# Thermodynamic analysis of combustion processes and pollutants emission using nonlinear optimization approach.

код для вставкиСкачатьASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING Asia-Pac. J. Chem. Eng. 2012; 7: 80–85 Published online 1 September 2010 in Wiley Online Library (wileyonlinelibrary.com) DOI:10.1002/apj.494 Research article Thermodynamic analysis of combustion processes and pollutants emission using nonlinear optimization approach Farshad Farshchi Tabrizi,1 * Ashkan Zolfaghari Sharak2 and Arsalan Zolfaghari Shahrak3 1 Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan, Iran Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran 3 Department of Chemical and Petroleum Engineering, University of Wyoming, Laramie, WY 8207, USA 2 Received 26 February 2010; Revised 6 June 2010; Accepted 11 June 2010 ABSTRACT: Mathematical formulation and modeling of combustion processes is an important tool in the understanding of this phenomenon. Determination of equilibrium temperature and composition is often the first stage in calculation of combustion characteristics. There are number of different techniques for simulation of combustion process. In this study a basic model has been developed based on the minimization of Gibb’s free energy to simulate the combustion processes. A nonlinear mathematical optimization has been developed based on Lagrange multipliers and solved using Quasi-Newton method written in MathCAD environment. The effect of various parameters such as initial temperature, pressure, and equivalence ratio on the equilibrium temperature and composition has been investigated. In contrast with the equilibrium constant method, obtained results out of this work show that the maximum flame temperature for normal paraffins occurs around the equivalence ratio of 1.05. In addition, from environmental point of view, effects of different conditions on the emission of pollutants in a combustion process have been studied. The simulation results showed that the NO and NO2 emission rates pass through a maximum point and there is an optimum point where the NO–CO emission could be minimized. 2010 Curtin University of Technology and John Wiley & Sons, Ltd. KEYWORDS: thermodynamic analysis; nonlinear optimization; Gibb’s free energy; pollutant; combustion processes INTRODUCTION Combustion is the first source of energy known to mankind and today about 90% of all energy consumed in the world is produced from combustion processes.[1] Therefore, a detailed knowledge of the combustion phenomena is essential in efficiency of fuel-consuming devices and prevention or at least minimization of the pollutant formation. Based on the principle of equilibrium in any irreversible process, total Gibb’s free energy of a system must be minimized at constant temperature and pressure. In such conditions, it is possible to calculate equilibrium temperature and compositions of the combustion reactions, using thermodynamic equations and mass balances. Sofyan et al .[2] and Chaikunchuensakun and Stiel[3] focused on determining the equilibrium compositions and ensuring convergence of chemical and phase equilibrium problems. One of the methods used to perform chemical equilibrium calculation is the equilibrium constant method, whereby the equations of mass and energy balances together with the equations *Correspondence to: Farshad Farshchi Tabrizi, Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan, Iran. E-mail: Farshchi@eng.usb.ac.ir 2010 Curtin University of Technology and John Wiley & Sons, Ltd. Curtin University is a trademark of Curtin University of Technology for equilibrium reactions is used to fulfill the calculations. This procedure is a traditional technique and needs a vast amount of data for various equilibrium equations. This technique has a relatively simple mathematical and thermodynamic basis but sometimes the thermodynamic basis of this method can be ill-defined especially if the number of species in the products is large and the equilibrium temperature is unknown. For example, Parishan Naddaf and Omidkhah[4] calculate the equilibrium composition and temperature in premixed flames using this method. The second method, which has a better defined mathematical and thermodynamic basis is the method of minimization of Gibb’s free energy. Yeow et al .