Humidity and Water Management in Fuel Cells s1

CACHE Modules on Energy in the Curriculum

Fuel Cells Module Title: Vapor Pressure / Humidity of Fuel Cell Gases Module Author: Jason Keith Author Affiliation: Michigan Technological University

Course: Thermodynamics

Text Reference: Sandler, 5.7, 7.1 Smith, Van Ness, and Abbott (7th ed.), section 6.1 and 6.4 Geankoplis (4th ed.), section 9.3

Concepts: Antoine Equation, Partial Pressure

Problem Motivation: Fuel cells are a promising alternative energy technology. One type of fuel cell, the proton exchange membrane fuel cell, reacts hydrogen and oxygen together to produce electricity. In this problem you will determine the effect of changing temperature and water content on the humidity of an air / water stream within a fuel cell. Balancing humidity in a fuel cell is critical to efficient operation.

Consider the schematic of a compressed hydrogen tank feeding a proton exchange membrane fuel cell, as seen in figure 1 below. The electricity generated by the fuel cell is used here to power a laptop computer. We are interested in determining the water content in a hydrogen feed to the fuel cell.

Computer (Electric Load)

H feed line 2 Air in

Anode Cathode Gas Gas Chamber Chamber

Air / H O out H out 2 2 H tank Fuel Cell 2

1st draft J.M. Keith June 14, 2007 Revision J.M. Keith July 26, 2007 Page 1 Problem Information Example Problem Statement: In this example problem you will use the concept of vapor pressure to help you determine the humidity of an air / water vapor mixture.

On a cool spring morning with a rainy forecast, the temperature is 67 oF, with a relative humidity of 79%. What is the temperature in degrees Celcius, saturated vapor pressure in kPa, partial pressure of water vapor in kPa, and humidity in kg H2O / kg dry air? Assume an atmospheric pressure of 1 bar. Note that 1 bar = 100 kPa.

Example Problem Solution: Step 1) We can convert the temperature to degrees Celcius using T(oC) = (T(oF) – 32) x 5/9. Thus, 67 oF is equal to 19.4 oC.

Step 2) The saturated vapor pressure of water in kPa can be determined using the Antoine equation (equation 6.76 on page 223 of the 7th edition of Smith, Van Ness, and Abbott),

B log P  A  10 SAT T  C

where, PSAT = vapor pressure, mm Hg A = 8.10765 B = 1750.286 C = 235 T = temperature, °C

Substituting into this equation gives PSAT = 16.9 mm Hg. Recognizing that there 101.325 kPa = 760 mm Hg, we have PSAT = 2.26 kPa.

Step 3) The relative humidity is the ratio of partial water pressure (PW) and the total th vapor pressure (PSAT), (given by equation 9.3-4 on page 566 in the 4 edition of Geankoplis)

P   W PSAT

Thus, PW = (0.79)(2.26 kPa) = 1.79 kPa.

Step 4) Finally, the humidity is defined as the ratio of the mass of water vapor to the mass of dry air. The molar ratio can be written using the ideal gas law, and then with use

1st draft J.M. Keith June 14, 2007 Revision J.M. Keith July 26, 2007 Page 2 of the molecular weights of the gases, to give the mass ratio (given by equation 9.3-1 on page 565 of the 4th edition of Geankoplis) as:

18.02 P H  W 28.97 P  PW

With P = 100 kPa, we have H = 0.0113 kg H2O / kg dry air.

1st draft J.M. Keith June 14, 2007 Revision J.M. Keith July 26, 2007 Page 3 Home Problem Statement: You have an air /water mixture entering a fuel cell at a temperature of 20 oC, a relative humidity of 70%, a mass flowrate of mtotal = 3.0 g/s, and a feed pressure of 1 bar. Note that 1 bar = 100 kPa.

a) What is the saturated vapor pressure of water in kPa (this is the vapor pressure if the relative humidity was 100%)? Use the Antoine equation, B log P  A  10 SAT T  C

where, PSAT = vapor pressure, mmHg A = 8.10765 B = 1750.286 C = 235 T = temperature, °C

b) What is the partial pressure of the water vapor in the feed air in kPa? What is the water flowrate in g/s?

c) Assume that the air / water mixture exiting the fuel cell has a total flowrate of 3.0 g/s but with a water flowrate of 0.1 g/s. The total pressure is 1 bar, and the temperature of this stream is 50 oC. Is the relative humidity greater than 90% (considered a minimum value to maintain a properly humidified membrane)?

Home Problem Solution: Part a. The saturated vapor pressure is the vapor pressure if the relative humidity of the air was 100%.

Using the Antoine Equation to calculate the vapor pressure, we get:

1750.286 log P 8.10765 10 SAT 20  235

log10 PSAT 1.244

101.325 kPa P 17.54 mmHg( ) SAT 760 mmHg

PSAT = 2.338 kPa

1st draft J.M. Keith June 14, 2007 Revision J.M. Keith July 26, 2007 Page 4 Part b. Step 1) The problem statement provided the relative humidity. The relative humidity is the ratio of partial water pressure (PW) and the total vapor pressure (PSAT).

P   W PSAT

PW  PSAT

PW = (0.7) (2.338kPa)

PW = 1.64kPa

Step 2) The water partial pressure can be used to obtain the humidity: 18.02 P H  W 28.97 P  PW

With P = 100 kPa and PW = 1.64 kPa, we have H = 0.0103 kg H2O / kg dry air.

Step 3) We can also use humidity to obtain the mass of water: m H  W mTOT  mW

With mTOT = 3.0 g/s and H = 0.0103 kg H2O / kg dry air, we can solve for mW = 0.0304 g/s.

Part c. Step 1) Again, the Antoine equation can be used to determine the vapor pressure at the new temperature.

1750.286 log P 8.10765  10 SAT 50  235

PSAT = 12.34 kPa

Step 2) We can use the humidity definition: m H  W mTOT  mW

With mTOT = 3.0 g/s and mW = 0.01 g/s, we have H = 0.0345 kg H2O / kg dry air.

1st draft J.M. Keith June 14, 2007 Revision J.M. Keith July 26, 2007 Page 5 Step 3) From the humidity we can solve for the water partial pressure: 18.02 P H  W 28.97 P  PW

With P = 100 kPa, and H = 0.0345 kg H2O / kg dry air, we have PW = 5.26 kPa.

Step 4) We can solve for the relative humidity: P   W PSAT

With PW = 5.26 kPa, and PSAT = 12.34 kPa,  = 0.43.

Step 5) Analysis: The water flowrate of 0.1 g/s is too low to keep the membrane humidified.

1st draft J.M. Keith June 14, 2007 Revision J.M. Keith July 26, 2007 Page 6