Air Fuel Ratio It is expressed on a mass basis and defined as:
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1 Cemical Reactions Wen analyzing eacting systems, we need to conside te cemical intenal enegy, wic is te enegy associated wit te destuction and omation o cemical bonds between te atoms. Temodynamic analysis o eactive mixtues is imaily an extension o te inciles we ave leaned tus a; oweve, it is necessay to modiy te metods used to calculate seciic entaly, intenal enegy and entoy. Deinitions Fuel: any mateial tat can be buned to elease temal enegy. Most amilia uels ae ydocabons and ae denoted by te geneal omula o C n H m. Fo examle octane is C 8 H 18. Combustion: is a cemical eaction duing wic a uel is oxidized and a lage quantity o enegy is eleased. Te oxidize is oten ai. Reactants: ae te comonents tat exist beoe te eaction. Poducts: ae te comonents tat exist ate te eaction. Ignition temeatue: te minimum temeatue at wic a uel stats to bun. Dy ai is comosed o 0.9% O, 78.1%, 0.9% A, and small amounts o CO, He, e, H. In combustion analyses, A is teated as, and ote gases ae neglected. Ten dy ai can be aoximated as 1% O and 79% by mole numbes. 1 kmol O kmol = 4.76 kmol ai (0.79/0.1 = 3.76) ote: om te Amagat model, we know tat a mixtue at a known T and P (as is te case wit combustion eactions): ni Vi n V Teeoe, by exessing a mixtue in tems o te numbe o moles we ae also exessing it in tems o a volume action. Duing combustion, nitogen beaves as an inet gas and does not eact wit ote elements. Howeve; geatly aects te come o a combustion ocess, since it entes in lage quantities and at low temeatue, absobing otion o te cemical enegy eleased duing combustion. In most combustion ocesses, te moistue in ai and te H O tat oms duing combustion can be teated as an inet gas, like nitogen. It is imotant to edict te dewoint temeatue o te wate vao since te wate dolets oten combine wit te sulu dioxide (tat may be esent) oming suluic acid wic is igly coosive. Ai Fuel Ratio It is exessed on a mass basis and deined as: m AF m ai uel ai uel M M ai uel M ai kg / kmol M. Baami ESC 461 (S 11) Cemical Reactions 1
2 Wee is te numbe o moles and M is te mola mass. Teoetical (Stoiciometic) Ai Te minimum amount o ai needed o te comlete combustion o a uel is called te stoiciometic o teoetical ai. A combustion ocess is comlete i all te cabon in te uel buns to CO, all te ydogen buns to H O, and all te sulu (i any) buns to SO. Tat is, all te combustible comonents o a uel ae buned to comletion duing a comlete combustion ocess. Te ideal combustion ocess duing wic a uel is buned comletely wit stoiciometic ai is called teoetical (o stoiciometic) combustion. Fo examle, te teoetical combustion o metane is: CH wee C : H : O : : 4 a O b 1 c 4 b c a d 3.76a 3.76 bco ch O d Solving tese equations, te balanced cemical eaction is: O 3.76 CO H O 7. CH 4 5 Te amount o combustion ai is moles o oxygen lus x 3.76 moles o nitogen, giving a total o 9.5 moles o ai e mole o uel. Te ai uel (AF) atio o te above combustion on a mass basis is: AF kg ai / kg uel Tat means kg o ai is used to bun eac kilogam o metane. In actual combustion ocesses, it is common actice to use moe ai tan te stoiciometic amount to incease te cances o comlete combustion o to contol te temeatue o te combustion cambe. Te amount o ai in excess o te stoiciometic amount is called excess ai. Te amount o excess ai is usually exessed in tems o te stoiciometic ai as ecent excess ai o ecent teoetical ai. Fo examle 150% = 1.5 te teoetical ai. Also, it may be eeed to as 0% excess ai; i.e., 10% stoiciometic ai. Te amount o ai used in combustion ocesses is also exessed in tems o te equivalent atio: Equivalent atio AF AF actual teoetical 1 1 lean mixtue (excess ai) ic mixtue (not enoug ai) M. Baami ESC 461 (S 11) Cemical Reactions
