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Optimization of the Arrhenius Parameters in a Pseudo-detailed Mechanism for Jet Fuel Thermal Oxidation Using Genetic and Simplex Algorithms Andrew S. Wade,* Adrian G. Kyne, Nicolae S. Mera, and Mohammed Pourkashanian Energy and Resources Research Institute, University of Leeds, Leeds, United Kingdom
Derek B. Ingham and Sean Whittaker Department of Applied Mathematics, University of Leeds, Leeds, United Kingdom Received July 30, 2004. Revised Manuscript Received September 10, 2004
In this paper we present a novel way to determine new Arrhenius parameters and unknown initial reactant concentrations in a pseudo-detailed reaction mechanism for the autoxidation of aviation fuel. The technique employed is a specialized optimization procedure known as a genetic algorithm (GA), which utilizes an abstraction of the Darwinian principle of survival of the fittest to “breed” good solutions over a predefined number of “generations”. Temporal O2 consumption profiles for a given fuel or paraffin blend, which have been measured experimentally over a range of conditions, are reproduced by integrating the governing set of differential equations that result from the chemical kinetic mechanism and the optimized set of rate constants and initial reactant concentrations obtained using a GA inversion process. A simplex algorithm is then applied to further improve the GA-optimized parameters. The new set of rate constants lie within chemically reasonable predefined boundaries based upon values found for analogous reactions in the literature. This powerful method also offers the ability to optimize unknown reactant concentrations in real fuels which cannot be measured with current experimental techniques simultaneously with the reaction rate parameters. Such a process can lead to the development of reaction mechanisms whose newly optimized rate constants and reactant concentrations reproduce closely all the experimental data available, enabling a greater confidence in their predictive capabilities. The process is also shown to be an effective tool to facilitate the elucidation of areas of particular success or failure of the mechanism to simulate the autoxidation characteristics of jet fuels. A GA-optimized pseudo-detailed oxidation reaction mechanism for a “clean” jet fuel, approximated by paraffin blends virtually devoid of antioxidants, is presented, along with optimized values of reactant concentrations for several real fuels. This mechanism offers a remarkable improvement over previous mechanisms in its generality, i.e., its ability to simulate autoxidation behavior for a range of fuels and their blends. In addition, the new mechanism is capable of predicting autoxidation characteristics for fuel blends that were not part of the optimization process.
Introduction Prior to entering the combustion chamber in an aircraft engine, aviation fuel acts as the primary coolant for several engine and airframe components as well as electronic equipment. This function causes elevation of the fuel temperature and, in the presence of dissolved O2, results in the thermal-oxidative stressing of the fuel. The autoxidation process involves a complex series of free radical chain reactions which produce oxygenated species, such as hydroperoxides, alcohols, ketones, aldehydes, and acids. Subsequent reactions lead to the production of solids and gums, which may go on to foul engine components. Such reaction products have been implicated in observed reductions in the efficiency of heat exchangers and can ultimately lead to blocked fuel * To whom correspondence
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system filters and other undesirable disturbances within the fuel flow.1 Furthermore, the fouling of close-tolerance valves can lead to catastrophic engine failure. For many years, antioxidants have been used as fuel additives to reduce the extent of autoxidation in jet fuels, during both room temperature storage and hightemperature thermal stressing in heat sink applications. The various types of antioxidants used in liquid fuels include hindered phenols, phenylenediamines, peroxide decomposers, and metal deactivators. All of these antioxidants act by preventing the formation of, or rapidly removing, chain-carrying radical species; see Zabarnick.2 Hindered phenols and phenylenediamines are primary antioxidants which are believed to slow autoxi(1) Hazlett, R. N. Thermal Oxidation Stability of Aviation Turbine Fuels; ASTM Monograph 1; ASTM: Philadelphia, 1991. (2) Zabarnick, S. Pseudo-Detailed Chemical Kinetic Modelling of Antioxidant Chemistry for Jet Fuel Applications. Energy Fuels 1998, 12, 547-553.
