Calculate the heating value of a gas that contains methane
(94.44 percent), ethane (3.4 percent), propane (0.55 percent), butane (0.5
percent), carbon monoxide (0.01 percent), carbon dioxide (0.57 percent),
hydrogen (0.03 percent) and nitrogen (0.5 percent).
Solution:
Let’s consider one mole of this gas as a basis of
calculations.
Heating value of a compound is heat obtained when that
compound is burnt completely. Its value
is same as the negative of heat of formation for that reaction when components
are in the natural state represented by 1 atmosphere and 25 degrees C.
Let’s find heat of reaction when one mole of methane is
combusted. One mole of methane reacts
with 2 moles of oxygen to produce 1 mole of carbon dioxide and 2 moles of water
(liquid state). Heat of formation of
methane is negative 17,889 calories, of oxygen is zero (pure element), and
water is negative 68,317 calories per mole.
So heat of reaction is equal to sum of heat of formation of products
minus sum of heat of formation of reactants.
This value is equal to 1 times negative 94,052 plus 2 times negative
68,317.4 minus 1 times negative 17,889 minus 2 times zero. Please note that in this calculation, there
is 1 mole of carbon dioxide, 2 moles of water are produced. Heat of reaction involving combustion of
methane is found to be negative 212,798 calories.
However, in this problem methane is 94.44 percent. So methane’s contribution is 94.44
percent. We could calculate the
contributions from other components ethane, propane, etc using the approach
discussed, or calculate the total number of carbon dioxide, and water produced
and oxygen consumed. Since, heat of
formation of oxygen is zero, there is no need to calculate amount of oxygen for
heat of reaction calculations.
It can be seen that heat of formation of hydrogen is zero
(elemental). Total carbon dioxide
produced in the combustion reaction is found to be 1.049 moles. Similarly, 2.038 moles of water are
produced. Please remember that
combustion of hydrogen results in water (liquid state).
Enthalpy of feed is enthalpy of all components reacting in
the combustion reaction is negative 18,407 calories.
Heat of reaction is equal to heat of formation of products
(carbon dioxide and water) minus heat of formation of reactants (methane,
ethane, propane, butane, carbon monoxide, and hydrogen). Heat of formation of carbon dioxide is 1.049
times negative 94,052 is equal to negative 98,660.5 calories. Similarly, heat of formation of water is
2.038 times negative 68,317.4 and is equal to negative 139,230.9 calories. The resulting value for the reaction mixture
is negative 219,492 calories per mol.
This value can be converted to BTUs per mole by multiplying it with
1.8. Heating value is equal to the
negative of heat of reaction and is equal to 3.951 times 10 to the power 5 BTUs
per lb mole. This value is termed as
high heating value and it is assumed that the water is available in the liquid
state.
In the actual situation, water is present in the vapor state
after gas is combusted. So heat of
vaporization is taken away from the combustion gases. This is termed as low heating value and is obtained by
subtracting latent heat of vaporization (1050 BTU per lb). There are 2.038 moles of water
produced, so low heating value (LHV) is
calculated to be 3.566 times 10 to the power 5 BTU per lb mole or 942.1 BTU per
dry standard cubic foot.