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

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ASIA-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. Comput. Chem. Eng.,
2002; 26, 1703–1724.
[7] T. Huiqing, K. Kuniyuki. Chem. Eng. J., 2005; 106, 261–267.
[8] S. Jarungthammachote, A. Dutta. Energy Conversion Manage., 2008; 49, 1345–1356.
[9] M. Zhou, J.E.D. Gauthier. Fuel, 1999; 78, 471–478.
[10] X. Gao, M. Zhang. NOx emissions of an opposed wall-fired
pulverized coal utility boiler. Asia-Pac. J. Chem. Eng., 5(3),
447–453.
[11] X. Wang, H. Tan, Y. Niu, E. Chen, T. Xu. Asia-Pac. J. Chem.
Eng., 2010; (DOI: 10.1002.apj.420).
[12] K.J. Hughes, A.S. Tomlin, V.A. Fupont, M. Pourkashian.
Faraday Discuss., 2001; 119, 337–352.
[13] R.H. Kalil, A. Sakhrieh, M. Hamdan, J. Asfar. Jordan J.
Mech. Ind. Eng., 2010; 4(1), 21–28.
[14] K. Kuan, Y. Kuo. Principles of Combustion, Wiley: 1986.
[15] I. Glassman. Combustion, Academic Press: 1977.
[16] A.G. Gaydon, H.G. Wolfhard. Flame, Their Structure, Radiation Temperature, 4th edn, Chapman & Hall: 1977.
[17] C. Ferguson. Internal Combustion Engine, Wiley: 1988.
[18] J.A. Barnard, J.N. Bradley. Flame and Combustion, 2nd ed,
Chapman & Hall: 1985.
[19] JANAF thermochemical tables, 2nd edn, 1971.
Asia-Pac. J. Chem. Eng. 2012; 7: 80–85
DOI: 10.1002/apj
85
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