10.1021/ef049814h CCC: $27.50 © 2004 American Chemical Society Published on Web 10/09/2004
GA Optimization of a Jet Fuel Oxidation Mechanism
dation by intercepting the chain-carrying alkylperoxy free radicals. Peroxide decomposers are secondary or preventative antioxidants which react with hydroperoxides and prevent their decomposition into free radicals. Metal deactivators are chelating agents, i.e., chemical compounds that form stable complexes with specific metal ions, and as such, they prevent the catalysis of free radical forming reactions. In the past, the chemical kinetic modeling of autoxidation processes has failed to include the effects of antioxidant species. Global models of aviation fuel degradation utilized a single reaction to account for the entire autoxidation process. Such a description is a vast oversimplification of a highly complex process which is central to the detrimental deposition problem within fuel-handling systems. Using their modified global model, Katta et al.3 had some success in simulating fuel stability characteristics for fuel blends, but Wade et al. 4 exposed the inadequacy of the single-step autoxidation reaction while endeavoring to optimize this mechanism using a GA inversion process. The clear conclusion was that, where it is available, further detail must be added to the global mechanism of Katta et al.2 to produce a truly robust chemical kinetic mechanism for jet fuel oxidation and deposition. Fortunately, the phenomenon of autoxidation has been studied extensively, and recently, Zabarnick5 developed a chemical kinetic model of antioxidant action for jet fuel applications, employing a so-called pseudo-detailed model involving 16 reactions. Later, Zabarnick2 added another step to account for the action of sulfuric peroxide-decomposing species, and subsequently, Kuprowicz et al.6 have added two further reactions accounting for further predicted behavior of radicals. Recently, Balster et al.7 went on to add some global surface reactions to model the deposition process. Recent modeling efforts have shown a good degree of success in simulating the autoxidation of straight-run and additized jet fuels.2,5-7 However, the calibration of these chemical kinetic schemes for jet fuel autoxidation has previously been achieved through a combination of theory, experiment, and trial-and-error. Such schemes have had a good degree of success in predicting O2 consumption behavior for paraffin blends at various temperatures and initial dissolved O2 concentrations, see Kuprowicz et al.,6 but have never been applied adequately to real-world fuels due to lack of analytical techniques to identify and measure the important reactants. Such calibration techniques also fall short of offering a truly robust reaction mechanism for fuel (3) Katta, V. R.; Jones, E. G.; Roquemore, W. M. Modelling of Deposition Process in Liquid Fuels. Combust. Sci. Technol. 1998, 139, 75-111. (4) Wade, A.; Ingham, D. B.; Kyne, A. G.; Mera, N. S.; Pourkashanian, M.; Wilson, C. W. Optimisation of the Arrhenius Parameters in a Semi-Detailed Mechanism for Jet Fuel Thermal Degradation Using a Genetic Algorithm. In Proceedings of ASME EXPO 2004, Vienna, June 2004; ASME: Fairfield, NJ, 2004; Paper No. GT2004-53367. (5) Zabarnick, S. Chemical Kinetic Modelling of Jet Fuel Oxidation and Antioxidant Chemistry. Ind. Eng. Chem. Res. 1993, 32, 10121017. (6) Kuprowicz, N. J.; Ervin, J. S.; Zabarnick, S. Modelling the LiquidPhase Oxidation of Hydrocarbons Over a Range of Temperatures and Dissolved Oxygen Concentrations with Pseudo-detailed Chemical Kinetics. Fuel 2004, 83, 1795-1801. (7) Balster, L.; Zabarnick, S.; Ervin, J.; Striebich, R.; DeWitt, M.; Doungthip, T. Predicting the Thermal Stability of Jet Fuel: Analytical Techniques Toward Model Validation. Proceedings of the 8th International Conference on Stability and Handling of Liquid Fuels, US Department of Energy: Steamboat Springs, CO, 2003; pp 779-794.
