Power Plant Engineering

220 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 – mwhfg ...(7.1a)

or LHV = HHV – 9mh 2 hfg ...(7.1b)

where

mw = mass of water vapor in products of combustion per unit mass of fuel (due to the combustion
of HZ in the fuel i.e., not including initial H 2 O in fuel).
mH 2 = mass of original hydrogen per unit mass of fuel, known from ultimate analysis.
hfg = 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.

Table 7.1 : Proximate and ultimate analysis of some U.S. coals

Analysis Bituminous

mass percent Anthractive medium velocity Subiluminous Lagnite

Proximate

Fixed carbon 83.8 70.0 45.9 30.8

Volatile matter 5.7 20.5 30.5 28.2

Moisture 2.5 3.3 19.6 34.8

Ash 8.0 6.2 4.0 6.2

(Contd.)