CRANFIELD REPORT N O . S . M * E . 6
VLiLu.c;
BSL::.. ..-Kluyvorwscj 1 - DZL'T
CRANFIELD s SEP m
INSTITUTE OF TECHNOLOGY
CALCULATED ADIABATIC COMBUSTION TEMPERATURES
OF HYDROCARBON - AIR MIXTURES
by
Cranfield Institute of Technology
CALCULATED ADIABATIC COMBUSTION TEMPERATURES
OF HYDROCARBON-AIR MIXTURES
by
E.M. Goodger
M.Sc.(Eng.), Ph.D., M.I. Mech.E., M. Inst.F., M.I.E. Aust., A.F.R.Ae.S., F.Inst.Pet.
Summary
Manually calculated values of adiabatic combustion temperature are presented, using a slightly modified version of Penner's method, for the simple cases of non-dissociation, and of dissociation to CO, H and 0 only, for a wide range of gasseous-phase hydrocarbon compounds in stoichiometric admixture with air. The variations in combustion temperature with carbon number are found to match most closely those
of the reaction enthalpy plotted on a basis of unit mass of stoichiometric mixture. Non-dissociated and dissociated stoichiometric temperatures
are found to average out approximately to 2460 K and 2340 K respectively.
The effects of variations in mixture strength, initial reactant temperature, and reaction pressure are also investigated.
CALCULATED ADIABATIC COMBUSTION TEMPERATURES Ot" HYDROCARBON-AIR MIXTURES
P a g e No.
1. Introduction 1 2. The Hydrocarbons 1 3. Kinetic Equilibrium 3 4. Equilibrium Product Composition in Fuel-Air Combustion 4
Stoichiometric Mixture, No Dissociation 4 Fuel-Weak Mixture, No Dissociation 4 Fuel-Rich Mixture, Water-Gas Balance 5 General Mixture, With Dissociation to CO, H. and 0^ 5
5. Equilibrium Temperature in Adiabatic Combustion 6 6. The Itffluence of Fuel Type upon Equilibrium Combustion
Temperature 7 7. The Influence of Operating Parameters upon Equilibrium
Combustion Temperature 8
References 10 Appendix - Specimen Calculations of Equilibrium Product
Composition and Temperature 11 4.1
4.2 4.3 4.4
1. INTRODUCTION
The combustion of mixtures of hydrocarbon fuels with air is widely used for the transfer of both work and heat, and knowledge of the equilibrium temperature reached in the flame is a key factor in assessing the
performance of the fuel in the given application. For reference purposes, zero heat losses are assumed, hence the resulting temperature is a maximum value for each condition, and since constant pressure is widely used in chemical and some engine combustion processes, the results presented in this note are both adiabatic and isobaric.
Normally, calculations of this magnitude lend themselves to computer treatment, but if one or two cases only need to be considered, manual iteration may be more practicable, despite the need to solve both linear and non-linear equations simultaneously. As a preliminary exercise to the completion of an all-purpose computer programme, therefore, the manual method of Penner (ref. 1) has been developed and rationalised in order to permit the simple and relatively rapid calculation of the adiabatic equilibrium temperatures of a number of light hydrocarbons burning with air. The results are presented over ranges of fuel type, mixture strength, initial temperature and operating pressure.
2. THE HYDROCARBONS
Most commercial liquid fuels are blends of many different types of hydro-carbon derived from petroleum. Individual hydrohydro-carbons comprise members of various groups, or series, each member differing from other members
of the same series but having a general formula and structural characteristic in common (table 1). The main series range from the paraffins, represented by the general formula C H „ and having the maximum possible hydrogen content for any hydrocarbon, through the naphthenes and olefins, both C H. ,
n zn the acetylenes, C H» _„, and eventually the aromatics, with general formula of C H„ , in their single nuclear configuration. They hydrogen content falls further when benzene rings combine to form the polynuclear aromatics, for example, naphthalene, C H„ ,„(n=10), and anthracene, C H-
,-n 2,-n-12 ,-n 2,-n-18 (n>14).
Evaluating the carbon/hydrogen mass ratio of a hydrocarbon C H as follows: C/H = 12x/y (or, more accurately, as 12.Olx/1.008y)
gives a set of curves as in figure 1. With increase in carbon number (that is, the number of carbon atoms in the molecule), these curves show a general tendency towards a C/H mass ratio of 6, that is, to a common formula C H„ . The polynuclear aromatics are the exceptions, with an extensive increase in C/H mass ratio tending towards 20+. Note that the aliphatic alcohols (for example, methyl alcohol CH OH, ethyl alcohol C„H OH) lie on the paraffin curve.
Since the reaction enthalpy (the calorific value) of hydrogen is about four times that of carbon (see table 1), an increase in C/H mass ratio indicates, broadly, a lower reaction enthalpy, but this is dependent also upon the structure of the molecule and the strength of the internal bonds. In practice, an increase in C/H ratio is also associated with greater
tendencies to smoke formation, carbon deposition and flame radiation. The latter is necessary in a furnace, but undesirable in an engine combustion chamber.
-2-The enthalpy of formation of a molecule is the energy change that
accompanies the formation of the molecule from its constitutent elements at the standard conditions of 25 C (298.16K) and 1 atm. The enthalpy of reaction of a combustion process is therefore seen to be the difference between the enthalpies of formation of the products and the reactants,
thus:
AH° = J:AH° Products - ZAH° Reactants,
r f f ' where the superscript o indicates that the conditions are standard.
The sign convention in thermochemistry, as in thermodynamics, is for positive heat addition and negative heat rejection. Thus the desired heat release from combustion is a negative quantity. In fuel technology and engineering generally, however, heat released is viewed in the
positive sense, consequently the curves of reaction enthalpy (values from ref. 2) in figure 2A have been inverted, and these show rising molar values with increasing molecular size. The results for the five series of hydrocarbons considered, together with the alcohols, all lie within a narrow straight-line band. Plotting on a mass basis shows a similar narrow band, but with a slightly reducing trend as molecular size
increases, with the exception of the aromatics and alcohols which release less heat (due to their lower hydrogen content, and their oxygen content, respectively) and show an increase in heat release with molecular size.
3. KINETIC EQUILIBRIUM
Generally, the reaction temperature of hydrocarbon fuels with air exceeds the 2000 K level at which the product molecules become unstable and begin to dissociate back into their reactant form. Hence a dynamic equilibrium is envisaged at which the rate of forwards reaction (conbustion) is just equal to the rate of reverse reation (dissociation). Development of the kinetic theory of gases permits the calculation of these reaction rates in both directions, and thus of the proportion of reaction products in
equilibrium at any given temperature level. Once this has been established, the quantity of heat released by the partial combustion of the fuel-air reactants can be compared with the quantity of heat absorbed by the equilibrium mixture of products. By making such comparisons at selected temperature levels, the equilibrium temperature, T^,, is found, by
interpolation, at which these two heat quantities are indentical.
