Chapter 3 Thermochemstry of Fuel Ar Mxtures 3-1 Thermochemstry 3- Ideal Gas Model 3-3 Composton of Ar and Fuels 3-4 Combuston Stochometry t 3-5 The1 st Law of Thermodynamcs and Combuston 3-6 Thermal converson effcency 3-7 Chemcally eactng Gas Mxtures 1
The composton and thermodynamc propertes of the pre- and postcombuston workng fluds n engnes The energy changes assocated wth the combuston processes
An deal gas exhbts certan theoretcal propertes. Specfcally, an deal gas Does not condense nto a lqud when cooled. Shows perfectly straght lnes when ts V vs. T & vs. T relatonshps are plotted on a graph. In realty, there are no gases that ft ths defnton perfectly. We assume that gases are deal to smplfy our calculatons. If temperature s not too low or pressure not to hgh, the deal gas model can be appled.
Gas speces (workng fluds n engnes (e.g., O, N, fuel vapor, CO, water vapor, etc. may be treated as deal gases. pv mt m ~ M ~ T nt where m mass of gas gas constant (J/kg K n number of moles ~ Unversal gas constant 8.3143 J/mol K or 1,543.3 ft lbf/lb-mole M Molecular weght 4
Ar typcally contans about 1-3 percent by mass of vapor 5 % varaton from normal ar Normal Ar
TABLE 3.1 rncple consttuents of dry ar Gas ppm by volume Molecular weght Mole fractons Molar rato O 09,500 31.998 0.095 1 N 780,900 8.01 0.7905 3.773 A 9,300 38.948 CO 300 44.009 Ar 1,000,000 8.96 1.0000 4.773 6
Atmospherc Ntrogen ~ ~ M X M X M ar where Molecular weght of ar O O an X ~ s a mole fracton of gas wth respect to total number of mole of the mxture gas. M an ar ~ M ~ X O X an an M 8.96 0.095 31.998 1 0.095 O M an 8.16 7
TABLE 3- Molecular weghts 8
The fuels most commonly used n IC engnes are blends of many dfferent hydrocarbon compounds obtaned by refnng petroleum or crude ol. These fuels are predomnantly carbon and hydrogen though desel fuels can contan up to about 1 percent sulfur. Other fuels of t nterestt are alcohols, l gaseous fuels (natural gas and lquefed petroleum gas, and sngle hydrogen compounds (e.g., methane, propane, sooctane. 9
Substances contaned n a crude ol have dfferent bolng ponts, the substances n crude ol can be separated usng fractonal dstllaton. The crude ol s evaporated and ts vapours are allowed to condense at dfferent temperatures n the fractonatng column. Each fracton contans hydrocarbon molecules wth a smlar number of carbon atoms. 10
- araffns 11
1
13
- Olefns 14
- Alcohol What s the component of alcohol that dffers from other fuels? 15
elatonshps between composton of reactants (fuel and ar and composton of products For example, overall chemcal equaton for the complete combuston of one mole of propane C 3 H 8 : C 3 H 8 5 O 3 CO 4 H O 16
What mass of O s requred for the complete combuston of 8.58 gofc 4 H 10? C 4 H 10 13O --> 8CO 10H O 4 10 Moles of C 4 H 10 : Molecular weght 4 10 of C 4 H 10 moles of C 4 H 10 requre 13 moles of O 8.58 g 58.13 g/mol moles of C 4 H 10 requre 13 moles of O 0.1476 mole 4 10 0.1476 mol x (13/ 0.9595 mole O 0.9595 mol x 31.998 g/mol 30.7 g O Ans 17
Stochometrc Mxture of products contan CO, H O and N C b b b ( N 4 4 a H b a ( O 3.773N aco H O 3.773( a CH y Ar or y y y ( 1 ( O 3.773N CO H O 3.773 1 N 4 4 where y b a 18
CH y y y y ( 1 ( O 3.773N CO H O 3.773 1 N 4 4 The stochometrc ar/fuel or fuel/ar ratos A F s F A 1 s Molecular weght of ar A F s (1 y / 4(1 3.773 8.96 1.011 1.008y 34.56(4 y 1.011 1.008y 19
