CACHE Modules on Energy in the Curriculum
Hydrogen as a Fuel
Module Title: Theoretical Fuel Consumption and Power
Module Author: Dr. Daniel A. Crowl
Author Affiliation: Michigan Technological University
Course: Stoichiometry, process design
Text Reference: Felder and Rousseau, Elementary Principles of Chemical Processes, 3rd ed.,
New York: John Wiley and Sons, 2005.
Concepts: Fuel consumption
Problem Motivation:
The cylinders in an internal combustion engine have a displacement that is the total volume of all
cylinders when they are at maximum volume. The displacement is measured in liters, with
typical values from 4 to 12 L.
During the operation of the combustion engine, air and fuel are either drawn into the engine
through a carburetor or mixed in the cylinder by fuel injection. If we know the total volumetric
flow rate of air and the concentration of the fuel, we can calculate the fuel consumption. The
volumetric flow rate can be calculated from the RPM of the engine and the engine displacement.
Finally, knowing the enthalpy of combustion of the fuel, and the fuel flow rate, we can calculate
the theoretical power.
These numbers provide a quick screening method to look at different fuels and their
performance. This evaluation does not consider the burning rate of the fuel nor the maximum
pressure generated by the combustion. This varies from fuel to fuel and would have an effect on
the engine performance.
This calculation also assumes that all the thermal energy generated by the combustion is
available to do mechanical work. In reality, the 2nd Law of Thermodynamics applies and reduces
the efficiency of conversion of the thermal energy to mechanical energy. There are also losses
due to friction in the mechanical parts.
Basic Definitions:
 Theoretical Fuel Consumption
Fuel consumption based entirely on volumetric air flow through the combustion engine and
stoichiometric combustion.
 Theoretical Power
The power delivered based entirely on the theoretical fuel consumption.
2nd Draft
D. A. Crowl
Page 1
June 25, 2010
Problem Information
Example Problem Statement:
An internal combustion engine with a displacement volume of 4 L has a rotational speed of 1500
rpm.
a. If hydrogen is used as a fuel, calculate the theoretical hydrogen consumption rate at this
rpm. Remember that each cylinder fires once every two revolutions. Assume that the
combustion occurs stoichiometrically. Assume that the air – fuel mixture enters the
engine at 300 K and 1 atm.
b. If the heat of combustion for the hydrogen is 241 kJ/mole, what is the theoretical power
delivered by this engine, in HP?
Example Problem Solution:
a. First, let’s calculate the volumetric flow of the air – fuel mixture. The engine operates at
1,500 rpm, but the cylinders only fire every other rotation. Thus, the volumetric flow is:
 1,500 rpm 

  4 L   3, 000 L/min  50 L/s
2


The stoichiometry of the combustion is as follows:
BASIS: 1 mole of hydrogen combusting
The hydrogen in pure oxygen combusts according to the following reaction:
H2 + ½ O2 H2O
With air the following can be written”
 79 
H2 + ½ O2+(1/2)   N2  H2O + 1.88 N2
 21 
We then have the following mixture, from which we can calculate the mole fractions and the
volumetric consumption of each species.
Species
H2
O2
N2
Moles
1
0.5
1.88
3.38
Mole Fraction
0.295
0.148
0.556
0.999
Volumetric
Consumption
(Liters/min)
885 = (0.295)(3000 L/min)
444
1,668
2,997
At 300 K and 1 atm the molar volume is
P
1 atm


 40.62 mol/m3
5
RgT  8.2057 10 m3 atm/mol K   300 K 
2nd Draft
D. A. Crowl
Page 2
June 25, 2010
The molar flow of hydrogen is
 0.885 m /min  40.62 mol/m   35.95 mol/min
3
3
The hydrogen consumption rate is then
35.95 mol/min  0.002 kg/mol  0.0719 kg/min  4.31 kg/hr
b.
The power rate is the energy release rate from the combustion reaction
1 min  241 kJ  1 HP

 35.95 mol/min  


  194 HP
 60 sec  mol  0.7457 kJ/s 
2nd Draft
D. A. Crowl
Page 3
June 25, 2010
Home Problem Statement:
An internal combustion engine with a displacement volume of 4 L has a rotational speed of 1500
rpm.
a. If propane is used as a fuel, calculate the theoretical propane consumption rate at this
rpm. Remember that each cylinder fires once every two revolutions. Assume that the
combustion occurs stoichiometrically. Assume that the air – fuel mixture enters the
engine at 300 K and 1 atm.
b. If the heat of combustion for the propane is 2043 kJ/mole, what is the theoretical power
delivered by this engine, in HP?
2nd Draft
D. A. Crowl
Page 4
June 25, 2010