Numerical Analysis of the Natural Gas Combustion Products

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1 Energy and Power Engneerng, 2012, 4, Publshed Onlne September 2012 (http://wwwscrporg/journal/epe) Numercal Analyss of the Natural Gas Combuston Products Fernando Rueda Martínez 1, Mguel Toledo Velázquez 1, Georgy Polupan 1, Juan Abugaber Francs 1, Gullermo Jarquín López 2, Celerno Reséndz Rosas 3, José Ángel Ortega errera 4 1 Researchng and Graduate Secton, Appled ydraulcs and Thermal Engneerng Laboratory, ESIME-IPN, Mexco Cty, Mexco 2 Researchng and Graduate Secton, ESIME Culhuacan-IPN, Mexco Cty, Mexco 3 Researchng and Graduate Secton, Pachuca Technologcal Insttute, Pachuca dalgo, Mexco 4 Researchng and Graduate Secton, Desgn Department, ESIME-IPN, Mexco Cty, Mexco Emal: Receved June 5, 2012; revsed July 8, 2012; accepted July 22, 2012 ABSTRACT The combuston ucts of fuels contanng the elements C,, O, N and S are calculated The methodology s based on the equatons obtaned n the stochometrc balance of atoms The adabatc flame temperature s determned consderng that the pressure of the boler furnace remans constant The scope of ths work s lmted to the analyss of natural gas (methane) wth molecular formula C 4 The methodology can, however, be employed for the calculaton of combuston ucts of a great varety of hydrocarbons under the establshed restrctons In the development of the methodology two cases are contemplated: Φ 1 (lean and stochometrc mxture) and Φ > 1 (rch mxture) In the frst case t s consdered that when the combuston s complete, the combuston ucts are O 2, 2 O, CO 2, N 2, SO 2, and the soluton follows drectly When the combuston s ncomplete, however, the ucts, O, N, 2, O, CO, NO, O 2, 2 O, CO 2, N 2 and SO 2 can be generated, accordng to Stephen R Turns (2000) When balances of atoms are performed, four conservaton equatons are obtaned, one for each of the C, O, and N elements An addtonal restrcton requres that the sum of the molar fractons of the ucts equals one mol Fnally, seven equlbrum constants, correspondng to the seven chemcal ons of combuston, are ntroduced All ths provdes a system of four nonlnear equatons whch s solved wth the Newton-Raphson method Keywords: Combuston Products; Adabatc Flame; Stochometrc Mxture 1 Introducton It was therefore decded here to develop a specfc purpose computatonal program for the calculaton of the combuston ucts of bolers burnng natural gas and fuel ol Informaton about computatonal codes that handle combuston problems are referenced n the lterature There s for example the one developed by Olkara and Borman [1], the CEC76 [2], developed by NASA and the powerful CEC86 [3] also from NASA (CEC stands for Chemcal Equlbrum Code) A more recent code reported n the lterature s the STANJAN developed by the Stanford Unversty n 1986 [4] All these codes are, as mentoned above, extensve and dffcult to obtan Ths motvated the development of the present methodology, mplemented as a computatonal program for the calculaton of the combuston ucts n bolers For ths specfc case the, composton of the natural gas s: 2 = 84%; C 4 = 802%; CO 4 = 05%; C 2 4 = 20%; C 2 6 = 45%; C 3 6 = 06%; C 3 8 = 03%; C 4 4 = 34% and S = 01% Ths data corresponds to the power plant named Jorge Luque, located n the State of Mexco, n Mexco In the course of development of the system of equatons the equvalence rato Φ s taken nto account as a varable whch can take dfferent values accordng to the fuel-ar ratos of the boler The contamnants (CO, SO 2, NO) are calculated These orgnate n the complete and ncomplete combuston of the fuel-ar mxture n chemcal equlbrum condtons Furthermore, the requred equlbrum constants are computed as functon of the temperature employng least squares polynomal fttng The data employed for the fttng s taken from the tables of thermo-chemcal propertes of JANAF (1985) The range of temperatures for the fttng polynomals s from 600 K to 4000 K 2 Methodology In the thermodynamcs of equlbrum, the mxng of fuel wth composton C n, m, O l, N k, S j (accordng to Davd R Lde [5]) wth ar, n an equvalence rato of, releases combuston ucts n a state of equlbrum at