Fuel/ar equvalence rato φ elatve ar/fuel rato φ λ λ φ 1 ( F / ( F / A actual A ( A / F ( A/ s actual F s Fuel-lean mxtures Stochometrc mxtures φ < 1, λ > Fuel-rch mxtures φ > 1, λ < 1 1 φ λ 1 0
Examples of Stochometrc combuston equaton: Methyl alcohol (methanol CH 1 N 3OH.5( O 3.773N CO HO 5. 66 1.5(1 3.773 8.96 ( A / F s (1 3 16 1 6.47 Ar molecular weght Hydrogen Fuel H 0 N.5( O 3.773N HO 1. 887 ( A / F s 34.3 1
Hydrocarbon fuel of composton 84.1 percent by mass C and 15.9 percent by mass H has a molecular weght of 114.15. Determne the number of moles of ar requred for stochometrc combuston and the number of moles of products produced per mole of fuel. Calculate (A/F S and the molecular weght of the reactants and products. Assumng fuel chemcal formulaton s of the form C a H b, we have the relaton 114.15 1.011a 1.008b (1
From mass fracton, b a 15.9/1.008.55 ( 84.1/1.011 From equatons (1 and (, we obtan, a 8 and b18 Chemcal balance equaton C 8H18 1.5( O 3.773N 8CO 9HO 47. 16N 3
By mol: By mass: 1 1. 5(1 3. 773 8 9 47. 16 1 59.66 64. 16 Molecular weght of Ar 1 114.15 59.66 8.96 8 44.01 9 18.0 47.16 8. 16 Based on 1 kg of fuel: 114.15 177.8 184.3 (both sdes are equal 114.15 114.15 177.8 114.15 1 15.14 16.14 184.3 114.15 4
From the above equaton, 1 mol of fuel requres 59.66 mol of ar to get 65.16 mol of products. 15.14 ( A / F s 15.14 1 1 ( F / A s 0.0661 15.1414 Ans Ans Molecular weght of reactants ( M and molecular weght of products ( M are M M 1 1 nm (1 114.15 59.66 8.96 60.66 ntot 36 30. Ans 1 1 nm (8 44.01 9 18.1 47.16 8.16 n 64.16 tot 8.71 Ans 5
3.5 THE FIST LAW OF THEMODYNAMICS AND COMBUSTION 3.5.1 Energy and Enthalpy Balances eactants Combuston roducts System changng from reactants to products 6
The frst law of thermodynamcs: relatng changes n nternal energy (enthalpy to heat and work transfer nteracton Q W U U or U work transfer to the system, - work transfer from the system Combuston process Constant volume ntal and fnal temperature T ( W pdv 0 7
ΔU V,T T Q U U ( ΔU V, T U U < ( U < U 0 ( heat of reacton at constant volume at temperature T Constant pressure Q Q W p ( V V W W ( W W pdv U U U U 8
Q p V V Q ( U U Q U U p( V V Q U pv ( U p V ( H H ( Δ H H p, T ( p, T ΔH heat of reacton at constant pressure at T 9
or eactants roducts or or or Schematc plot of nternal energy (U or enthalpy (H of reactants and products as a functon of temperature 30
The dfference between From ( Δ H p, T and ( Δ U V, T h u pv <- Thermodynamcs ( H H ( U U Δ H p, T ( ΔU V, T (, T, T ( U pv ( U pv ( ΔU V, T therefore p ( V V ( U U ( ΔU V, T Δ H p, T ( ΔU V, T canceled out! ( p V V ( 31
If all the reactant and product speces are deal gases ~ ( ( n n T Δ H p, T ( ΔU V, T One of the products H O, can be n the gaseous or lqud phase. The nternal energy (or enthalpy of the products wll depend on the relatve proportons of water n gaseous or lqud phase. 3
Internal energy dfference between curves ( Δ U V, T, H Olq ( ΔU V, T H Ovap m H O u fgh O V, mh O mass of water n the products u fgh O nternal energy at T & p of the products The relatonshps appled for enthalpy ( ΔH ( Δ H m h p, T, H Olq p, T, H Ovap H O fgh O 33
eactants roducts Vapor Lqud eactants Vapor fuel roducts Lqud Fuel (a (b Schematc plots of nternal energy of reactants and products as a functon of temperature. (a Effect of water n products as ether vapor or lqud. (b Effect of fuel n reactants as ether vapor or lqud. 34