3 Amounts o ai less tan te stoiciometic amount ae called deiciency o ai and oten exessed as ecent deiciency o ai. Entaly o Fomation Duing a cemical eaction, some cemical bonds tat bind te atoms into molecules ae boken, and new ones ae omed. Tus a ocess tat involves cemical eactions involves canges in cemical enegies, wic must be accounted o in an enegy balance. It is necessay to coose a common base as te eeence state and assign a value o zeo to te intenal enegy o entaly o a substance at tat state. Te cosen eeence is known as standad eeence state: 5 C and 1 atm. Poety values at te standad eeence state ae indicated by a suescit ( ), e.g. and u. Entaly o eaction, R : te dieence between te entaly o te oducts at a seciied state and te entaly o te eactants at te same state o a comlete eaction. Entaly o combustion, C : te amount o eat eleased duing a steady-low combustion ocess wen 1 kmol (o 1 kg) o uel is buned comletely at a seciied temeatue and essue R = C =H oducts - H eactants Entaly o omation, cemical comosition. : te entaly o a substance at a seciied state due to its We assign te entaly o omation all stable elements (suc as O,, H ) a value o zeo at te standad eeence state o 5 C and 1 atm. Conside te omation (buning) o CO om its elements at 1 atm duing a steady-low ocess: C + O CO Te entaly cange duing tis ocess was detemined to be 393,50 kj/kmol. Howeve; H eact = 0. Tus te entaly o omation o CO at standad eeence state is:, CO - 393,50 kj/kmol Te negative sign is due to te act tat cemical enegy is eleased (exotemic ocess) duing te omation o CO. Te ositive value indicates eat is absobed (endotemic ocess). See Table A-6 o te entaly o omation o cemical substances. Heating Value: is deined as te amount o eat eleased wen a uel is buned comletely in a steady-low ocess and te oducts ae etuned to te state o te eactants. Tat is te absolute value o te entaly o combustion o uel. Hige Heating Value (HHV): wen te wate in te oducts is in te liquid om. Lowe Heating Value (LHV): wen te wate in te oducts is in te vao om. M. Baami ESC 461 (S 11) Cemical Reactions 3
4 HHV LHV m kj kg uel / g H O HHV and LHV o common uels ae given in Table A-7. Fist Law Analysis o Reacting Systems 1) Steady-low System We exess te entaly in suc a om tat is elative to te standad eeence state and te cemical enegy tem aeas exlicitly. Tus it educes to te entaly o omation at te standad eeence state lus sensible entaly elative to a eeence state, i.e., 5 C and 1 atm: kj kmol Entaly / Wee te tem in te aenteses eesents te sensible entaly elative to te standad eeence state. Q Reactants Combustion cambe Poducts Fig.1: Te ist-law o eacting mixtues. Te ist-law o a cemically eacting steady-low system can be exessed as: Q in W in n Q W n Wee n and n eesent te molal low ates o te oducts and te eactants, esectively. O on a mole o uel basis: Q in W in Q W Wee and eesent te numbe o moles o te eactants and te oduct, esectively. Te ist-law can also be witten as: Q W H H kj kmol uel Wee H H od eact od eact / kj / kmol uel kj / kmol uel M. Baami ESC 461 (S 11) Cemical Reactions 4
5 Remembe tat te eat tanse to te system and wok done by te system ae consideed ositive quantities. ) Closed System Te enegy balance o a cemically eacting closed system can be exessed as: Q W = U od - U eact wee U eesents te intenal enegy. To avoid using anote oety te intenal enegy o omation- we use te deinition o entaly u = Pv. Tus, te ist-law becomes o closed systems: Q W Tem gas. Examle Pv Pv Pv is negligible o solids and liquids, and can be elaced by R u T assuming ideal Liquid oane (C 3 H 8 ) entes a combustion cambe at 5 C at a ate o 0.05 kg/min wee it mixed and buned wit 50% excess ai tat entes te combustion cambe at 7 C. An analysis o combustion cambe eveals tat all te ydogen in te uel buns to H O but only 90% o te cabon buns to CO wit te emaining 10% oming CO. I te exit temeatue o te combustion gases is 1500 K, detemine a) Te mass low ate o ai b) Te ate o eat tanse om te combustion cambe. Assumtions: Steady oeating condition Ai and te combustion gases ae ideal gases Kinetic and otential enegies ae negligible. Analysis: Te teoetical amount o ai is detemined om te stoiciometic eaction: C 3 H 8 + a t (O ) 3CO + 4 H O a t O balance gives a t = 3 + = 5 Ten te balanced equation o te actual combustion ocess wit 50% excess ai and some CO becomes (5 x 1.5 = 7.5): C 3 H (O ).7CO CO + 4 H O +.65 O + 8. a) te ai-uel atio o tis combustion ocess is: M. Baami ESC 461 (S 11) Cemical Reactions 5