Reation rates are found by experiment to be directly proportional to the instantaneous concentrations of the reacting materials, raised to some power. Thus, in a reversible reaction such as:
A + B «ssste C,
the instantaneous rate of forward reaction after a given time period might be found by experiment to be in the following terms:
Forward r e a c t i o n r a t e °^ [AI [BJ
instantaneous molar concentration of reactant X, rate constant for the forward reaction.
the reverse reaction may well be found by experiment to be given where [xj =
and k = r Similarly,
in the form:
Reverse reaction rate • k IQ] wluMB k » rate constant for the reverse reaction.
K
At the dynamic equilibrium condition for any given temperature, the two rates are equal, hence
'^F W W -
^RW
where K' is known as the concentration equilibrium constant for the given reaction. In what follows, reaction products are located in the numerator of the equilibrium constant expressions, but it should be noted that
some authors use the reciprocal form, whereas others use a squared version, with combustion equations written in the form 2X + 0„ = 2 XO,
instead of the form X + i 0 = XO
Since, from Avogadro's principle, molar concentrations of gases are proportional to partial pressures;
P = partial pressure of material A = total pressure
A.
(
moles of A \ total moles/
Hence, the equilibrium condition can also be represented by;
P„ P P
A B
K, known as the partial pressure equilibium constant for the given
reaction. These are the values normally tabulated in the literature, hence the Avogadro correction of (pressure x mole ratio) is usually necessary to determine the molar concentrations.
With hydrocarbon fuels, generally, dissociation occurs with the
combustion of hydrogen to H O , and with the second, high-teraperature, stage of combustion of carbon from CO to C0„, thus:
H^ + i O^^^nSsH^O, and CO + iO^-s^sÜ CO^, leading to the following expressions for equilibrium:
K. = \ ^ . .
H O 1, for the association of H„ and 0 , and
P (P )^ «2 °2
P
K = CO
CO 2 , for the assocation of CO and 0 P (P )
CO "• 0^
Since both reactions are occurring together, the half mole of oxygen produced by dissociation of the mole of C0„ may be considered as the oxygen required by the mole of H„. Combination of the two combustion equations then gives:
-4-which is the water-gas reaction, leading to the water-gas reaction equilibrium constant: ^ C P P CO H^O ~p p CO2 H2
Since, in this case, the mathematical products of the powers of the pressure terms in the numerator and denominator are equal, the value of K^ is numerically equal to that of K A .
Further dissociation to radicals and atomic species is unlikely to be extensive at the relatively low temperatures of combustion of hydrocarbons with air, due to the massive proportion of diluent nitrogen.
4, EQUILIBRIUM PRODUCT COMPOSITION IN FUEL-AIR COMBUSTION
Once the type of fuel is known, the general formula C H and the C/H ^ y
ratio can be evaluated, together with the relative molecular mass given by 12x + y (or, more accurately, by 12.01x + l,008y). Atmospheric air is represented by a mixture of 0.789 mole N and 0.210 mole 0 , with a nitrogen/oxygen mole ratio of 3.76, and a mean value of relative
molecular mass (allowing for trace constituents) of 28.966. Consequently, (m) mole of. oxygen are contained in (4.76 m) mole of air. At any
given temperature, the use of published values of partial pressure equilibrium constants permits the derivation of the relative molar quantities of reactant and product coexisting in equilibrium. In what follows, all reactants and products are assumed to be in the gaseous phase.
4.1. STOICHIOMETRIC MIXTURE. NO DISSOCIATION
In this hypothetical case, which can be approached in practice only when the temperature is low and pressure high, fuel bums in air without dissociation, and the stoichiometric combustion equation is given by:
C H + m (0„ + 3.76 N„) + x C0_ + ('y/2) H„0 + (3.76 m ) N„.
x y s 2 2 2 ' ^ ' 2 si
Stoichiometric mole oxygen (per mole fuel) =* m = x + y/4
Stoichiometric fuel/air mass ratio =« (F/A) = 12.01 x + l.OOSy ^ 4.76 (28.966) m
s = 12.01 x + 1.008y
137.88 (x+ y/4)
Values of m and(F/A) for the lighter members of the various hydrocarbon s s
series are included in table 1.
4.2 FUEL-WEAK MIXTURE. NO DISSOCIATION
The value of m. is now in excess of m , resulting in unreacted oxygen as a product, and the combustion equation appears as follows:
C H + m (O- + 3.76 N_) =• x CO. + Cy/2)H„Ö + (m - x - y/4) 0„ +
x y 2 2 2 ' 2 2
(3.76m) N^
The fuel/air mass ratio = F/A = 12.01 x + 1.008 y 137.88m and the equivalence ratio » 0 =« F/A » m /m.
(F/A)^ «
4.3 FUEL-RICH MIXTURE. WATER-GAS BALANCE
The value of m is now less than m and, although dissociation to molecular oxygen is ignored here, some dissociation of products to fuel components, as
in the water-gas reaction, must be considered in order to determine the extent to which the carbon and hydrogen share the available oxygen at any given temp-temperature. The combustion equation therefore contains four unknowns, as follows:
C H + m(02 + 3.76 N^) = n^ CO2 + n2 H2O + n^ CO + n^ H2+ (3.76 m) N2
The four equations required for solution are provided as follows:
From carbon mole balance, n + n- = x From hydrogen mole balance, n„ + n, = y/2
From oxygen mole balance, 2 n^ + n„ + n„ • 2 m, thus, n^ + n_ = 2 m - X From water-gas reaction, KA " 3 2 - K^
"1 "4
At the given temperature, therefore the corresponding value of K^^ permits derivation of the equilibrium concentrations of all the products, as in the following procedure:
(a) At given temperature, read K^ from table 2.
(b) Assume value of n^ (slightly below stoichiometric value). (c) Evaluate n„, n. and n,.
2 3 4
(d) Evaluate (n n./n^n.) and compare with K^
(e) Repeat from (b) until equality.