[5] applied direct search optimization to Gibb’s free energy minimization to determine phase compositions at equilibrium. This method was also reported by Dan Vladimir[6] to be very effective for complicated phase equilibrium and chemical equilibrium problems. Tang and Kitagawa[7] studied a thermodynamical analysis for superficial water gasification of biomass based on the direct use of Gibb’s free energy minimization. In Jarungthammachote and Dutta’s[8] research, temperature and equilibrium compositions are calculated without reaction mechanism consideration.[8] Asia-Pacific Journal of Chemical Engineering NONLINEAR OPTIMIZATION APPROACH Several other methods had been proposed to simulate the combustion processes and investigate the effective parameters. For instance, a new method for the estimation of adiabatic flame temperature of hydrocarbon fuels is presented by Zhou and Gauthier.[9] They used the application of artificial neural networks to adiabatic flame temperature prediction, and investigate the effect of various operating conditions such as pressure, fuel composition, equivalence ratio, and input temperature of reactants. They showed that neural network models can provide the adiabatic flame temperature prediction with a good level of accuracy over a wide range of operating conditions. Gao and Zhang[10] have investigated the effects of operational variables on NOx emission level of an opposed wall-fired pulverized coal utility boiler. They found that the oxygen level was significant parameter to affect the NOx emission. Also, based on their research, increasing the O2 level led to a linear increase of NOx emission. Wang et al .[11] described the influence of SO2 on NO reduction processes. Addition of SO2 inhibits the formation of NOx . According to the results of experimental and kinetic analysis, Hughes[12] indicated that in the premixed methane flames, SO2 imposed an inhibiting effect on NO generation under the fuel-lean or weak fuel-rich condition. In another study, the effect of pressure of premixed flames on the adiabatic flame temperature of a methane-air flame was studied by Khalil et al .[13] They used FLUENT software to simulate the variation of adiabatic flame temperature as a function of pressure in the range of 2–10 atm. They found that in general, the adiabatic flame temperature increases with pressure and FLUENT software is a suitable tool to simulate the turbulent premixed flames. In this study, a general mathematical model based on the implementation of minimization of Gibb’s free energy method is proposed to simulate the combustion processes. As the model results were in good agreement with the available literature, the effect of various parameters such as equivalence ratio, pressure, and the number of selected species was investigated. At the end, environmental studies on CO and NOx emission are reported. MATHEMATICAL MODELING energy. This may arise solving of the nonlinear equations system, which is solved here based on the QuasiNewton method. Minimization of the Gibb’s free energy function based on its variables must respect problem constraints for the mass balance of each species. Therefore, an unknown coefficient called the Lagrange coefficient is used. By multiplying this parameter to the constraints of the problem and adding to the G function, a new function F could be obtained. So if this function is implemented for the minimization with respect to its variables, the results minimize the free energy function and will honor the appropriate assigned limitations. Mass balance constraint could be written based on the input and output stream of the system as well as production of species during the reaction. Hence a balance equation is required for every species presented in the study. ‘k ’ and ‘a’ stand for each atomic species and number of components which have that atomic species, respectively. a is a known parameter, and aik is the number of atoms of element k in the molecular specie i , hence mass balance for the element k could be written as: ni .aik − Ak = 0 k = 1, 2, 3, . . . (2) i Now for each species, the Lagrange multiplier λk is introduced and the final form for function F could be derived as: F =G+ (3) λk ni .aik − Ak k i The unknown parameters for this problem are ni , λk , and T . To solve the problem, we need the same number of independent equations. ‘ni ’-independent equations can be written based on the derivation of the F fuction with respect to the ni , as: (∂F /∂ni )T ,P ,nj ,λk = (∂G/∂ni )T ,P ,nj + λk aik = 0 k (4) Additional λk -independent equations could be obtained based on the derivative of the F function with respect to the λk as: (∂F /∂λk )T ,P ,ni ,λj = ni aik − Ak = 0 (5) i The Gibb’s free energy for a system containing just one phase at constant temperature and pressure depends only on the number of