2 354 F RUEDA MARTÍNEZ ET AL temperature T and pressure P The numbers n and m cannot be zero; l, k and j, on the other hand, could or could not be zero Furthermore, accordng to Stephen R Turn [6], twelve combuston ucts are formed when there s dssocaton due to hgh temperature The resultng combuston equaton for these elements s: (Equaton (1), below) The equvalence rato s commonly employed to quanttatvely ndcate f the fuel-ar mxture s rch, lean or stochometrc The equvalence rato s defned as: AF Stoch F A AF F A (2) Stoch Ths defnton shows that for rch fuel mxtures > 1 whle for lean fuel mxtures < 1; for a stochometrc mxture = 1 In many combuston applcatons, the equvalence rato s the most mportant factor for the determnaton of the system s effcency The values of 1 through 12 are the molar fractons of the combuston ucts; the value of 13, on the other hand, represents the number of moles of fuel requred to obtan one mol of combuston ucts Equaton (1) can be smplfed to obtan 13 nc m js ro2 rn 2 1 2O 3N 42 5O 6CO 7NO (3) O O CO N SO where n j l k r r 4 2 0; r 376 r0; r0 2 2 Performng a balance of atoms for each element of the fuel one obtans C :n (4) :m 2 2 (5) O:2r (6) N :2r 2 (7) S :j13 12 (8) An addtonal condton s mposed to the former system, namely that the sum of all molar fractons of the ucts must be equal to one mol That s 12 1 (9) 1 Atmospherc ar s an Oxygen and Ntrogen mxture wth slght quanttes of Carbon Anhydrous, Argon and Water Steam Its composton slghtly vares wth humdty and alttude When water steam presence s not consdered n atmospherc ar composton, t s known as dry ar Ths work consders the dry ar composton as follows 21% Oxygen and 79% Ntrogen Thus the 79% N 2 fracton refers to N 2, CO 2 and Ar mxture, whch s known as atmospherc Ntrogen That way, there s 021 mol of Oxygen and 079 mol of Ntrogen n each dry ar mol That s to say: 1DA = 021O N 2 Determnng the Adabatc Flame Temperature (Frst Law of the Thermodynamcs) The combuston ucts are determned for a pressure of one atmosphere and at the adabatc flame temperature For ths reason, the frst thng to do s to determne the temperature of the adabatc flame for complete methane s combuston Assumptons n the applcaton of the frst law of the thermodynamcs for the boler furnace (Fgure 1): 1) The control volume s fxed to the coordnate system; 2) The flud propertes at each pont wthn the control volume do not change wth tme; 3) The flud propertes are unform at all nlet and outlet flows; 4) There s only one nlet and one ext for the flud n the control volume consdered Thus, the frst law can be wrtten as h h (10) 0, T P T, P (11) The enthalpy of the ants s Nh Nfuelhfuel NO ho NN hn (12) ad kJ kmol dm 0, de cv cv 0 dt m e P dt m e P e Inlet, Q W Ext, e Fgure 1 Control volume for the statonary flow n the boler furnace n e Cn m Ol Nk Sj O2 376N2 O N O CO NO O O CO N SO (1)

3 F RUEDA MARTÍNEZ ET AL 355 The enthalpy of the ucts s Nh (13) N h c T f, p, ad Tad Tad Tad 298 Equatng wth, and solvng for T ad gves T K ad Once the adabatc flame temperature s determned the next step s to calculate the combuston ucts Below the flow dagram of computatonal FORTRAN program for complete combuston s presented START Φ = 01 C = 10 S = 00 N = 00 = 40 O = 00 n j r l r r0 2 k r' 376r m r 2 r ' 4 8 r13 025m13 n13 j m13 10 n r13 12 j13 SUM , 9, 10, 11, 12,, SUM COMB END 3 Results Sample solved example 1: Fuel: C 4; Equvalence rato : 10; Total pressure: 1 atm; Reactants temperature: 298 K; Adabatc flame temperature: K; Sample solved example 2: numercal soluton; Fuel: C 4 ; Equvalence rato : 110; Total pressure: 1 atm; Reactants temperature: 298 K; Adabatc flame temperature obtaned per teraton: 2195 K The results of the numercal soluton, Tables 1 and 2 above, were used n order to make some adjustments to the geometry and confguraton of a combuston gas turbne, Fgure 2, based on some qualtatve conclusons and quanttatve results obtaned from the theoretcal study of thermodynamcs, flud mechancs and chemcal knetcs appled to turbulent combuston phenomena order to optmze ts performance and reduce the gaseous pollutants Table 1 Results of the combuston ucts for Φ = 1 Results of the combuston ucts burnng natural gas at Φ = 10 X (O 2 ) E+000 X ( 2 O) X (CO 2 ) X (N 2 ) X (SO 2 ) X (COMB) E E E E E 002 SUM Table 2 Results of the combuston ucts for Φ = 110 X ( 2 ) X (CO) X (O 2 ) X (N 2 ) E E E E 001 X () E 002 X (O) E 003 X (N) X (O) X (NO) X ( 2 O) X (CO 2 ) X (SO 2 ) SUM E E E E E E E 001

