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3.4 Thermodynamics of Combustion System 83

Since a typical flue gas or engine exhaust is at temperature greater than 100 °C,
where water exists as vapor, LHVs are more relevant than HHVs to fuel com-
bustion analysis. The heating values of typical fuels are available in the literature,
for example, Fundamentals of Combustion Processes by McAllister et al. [12].
Table A.5 shows the HHV and LHV of some typical fuels.
The LHV can be related to the enthalpy of formation of a fuel. Enthalpy of
formation is available at certain temperature, typically T = 298 K.

" #
1 X o X o
LHV 298KÞ ¼ n i h f ;i n i h f ;i ¼ DH R 298Kð Þ ð3:59Þ
ð
n f
R P
where the enthalpy of formation of the fuel is used for the calculation of the total
enthalpy of the reactants.
Example 3.9: Heating values
Consider stoichiometric combustion of methane with pure oxygen proceeds as
CH 4 þ 2O 2 ! CO 2 þ 2H 2 O. The mass-based HHV of methane is 55.65 MJ/kg at
298 K and 1 atm, estimate (a) LHV of CH 4 , (b) enthalpy of formation of methane.
Solution
The conversion from HHV (MJ/kg) to HHV (MJ/kmole) is needed by considering
the molar weight of the fuel given based on mass, and it can be converted by

HHVðMJ=kmoleÞ¼ HHVðMJ=kgÞ M fuel
¼ 55:65ðMJ=kgÞ 16 ðkg=kmoleÞ
¼ 890:4MJ=kmole at 298KÞ
ð

(a) The LHV can be determined by considering the latent heat of vaporization of
water at 298 K, which is h fg ¼ 43:92MJ=kmole.

n H 2 O
LHV ¼ HHV h fg
n fuel
¼ 890:4 2 43:92 ð MJ=kmoleÞ
ð3:60Þ
¼ 802:6 ð MJ=kmoleÞ
¼ 802:6 ð MJ=kmoleÞ or 50:1MJ=kg

(b) The combustion CH 4 þ 2O 2 ! CO 2 þ 2H 2 O gives

h o þ n H 2 O h o h o h o ð3:61Þ
f ;H 2 O n CH 4 f ;CH 4 þ n O 2 f ;O 2
LHV ¼ n CO 2 f ;CO 2