CACHE Modules on Energy in the Curriculum
Fuel Cells
Module Title: Hydrogen Purification
Module Author: Jason Keith
Author Affiliation: Michigan Technological University
Course: Separations
Text Reference: Wankat (2nd edition), Section 17.1
Concepts: Given a mixture of hydrogen and methane and adsorption isotherms determine
the effluent from a pressure swing adsorption system.
Problem Motivation:
Fuel cells are a promising alternative energy conversion technology. One type of fuel
cell, a proton exchange membrane fuel cell (PEMFC) reacts hydrogen with oxygen to
produce electricity (Figure 1). Fundamental to a hydrogen economy powered by fuel cells
is the generation of high purity hydrogen.
Consider the schematic of a compressed hydrogen tank (2000 psi, regulated to 10 psi)
feeding a proton exchange membrane fuel cell, as seen in Figure 2 below. We will now
focus on hydrogen purification (to fill the compressed tank).
-
-
e
e
H2
H2O
O2
H+
H2
H2O
H2
O2
O2
+
H
H2
Computer
(Electric
Load)
Pressure
regulator
H2 feed line
Air in
H2
H2
H2
H2
H2
H2O
H2O
+
H
H+
O2
Anode
Cathode
Electrolyte
Figure 1. Reactions in the PEMFC
H2 out
H2 tank
Fuel Cell
Air / H2O out
Figure 2. Diagram for fueling a laptop.
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The PEMFC reactions are:
Anode:
Cathode:
Overall:
H2
→ 2H+ + 2e½ O2 + 2H+ + 2e- → H2O
H2 + ½ O2
→ H2O
For each mole of hydrogen consumed, two moles of electrons are passed through the
electric load. To convert electron flow (moles of electrons/s) to electrical current
(coulombs/s or amps), one would use Faraday’s constant: F  96,485 coulombs / mole of
electrons. The primary objective of a fuel cell is to deliver energy to the electric load. To
calculate the energy delivery rate (also know as power) one would multiply the current
times the cell voltage: Power = Current · Voltage. (Recall the unit conversions:
Coulomb  Volt  Joule and Joule / s  Watt ).
Background
Natural gas has been proposed as a source of hydrogen for fuel cell vehicle applications
because of the existing infrastructure. Let us suppose that natural gas is “reformed” into
hydrogen at a service station.
Figure 3 shows a black box diagram of a pressure-swing adsorption process which
purifies the hydrogen so it can be charged into compressed tanks on board a vehicle. A
feed F (kgmol/h) with hydrogen mole fraction xF,H and methane mole fraction xF,M = 1 –
xF,H enters the unit. As more methane than hydrogen is adsorbed within the process
(using, for example, activated carbon), the hydrogen product stream H (kgmol/h) exits
with a higher hydrogen mole fraction xH,H. The waste gas W (kgmol/h) with methane
mole fraction xW,M is used as fuel in the reformer.
Product, H
Feed, F
Waste Gas, W
Figure 3. Pressure-Swing Adsorption Process Diagram
The amount of gas A adsorbed qA (mmol/g adsorbent) is given by either the linear
isotherm or the Langmuir isotherm. The linear isotherm is given by:
qA  K A pA
(1)
where KA is the equilibrium coefficient and pA is the partial pressure of gas A (kPa).
The Langmuir isotherm is given by:
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qA 
q A,max K A p A
(2)
1 K A pA
where qA,max (mmol/g adsorbent) is the maximum possible adsorption (the adsorbent is
“saturated”).
For simplicity we will assume that the adsorption isotherms for methane and hydrogen
are not dependent upon each other.
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Example Problem Statement: The feed to an adsorption column for a small hydrogen
production system has a flow rate of 43 kgmol/h with a hydrogen mole fraction of 0.953.
The feed is at a pressure of 2000 kPa and temperature 75 oC. Assume that all material
adsorbed exits in the waste gas stream.
Hydrogen adsorption is described by the linear isotherm:
q H 2 (mmol/g )  2.7  10 4 p H 2 (kPa )
(3)
Methane adsorption is described by the Langmuir isotherm:
q M (mmol/g ) 
6  5  10 3 p M (kPa )
1  5  10 3 p M (kPa )
(4)
a) Choose a basis of 1 kg adsorbent and determine the kgmol of hydrogen and
methane adsorbed.
b) There are two beds in the system. It is assumed that one bed traps material for 10
minutes while the other is being regenerated. There are 200 kg of carbon in each
bed. Consider gas flow through one bed for ten minutes (trapping). This allows
for one “cycle” of gas to exit as product H and waste gas W. Determine the exit
flow rates H and W and the corresponding hydrogen mole fractions.