4 356 F RUEDA MARTÍNEZ ET AL formaton rate The model that was taken as a startng pont s the tubular combuston chamber whch s located the Appled Thermal and ydraulcs Engneerng Laboratory (LABINTAP) of the Mechancal Engneerng School, Natonal Polytechnc Insttute The specfc objectve of these amendments s to mnmze the concentraton of unburned hydrocarbons, carbon monoxde and ntrogen oxdes n the combustor exhaust by reachng a unform temperature dstrbuton wthn t by adaptng the ar and fuel flow patterns, Fgure 3 In order to have a reference for comparson, only modfcatons were made n the flame tube of the chamber, leavng unchanged the case The geometry of the prmary zone nlet secton as well as the sze and layout of the dluton holes were changed and an annular confguraton was used for fuel njecton The proposed geometry for the camera was drawn usng the mesh generaton software GAMBIT The smulaton of ts operaton, as well as measurement of ts performance parameters were carred out usng the computatonal flow smulaton tool FLUENT The results of computer smulaton show that the geometry of the prmary zone, the nlet temperature and Fuel nlet Prmary ar Secondary ar Flame tube Tertary Injector Swrl vanes Combuston Mxture and dluton zone Zone Fgure 2 Schematc dagram of a contnuous combuston chamber ar Towards gas turbne Fgure 3 Temperature feld of the modfed prmary zone locaton of the fuel njector have a consderable nfluence on the performance parameters of the camera Wth these smple adjustments to the combuston chamber there was an effcency ncrease from 76% to 9999% whle the ntrc oxde levels were reduced from 105 to 12 ppm wth respect to the actual model 4 Conclusons The development of the equatons s based n balances from atom s conservaton, consderng that the chemcal composton of the fuel contans only the elements C,, O, N and S The ar s dry, contanng only ntrogen and oxygen Furthermore, for a complete combuston (Φ = 1) t s possble to get n the soluton a maxmum of fve ucts; for an ncomplete combuston (Φ = 110), on the other hand, up to twelve ucts can be present n the soluton The polynomals for the equlbrum constants as functon of the temperature were obtaned employng least squares fttng method The range of temperature for whch the polynomals are vald s 600 K through 4000 K n accordance wth the data of JANAF tables (1986) The molar fractons of the combuston ucts are obtaned for the adabatc flame temperature In order to compute the ucts the methodology s dvded n two parts: one s for 1 and the other for > 1 The developed methodology can be employed n the calculaton of the combuston ucts for dfferent values of the equvalence rato Φ Ths can be done for a great varety of hydrocarbons wth known molecular formulas and whch meet the establshed restrctons Ths methodology has been appled to engneerng n order to make some adjustments to the geometry and confguraton of a gas turbne combuston optmzng ts performance and reducng the gaseous pollutants formaton rate and mnmzng the concentraton of unburned hydrocarbons, carbon monoxde and ntrogen oxdes n the combustor exhaust by reachng a unform temperature dstrbuton wthn t by adaptng the ar and fuel flow patterns REFERENCES [1] M J Moran and N Shapro, Fundamentals of Engneerng Thermodynamcs, John Wley and Sons, New York, 2000 [2] J Mathews, Numercal Methods for Mathematcs, Scence and Engneerng, 2nd Edton, Prentce all, Englewood Clffs, 1992 [3] G Zrkel and E Berlnger, Understandng Fortran 77 and 90, PWS Publshng Company, Boston, 1994 [4] J Warnatz, U Maas and R W Dbble, Combuston Physcal and Chemcal Fundamentals, Modelng and Smulaton, Experments, Pollutant Formaton, 3rd Edton,

5 F RUEDA MARTÍNEZ ET AL 357 Sprnger-Verlang, Berlín edelberg, 2001 [6] S R Turns, An Introducton to Combustón Concepts [5] D R Lde, CRC andbook of Chemstry and Physcs, and Applcatons, 2nd Edton, McGraw ll, New York, 71st Edton, Nomenclature α Rato of oxygen contents to fuel contents, kmol/kmol f Nonlnear functons for the molar fractons Φ Equvalence rato for the fuel-ar mxture h Enthalpy per mol of ucts K p Equlbrum constants for partal pressures M Number of atoms of ydrogen n the molecule of fuel n Number of atoms of Carbon n the molecule of fuel l Number of atoms of Oxygen n the molecule of fuel k Number of atoms of Ntrogen n the molecule of fuel j Number of atoms of Sulfur n the molecule of fuel P Total pressure, Pa P Partal pressures of ucts, Pa T Temperature, K f A, j Coeffcents of the Jacoban matrx j T, j Dervatves of molar fractons j 1 Molar fracton of the monatomc hydrogen () ucts 2 Molar fracton of the monatomc oxygen (O) ucts 3 Molar fracton of the monatomc ntrogen (N) ucts 4 Molar fracton of the hydrogen ( 2 ) ucts 5 Molar fracton of the hydroxyl (O) ucts 6 Molar fracton of the carbon monoxde (CO) ucts 7 Molar fracton of the ntrogen oxdes (NO) ucts 8 Molar fracton of oxygen (O 2 ) n the ucts 9 Molar fracton of water vapor ( 2 O) n the ucts 10 Molar fracton of carbon doxde (CO 2 ) n the ucts 11 Molar fracton of ntrogen (N 2 ) n the ucts 12 Molar fracton of sulfur doxde (SO 2 ) n the ucts 13 Amount of moles of combustble to form one mol of ucts

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