species moles. (G)T,P = G(n1 , n2 , n3 , . . . , nN ) (1) To calculate the moles of each species at equilibrium, one must consider the energy and mass balance equations as well as the minimization of the Gibb’s free 2010 Curtin University of Technology and John Wiley & Sons, Ltd. And finally, energy equation as: ◦ H ◦ = HR◦ + H298 + HP◦ (6) The first term on the right hand side of Eqn (4) is the chemical potential. Therefore, for the gaseous phase reaction it can be written as: (∂G/∂ni )T ,P ,nj = µi = Gi◦ + RTLn(yi ϕi p) (7) Asia-Pac. J. Chem. Eng. 2012; 7: 80–85 DOI: 10.1002/apj 81 82 F. F. TABRIZI, A. Z. SHARAK AND A. Z. SHAHRAK Asia-Pacific Journal of Chemical Engineering The exhausted gaseous mixture in the combustion processes has low to moderate pressure. Also, as the temperature of gaseous mixture is sufficiently high, one can safely assume the fugacity coefficient of species i in the gaseous mixture to be unity. Assuming the adiabatic condition for the flame, Eqn (6) is set equal to zero and thus the maximum flame temperature is calculated. If the calculations are performed on the basis of mole fractions, yi , a further equation for the evaluation of ni is needed. This equation is: yi − 1 = 0 (8) Now, based on the appropriate numerical method for solution of the nonlinear equations system, one can find the final solution based on the various input parameters. RESULTS AND DISCUSSION After solving the equations using MATHCAD software based on the Quasi-Newton method, the results have been compared with a number of references. Tables 1 and 2 summarize some parts of the achieved results and the appropriate comparisons with the published experimental data. These data show very good agreement between the model results and published data. After justifying the accuracy and capability of the algorithm, it is possible to investigate the various parameters that affect the equilibrium condition in a combustion process. The small relative differences between our results and references can be explained based on the following reasons: (1) The main reason is the various references implemented different calculation techniques for their calculations. Some references have used the equilibrium constant method for their calculations, whereas in this study, minimization of Gibb’s free energy is used. (2) The accuracy of thermodynamic data for the Gf◦ , CP can also affect the final results. In this work, JANAF tables[19] have been used. (3) The numerical method implemented for obtaining solution can also affect the final results, for example Gaydon and Wolfhard[16] used an iterative procedure for the calculations, whereas in the present study, the nonlinear set of equations were solved base on the Quasi–Newton method. Investigation of effective parameters on equilibrium conditions The accuracy and capability of the algorithm has been justified in the previous section, it is now possible to investigate the various parameters that affected the equilibrium conditions in the combustion processes. Equivalence ratio One of the main parameters in the combustion process is the fuel/air ratio. In comparing the combustion characteristics of different fuels, it is sometimes convenient to express the mixture in terms of an equivalence ratio . The equivalence ratio is the actual fuel/air ratio divided by the stoichiometric fuel/air ratio. This parameter is usually presented as the equivalence ratio (ϕ). For ϕ > 1, the amount of oxidizer or air is in excess and hence a large amount of the released energy is absorbed that results in lowering of the flame temperature with respect to ϕ = 1 conditions. At condition when ϕ < 1, the total available energy will not be released due to the shortage of oxidizer and hence the flame temperature will again Table 2. Temperature and composition results for acetylene and comparison with a reference ( = 1 and P = 1 atm). Result This work Adiabatic flame temp. (K) YH2O YCO2 YCO YO2 YH2 YNO YN2 YO YH YOH Gaydon–Wolfhard[16] 2515 2532 0.07 0.1166 0.0404 0.0163 0.004 0.0069 0.7346 0.0022 0.0019 0.0072 0.07 0.12 0.04 0.02 0.00 0.01 0.73 0.00 0.00 0.01 Table 1. Adiabatic flame temperature of hydrocarbons in comparison with different references ( = 1 and P = 1 atm). Fuel CH4 C2 H6 C3 H8 C4 H10 C2 H2 Kuan[14] Glassman[15] Gaydon–Wolfhard[16] Ferguson[17] Barnard Bradley[18] This work 2222 – – – 2545 2210 – – – – 2222 2244 2250 2256 2532 2227 – 2268 – 2540 2222 – – – 2513 2207 2240 2247 2249 2515 2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. 