4.4. GENERAL MIXTURE, WITH DISSOCIATION TO CO, H and 0
In the more general and realistic case where the fuel and air burn with dissociation to carbon monoxide and free hydrogen and oxygen, the following combustion equation, incorporating five unknowns, applies to all mixture r.Ttios: C H + m (0^ + 3.76 N„) = n, CO. + n„ H„0 + n„ CO + n, H„ + n^ 0„ + (3.76 m) N,,
x y 2 2 L z z /. J H z D z z In addition to the two equations provided by mole balances of carbon and
hydrogen, the oxygen mole balance equation is amended to:
2 n^ + n2 + n3 + 2^3 = 2 m,
and two further equations result from the dissociation of CO and H„0, as follows CO, P3 (P5) n^ (P n^/n^) and ^2!^
P4 (V
n^ (P n^/n^) where andP = total pressure of the mixture,
= total number of moles of products present.
Since both linear and non-linear equations are involved, solution follows by iteration, as in the following procedure:
(a) At given temperature, read K and K^ from table 2. (b) Assume (nj./n ) and evaluate (P n^/n )
(c) Evaluate n^/n^ - (P n^/n^)^ K^^ , and n2/n^ » (P n^/n^)^ K^^ ^ (d) Evaluate n, also (e) Evaluate n 1 + n^/n3
JIL
1 + n2/n^ and n, and n, X - n 3' y/2 - n^. 2 m - X - (n + n ) (f) Evaluate n and (n^/n^)compare with En = (3.76 m + I n - ) , where
j = 1 to 5.
(g) Repeat from (b) until equality.
5 EQUILIBRIUM TEMPERATURE IN ADIABATIC COMBUSTION
Solution of the above combustion equations at selected temperature levels permits the derivation of the equilibrium temperature, T (that is, the adiabatic flame temperature), since this is seen to represent a thermal balance between the enthalpy released by combustion of the reactants, and the rise in enthalpy of the resulting products. Hence:
Enthalpy released by reactants AH° A H ° | = En. Em. 1 where AH„
'AH! AH°1
Jenthalpy absorbed by products AH°
AH
m.
rise in sensible enthalpy from 298.16 K to T K T 298.16
(H"
-
H")_- (H°
o T o''298.16
standard enthalpy of combustion initial temperature of reactantt equilibrium temperature of products moles of reactant i
Since the standard enthalpy of combustion reaction is given by the difference in enthalpies of formation of the products and reactants, the thermal balance can be expressed in terms of total enthalpies (that is, formation plus sensible .ibove the standard condition of 298.16K and 1 atmosphere), as follows:
Total enthalpy of products - total enthalpy of reactants = EAH = 0 ,
where AH^ = standard enthalpy of formation.
that is. En. | AH";: + AHl f - Em. | AHX + AH°
o - . . . J? . . -L. Ji
0.
Total enthalpies for oxygen, mitrogen and the hydrocarbon combustion products are included in table 2.
The method of solution is to determine the product composition at two bracketing temperatures, and to test for EAH - 0, the equilibrium values of T , and henco of product composition, being found be linear interpolation between the values of EAH at the bracketing temperatures. The following procedure permits solution:
(a) At given temperature, determine product composition, as above.
(b) At same temperature, read all values of total enthalpy from table 2.
(c) Weight each value of total enthalpy from(b) with appropriate concentration from (a) , and check for EAH =• 0.
(d) Repeat from (a) with bracketing value of temperature.
(e) Determine (fi) T (and molar concentrations if required) by linear interpolation.
6. THE INFLUENCE OF FUEL TYPE UPON EQUILIBRIUM COMBUSTION TEMPERATURE
For stoichiometric mixtures with air, the equilibrium combustion temperature?, with their related product concentrations, have been calculated by the procedures outlined in the previous sections, for both dissociated and non-dissociated cases, at the standard initial temperature of 298.16K, and constant reaction pressure of 1 atm. The equilibrium combustion temperature is seen to be a function of both the heat released by the fuel-air mixture (the enthalpy of reaction) and the heat absorbed by the resulting products. The following comments can be made regarding the influence of fuel type upon these two parameters.
(A) Heat released by reactants. In broad terms, this would be expected to vary directly with the hydrogen content of the fuel, and therefore inversely with
C/H ratio. However, the total output of energy is influenced also by such factors as ring strain and resonance, and the results in figure 2A, plotted per unit mass of fuel, showed an almost unique reduction in reaction enthalpy with increase in carbon number. The reaction enthalpy released per unit mass of stoichiometric mixture, on the other hand, is also directly dependent upon the stoichiometric fuel/air mass ratio, and the reaction enthalpy mixture curves in figure 2B show a separation between the various fuel types, together with a general reduction as carbon number increases. The curves also show the lightest acetylenes to have the highest reaction enthalpy on a mixture mass basis.
(B) Heat absorbed by products. This is controlled entirely by the relative concentrations of the various combustion products, together with their
individual levels of specific heat capacity. The following values of specific heat capacity apply to the three major combustion products at a representative
temperature of 2500K: „^ , ^ ^^/ \ „ ^/ N
C02(g) CO(g) H20(g)
The carbon products are seen to have specific heat capacities less than half that of the hydrogen product, consequently the combustion temperature would be expected to vary directly with C/H ratio. The percent molar concentrations of CO and H.O resulting at the equilibrium temperatures of stoichiometric fuel-air mixtures are shown in table 3 and plotted in
figure 3. These indicate the trends expected from the variations in C/H ratio and, from the preponderance of C0„ over H„0 in the case of acetylene and of benzene, suggest that the equilibrium temperatures of these two fuels may be high.
The above discussion shows the overall relationship between equilibrium temperature and molecular structure to be rather complex, and its
prediction not necessarily straightforward. However, the calculated results presented in figures 4A and B permit the following conclusions:
i) In general, the non-dissociated values of equilibrium temperature tend to an average level of about 2460 K, and the dissociated values to about 2340 K, giving the approximate average relationship,
(D) T„<^ (N-D) T - 120 K.
(Spot calculations with more intensive dissociation to atomic 0 and H, and to the radicals OH and NO, show a further reduction in
(D) T of about 23 K, but the general trends of T with carbon number are, of course, unchanged).
ii) For most fuels shown, the trends of T values follo\^ broadly those of the reaction enthalpies plotted on a stoichiometric mixture mass basis (figure 2B). Exceptions include the aliphatic alcohols, which show a rising temperature with carbon number, and the
relative levels of the aromatic and olefin curves.
iii)The highest combustion temperatures are given by acetylene,C_H„, with stoichiometric values of (N-D) T = 2909 K, and (D) T = 2583 K.
Values are also included in figures 2B and 4 for the parent fuel elements hydrogen (gaseous) and carbon (as graphite).
In some cases where the hydrocarbon fuels normally exist in the liquid phase at the standard conditions, further calculations have been made
to allow for the latent heat of vaporisation (from ref. 4). These permit the following conclusion:
iv) Comparison of values of combustion temperature for fuels in the
liquid and gaseous phases show reductions in (D) T of the following order; Paraffins 47 K; Aliphatic Alcohols 60 K; Napthenes 10 K; Olefins 11 K, Aromatics 58 K.