3.5. Enthalpes of Formaton Δh ~ f The enthalpy of formaton of a chemcal compound s the enthalpy ncrease assocated wth the reacton of formng one mole of the gven compound from ts element n the thermodynamcs standard [98.15 K(5 C, 1 atm] ο f roducts: H ο n Δ h products ~ ο f, eactants: H ο n Δh reactants ~ ο f, 35
ο ο T H H H Δ ( Δ Δ f f h n h n ~ ο ~ ο T p H H H Δ 0, ( r f f,, (enthalpy that ncreases from ( ( ( T V T V V p U H Δ Δ ( ( (,, T V T V V p U (already dscussed prevously ( y p y ( ( ( 0 0 T p T V V V p H U Δ Δ ( ( ( 0 0,, T p T V p The case of deal gas The case of deal gas 0 ( ~ ( ( 0 0 T n n H U T p T V Δ Δ 36 0,, ( ( ( 0 0 T p T V
TABLE 3. Standard enthalpes of formaton (5 C, 1 atm Speces State ο Δh ~ f O Gas 0 N Gas 0 H Gas 0 C Gas 0 CO Gas -393.5 H O Gas -41.83 H O Lqud -85.84 CO Gas -110.54 CH 4 Gas -74.87 C 3 H 8 Gas -103.85 CH 3 OH Gas -01.17 CH 3 OH Lqud -38.58 C 8 H 18 Gas -08.45 C 8 H 18 Lqud -49.35 MJ/kmol 37
3.5.3 Heatng Values Q HV Heatng value of a fuel s a magntude of heat of reacton that s measured drectly at a standard temperature (5 C or 77 F for complete combuston of unt mass of ffuel. eacton at constant pressure Q HV ( Δ H p, T 0 eacton at constant volume Q HVV ( ΔU V, T 0 38
Hgher heatng value (HHV H O formed n products s condensed to lqud phase Lower heatng value (LHV H O formed n products s n vapor phase 39
HHV and LHV are related by Q (constant pressure HHV m H O Q LHV ( h fg H p p m f O (constant volume Q HHV m H O Q LHV ( u fg H v v m f O mh O m f : rato of mass of H O produced to mass of fuel burned 40
Heatng values of fuels are measure n calormeter For gaseous fuels, usng contnuous-flow atmosphere pressure calormeter. An enterng fuel s saturated wth water vapor and mxed wth suffcent saturated ar for complete combuston at reference temperature. For lqud and sold fuels, fuel s burned wth oxygen under pressure at constant volume n a bomb calormeter. 41
Used for sold/lqud fuels Burnng under pressure at constant volume Obtan HHV 4
Example 3.Lqud kerosene fuel of the heatng value, (determned d n a bomb b calormeter of 43. MJ/kg and average molar H/ C rato of s mxed wth the stochometrc t ar requrement at 98.15 KCl K. Calculate lt the enthalpy of the reactant mxture relatve to the datum of zero enthalpy for C, O, N and H at 98.15 K. N In bomb, const volume Q Δ ( U 43. MJ/kg HHV V, T { V 0 98.15 The combuston equaton per mole of C can be wrtten 3 CH ( O 3.77. N CO H O 5. 66 N 43
3 CH ( O 3.77. N CO H O 5. 660 N kmol 7.160 kmol 7.66 fuel ar kg 07.4 kg kmol kg 1 14 1.4 products The heatng value gven s at constant volume, ο ο (ΔH H p ( Δ U ο ( n p n T V, T ~ ο (ΔU V 43. MJ/kg ο (ΔH p can be obtaned, notng that the fuel s n the lqud phase: 3 43. 8.3143 10 (7.66 7.160 98.15 14 43. 0.09 43.1 MJ / kg fuel 44
The enthalpy of the products per klogram of mxture s found from the enthalpes of formaton (wth H O vapor: ~ H ο n Δh f, ο products ο H 1( 393.5 1( 41.83 1.4.87 MJ / kg ( ΔH ο ( ο ο ΔH p, T H H 0 ο ο ο H H (Δ H p ο MJ 14 kg fuel H.87 43.1. kg fuel 1.4 kg product Enthalpy of the reactants per klogram of mxture 0.145 MJ/kg product Ans 45
3 CH ( O 3.77. N CO H O 5. 660 N kmol 7.160 kmol 7.66 fuel ar kg 07.4 kg kmol kg 1 14 1.4 products The heatng value gven s at constant volume, ο ο (ΔH H p ( Δ U ο ( n p n T V, T ~ ο (ΔU V 43. MJ/kg ο (ΔH p can be obtaned, notng that the fuel s n the lqud phase: 14 98.15 1.4 1.4 3 43. 8.3143 10 (7.66 7.160.73 0.00570057.74 MJ / kg product 46