2012; 7: 80–85 DOI: 10.1002/apj Asia-Pacific Journal of Chemical Engineering NONLINEAR OPTIMIZATION APPROACH Figure 1. Effect of relative amount of input air on the adiabatic flame temperature for propane. Figure 2. Effect of pressure on adiabatic flame temperature of propane. be lower compared to when ϕ = 1. Results based on the equilibrium constant method, equivalence ratio is estimated around ϕ = 1.[4] As the overall heat capacity of the products is lower than the reactants, it seems that the maximum flame temperature should be appearing in ϕ > 1. The equivalence ratio result reported by Gaydon and Wolfhard[16] is in ϕ = 1.05. Our results show that for normal paraffins, the maximum flame temperature occurs around ϕ = 1.05. Figure 1 represents the effect of relative amount of input air on the adiabatic flame temperature. leads to increase the flame temperature. Figure (2) illustrates the effect of pressure on the adiabatic flame temperature of propane. Table 3 represents the effect of pressure on flame temperature and composition for combustion products of propane with air. Increase in the pressure contributes to increase in the emission of carbon dioxide and decrease in emission of carbon monoxide. As in environmental studies, a trivial change in emission of both CO2 and CO is crucial; the operation should be done in an optimum pressure where the emission of both components is minimized. Pressure The effect of pressure on the equilibrium temperature and composition can be interpreted using the Le-chatellier principle. According to this principle, increasing pressure causes a shift towards reactions, which produce smaller moles of products. Minimization of Gibb’s free energy method shows that an increase in pressure causes an increase in adiabatic flame temperature. However, increasing the pressure contributes to reduce the rate of the decomposition reactions. This Number of selected species The number of selected species for calculation in the equilibrium mixture also has an effect on the final results. Increasing the number of species causes a decrease in the flame temperature and of course increases the accuracy of the calculations. The reason behind this behavior can be explained due to the fact that, the higher the combustion temperature, the more combustion products are at equilibrium. This is actually due to the fact that some of the species, Table 3. Effect of pressure on flame temperature and composition for propane–air mixture ( = 1). Pressure 1 atm 3 atm 5 atm 7 atm 9 atm Adiabatic flame temp. (K) YCO2 YCO YH2O YH2 YO2 YO YOH YH 3064 0.1358 0.1995 0.3108 0.0628 0.0967 0.0478 0.0946 0.0522 3209 0.1421 0.1976 0.3229 0.0597 0.0941 0.0427 0.0969 0.0440 3280 0.1457 0.1963 0.3289 0.0581 0.0928 0.0403 0.0976 0.0403 3327 0.1482 0.1953 0.3330 0.0570 0.0918 0.0387 0.0979 0.0380 3363 0.1501 0.1943 0.3361 0.0561 0.0911 0.0375 0.0981 0.0363 2010 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. 2012; 7: 80–85 DOI: 10.1002/apj 83 84 F. F. TABRIZI, A. Z. SHARAK AND A. Z. SHAHRAK Asia-Pacific Journal of Chemical Engineering for instant radicals, have higher activation energy. So, by increasing the number of possible products in our calculation, the results would mimic the reality better. However, as the decomposition reactions are endothermic, increasing the number of combustion species enhances the decomposition reactions. This fact decreases the flame temperature in these conditions. The investigations showed that considering ten species for calculation is sufficient for the most required engineering accuracy and if we abandon the environmental considerations, the usual commonly reported species are those of listed in Table 2. Any further increase in the number of species will have a negligible effect on the final flame temperature calculations. It is obvious that for the environmental studies, where a small amount of a particular species is vital and even very small concentrations of that species can be crucial, that species must be included in the species list for calculations. Table 4 illustrates the effect of number of species on the final results for combustion of propane with air at a unit of equivalence ratio. at flame temperature above 1300 K. Because the flame temperature for most gases is above 2200 K, NO emission must be taken into account seriously for them. NO2 is another component of nitrogen oxides family. In fact, NO oxidizes to NO2 as the exhaust gases leave combustion chamber. This is due to the fact that the oxidizing reaction is more favorable at low temperature. The transformation of NO into NO2 actually begins within the combustor and in the zone with considerable available excess air. The allowable concentration of the NO2 and NO in the air are 0.15 and 5 ppm, respectively.