7, THE INFLUENCE OF OPERATING PARAMETERS UPON EQUILIBRIUM COMBUSTION TEMPERATURE.
It is of some interest to know the effects of such parameters as mixture strength, initial temperature and reaction pressure upon the resulting combustion temperature. Since methane is the simplest basic molecule in the whole hydrocarbon range, it has been adopted here as one of the representative fuels to illustrate the effects of these variables.
Furthermore, since a particular isomer of octane (2,2,4-trimethylpentane) is commonly used as an upper reference fuel in the performance rating
of commercial hydrocarbon fuels, it has been adopted here as a second representative fuel. These two fuels together permit some degree of interpolation and extrapolation.
The results presented in figures 5,6, and 7 lead to the following additional conclusions:
v) The maximum values of (D) T_ ate reached at about 3% and 5% fuel-rich for methane and iso-octane respectively, representing reductions from the maximum (N-D) T values at stoichiometric of
E
about 70 and 100 K respectively. (With further enrichment of fuel, a progressive reduction in (D) T would arise due to more extensive
E dissociation to graphite).
vi) For stoichiometric mixtures, rises of about 302 K in the initial temperature promote rises in (D) T of only about 167 K for both methane and iso-octane, due to the increased dissociation at the higher temperatures.
vii)For stoichiometric mixtures, rises in reaction pressure to 50 atm
promote rises in (D) T of 54K for methane, and of 70 K for iso-octane, E
1 0
-REFERENCES
1. Penner, S,S. Thermodynamics for Scientists and Engineers Addison-Wesley Publishing Co. 1968
2. Weast, R.C. (Ed) Handbook of Chemistry and Physics
45th. Edition. The Chemical Rubber Co. 1964-5
3. Mayhew, Y.R. & Thermodynamic and Transport Properties of Fluids Rogers, G.F.C. 2nd Edition. Basil Blackwell. 1970
4. Cox, J.D.&. Thermochemistry of Organic and Organometallie Pilcher, G. Compounds.
Academic Press. 1970.
5. Anderson, J.W., Natl. Petrol News, Tech. S e c , Beyer, G.H. & 36: R 476 (July 5, 1944)
APPENDIX
SPECIMEN CALCULATIONS OF EQUILIBRIUM PRODUCT COMPOSITION AND TEMPERATURE
The follo'!«7ing calculations are made using iso-octane (2,2,4-trimethylpentane), the initial conditions being standard, except where stated.
For iso-octane, stoichiometric mole of oxygen = m = x + y/4 =12.5
Stoichiometric fuel/air mass ratio = (F/A) » 12.01 x + 1.008 y = 0.0663 ^ 137.88 m
s Standard enthalpy of formation, AH , kj/mol
2,2,4-trimethylpentane (g) -224.2869
C02(g) -393.7761 CO(g) -110.5973 H20(g) -241.9882 02(g), N2(g), H2(g) 0
A.l. Stoichiometric Mixture, No Dissociation (see paragraph 4.1.)
The combustion equation (all gases) becomes:
iCgH^g + 12.5 (O2 + 3.76 N2) - 8 CO2 + 9 H2O + 47 N2
At a selected temperature of 2500 K, values of total enthalpy from table 2 give:
EAH° = 8 (-271.346) + 9 (-144,007) + 47 (74.3856) - (-224.2869) = 253,58 kJ/mol
At a selcted temperature of 2400 K, the corresponding value of EAH is -15.19 kJ/mol
A check at other values of temperature shows that linear interpolation of EAH is entirely acceptable over a wide range, hence
(N-D) T^ = 2400 +/ 15.19"^ 100 = 2406 K + / 15JL9^ \268.77/
A.2 Fuel-Weak Mixture. No Dissociation (see paragraph 4.2)
With,say, lOZ excess air, equivalence ratio = <() = m /m = 0.09091, and m = 13.75. The combustion equation becomes:
iC-H,„ + 13.75 (0„ + 3.76 N„) - 8 CO. + 9 H.O + 1.25 0„ + 51.7 N„
o i o Z / Z Z Z Z
At selected temperature of 2300 K, EAH° = 120.60 kJ/mol, and
at selected temperature of 2200 K, EAH » -167,59 kJ/mol, using methods similar to those in the previous paragraph.
By linear interpolation, (N-D) T_, = 2258 K,
A. 3 Fuel-Rich Mixture. Water-Gas Balance (see p.aragraph 4.3)
With, say, only 90% of the stoichiometric air, ^ - 1/0.9 = 1.111, and m = 11.25
-12-iCgH^g + 11.25 (O2 + 3.76 N2) = n^ CO2 + n2H20 + n CO + n H2 + 42.3 N2
l''our equations are required for solution: C balance gives n + n = x = 8
H balance gives n + n, = y/2 = 9
0„ balance gives n + n = 2 m - x = 14.5 Equilibrium constant gives K^„ = n„ n
^ ^
Following the procedure outline in paragraph 4.3 gives: a) Set T = 2400 K, then K^^ = 5 . 8 6 from table 2.
b) Assume n = 6 (that is, slightly below the stoichiometric value of 8) c) n2 = 14.5 - n = 8.5 n = 8 - n = 2 n, = 9 - n- = 0.5 4 Z d) n n -^-=- = 2 x 8 . 5 = 5 . 6 , whereas K,,^ = 5.86 n,n, -7 7--r WG 1 4 6 x 0 . 5
e) By trial and error to give n n„
n, n, ° \ G
1 4
n^ = 5.988; n2 = 8.512; n = 21012; n = 0.488, and EAH° = 237.45 kJ/mol Similarly, setting T = 2300 K, where K^ = 5.6068 gives:
n^ = 6.004; n2 = 8.496; n = 1.966; n = o.504, and EAH° = -7.68 kJ/mol
By linear interpolation, (N-D) T_ = 2303 K E
A.4 General Mixture, With Dissociation to CO, H and 0„ (see paragraph 4.4)
Although the following treatment applies to any mixture strength, as indicated in the paragraph heading, the stoichiometric case is considered here for implicity.