6 m AF m tus; m ai ai uel AF 3kmol kmol9kg / kmol 1kg / kmol 4kmolkg / kmol m 1.18 kg ai / min uel 5.53 kg ai / kg uel b) Te eat tanse o tis steady-low combustion ocess is detemined om an enegy balance e unit mole o uel: Q Assuming te ai and te combustion oducts to be ideal gases, we ave = (T). Substance kj/kmol (Table A-6) 80 K 98 K 1500 K kj/kmol (Table A-18,19) kj/kmol C 3 H 8 (l) -118, O , ,073 H O (g) -41, ,999 CO -393, ,078 CO -110, ,517 ote tat: C H 3 8 l g g C H 3 8 kj/kmol Q = (1 kmol C 3 H 8 )[(-118, ) kj/kmol C 3 H 8 ] + (7.5 kmol O )[( ) kj/kmol O ] + (8. kmol ) [( ) kj/kmol ] (.7 kmol CO ) [(-393, ) kj/kmol CO ] (0.3 kmol CO) [(-110, , ) kj/kmol CO] (4 kmol H O)[(-41, , ) kj/kmol H O] (.65 kmol O )[(0 + 49,9 868) kj/kmol O ] (8. kmol )[(0 + 47, ) kj/kmol ] = 363,880 kj/kmol o C 3 H 8 = 363,880/44 = 870 kj/kg o C 3 H 8 Ten te ate o eat tanse o a mass low ate o 0.05 kg/min o oane becomes: Q mq 0.05kg / min870kj / kg 413.5kJ / min = 6.89 kw M. Baami ESC 461 (S 11) Cemical Reactions 6
7 Adiabatic Flame Temeatue Wen te combustion cambe is insulated (no eat loss to te suoundings), te temeatue o te oducts eaces a maximum wic is called te adiabatic lame o adiabatic combustion temeatue o te eaction. In combustion cambes, te igest temeatue to wic a mateial can be exosed is limited by metallugical consideation. Teeoe, te adiabatic lame temeatue is an imotant consideation in te design o combustion cambes, gas tubines, and nozzles. Te max temeatue can be contolled by adjusting te amount o excess ai wic seves as coolant. Q = 0 Ai Poducts Fuel T max Insulation Te adiabatic lame temeatue o a steady-low combustion ocess is detemined om an enegy balance wen Q = 0: H od H eact Te detemination o te adiabatic lame temeatue equies te use o an iteative tecnique suc as te one descibed below: An adiabatic temeatue (T adi ) is guessed. Ste 1: Calculate te H eact based on known values o T eact and T e. Ste : Calculate te H od based on te guessed value o T adi and T e. Ste 3: Reeat Ste, until H eact = H od. Te adiabatic lame temeatue o a uel is not unique; its value deends on: 1) Te state o te eactants ) Te degee o comletion o te eaction 3) Te amount o ai used. ote tat te adiabatic lame temeatue attains its maximum value wen comlete combustion occus wit te teoetical amount o ai (0% excess ai). Entoy Cange o Reacting Systems Te entoy balance o any system undegoes any ocess can be exessed as: M. Baami ESC 461 (S 11) Cemical Reactions 7
8 S S in et entoy tanse by eat and mass S gen S system Using quantities e unit mole o uel and taking ositive diection o eat tanse to te system; entoy balance becomes: Q T k k S gen S od S eact kj / K Fo an adiabatic ocess, we obtain: S gen S od S eact 0 It sould be noted tat o te entoy balance o a eacting system involves calculating te entoies o comonents (eactants and oducts) not te entoy canges. Tus, we need a common base o te entoy o all substances, as we did wit entaly. Te tid law o temodynamics ovides an absolute base o te entoy values o all substances. Accoding to te tid law o temodynamics, te entoy o a ue cystalline substance at absolute zeo temeatue is zeo. te entoy elative to tis datum (0 K) is called absolute entoy absolute entoy at 1 atm and temeatue T is denoted as s T s T s mass o e mole basis, o a e unit wile was only a unction o temeatue o ideal gases, we must account o te eects o bot T and P in entoy: T, P s T, P 0 Ru ln P P 0 Wee Ru = kj/kmol.k is te univesal gas constant. ote tat temeatue o a comonent is te same as te temeatue o te mixtue and te atial essue o a comonent is equal to te mixtue essue multilied by te mole action o te comonent: Ti Tmixtue Fo te comonent "i" Pi yi Pmixtue Fo te comonent i o an ideal-gas mixtue, tis elationsi can be witten as: s i i m T, P s T, P R ln kj / kmol K i i 0 u y P P 0 Wee P 0 = 1 atm, P i is te atial essue, y i is te mole action o te comonent, and P m is te total essue o te mixtue. M. Baami ESC 461 (S 11) Cemical Reactions 8
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