Example Problem Solution:
Part a)
Step 1) Determine the partial pressures in the feed gas using Dalton’s law of partial
pressures. For hydrogen,
p H 2  Px F , H  2000 kPa  0.953  1906 kPa
(5)
Step 2) For methane,
p M  Px F , M  2000 kPa  (1  0.953)  94 kPa
(6)
Step 3) Given the partial pressures, determine the amount of hydrogen adsorbed
according to the linear isotherm:
q H 2 (mmol/g )  2.7  10 4  1906 (kPa )  0.51 mmol/g
(7)
carbon
Step 4) Scale up according to the basis set in the problem statement:
q H 2 (kgmol/kg )  0.51mmol/g
carbon

1000 g carbon kgmol
 5.1 10 4 kgmol/kg
kg carbon 10 6 mmol
carbon
(8)
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Step 5) Given the partial pressures, determine the amount of methane adsorbed according
to the Langmuir isotherm:
6  5  10 3  94(kPa )
q M (mmol/g ) 
 1.92 mmol/g
1  5  10 3  94(kPa )
(9)
carbon
Step 6) Scale up according to the basis set in the problem statement:
q M (kgmol/kg )  1.92 mmol/g
carbon

1000 g carbon kgmol
 1.92  10 3 kgmol/kg
6
kg carbon 10 mmol
carbon
(10)
Part b)
Step 1) In 10 minutes of trapping the number of moles of hydrogen entering the column
is:
10 min 43 kgmol
h 0.953
 6.83 kgmol
h
60 min
(11)
Step 2) The amount of hydrogen that can be adsorbed in 200 kg carbon is:
200 kg carbon
5.1  10 4 kgmol
 0.102 kgmol
kg carbon
(12)
Step 3) Thus we expect 0.102 kgmol hydrogen to exit with the waste gas in 10 minutes,
or 0.612 kgmol/h.
Step 4) In 10 minutes the number of moles of methane entering the column is:
10 min 43 kgmol
h 1  0.953
 0.34 kgmol
h
60 min
(13)
Step 5) The amount of methane that can be adsorbed in 200 kg carbon is:
200 kg carbon
1.95  10 3 kgmol
 0.39 kgmol
kg carbon
(14)
Step 6) Since the amount of methane entering the column is less than the storage
capacity, we expect no methane in the hydrogen product stream. Thus, xH,H = 1.00 and
H
6.83 kgmol - 0.102 kgmol 60 min
kgmol
 40.37
10 min
h
h
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Step 7) An overall mass balance can be used to determine the waste gas flow rate:
W  F  H  43
kgmol
kgmol
kgmol
 40.37
 2.63
h
h
h
(16)
Step 8) The hydrogen mole fraction is given by:
xW , H 
0.612
 0.23
2.63
(17)
Summary: The hydrogen mole fraction in the waste gas is higher than the feed because
some of the hydrogen is adsorbed. We could define an “efficiency” of hydrogen
separation by Hx H , H / Fx F , H  40.31(1) /( 43)(0.953)  98.5% which indicates a good
separation.
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Home Problem Statement: The feed to an adsorption column for a small hydrogen
production system has a flow rate of 26.04 kgmol/h with the following composition:
hydrogen mole fraction of 0.768, methane mole fraction of 0.0384, carbon monoxide
mole fraction of 0.0015, and a carbon dioxide mole fraction of 0.192.
The feed is at a pressure of 2000 kPa and temperature 75 oC. Assume that all material
adsorbed exits in the waste gas stream.
Hydrogen adsorption is described by the linear isotherm:
q H 2 (mmol/g )  2.7  10 4 p H 2 (kPa )
(18)
Methane adsorption is described by the Langmuir isotherm:
q M (mmol/g ) 
6  5  10 3 p M (kPa )
1  5  10 3 p M (kPa )
(19)
Carbon monoxide adsorption is described by the Langmuir isotherm:
qCO (mmol/g ) 
0.45  4  10 1 pCO (kPa )
1  4  10 1 pCO (kPa )
(20)
Carbon dioxide adsorption is described by the Langmuir isotherm:
0.9  5  10 2 pCO 2 (kPa )
qCO 2 (mmol/g ) 
1  5  10 2 pCO 2 (kPa )
(21)
a) Determine the partial pressure of each gas in the feed stream
b) If you have two beds of 100 kg carbon each, determine the total kgmol of each
gas in the feed stream that can be adsorbed onto the carbon
c) Determine the flow rates of the feed chemicals in kgmol/hr
d) Determine the breakthrough time for methane, carbon monoxide, and carbon
dioxide. Based upon these results, what is the maximum regeneration time
allowed with pure hydrogen in the product stream? Also, estimate the exiting
waste stream flowrate and compositions.
For simplicity we will assume that the adsorption isotherms for methane, hydrogen,
carbon monoxide, and carbon dioxide are not dependent upon each other.
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