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).
The PEMFC reactions are: Anode: H2 → 2H+ + 2e-
Cathode: ½ O2 + 2H+ + 2e- → H2O
Overall: 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: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: and).
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.
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:
(1)
where KA is the equilibrium coefficient and pA is the partial pressure of gas A (kPa).
The Langmuir isotherm is given by:
(2)
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.
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:
(3)
Methane adsorption is described by the Langmuir isotherm:
(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,
(5)
Step 2) For methane,
(6)
Step 3) Given the partial pressures, determine the amount of hydrogen adsorbed according to the linear isotherm:
(7)
Step 4) Scale up according to the basis set in the problem statement:
(8)
Step 5) Given the partial pressures, determine the amount of methane adsorbed according to the Langmuir isotherm:
(9)
Step 6) Scale up according to the basis set in the problem statement:
(10)
Part b)
Step 1) In 10 minutes of trapping the number of moles of hydrogen entering the column is:
(11)
Step 2) The amount of hydrogen that can be adsorbed in 200 kg carbon is:
(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:
(13)
Step 5) The amount of methane that can be adsorbed in 200 kg carbon is:
(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
(15)
Step 7) An overall mass balance can be used to determine the waste gas flow rate:
(16)
Step 8) The hydrogen mole fraction is given by:
(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 which indicates a good separation.
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:
(18)
Methane adsorption is described by the Langmuir isotherm:
(19)
Carbon monoxide adsorption is described by the Langmuir isotherm:
(20)
Carbon dioxide adsorption is described by the Langmuir isotherm:
(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.
1st Draft J.M. Keith September 3, 2008
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