The enthalpy of the products per klogram of mxture s found from the enthalpes of formaton (wth H O vapor: ~ H ο n Δh f, ο products ο H ( ΔH ο 1( 393.5 1( 41.83 1.4.87 MJ / kg ( ο ο ΔH p, T H H 0 ο ο ο H H (Δ H p Enthalpy of the reactants per klogram of mxture ο H.87.74 0.146 MJ/kg product Ans 47
3.5.4 Adabatc Combuston rocess -> adabatc constant volume process adabatc constant t pressure process -> Constant volume -> ΔQ ΔW ΔU adabatc Δ Q pdv ΔU Δ { Q p( V V 1443 ΔU 0 0 ΔU 0 U U 0 48
or eactants roducts or Adabatc combuston process: constant-volume on U-T dagram and constant-pressure on H-T dagram 49
3.5.5 5 combuston effcency Control volume surroundng engne 50
Consder a mass m whch passes through the control Consder a mass m whch passes through the control volume, the net chemcal energy release due to combuston s combuston s [ ] Δ Δ ~ ~ ( ( ο ο f f A A h n h n m T H T H [ ], products,, reactants, ( ( f f A A where ο f h, ~ Δ enthalpy of formaton of speces f, py p 51
The combuston effcency η c The fracton of fuel energy suppled to the control volume around the engne whch s released by combuston η c m H ( T A H ( T A m Q f Q HV energy released due to combuston where HV s the amount of energy suppled to the control volume around the engne whch can be released by combuston Q f 5
Varaton of engne combuston effcency wth fuel/ar equvalence rato 53
3.6 Thermal converson effcency ηt Effcency whch relates the actual work per cycle to amount of fuel chemcal energy released n combuston process. η t Actual work per cycle Fuel chemcal energy release W η c c c t H Δ ( TA H ( TA (Δ H T ηc m f Q A HV W W Therefore η η η f c t Fuel converson effcency (seen before!! 54
Example 3.3 The brake fuel converson effcency s 0.3. The mechancal effcency s 0.8. The combuston effcency s 0.95. The heat losses to coolant and ol are 60 kw. The fuel chemcal energy enterng the engne per unt tme, s 190 kw. Whatpercentage ofths energy become? a brake work b frcton work c heat losses d Exhaust chemcal energy e Exhaust sensble energy Analyss: Fuel chemcal energy per unt tme b (1 frcton ( heat loss (3 Exhaust energy chemcal sensble (4 (5 55
a From η f, b b m& f Q HV b 0.3 190 57 kw 30% Ans b From η m b b g b f 0.8 57 57 f f 14.5 kw 14.5 100 7.5% Ans 190 56
c Heat loss 60 kw d Exhaust chemcal energy due to combuston neffcency 60 100 31.6% Ans 190 ( 1 η m& c Fuel chemcal energy f Q HV ( 1 0.94 190 11.4 190 100 6% 11.4 kw e Exhaust sensble energy 190 - (a b c d 190 57 14.5 60 11.4 47.35 kw 47.35 100 4.9% 190 Ans 57
3.7 CHEMICALLY EACTING GAS MIXTUES Dependng on problem and porton of engne cycle, chemcal reacton may: 1 to be very slow -> neglgble effect on mxture composton (frozen toberapd -> the composton remans n chemcal equlbrum 3 rate-controllng -> determne how composton changes wth tme 58
3.7.1 Chemcal Equlbrum The chemcal reacton by whch ndvdual speces n the burned gases react together,,produce and remove speces at equal rates. 1 CO O CO Consder a system undergong a constant-pressure, constant temperature process. In the absence of work transfer, the frst law gves 1 st Law ΔQ ΔH nd Law ΔQ TΔS Δ1443 H TΔS ΔG 0 ( ΔG G or p, T 0 59
Thus reactons can occur f Gbbs free energy At equlbrum, ( ΔG p, T 0 G < G or G G Consder general reacton whose stochometry s gven by υ M a a υbm b l l m m... υ M υ M... The mxture composton n equlbrum can be determned by equlbrum constant, t K ln Δ G K ~ T ο 60