Thus, the combustion equation becomes:
iCgH^g + 1 2 . 5 (O2 + 3 . 7 6 N2) = n^ CO2 + n2 H2O + n^ CO + n^ H2 + ^ ^ 0 2 + 47 N, From C and H„ b a l a n c e s , n^ + n_ = 8 , and n„ + n , = 9 , as b e f o r e b u t
n = 2 m - x - (n^ + n „ ) = 17 - (n^ + n _ )
2 2
Total mole products = En = 64 + n
Following the procedure outline in paragraph 4.5 gives:
a) Set T = 2300 K, then K.. = 83.25, and K„ ^ = 466.77
b) Assume (n /n ) = 0.01, then (P n /n ) ^ = 0.1
8 = 0.8579, and n = 8 - n = 7.1421 1 + 8.325 ^ -^ 9 - 0.1888 , and n = 9 - n - 8.8112 1 + 46.677 ^ ^ 17 - (7.1421 + 8.8112) - 0.5234 2 "5 = 0.5234 = 52.34, whereas En = 64.5234, hence n / En (n^/n^) 0.01
By trial and error, n^^/n = 0.00865 is found to give n = En, hence:
n^ = 7.085; n2 = 8.797; n^ = 0.915; n^ = 0.203; n^ = 0.559, and J;AH° = 21.029 kJ/mol Similarly, setting T = 2200 K gives n /n = 0.00568, together with
n^ = 7.4077; n2 = 8.862; n^ - 0.593; n^ = 0.138; n - 0.366, and EAH° = -350.257 kJ/mol
By linear interpolation, (D) T_ " 2294 K E
The equilibrium concentrations of products can also be found by linear interpolation between these two sets of values.
Values of T over a range of equivalence ratio are shown in table 4 for methane and iso-octane.
Table 4. Miaifture Results for Methane and Iso-Octane (K)
* 0.7692 0.8000 0.8333 0.8696 0.9091 0.9524 1 1.0526 1.1111 1.1765 1.25 1.-3333 1.42.86 (N-D)Tg 2330
CH^
(D) Tg 2213 2247 2253 2221 2,2,4-trimethylpentane (N-D) Tg (D) Tg 2019 2013 2073 2065 2131 2115 2192 2166 2258 2216 2329 2260 2406 2295 2357 2308 2303 2290 2242 2239 2182 2112 2036A.5 General Mixture. With Dissociation, at Non-Standard Initial Temperature
Using the stoichiometric mixture of iso-octane and air, as before, the combustion and mass balance equations appear as in the previous paragraph, together with the product compositions at each selected temperature. However, the total enthalpies of the reactants now include terms for the rise in
sensible heat from the standard temperature of 298.16 K to the new initial temperatures of 400, 500 and 600 K respectively. For atmospheric oxygen
-14-and nitrogen, -14-and for methane, these values of sensible heat are
included in ref. 1. For iso-octane, the corresponding rises in sensible heat have been found here from values of specific heat opacity, in terms of
2 3
c = a T + b T + c T , estimated by the additive-group method of Anderson, Beyer and Watson, (ref. 5).
The results are as follows:
Table 5. Results with Variable Initial Temperature
T^ K i 2 9 8 . 1 6 400 500 600
°2
0 3 . 0 2 5 4 6 . 0 8 9 3 9 . 2 5 0 3 T o t a l ^ 2 0 2 . 9 7 3 0 5 . 9 1 4 7 8 . 8 9 9 9 E n t h a l p i e s , k J / m o l ^ \ ^ ^ « 1 8 - 7 4 . 9 8 7 7 - 2 2 4 . 2 8 6 9 - 7 1 . 0 2 0 7 - 2 0 0 . 4 8 6 2 - 6 6 . 6 5 8 1 - 1 7 2 . 1 4 9 5 - 6 1 . 7 0 0 9 - 1 3 9 . 4 5 3 1 (D) ' \ 2247 2301 2356 2413^E ^ 1
iS«18
2294 2349 2904 2461A,6 General Mixture. With Dissociation, at Non-Standard Reaction Pressure ,,..•• , . 1 1 • • I i i. f . I , 1 .
Using the stoichiometric mixture of iso-octane and air, as before, the combustion and mass balance equations appear as in the two previous paragraphs, but the product compositions at the selected temperatures differ due to the different values of P in the term (P n./n )i.
Following the procedure outlined in paragraph 4,4 for the 25 atm cases gives:
a) Set T = 2300 K, then K = 83,25, and K^ ^ = 466.77
b) Assume (n /n ) = 0.003, then (P n /n )
i
0.2739. c) n /n = (0.2739) 83.25 = 22.8022, and n2/n^ = 127.8483 d) n, 8 1 + 22.8022 9 1 + 127.848 0.3361, and n r^ 8 - n = 7.6639 0.0698, and n e) n = 17 - (7.6639 + 8.9302) ^ 2 2 0.2030 9 - n, = 8.9302 4 f) n, "T/"5 0.2030 0.0030 - 67.6583, whereas En = 64.2030By trial and error, n /n = 0.00311 is found to give n = En, and EAH = -174.3686 kJ/mol. Similarly, at T = 2400K, EAH° = 143.6982 kJ/mol. By linear interpolation, (D) T = 2355 K. The results are as follows:
Table 6. Results with Variable Reaction Pressure P atm
1
10 25 50 CH, 4 2247 2284 2295 2301^Vl8
2294 2341 2355 2364TABLE 1^ THERMOCHEMICAL DATA FOR HYDROCARBON FUELS (GASEOUS P H A S E )
hx«y
C H ^ S»6 S"8 S»10 S«12hh'.
