CACHE Modules on Energy in the Curriculum
Hydrogen as a Fuel
Module Title: Fuel Energy Cost and Energy Density
Module Author: Dr. Daniel A. Crowl
Author Affiliation: Michigan Technological University
Course: Stoichiometry, process design, thermodynamics
Text Reference: Felder and Rousseau, Elementary Principles of Chemical Processes, 3rd ed.,
New York: John Wiley and Sons, 2005.
Concepts: Energy cost and energy density of fuels.
Problem Motivation:
Selection of a fuel energy source depends on a lot of parameters. This includes the fuel cost,
energy content, energy density, compatibilility with equipment, availability, transportation and
storage, waste, emissions, to name a few.
This module will look at the parameters of fuel cost (on an energy basis), and fuel density.
Basic Definitions:
 Energy density
Energy of the fuel per unit volume.
Problem Information
Example Problem Statement:
The following information is available on various fuels as of June, 2010:
Energy Source, unit
Crude Oil, barrel = 42 gallons
Gasoline, gallon
Natural gas, 1000 SCF @60oF
Bituminous coal, broken, short ton
Electricity, kWh
Hydrogen, kg
Ethanol, gallon
2nd Draft
kJ/unit
5.8 MM
132,000
1.05 MM
25.3 MM
3600
120,500
80,100
D. A. Crowl
Page 1
$/Unit
$78
$2.80
$4.90
$64
$.088
$4
$1.70
Density
kg/m3
900
720
Ideal gas
833
Ideal gas
789
June 25, 2010
a. Calculate the cost in $ per MJ of energy for each type of fuel? Which fuel is the best
bargain? What other considerations are important?
b. Calculate the energy density in MJ/m3 for each fuel source, except electricity. For natural
gas and hydrogen assume a pressure of 1 atm and a temperature of 298 K. Which fuel offers
the best energy density?
c. What pressure, in atm, must the natural gas and hydrogen be compressed to in order to
achieve the same energy density as gasoline? A pressure of 10,000 psi has been identified as
a potential storage pressure for hydrogen. What is the energy density of natural gas and
hydrogen at this pressure? Assume ideal gas behavior.
d. Estimate the compression energy required to compress hydrogen to 10,000 psi. What
percentage of the hydrogen fuel energy is used to do this compression? Assume a
compressor efficiency of 70%, an initial gas temperature of 80oF and a heat capacity ratio for
hydrogen of 1.41.
Example Problem Solution:
a. Crude oil:
$78



  $0.0134 /MJ
3
 5.8 10 MJ 
Gasoline:
 $2.80 

  $0.0212 /MJ
 132 MJ 
Natural gas:
$4.90



  $0.0047 /MJ
3
 1.05 10 MJ 
Bituminous coal:
$64



  $0.0025 / MJ
3
 25.3 10 MJ 
Electricity:
 $0.088 

  $0.0244 / MJ
 3.6 MJ 
Hydrogen:
$4



  $0.0332 /MJ
 120.5 MJ 
Ethanol:
 $1.70 

  $0.0212 /MJ
 80.1 MJ 
2nd Draft
D. A. Crowl
Page 2
June 25, 2010
The fuels can be ranked from least expensive to most expensive per MJ as follows:
Fuel
$/MJ
Coal
$0.0025
Natural Gas
$0.0047
Crude oil
$0.0134
Gasoline
$0.0212
Ethanol
$0.0212
Electricity
$0.0244
Hydrogen
$0.0332
Coal is clearly the best value, but results in a lot of emissions and carbon dioxide. Natural
gas is probably the most versatile and a very good value. Electricity and hydrogen are not
good values at these prices. Since ethanol is a gasoline replacement, it is no surprise that it
has the same energy cost.
b. Crude oil:
1 m3  264.2 gallons = 6.29 barrels
 5.8 103 MJ   6.29 barrels 
3


