CACHE Modules on Energy in the Curriculum
Fuel Cells
Module 4 (Final Draft): Generation of Electricity Using Recovered Hydrogen
Module Author: David Allen
Author Affiliation: University of Texas at Austin
Module Secondary Author: Valarie Thomas
Author Affiliation: University of Michigan
Course: Mass and Energy Balances
Text Reference: Section 4.7 of Felder and Rousseau, 2nd ed. (Combustion Reactions)
Concepts: Energy (balance) required to generate electricity using hydrogen as a fuel supplement
in a fuel cell is compared to that required when using the combustion heat energy of natural gas
in a power plant. In addition, efficiencies of these 2 differing methods at generating electricity
are compared.
Background/Introduction
A number of chemical manufacturing reactions produce hydrogen as a co-product. For example,
in a chloro-alkali facility, sodium hydroxide and molecular chlorine are produced from salt water
along with hydrogen as a co-product:
electrolysis
2NaCl + 2H2O
Cl2 + 2NaOH + H2
In ethylene production from ethane, hydrogen is also a co-product.
pyrolysis
CH3-CH3
CH2=CH2 + H2
At some of these facilities, excess hydrogen not used in other chemical manufacturing processes
is used as a fuel supplement.
Customarily hydrogen is utilized as a fuel supplement by converting the heat energy released
from its combustion into electricity. Alternatively, hydrogen can be used as a fuel supplement
by feeding it to a fuel cell, an energy conversion device that electrochemically generates
electricity. A fuel cell consists of an anode and cathode, separated by an electrolyte. Hydrogen
is fed to the anode and oxygen to the cathode. A diagram showing the operation of a typical
polymer-electrolyte membrane (PEM) fuel cell is shown below:
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Figure 1. PEM fuel cell. (U.S. Department of Energy,
http://www.eere.energy.gov/hydrogenandfuelcells/fuelcells/)
The overall reaction in the fuel cell produces water and heat. In the anode, hydrogen is
catalytically dissociated into protons and electrons. The electrons leave the anode via an external
circuit and re-enters the fuel cell via the cathode. In the cathode, oxygen that has been
catalytically reduced reacts with protons from the electrolyte and electrons from the external
circuit to form the reaction products water and heat.
For combustion, the conversion of hydrogen’s chemical energy into mechanical work is limited
by the laws of thermodynamics. In contrast, a fuel cell can, in principle, completely convert the
chemical energy of hydrogen into electricity, the flow of protons through the electrolyte and
electrons in an external circuit.
A comparison of how effective the two different methods are at utilizing hydrogen as a fuel
supplement can be made by calculating the overall energy efficiencies of processes. For this
problem, efficiency is defined as the ratio of electrical energy actually obtained to the energy
input.
Example Problem
The overall reaction occurring in the fuel cell is:
H2 + 0.5 O2

H2O
The maximum amount of electrical energy that can be generated by a fuel cell can be determined
from the ion (proton) flow. Every mole of molecular hydrogen (H2) fed to a fuel cell has the
potential to generate two moles of electrons at the anode. Every mole of electrons carries 9.65 *
104 Coulombs of charge (Faraday’s constant). A coulomb/sec is an ampere (1 amp of current).
The power generated by 1 amp of current depends on the voltage (V) at which the current is
generated (P=I*V).
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a.) Assume that the fuel cell generates electricity at a voltage of 1.2 V. Calculate the
ideal electrical power (in MW) that would be generated by the fuel cell if fed
hydrogen at a rate of 10,000 kilogram/hr.
b.) If the fuel cell operates at 50% efficiency, how much power could be generated if
10,000 kilograms/hr of hydrogen were fed to the fuel cell?
c.) If the same amount of electricity in part b) had been generated by a power plant
burning natural gas (with an efficiency of 35% in converting the heat of combustion
of the natural gas into electricity), how much natural gas would have been used (in
kg/hr and in BTU/hr)? Assume that the heating value of natural gas is 1000 BTU/scf.
d.) If the 10,000 kg/hr of hydrogen had been used as a combustion fuel, what heat would
have been provided (in BTU/hr)? Assume the heat of combustion is 61,000 BTU/lb.
e.) Calculate the net energy used producing electrical power with the fuel cell as opposed
to combusted natural gas at a power plant (energy content of the natural gas that
would be used at the power plant – heat of combustion that would have been liberated
if hydrogen had been combusted at a power plant).