S"l6 S«18 S"20 ^ l o " 2 2 S l » 2 4 S » 6h4"8
S«10 V l 2 S»14 \ ' 2 \ S«6h4»8
S»10 NAME P A R A F F I N S (ALKAUES) M e t h a n e E t h a n e P r o p a n e B u t a n e P e n t a n e Hexane Hep t a n e Oc t a n e Nonane Decane U n d e c a n e NAPHTHENES (CYCLANES) C y c l o p r o p a n e C y c l o b u t a n e C ^ c l o p e n t a n e C y c l o h e x a n e C y c l o h e p t a n e OLEFINS (ALKENES) E t h y l e n e ( E t h e n e ) Fropene I - B u t e n e 1 - P e n t e n e C/H MASS ( A p p r o x ) 3 4 4 . 5 4 . 8 5 5 . 1 4 5 . 2 5 5 . 3 3 5 . 4 5 . 4 5 5 . 5 6 6 6 6 6 6 6 6 f) R.M.M. 1 6 . 0 4 2 3 0 . 0 6 8 4 4 . 0 9 4 5 8 . 1 2 0 7 2 . 1 4 6 8 6 . 1 7 2 1 0 0 . 1 9 8 1 1 4 . 2 2 4 1 2 8 . 2 5 0 1 4 2 . 2 7 6 1 5 6 . 3 0 2 4 2 . 0 7 8 5 6 . 1 0 4 7 0 . 1 3 0 8 4 . 1 5 6 9 8 . 1 8 2 2 8 . 0 5 2 4 2 . 0 7 8 5 6 . 1 0 4 7 0 . 1 3 0 s 2 3 . 5 5 6 . 5 8 9 . 5 1 1 1 2 . 5 14 1 5 . 5 17 4 . 5 6 7,5 9 1 0 . 5 ' 3 4 . 5 6 7 . 5 ( F / A ) ^ 0 . 0 5 8 1 7 0 . 0 6 2 3 1 0 . 0 6 3 9 6 0 . 0 6 4 8 5 0 . 0 6 5 4 1 0 . 0 6 5 7 9 0 . 0 6 6 0 6 0 . 0 6 6 2 7 0 . 0 6 6 4 4 0 . 0 6 6 5 7 0 . 0 6 6 6 8 0 . 0 6 7 8 2 0 . 0 6 7 8 2 0 , 0 6 7 8 2 0 . 0 6 7 8 2 0 . 0 6 7 8 2 0 . 0 6 7 8 2 0 , 0 6 7 8 2 [ 0 . 0 6 7 8 2 0 . 0 6 7 8 2 AH° ! k J / m o l - 7 4 . 8 9 7 7 - 8 4 . 7 2 4 1 - 1 0 3 . 9 1 6 4 - 1 2 4 . 8 1 6 9 - 1 4 6 . 5 3 8 0 - 1 6 7 . 3 0 4 5 - 1 8 7 . 9 4 5 5 - 2 0 8 . 5 8 6 4 - 2 2 9 . 1 8 5 4 - 2 4 9 . 8 2 6 4 - 2 7 4 . 6 5 4 1 - 7 7 . 2 8 8 3 - 1 2 3 . 2 1 7 5 5 2 . 3 1 8 3 2 0 . 4 2 7 4 1 . 1 7 2 3 - 2 0 . 9 3 4 0 -M J / B O I 0 . 8 0 2 9 1 . 4 2 8 8 2 . 0 4 5 4 2 . 6 6 0 2 3 . 2 7 4 3 3 . 8 8 9 3 4 . 5 0 4 4 5 . 1 1 9 5 5 . 7 3 4 7 6 . 3 4 9 8 6 . 9 6 0 7 3.1015 3 . 6 9 1 4 1 . 3 2 3 8 1 . 9 2 7 7 2 . 5 4 4 2 3 . 1 5 7 9 AH° r MJ/kg 5 0 . 0 4 7 1 4 7 . 5 1 8 7 4 6 . 3 8 6 5 4 5 . 7 7 1 3 4 5 . 3 8 4 0 4 5 . 1 3 3 8 4 4 . 9 5 4 9 4 4 . 8 2 0 0 4 4 . 7 1 4 9 4 4 . 6 3 0 2 4 4 . 5 3 3 9 4 4 . 2 2 5 5 4 3 . 8 6 3 4 4 7 . 1 9 2 6 4 5 . 8 1 3 0 4 5 . 3 4 8 5 4 5 . 0 2 9 1 r DISSOCIATED " 5 / n , 0 . 0 0 6 4 3 0 . 0 0 7 7 5 0 . 0 0 8 1 4 0 . 0 0 8 3 2 0 . 0 0 8 4 2 0 . 0 0 8 5 1 0 . 0 0 8 4 9 0 . 0 0 8 6 8 0 . 0 1 1 1 6 0 . 0 1 0 6 5 0 . 0 0 9 4 0 0 . 0 0 8 9 9 0 . 0 1 2 7 0 0 . 0 1 1 1 6 0 . 0 1 0 6 5 0 . 0 0 9 4 0 STOICHIOMETRIC (K) (N-D) Tg 2 3 3 0 2 3 8 3 2396 2402 2405 2 4 0 8 2 4 1 0 2411 2413 2 4 1 4 2 4 1 3 2439 2 4 2 3 2 5 6 8 2 5 0 8 2480 2 4 7 1 ( D ) T ^ 2247 2282 2289 2 2 9 3 2295 2296 2299 2300 2310 2305 2420 2362 2348 2339C H X y V l 2 S»14 S»16 S»18 So«20 ' ^ l l ' ' 2 2 S2"24 S«2 C3H4 ^ih S"8 ^ 6 » 1 0 S«12 S»14 S»16 '^10«18 ^ 6 » 6 ^ 7 » 8 S«10 NAie 1 - Hexene 1 - H e p t e n e 1 - O c t e n e 1 - Nonene 1 - D e c e n e 1 - U n d e c e n e 1 - D o d e c e n e ACETYLENES ( A l k y n e s ) ' A c e t y l e n e ( E t h y n e ) P r o p y n e 1 - B u t y n e 1 - P e n t y n e I - Hexyne 1 - H e p t y n e 1 - O c t y n e 1 - Nbnyne 1 - Decyne AROMATICS B e n z e n e T o l u e n e X y l e n e ( a v e r a g e ) C/H MASS 6 6 6 6 6 6 6 12 9 8 7 . 5 7 . 2 7 6 . 8 6 6 . 7 5 6 . 6 7 12 1 0 . 5 9 . 6 R.M.M. 8 4 . 1 5 6 9 8 . 1 8 2 1 1 2 . 2 0 8 1 2 6 . 2 3 4 1 4 0 . 2 6 0 1 5 4 . 2 8 6 1 6 8 . 3 1 2 2 6 . 0 3 6 4 0 . 0 6 2 5 4 . 0 8 8 6 8 . 1 1 4 8 2 . 1 4 0 9 6 . 1 6 6 1 1 0 , 1 9 2 1 2 4 . 2 1 8 1 3 8 . 2 4 4 7 8 . 1 0 8 9 2 . 1 3 4 1 0 6 . 1 6 0 "% 9 1 0 . 5 12 1 3 . 5 15 1 6 . 5 18 2 . 5 4 5 . 5 7 8 , 5 10 1 1 . 5 13 1 4 . 