Modern Engineering Thermodynamics

15.4 Fuel Modeling 599
Hydrocarbon fuels refined from petroleum normally contain a mixture of many organic components. Gasoline,
for example, is a mixture of over 30 compounds. It is, however, convenient to model these fuels as a single
average hydrocarbon compound of the form C n H m , as discussed in the following section.
15.4 FUEL MODELING
It is fairly easy to obtain accurate composition analysis of combustion products with modern gas chromatography
or mass spectroscopy techniques. With an accurate combustion analysis of a fuel that is in reality a complex
mixture of hydrocarbons, an equivalent or average hydrocarbon model of the form C n H m can be determined
from a chemical element balance. For example, if the combustion products contain only CO 2 ,CO,O 2 ,H 2 O,
and N 2 , then Eqs. (15.3a–c) could be used to determine the composition parameters n and m when the stoichiometric
coefficients of the products are measured. Since the fuel model formula C n H m represents an average of all
the different hydrocarbon compounds present in the fuel mixture, n and m usually do not turn out to be integers
and the resulting model does not represent any real hydrocarbon (except possibly when n and m are
rounded to integers).
EXAMPLE 15.2
A new hydrocarbon fuel is being developed that consists of 1.00 kgmole of methane (CH 4 )mixedwith3.00kgmolesof
propane (C 3 H 8 ). Determine the hydrocarbon fuel model for this mixture.
Solution
This mixture is assumed to produce 1.00 kgmole of the fuel model C n H m ,so
An element balance for this equation gives
1CH 4 + 1C 3 H 8 = 1C n H m
Carbon balance: 1 + 3ð3Þ = 10 = n
Consequently, the hydrocarbon fuel model is C 10 H 28 .
Hydrogen balance: 4 + 3ð8Þ = 28 = m
Exercises
4. Determine the hydrocarbon fuel model in Example 15.2 if only 2.00 kgmoles of propane are used in the mixture.
Answer: Hydrocarbon fuel model = C 7 H 20 .
5. Determine the hydrocarbon fuel model in Example 15.2 if ethane (C 2 H 6 ) is used in place of the methane. Answer:
Hydrocarbon fuel model = C 11 H 30 .
6. 1.00 lbmole each of methane (CH 4 ), propane (C 3 H 8 ), and butane (C 4 H 10 ) are mixed to form 1.00 lbmole
of a new super fuel. Determine the hydrocarbon fuel model for this mixture. Answer: Hydrocarbon fuel
model = C 8 H 22 .
Often, you do not know the exact hydrocarbon composition of a fuel. However, you can analyze the products of
the fuel’s combustion and deduce the fuel model. Several modern instruments produce an accurate exhaust gas
analysis. For example, gas chromatography and mass spectrometry are commonly used in exhaust gas analysis
today. But perhaps the quickest, simplest, and most inexpensive method of obtaining an approximate combustion
analysis is with an Orsat analyzer. This gas analyzer uses a chemical absorption technique to determine the volume
fractions (which are equivalent to the mole fractions) of CO 2 ,CO,andO 2 in the exhaust gas (see Figure 15.4).
Since it cannot measure the H 2 O content, the exhaust gas sample is always cooled to room temperature, or below
the dew point of any water vapor present, so that most of the water in the combustion products condenses out.
Therefore, the Orsat technique is said to produce a dry products analysis. Also, the Orsat technique cannot detect
unburned hydrocarbons (typically CH 4 ) and free hydrogen (H 2 ) in the exhaust gas. These are usually small and
can normally be neglected. However, studies have shown that the mole fractions of methane and hydrogen in the
combustion products of a hydrocarbon can be approximated as χ CH4 ≈ 0:0022 and χ H2
≈ 0:5ðx CO Þ, and these relations
can be used with an Orsat analysis if necessary.