  36,500 MJ/m
3
3
1m
m



Gasoline:
1 m3  264.2 gal
 264.2 gal   132 MJ 
3
  34,900 MJ/m


3
 m
  gal 
Natural gas:
1000 ft 3  28.32 m3
3
 1050 MJ   1000 ft 
 37.1 MJ/m3

3 
3 
 1000 ft   28.32 m 
Coal:
1 ton = 2000 lbm = 907.2 kg
 25.3 103 MJ   833 kg 
3


  23, 200 MJ/m
3
 907.2 kg   m 
Hydrogen: Need to calculate volume of 1 mole of gas at 1 atm and 60oF = 288 K
V
nRgT

1 mole  8.2057 105 m3 atm/mol K   288 K 
P
 0.241 MJ 
 10.2 MJ/m3

3 
0.0236
m


2nd Draft
1 atm
D. A. Crowl
Page 3
 0.0236 m3
June 25, 2010
Ethanol:
 264.2 gal   80.1 MJ 
3
  21, 200 MJ/m


3
 m
  gal 
The table below shows the ranking of the various fuels, with the highest density at the top:
Fuel
Crude oil
Gasoline
Coal
Ethanol
Natural gas
Hydrogen
Energy Density
MJ/m3
36,500
34,900
23,200
21,200
37.1
10.2
Clearly, crude has the highest energy density, with hydrogen gas having the lowest energy
density. Note that ethanol has 21,200/34,900 = 0.61 or 61% of the energy content of
gasoline on an identical volume basis.
c. The pressure required for hydrogen and natural gas to achieve the same energy density as
gasoline can be found from the ideal gas law. The energy density of gasoline is 34,900
MJ/m3. Thus, the pressure required is:
For natural gas:
 P 
34,900 MJ/m3   37.1 MJ/m3   2 
 1 atm 
P2  941 atm
For hydrogen:
 P 
34,900 MJ/m3  10.2 MJ/m 3   2 
 1 atm 
P2  3421 atm
Clearly, the pressure required for hydrogen is much too high for any practical application.
Commonly suggested pressures for hydrogen storage are 5,000 psi and 10,000 psi. At 10,000
psi = 681 atm, the energy density for hydrogen is:
atm 
3
10.2 MJ/m3   681
  6,950 MJ/m
1 atm 
2nd Draft
D. A. Crowl
Page 4
June 25, 2010
This is higher than the energy density of natural gas and crude oil, but still a lot less than
gasoline or ethanol.
The ideal gas law is not likely to be valid at these pressures, so this is an approximation.
d. The energy of compression for an ideal gas for adiabatic compression is given by:
 1/  

    P2 


W  Rg T1 

1




   1   P1 
Substituting the known quantities, and converting 80o F=300 K ,
 0.41/1.41

 1.41   10, 001 atm 
W   8.314 J/mol K  300 K  

1

  48.6 kJ/mol
 

 0.41   1 atm 

For a compressor efficiency of 70%, the total work is:
48.6 kJ/mol
W
 69.4 kJ/mol
0.70
The energy per mole of hydrogen is
 120,500 kJ   0.002 kg 


  241 kJ/mol
kg

  mol 
The fraction of the energy required to compress the hydrogen to 10,000 psi is
69.4 kJ/mol
 0.288 or 28.8%
241 kJ/mol
28.8% of the energy is used for the compression – this is a large fraction of the total energy
content.
2nd Draft
D. A. Crowl
Page 5
June 25, 2010
Home Problem Statement:
Liquefied fuels such as liquefied natural gas (LNG) or liquid propane have become important
energy carriers throughout the world. These fuels are used mostly for fleet vehicles in large
cities.
a. LNG has become an important fuel because it has a much higher energy density than gaseous
natural gas. The density of LNG is 450 kg/m3. If the LNG is considered to be all methane,
calculate the energy density of LNG in MJ/m3. The heat of combustion for methane is 50
MJ/kg.
b. Redo part a with liquid propane. The heat of combustion (LHV) for propane is 46.3 MJ/kg
and its density is 583 kg/m3.
c. Redo part a for gaseous propane at 1 atm and 298 K.
d. Comment on the motivation to use liquefied fuels rather than gaseous fuels.
2nd Draft
D. A. Crowl
Page 6
June 25, 2010