5 7 . 5 9 1 0 . 5 ( F / A ) ^ 0 . 0 6 7 8 2 0 . 0 6 7 8 2 0 . 0 6 7 8 2 0 . 0 6 7 8 2 0 . 0 6 7 8 2 0 . 0 6 7 8 2 0 , 0 6 7 8 2 0 . 0 7 5 5 3 0 . 0 7 2 6 4 0 . 0 7 1 3 2 0 , 0 7 0 5 7 0 . 0 7 0 0 9 0 , 0 6 9 5 5 0 , 0 6 9 4 9 0 . 0 6 9 3 0 0 . 0 6 9 1 5 0 . 0 7 5 5 3 0 . 0 7 4 2 5 0 . 0 7 3 3 3 k J / m o l - 4 1 . 7 0 0 5 - 6 2 . 1 7 4 0 - 8 2 . 9 8 2 4 - 1 0 3 . 5 8 1 4 - 1 2 4 . 2 2 2 4 - 1 4 4 . 8 6 3 3 - 1 6 5 . 4 6 2 3 2 2 6 , 8 9 9 4 1 8 5 . 5 5 4 8 1 6 6 . 2 1 6 0 1 4 4 . 4 4 4 6 1 2 3 . 7 1 9 9 1 0 3 . 0 7 9 0 8 2 . 4 8 0 0 6 1 . 8 3 9 0 4 1 . 2 4 0 0 8 2 . 9 8 2 4 5 0 . 0 3 2 3 1 8 . 0 5 9 1 -AH° r _ . K I / B o l 3 . 7 7 2 9 4 . 3 8 8 2 5 . 0 0 3 1 5 . 6 1 8 3 6 . 2 3 3 4 6 , 8 4 8 5 7 . 4 6 3 7 1 . 2 5 6 4 1 , 8 5 0 9 2 . 4 6 7 3 3 . 0 8 1 3 3 , 6 9 6 3 4 . 3 1 1 4 4 , 9 2 6 6 5 . 5 4 1 7 6 , 1 5 6 9 3 . 1 7 1 6 3 . 7 7 4 4 4 . 3 7 8 0 MJ/kg 4 4 . 8 3 2 0 4 4 . 6 9 4 3 4 4 . 5 8 8 0 4 4 . 5 0 7 0 4 4 . 4 4 1 9 4 4 . 3 8 8 6 4 4 . 3 4 4 5 4 8 . 2 5 7 8 4 6 . 1 9 9 9 4 5 . 6 1 6 1 4 5 . 2 3 7 1 4 5 . 0 0 0 2 4 4 . 8 3 3 3 4 4 . 7 0 9 3 4 4 . 6 1 2 9 4 4 . 5 3 6 4 4 0 , 6 0 5 4 4 0 . 9 6 6 6 4 1 . 2 7 5 7 DISSOCIATED - 5 / n , 0 . 0 0 8 9 9 0 . 0 0 9 9 2 0 . 0 0 9 8 0 0 . 0 0 9 6 4 0 . 0 0 9 5 3 0 . 0 2 4 7 7 0 . 0 1 7 0 4 0 . 0 1 4 6 6 0 . 0 1 3 2 8 0 . 0 1 2 7 1 0 . 0 1 1 5 6 0 . 0 1 1 0 2 0 . 0 1 2 3 3 0 . 0 1 1 5 7 0 . 0 1 1 0 4 STOICHIOfBTRIC (K) (N-D)Tg 2 4 6 5 2 4 5 9 2 4 5 5 2 4 5 1 2 4 4 8 2 4 4 6 2 4 4 4 2 9 0 9 2 7 0 0 2 6 1 1 2 5 7 3 2 5 5 2 2 5 3 3 2 5 1 8 2 5 0 7 2 4 9 8 2 5 2 9 2504 2487 (D) Tg 2 3 3 3 2329 2 3 2 6 2322 2 3 1 9 2 5 8 3 2 4 7 6 2432 2 4 0 6 2394 2 3 6 6 2 3 5 4 2 3 6 6 2 3 4 8 2342
TABLE 1 . CONTINUED
C H
X y
NAME C/H MASS R.M.M. (F/A),
kJ/oDl -4H MJ/nol MJ/kg iTOKmiOMETRIC (K) DISSOCIATED "5/n, (N-D)T, (D) T„ ^10«8 CH-OH CjHjOH CjH^OH H2(8) C(8r) Naphthalene ALIPHATIC ALCOHOLS Methanol Ethanol Propanol PARENT ELEMENTS Hydrogen (gas) Carbon (graphite) 15 3 4 4 . 5 128.164 32.042 46.068 60.094 2.016 12,010 12 1.5 3 4.5 0 . 5 1 0.07746 0.15493 0.11137 0.09685 0.02924 0.08710 150.9341 -201.3013 -235.4656 -235.1066 0 0 5.0566 0.6765 1.2781 1.8932 0.2420 0.3938 39.4545 21.1114 27.7427 31.5036^ 120.0338 32.7873 0.01261 0.00725 0.00762 0.00804 0.01131 0.01120 2534 2335 2356 2377 2534 2458 2367 2243 2258 2273 2444 2309
(a) EQUILIBRIUM CONSTANTS (PARTIAL PRESSURE - atm)' TEMP K '^C02 \ ^ ^ G 2000 730.62 3.3931 xlO^ 4.6441 2100 330,00 1.6458 xlO"^ 4.9873 2200 165.69 852.12 5.1429 2300 83.250 466.77 5.6068 2400 45.814 268.47 5.8600 2500 26,443 161.27 6.0988 2750 7.2828 53.272 7.3148 3000 2.9451 20.999 7.1301
(b) TOTAL ENTHALPY OF COMPOUNDS = (AH° + Ali^ ) kJ/mol
co^
H20 CO -302.077 -169.714 - 53.8101 -295.965 -164.674 - 50.1718 -289.852 -159.570 - 46.5251 -283.739 -154.420 - 42.8617 -277.543 -149.237 - 39.1898 -271.346 -144.007 - 35.5096 -255.771 -130.777 - 26.2652 -240.113 -117.254 - 16.9747(c) TOTAL ENTHALPY OF ELEMENTS = AH° kJ/mol
«2 O2 ^7 TEMP K 52.9538 59.2357 56,1973 2000 56,3928 63,0247 59,8076 2100 59.8637 66.8473 63.4334 2200 63.3647 70.6824 67.0725 2300 66.8942 74.5426 70.7234 2400 70.4500 78,4196 74.3856 2500 79,4558 88.2209 83.5840 2750 88.6011 98.1604 92,8343 3000 I
TABLE 3. PERCENT MOLE CONCENTRATIONS AT (D) T, 1 C H X y PARAFFINS
™4
S»6
S « 8
, ^ 4 « 1 0S " l 2
^6^14S«16
'^8"l8V 2 0
^ l o " 2 2 NAPHTHENESS"lO
V 1 2
OLEFINSS»4
S»6
^ 4 " 8S"lO
"^6^12S»14
' S " l 6
