Power Plant Engineering

7.3.2 ULTIMATE ANALYSIS
A more scientific test than proximate analysis, ultimate analysis gives the mass percentages of
the chemical elements that constitute the coal. These include carbon, hydrogen, nitrogen, oxygen, and
sulfur. Ash is determined as a whole, sometimes in a separate analysis. Ultimate analysis is given by
ASTM Standards D 3176.
7.3.3 HEATING VALUE
The heating value, Btu/lbm or J/kg of fuel, may be determined on as-received, dry, or dry-and-
ash-free basis. It is the heat transferred when the products of complete American National Standards
Institute/American Society for Testing and Materials.
combustion of a sample of coal or other fuel are cooled to the initial temperature of air and fuel.
It is determined in a standard test in a bomb calorimeter given by ASTM Standards D 2015. There are

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POWER PLANT ENGINEERING
two determinations: the higher (or gross) heating value (HHV) assumes that the water vapor in the
products condenses and thus includes the latent heat of vaporization of the water vapor in the products;
the lower heating value (LHV) does not. The difference between the two is given by
LHV = HHV – m
w
h
fg
...(7.1a)
or
LHV = HHV – 9m
h2
h
fg
...(7.1b)
where
 m
w
= mass of water vapor in products of combustion per unit mass of fuel (due to the combustion
of H
Z
in the fuel i.e., not including initial H
2
O in fuel).
m
H2
= mass of original hydrogen per unit mass of fuel, known from ultimate analysis.
h
fg
= latent heat of vaporization of water vapor at its partial pressure in the combustion products,
Btu/lb. H
2
O or J/kg H
2
O.
The partial pressure of water vapor in the products of combustion is obtained by multiplying the
mole faction of H
2
O in the products, which is obtained from the combustion equation in the usual
manner, by the total pressure of the products. The 9 in Eq. (7.1b) is the ratio of the molecular masses of
H
2
O and H
2
and represents the mass of H
2
O vapor obtained from a unit mass of H
2
.
Because gases are not usually cooled down below the dew point in steam generators (or engines),
it does not seem fair to charge them with the higher heating value in calculating energy balances and
efficiencies of cycles or engines. Some, however, argue that they should be charged with the total energy
content of the fuel. A uniform standard had to be agreed upon, whereupon everybody uses the HHV in
energy balances and efficiency calculations. (The LHV is the standard used in European practice, how-
ever.)
As indicated above, heating values are obtained by testing. However, a formula of the Dulong
type (which does not include the effects of dissociation) is used to give approximate higher heating
values of anthracite and bituminous coals in Btu/lbm.
HHV = 14,600C + 62,000(H – O/8) + 4050S
...(7.2)
where C, H, O, and S are the mass fractions of carbon, hydrogen, oxygen, and sulfur, respectively, in the
coal. For lower-rank fuels, the above formula usually underestimates the HHV.
Table 7.1 gives the proximate and ultimate analyses of some typical U.S. coals.