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autoxidation which, with suitably accurate knowledge of fuel composition, would give sufficiently accurate predictions over the entire spectrum of fuels and conditions found in aircraft fuel-handling systems. As the concentrations of certain reactants within the fuels of interest which are central to these pseudo-detailed mechanisms are unknown, they have previously been altered to match experimental data as part of the calibration procedure since no current experimental methods are available for measurement of these important quantities. It is of great importance that such reactants are identified and quantified as marked differences in the oxidation and deposition characteristics from batch to batch of jet fuel are caused by variations in fuel composition. We attempt to optimize the reaction rate parameters and unknown reactant concentrations within jet fuels using a process based upon an abstraction of the Darwinian principle of survival of the fittest which has inspired a class of algorithms known as genetic algorithms (GAs). Genetic algorithms attempt to find the best solution to a problem by imitating the process of evolution in nature. Thus, a typical algorithm will repeatedly “breed” populations of individuals which represent possible solutions to a particular problem. The reaction rate parameters are each encoded into “genes” which are then concatenated to form the “chromosomes” of the individuals of a population of possible solutions to the problem. The simple chemical kinetic modeling package “Acuchem” (see Braun et al.8) can be run using a kinetic scheme defined by decoding the genetic data within each individual chromosome and the resulting O2 consumption outputs compared to known experimental data. The fittest individuals within a population are identified according to an objective or “fitness” function and subsequently used to provide offspring for the next generation. As this process is repeated, increasingly superior solutions are discovered. The GA optimization technique has been applied successfully to many chemical kinetic problems (for example, see Polifke et al.,9 Harris et al.,10 Elliott et al.,11 and Wade et al.4). It is the purpose of this study to optimize the reaction rate parameters and unknown reactant concentrations for the 19-reaction pseudo-detailed autoxidation mechanism of Kuprowicz et al.6 A method is presented for the prediction of unknown reactant concentrations within fuels of interest by utilizing a GA inversion process on experimental data for fuel blends. Such concentrations for a given fuel could then be used effectively as inputs in an optimized mechanism to predict autoxidation characteristics of interest. It is (8) Braun, W.; Herron, J. T.; Kahaner, D. Acuchem: A Computer Program for Modelling Complex Reaction Systems. Int. J. Chem. Kinet. 1988, 20, 51-62. (9) Polifke, W.; Geng, W.; Do¨bbeling, K. Optimisation of Reaction Rate Coefficients for Simplified Reaction Mechanisms with Genetic Algorithms, Combust. Flame 1998, 113, 119-135. (10) Harris, S. D.; Elliott, L.; Ingham, D. B.; Pourkashanian, M.; Wilson, C. W. The Optimisation of Reaction Rate Parameters for Chemical Combustion Using Genetic Algorithms. Comput. Methods Appl. Mech. Eng. 2000, 190, 1065-1090. (11) Elliott, L.; Ingham, D. B.; Kyne, A. G.; Mera, N. S.; Pourkashanian, M.; Wilson, C. W. A Real Coded Genetic Algorithm for the Optimization of Reaction Rate Parameters or Chemical Kinetic Modelling in a Perfectly Stirred Reactor. Genetic and Evolutionary Computation Conference, Late Breaking Papers; GECCO: New York, 2002; pp 138-144.
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hoped that, once a truly robust mechanism for accurately predicting fuel oxidation has been realized, subsequent addition and GA optimization of more global deposition reactions will allow reliable prediction of deposition profiles over a wide range of operating conditions. The near-isothermal experimental measurements of Jones et al.12 and Jones and Balster13 were used to tune and hence improve upon the Arrhenius parameters used in the pseudo-detailed autoxidation reaction mechanism of Kuprowicz et al. The Jet-A fuels used by Jones et al.12 to study fuel blends were POSF-2827 and POSF-2747. POSF-2827 is a straight-run (non-hydrotreated) Jet-A fuel containing significant amounts of naturally occurring antioxidant species. Such straight-run fuels produce relatively low hydroperoxide concentrations and oxidize relatively slowly upon encountering elevated temperatures in the presence of dissolved O2. POSF-2747 is a Jet-A fuel which has been hydrotreated; i.e., it has been processed to remove deleterious trace species and as such has had many of its indigenous antioxidants removed, causing it to oxidize quickly. POSF-3084 was used in the subsequent work of Jones and Balster13 on the interaction between the synthetic antioxidant BHT and naturally occurring antioxidants in the autoxidation of paraffins. This Jet-A fuel was selected as a source of polar species which act as natural antioxidants and also reduce the thermal stability of this fuel, i.e., increase its tendency to foul surfaces.13 The paraffinic solvent used in this study was Exxsol-D110, obtained from the Exxon Corp. to serve as a fuel diluent and a baseline hydrocarbon. It consists of ∼50% paraffins, ∼50% cycloparaffins, and