Solution to Example Problem
a.) The ideal current generated from 10,000 kg of hydrogen fed to a PEM fuel cell in an
hour is calculated by first converting the mass flow to molar flow per second:
(10,000 kg/hr) * (1000g/kg) *(1 mole/2g) * (1 hr/3600 sec) = 5 x 103/3.6 mol/sec
The current carried by that number of moles of hydrogen is determined by
multiplying the molar flow by Faraday’s constant accounting for the fact that every
mole of molecular hydrogen generates 2 electrons:
(5 x 103/3.6 mol/sec) * (2 electrons/mole)* 9.65 * 104 Coulombs/mole =
(9.65 x 108)/ 3.6 coulomb/sec (A= amp) = 270 MA
If the power is the product of the current and voltage (I*V) and the current is generated at
1.2 V, then the power is 320 * 106 A*V (320 MW).
b.) If the fuel cell operates at 50% efficiency, 160 MW (0.5*320 MW) of power would
be provided.
c.) To yield 160 MW of electrical energy (the same as that from the fuel cell) from a
thermoelectric conversion process converting the heat of combustion of natural gas to
electricity at 35% efficiency, the energy input would have been:
160 MW= 0.35 x (total thermal power available) or 460 MW total thermal power was
available.
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This total thermal power must be converted to the equivalent heat of combustion in
order to determine the amount of natural gas required for the 160 MW electrical
energy yield.
Converting to BTU/hr: 460 MW * (3.415 BTU/hr per watt) = 1570 *106 BTU/hr
of heat of combustion required from natural gas to generate the same electrical
power as the fuel cell
This will require the following volume of natural gas:
1570 *106 BTU/hr * 1000 BTU/scf of natural gas = 1.57 * 106 scf/hr natural gas
Converting this to a mass flow rate, using the ideal gas law:
1.57 * 106 scf natural gas * 28.3 L/ft3 * 1 mole/22.4 L * .016 kg/mole = 32000 kg/hr
of natural gas would be used to generate the same electrical power as the fuel
cell
d.) If the heat of combustion of hydrogen is assumed to be 61,000 BTU/lb then the heat
generated from the combustion of the molecular hydrogen mass flowrate of 10,000
kg/hr would be:
10,000 kg/hr * 2.2 lb/kg * 61,000 BTU/lb = 1340*106 BTU/hr
heat of combustion would be liberated per hr if that mass flowrate of molecular
hydrogen was combusted.
e.) The energy balance of producing electrical energy changes when a fuel cell is used.
Normally to produce the electrical energy generated by the fuel cell, 1570 x 106
BTU/hr of heat energy would be needed from the combustion of natural gas. And,
the 10,000kg/hr of recovered hydrogen would have been combusted to generate 1340
x 106 BTU/hr of heat energy. Thus, the use of the fuel cell to electrochemically
oxidize hydrogen rather than combust natural gas to generate electrical power causes
a net energy change of
(1570 x 106 BTU/hr of avoided thermal energy from natural gas use – 1340 x 106
BTU/hr of thermal energy that is fed to the fuel cell rather than combusted) =
230 x 106 BTU/hr, an energy savings.
Thus, using a fuel cell to produce electricity from hydrogen by-product gas in a
chloro-alkali or ethylene manufacturing facility increases the efficiency of generating
electrical power by 15%, (230* 106 BTU/hr)/ (1570 x 106 BTU/hr).
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Problem Statement
1. Repeat parts a.) – e.) above, however now assume that the natural gas power plant is 40%
efficient. With these assumptions, does using the fuel cell increase overall energy efficiency?
2. In a subsequent module in this series on fuel cells (Module 7) you will calculate that the
thermodynamic limit to fuel cell efficiency is approximately 80% for some types of fuel cells. If
the fuel cell efficiency is 80%, what is the improvement in energy efficiency due to using the
fuel cell? Assume that the power plant is 40% efficient.
3. Carbon dioxide is a known greenhouse gas, and some facilities are attempting to reduce
emissions of carbon dioxide. What percentage change in carbon dioxide emissions results from
the scenario described in the sample problem?
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Description of the Module:
Resources:
Basic background information on fuel cells is available at a Department of Energy web site:
http://www.eere.energy.gov/hydrogenandfuelcells/fuelcells/
Information on the use of fuel cells to generate electricity from chemical by-products:
Dow Chemical Company, in partnership with General Motors Corporation is demonstrating the
use of hydrogen fuel cells in generating electricity from by-product hydrogen in chemical
manufacturing operations. This partnership is described in the attached press release, which can
also be found at the Dow web site:
http://www.dow.com/dow_news/corporate/2003/20030507c.htm
Fuel cell trailer at the Dow Freeport facility
From: http://www.dow.com/commitments/studies/fuelcell/press.htm?filepath=&fromPage=BasicSearch
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Fuel cell trailer at the Dow Freeport facility
From: http://www.dow.com/commitments/studies/fuelcell/press.htm?filepath=&fromPage=BasicSearch
Notes to Instructor:
The time required to read the problem and perform the problem should be under 1 hour. If the
students are also required to visit the web sites and learn the basics of fuel cells prior to
completing the problem, 2 hours would be required. The problem could be expanded by asking
students to research fuel cell efficiencies, determining whether the 50% efficiency used in the
problem is an appropriate value, or by having the students perform Module 7 in this series. The
students will discover that higher efficiencies may be possible, particularly if waste heat is
recovered from the fuel cell.
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