S»18
^ 1 0 ^ 2 0 ^ 1 1 ^ 2 2 ACETYLENESS"2
S^
^4»6S"8
1 J \J ^ 6 » 1 0S»12
S»14
S " l 6
•^lo^is
CO2 8 . 5 3 9 . 7 3 1 0 . 2 5 1 0 . 5 3 1 0 . 7 1 1 0 . 8 3 1 1 . 0 0 1 1 . 0 8 1 1 . 4 0 1 1 . 4 7 1 0 . 8 0 1 1 . 0 8 1 1 , 1 7 1 1 . 2 4 1 1 . 2 7 1 1 . 3 0 1 1 . 3 2 1 1 . 3 5 1 1 . 3 7 1 1 . 2 4 1 1 . 7 1 1 1 . 6 9 1 1 . 6 7 1 1 . 6 1 1 1 . 6 1 1 1 . 5 8 H^O 1 8 . 5 2 1 6 . 0 4 1 5 . 0 4 1 4 . 5 0 1 4 . 1 6 1 3 . 9 3 1 3 . 6 4 1 3 . 4 5 1 2 . 6 6 1 2 . 6 8 1 2 . 5 0 1 2 . 5 8 1 2 . 6 0 1 2 . 6 2 1 2 . 6 3 1 2 . 6 3 1 2 . 6 4 1 2 . 6 5 1 1 2 . 6 5 7 . 4 0 9 . 4 1 1 0 . 3 0 1 0 . 8 1 1 1 . 1 3 1 1 . 5 4 1 1 . 7 7 CO j 0 . 9 1 1.19 1.29 1 . 3 3 1.36 1 . 3 8 1.39 1 . 4 3 1.57 1 . 5 0 2 . 1 2 1.86 1 . 7 8 1.72 1 . 6 8 1 . 6 6 1 . 6 4 1 . 6 1 1.59 4 . 4 9 3 . 0 1 2 . 5 5 2 . 2 9 2 . 1 8 1.97 1.87 »2 0 . 3 6 0 . 3 6 0 . 3 4 0 . 3 3 0 . 3 2 0 . 3 2 0 . 3 1 0 . 3 1 0 . 3 1 0 . 3 0 0 . 4 2 0 . 3 7 0 . 3 5 0 . 3 4 0 . 3 3 0 . 3 3 0 . 3 2 0 . 3 2 0 . 3 1 0 . 4 7 0 . 4 0 0 . 3 8 0 . 3 6 0 . 3 6 0 . 3 4 0 . 3 3°2
0 . 6 4 0 . 7 8 0 . 8 1 0 . 8 30.84
1 0 . 8 5 0 . 8 5 0 . 8 7 0 . 9 4 0 . 9 0 1.27 1.12 1.06 1 . 0 3 1 . 0 1 0 . 9 9 0 . 9 8 0 . 9 6 0 . 9 5 2 . 4 8 1 . 7 0 1,47 1 , 3 3 1,27 1.16 1.10C H X y AROMATICS
S«6
S«8
S«10
^10»8 ALCOHOLS CH^OK C^H^OH C^H^OH ELEMENTS «2 C(gr) CO^ 13.69 13.35 13.11 14.36 10.46 11.02 11.17 0 18.53 H^O 7.74 8.58 9.18 6.50 22.56 17.94 16.25 50.33 0 CO 2.25 2.08 1.97 2.34 1.03 1.17 1.41 0 2.24h
0.22 0.23 0.24 0.18 0.42 0.35 0.34 2.26 0°2
1.23 1.16 1.10 1.26 0.73 0.76 0.80 1.13 1.12(ANTHR/CENE) 16 \L (NAPHTHALENE) (ACETYLENE) 12 UI < Z (CYCLOPROPANE) ACETYLENES NAPHTHENES ' I 11
"¥
'—5—'—r
CARBON NUMBERFIG. 1. C/H RATIO OF LIGHT HYDROCARBONS
PARAFFINSi INCREASING \ IHEAT RELEASE) ACETYLENES (NAPHTHALENE) OLEFINS AROMATICS NAPHTHENES
ALCOHOLS MOLE BASIS
40-PARAFFINS HI • • <l J—ACETYLENES NAPHTHENES OLEFIN^ AROMATICS '(NAPHTHALENE) CREASING \ HEAT R E L E A S E ] «ALCOHOLS MASS BASIS
&09-D X 1 "5 E 007 35 275-ACETYLENES AROMATICS -« « » « ^t M H „ OLEFINS PARAFFINS -HJg) / INCREASING \ I ^ A T RELEASE/ MOLE BASIS C(gr) — T -3 i » t T 7 9 CARBON NUMBER 11 •Hjlgl MASS ^ASIS ALCOHOLS PARAFFINS • t ' ' T * H 1 » ^ • • • N A P H I H E N E S PARAFFINS OLEFINS
C(gr)-FIG.2B STANDARD ENTHALPIES OF REACTION FOR STOICHIOMETRIC F U E L - A I R MIXTURES is: \ VALCOHOLS < —I o z 11 o 7 oc ' 14^ ty Cn H2n • 2 (RM?AFFINS) X « H2O * K CO2 (NAPHTHENES / OLEFINS) Cn H2n CO2 /H2O . ^ ' A -
-zt^-- -^ = ^
Cn H2n-2 (ACETYLENES) (NAPHTHALENE) Cn H2n-6 (AROMATICS) . - V ' ' H 2 0 ~-v (NAPHTHALENE) 7 9 CARBON NVMSER 11FIG. 3. PERCENT MOLAR CONCENTRATIONS OF CO2AND HgO AT STOICHIOMETRIC Tg
2800
(ND)TE
-
2600-
2UX)-\
A FUELS IN GASEOUS PHASE
\ •-H2 \ \ N ^ •x^ ^ ^ - (NAPHTHALENE) gv - A.-*. 7 ^ ^ - - ^ " ^ ~ -A ACETYLENES 'AROMATICS ^ NAPHTHENES ' OLEFINS ^ _ , •_ - • 8 - - • - -«PARAFFINS ^'' ^ 2 , 2 . 4 - T M P / ^ u^-^UXOHOLS 2200. I I I » I 1 I 5 7 9 II 13 I I I CARBON NUMBER
FIG. 4A NON-DISSOCIATED STOICHIOMETRIC EQUILIBRIUM TEMPERATURE
2600 (D)T,
FUELS IN GASEOlg PHASE
2a)a
(NAPHTHALENE) ACETYLENES NAPHTHENES Ckr FINS 2.2,t-TMP PARAFFINS 'ALCOHOLS 2200 I ' 1 ' ' r I I • I r ' I ' 'I I è ' T 9 fl 13 CARBON NUMBER] ^T
FIG. 4B DISSOCIATED STOICHIOMETRIC EQUILIBRIUM TEMPERATURES
Tp K
\ (N-D) TE
2,2.4-IMP
600
FIG. 6. INFLUENCE OF INITIAL TEMPERATURE ON DISSOCIATED Tg
2400
FUEL WEAK FUEL RICH
EQUIVALENCE RATIO (f>
atm