υ M a a υ M... υ M υ M... b b l l m m The equlbrum constant for a specfc reacton s obtaned va the relaton reacton log K log10( K 10( reacton ν ( K equlbrum constant of reacton ( K equlbrum constant of formaton of speces ν stochometrc coeffcents ostve ( for product speces Negatve (- for reactant speces 61
1 Ex CO O CO reacton r 1 at,500 K K log ( K 10 p reacton r1 ν log 10 ( K 1 1log ( K CO 10 1log ( log ( 10 K CO K 10 O can also be obtaned from partal pressure K ν ν1 ν ν 3 p p p p ->... p 0 p0 p0 p0 Π multplcaton p partal pressure of speces 6
where e K p p ( % χ ( % χ p p ν ν ν p ~ 0 0 χ mole fracton p 0 standard state pressure If ν 0, K ~ χ An equlbrum constant, K c c ν gmole cm 3 K (, based on concentratons [ M ] ν elaton between K Hence f K & K C K ~ ν ( T ~ C 0, ν p K ; -> unversal gas const K C 63
Example 3.4 In fuel-rch combuston product mxtures, equlbrum between the speces CO, H OCOand O, H s often assumed to determne the burned gas composton. For φ 1., for C 8 H 18 -ar combuston products, determne the mole fractons of product speces at 1,700 K Analyss: The reacton relatng these speces often called the water gas reacton. CO H CO H O 64
Queston What s the chemcal equaton for a stochometrc combuston of C 8 H 18? C 8H18 1.5(O 3.773N 8CO 9HO 47.16N emember that these gases are the products for stochometrc combuston!! The combuston of C 8 H 18 wth ar for φ 1. can be wrtten as 1.5 C 8 H18 ( O 3.773 N aco bh O cco dh 3930 39. 30 N 1. 65
A carbon balance: c 8 A hydrogen balance: d 18 a ( b (3 A oxygen balance: b c 0. 83 a (4 Combuston products are n chemcal equlbrum. CO H CO H O Ths chemcal reacton s called water gas reacton. At 1,700 K, log 10 K 0.510 K 3. 36 K The equlbrum relaton then gves K p p ( % χ ( % χ ν ν p ν p 0 p 0 (5 66
What s K p for ths reacton? p CO H CO H O In ths case, ν? ν 1 1 1 1 0 Thus K p 0 p ( ν ν χ p % 0 K ~ ν χ 67
K CO H CO H O ~ χ ν ~ χ 1 CO 1.5 C 8 H18 ( O 3.773 N aco bh O cco dh 3930 39. 30 N 1. ~ χ 1 H ~ χ 1 CO ~ χ 1 H O ~χ CO a b ~χ H O ~ c d χ CO ~χ H n n n n n p a b c d 39.30 Therefore K p c n a n b n d n 68
K p c n a n b n d n cb 3.36 (6 ad From the equatons (, (3, (4 and (6 we can solve for a 5.14, b 7.69, c.86, d 1.31 n p a b c d 39.3030 5.14 7.69.86 1.31 56.30 39.30 69
Mole fractons of products become ~ χ ~ χ ~ χ ~ χ CO H CO H a 5.14 56.30 b n n 7.69 56.30 O n c n d n.86 56.30 1.31 56.30 0.137 0.051 0.03 0.091 Ans Ans Ans Ans ~ χ N 39.3030 56.30 0.698 Ans 70
For a chemcal reacton that s not n equlbrum, the processes are controlled by rates at whch the actual reactons occur. For a chemcal reacton ν M ν M ν M ν M a a b b c c d d The reacton rate n forward ( drecton: d dt [ M ] a d [ M ] c dt The reacton rate n backward ( - drecton: d dt [ M ] c d [ M ] dt a k k υ [ ] [ ] a υ M M b a b ν [ ] [ ] c ν M M d c d k and k - are the rate constants n forward and reverse drectons 71
The net rate of producton of products or removal of reactants: k ν [ ] [ ] [ ] [ ] a ν b ν M M k M c ν M d a b c d k E A Aexp T A: pre-exponental factor E A : actvaton energy At equlbrum, 0 k [ M ][ M ] k [ M ][ M ] a b ν c [ M c ] [ M d ] ν a [ M ] [ M ] ν c d equlbrum constant, based d k K on concentraton ν c b k M a M b (learned before!! 7
k f 1 N O NO N N O k f NO O eacton rates of NO and N d dt [ NO] k [ N ][ O] k [ N ][ ] f 1 f O d [ N ] k [ ][ ] [ ][ f 1 N O kf N O] dt 1443 consumed 73