking, 3-phase trickle bed reactor, batch and fed-batch fermentation, reactive system, ethylene oxide reactor, coal-water slurry gasifier, reaction network, CSTR, radial flow packed bed reactor, FT synthesis slurry reactor, reactive extraction, terephthalic acid production, ammonia synthesis.
Power Generation: Photovoltaic, power system, dispatch problem, wind power, solar cell/power, SOFC and PEM fuel cells, reheat regenerative power cycle
Other Applications: Reservoir, cooling tower, Cr(VI) removal from wastewater, ionic liquids, biochemical system, partition coefficient estimation, solubility parameter estimation, PID controller tuning, phase equilibrium and stability, VLE modeling, model discrimination, soft sensor, slurry flow
Common Objective Functions: Misfit, error, relative error, total relative error, absolute error, mean squared error, sum of squared error, root mean square error, mean absolute percentage error, integral error, integral time weighted absolute error, fitting error, Gibbs free energy, deviation from set point, error-in-variable, standard deviation of error, cross correlation of error.
Table 1.4 Recent applications of DE in process design and optimization Reactors: Fluidized and fixed bed reactors, methanol synthesis, CO2 conversion to methanol, dimethyl ether production, (packed bed) membrane reactor, thermally coupled reactors, thermally coupled dual membrane reactor, copolymerization reactor, naphtha reformer, naphtha pyrolysis, ethylene cracking furnace, alkylation process, Williams-Otto process, ethylene oxide reactor, Fischer-Tropsch reactor, cyclohexane dehydration, auto-thermal ammonia reactor, hydrogen production, styrene reactor Fermentation Processes: Fermentation, fed-batch fermentation, fermentation-pervaporation and fermentation-extraction processes
Separation Processes: Bixin extraction, filtering hydrocyclone, intensified distillation column, extractive distillation, middle vessel batch distillation, ethanol dehydration, solvent design for ethanol extractive fermentation, lactic acid production/recovery Power Generation: Distributed generation, electric power network, solar plant with storage, hydrothermal power system, supercritical CO2 Brayton cycles, renewable distributed generation, coal fired power plant, PEM fuel cell, power cycle with waste heat and LNG (liquefied natural gas) cold energy, solar thermal refrigeration systems Other Applications: Heat exchangers, HEN retrofitting, photovoltaic water pumping, water distribution, scheduling, blending process, pressure vessel design
Common Objective Functions: Expected global cost, life cycle cost, total (annual) cost, profit, operating cost, efficiency, fuel cost, utility cost, primary energy consumption, emissions, production rate, purity, effectiveness, yield, productivity, conversion, recovery, selectivity, fugacity, activity, outlet mole fractions
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Introduction 17
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