[15] The other nitrogen oxides components are produced in a little concentration in the gaseous combustion reactions and can be neglected. Figures 3 and 4 show the effect of temperature on NO and NO2 mole fraction, respectively. As it can be seen from Figs 3 and 4, NO and NO2 emission passed from a climax. The reason behind this behavior can be interpreted as a result of the Environmental studies Using the above method for calculation of the equilibrium condition, it is possible to determine the concentration of the pollutants in combustion processes. Therefore, instead of performing very expensive and difficult experiments, it is most desirable to use mathematical simulation to determine the amount of pollutants exhausted in gaseous fuel combustion processes. Emission of NOx The family of nitrogen oxides (NOx ) has a critical role in the air pollution. The most important species of these types is nitrogen monoxide (NO). Experimental studies demonstrate that the NO emission became significant Figure 3. Effect of temperature on emission of NO for propane–air mixture. Table 4. Effect of number of species on the final results for propane–air mixture ( = 1 and P = 1 atm). Number of species Adiabatic flame temperature (K) YH2O YCO2 YN2 YCO YO2 YH2 YNO YO YOH YH N =3 N =7 N = 10 2324 2262 2247 0.1401 0.1111 0.7407 – – – – – – – 0.1583 0.1026 0.7215 0.0127 0.0057 0.0024 0.0027 – – – 0.1484 0.1028 0.7210 0.0124 0.0058 0.0033 0.0025 0.0003 0.0032 0.0005 2010 Curtin University of Technology and John Wiley & Sons, Ltd. Figure 4. Effect of temperature on emission of NO2 for propane–air mixture. Asia-Pac. J. Chem. Eng. 2012; 7: 80–85 DOI: 10.1002/apj Asia-Pacific Journal of Chemical Engineering NONLINEAR OPTIMIZATION APPROACH the reactants. However, in the equilibrium constant method, the reported maximum flame temperature is at = 1. • Increasing the pressure contributes to increase in the adiabatic flame temperature and CO2 emission, whereas, the emission rate of the carbon monoxide decreases. • Both NO and NO2 emission rates pass through a maximum point after T = 3000 ◦ C. So, for the conventional industrial combustion processes, it is reasonable to work at lower temperatures to reduce the NOx emissions. • Increasing the number of selected product’s species in the calculations decreases the maximum attainable flame temperature. Figure 5. Effect of equivalence ration on CO and NO emission for propane–air mixture. decomposition of NOx into the lighter products. As the flame temperature rarely reaches to the 3000 ◦ C, it is better to work at a lower temperature to reduce the nitrogen pollutants concentration in the products composition. Emission of CO Carbon monoxide is another combustion-generated pollutant. The effect of excess input air on the CO and NO emission for a propane–air mixture are shown in Fig. 5. It shows that increase in the equivalence ratio contributes to increase in emission of CO sharply, however, the emission of NO passes through a maximum around ϕ = 0.7. The optimum equivalence ratio of air can be therefore determined using this figure to minimize the NO–CO emission. CONCLUSION In this paper a nonlinear optimization method has been used for the calculation of equilibrium temperature and composition of the exhausted gaseous mixture. The results are in good agreement with published data. The effects of various parameters have been scrutinized. The conclusions summarized below shows the main findings of this paper: • For normal paraffins, maximum flame temperature occurs around = 1.05. This is due to the fact that the overall heat capacity of the products is lower than 2010 Curtin University of Technology and John Wiley & Sons, Ltd. It is also possible to use this program to simulate the pollutant emission, and particularly to optimize the air/fuel ratio and minimize the concentration of different types of pollutants. REFERENCES [1] BP statistical review of world energy, http://www.bp.com/ productlanding.do?categoryId=6929&contentId=7044622 (16 July 2010). [2] Y. Sofyan, A.J. Ghaja, K.A.M. Gasem. Ind. Eng. Chem. Res., 2003; 42, 3786–3801. [3] S. Chaikunchuensakun, L.I. Stiel. Ind. Eng. Chem. Res., 2002; 41, 4132–4140. [4] A. Parishan Naddaf, N. Omidkhah, R. Mohammad. J. Iranian Chem. Chem. Eng., 2006; 1. [5] L. Yeow Peng, R. Gade Pandu, L. Rein. Comput. Chem. Eng., 1999; 23, 1183–1191. [6] N. Dan Vladimir, S. Gomez, E. Luna. 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