CACHE Modules on Energy in the Curriculum: Fuel Cells

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1 Abtract CACHE Module on Energy in the Curriculum: Fuel Cell In thi paper we demontrate how new technologie, in thi cae fuel cell, can be rapidly infued into the chemical engineering curriculum. Coure pecific module have been developed that apply fundamental chemical engineering principle to the analyi of fuel cell ytem. The module with be delivered though the CACHE web ite. Each module contain a problem motivation, reference to material from textboo widely ued in the chemical engineering curriculum, an example problem tatement, example problem olution, home problem tatement, and home problem olution. The module [will be available via the CACHE webite by the time the final paper i ubmitted] and are available for ue by any chemical engineering faculty member in their coure. To date we have developed material for the following coure: ma and energy balance, thermodynamic, fluid mechanic, heat and ma tranfer, and inetic and reaction engineering. In addition to preenting the module, we will preent ome preliminary aement on thee educational module. Objective and Motivation The earch for alternative energy ource i an area that ha received great attention in the lat few year, beginning with the January 003 State of the Union addre by Preident George W. Buh, approving federal funding for hydrogen fuel cell reearch for paenger vehicle. Similar announcement were made by tate governor, mot notably Michigan Governor Jennifer Granholm, tating not only will we build thee car in Michigan, our Automotive Technology Corridor will help develop the fuel cell technology thoe car will run on. Inherent within the nation initiative hould be the development of educational program related to fuel cell and other apect of the hydrogen economy. Although it i common for engineering curricula to lag behind technology in emerging field, there ha been a thrut to develop coure material for hydrogen technology reearch within the chemical undergraduate curriculum. Thi paper decribe thee effort. Fuel Cell Overview A fuel cell i device that convert a fuel into electricity with heat a a byproduct. There are everal type of fuel cell, with the mot liely fuel cell to be ued for tranportation application being the proton exchange membrane fuel cell. In thi device, the hydrogen fuel react with oxygen from the air and produce water. A ingle cell of a fuel cell produce about 0.7 V of potential; for many application the cell are taced together to give a higher voltage to power an electric motor. A uch, the majority of deign and analyi of fuel cell ytem focue on a ingle cell. A cartoon i hown in figure 1 below.

2 Bipolar Plate Ga Diffuion Layer Anode Bipolar Plate Ga Diffuion Layer Cathode Electrolyte Figure 1. Schematic of one cell of a proton exchange membrane fuel cell. The lanted line are the bipolar plate, the horizontal line are the ga diffuion layer, the vertical line are the electrode (left bloc i the anode; right bloc i the cathode), and the grid repreent the electrolyte. Within a ingle cell of a fuel cell are bipolar plate which function to eparate one cell from the other. The bipolar plate have channel etched on either ide to allow for reactant and product gae to flow. The plate alo need to have low hydrogen permeation, high thermal conductivity, and high electrical conductivity. Within the channel the chemical reach a ga diffuion layer, and are tranported through thi layer, after which where they encounter the electrode. The electrode contain a platinum catalyt which facilitate the converion of the fuel into proton and electron. The proton pa through a ulfonated polymer electrolyte membrane. Meanwhile, the electron are conducted bac through the ga diffuion layer, bipolar plate, and electric load where they react with the proton and oxygen to form water. For more information regarding fuel cell contruction, the reader i referred to the text of Larminie and Dic 1 or the Lo Alamo National Laboratory fuel cell webite. Bringing Fuel Cell Concept into Engineering Curricula In thi ection we will briefly review our effort in bringing fuel cell technology into the undergraduate and graduate chemical engineering curriculum. At Michigan Tech, fuel cell concept have been incorporated in everal way: Alternative Fuel Group Enterprie thi introduce tudent to alternative energy technology through project wor. Project have been ponored by the United State Army Tan Automotive and Armament Command (TACOM) and Army Reearch Laboratory (ARL), and have focued on integration of commercially available fuel cell into mall and large vehicle. More information on thi curriculum i available elewhere 3-5.

3 Fuel Cell Fundamental Coure thi i a 1 credit elective coure introducing fuel cell technology to chemical, mechanical, and electrical engineering tudent. More information on thi coure i available elewhere 3-5. Fuel Cell Problem Set thee are problem for CM310 Tranport / Unit Operation (heat and ma tranfer and related unit operation). Thee include traditional homewor problem and calculation uing finite element oftware 6. At the Univerity of Michigan, fuel cell concept have been incorporated in everal way: Item 1 Item At the Illinoi Intitute of Technology, fuel cell concept have been incorporated in everal way: Fuel Cell Sytem Deign and Control coure Item Fuel Cell Module Development In the ummer of 006, J. Keith initiated a collaboration with Prof. Scott Fogler of the Univerity of Michigan and Prof. Don Chmielewi of the Illinoi Intitute of Technology. Thi Fuel Cell Curriculum Development Project ha been partially funded by the CACHE Corporation (Computer Aid for Chemical Engineering), and the project tatu wa preented by J. Keith during an invited eion at the November 007 American Intitute of Chemical Engineer Annual Meeting 7. To be mot effective in teaching the tudent, each module conit of a problem motivation, example problem tatement, example problem olution, home problem tatement, and home problem olution. The module alo have additional information that lit the chemical engineering coure that the problem can be ued in, ection of popular textboo to aid intructor in nowing when to ue the problem, and common tumbling point for tudent (baed upon beta-tet at Michigan Technological Univerity). The module are currently online at the following ite 8 : but will eventually be moved over to the CACHE webite 9 : ( There are two example module hown in the appendix at the end of thi paper, for the material and energy balance coure and for the tranport phenomena coure. Current module are available for the coure, and topic area a een in table below. Thee module are currently under peer review from leading educator around the nation a well a indutrial member of the CACHE Corporation.

4 Chemical Engineering Core Coure Material and Energy Balance Material and Energy Balance Material and Energy Balance Material and Energy Balance Thermodynamic Thermodynamic Thermodynamic Heat and Ma Tranport Heat and Ma Tranport Module Title Application of Heat of Reaction: Hydrogen v. Gaoline Material Balance on a Fuel Cell Energy Balance on a Fuel Cell Generation of Electricity Uing Recovered Hydrogen Equation of State for Fuel Cell Gae Thermodynamic and Fuel Cell Efficiency Vapor Preure / Humidity for Fuel Cell Gae Conduction and Convection Heat Tranfer in Fuel Cell Microcopic Balance Applied to Fuel Cell Diffuion Coefficient for Fuel Cell Gae Preure Drop in Fuel Cell Bipolar Plate Nernt Equation and Fuel Cell Kinetic Uing Plug Flow Reactor Equation for Fuel Cell Voltage Table. Current chemical engineering fuel cell module Heat and Ma Tranport Fluid Mechanic Kinetic and Reaction Engineering Kinetic and Reaction Engineering Preliminary Aement During fall of 007, twenty-three tudent enrolled in the Fuel Cell Fundamental Coure at Michigan Technological Univerity. The homewor aignment for thi coure are hown in the following lit: Application of Heat of Reaction: Hydrogen v. Gaoline (full module) Equation of State for Fuel Cell Gae (full module) Thermodynamic and Fuel Cell Efficiency (full module) Nernt Equation and Application in Chemical Kinetic (problem only) Fuel Cell Ma Balance (problem only) Vapor Preure / Humidity for Fuel Cell Gae (full module) Conduction and Convection Heat Tranfer in Fuel Cell (full module) In five of thee aignment, the full module wa given (with the exception of the home problem olution). Example of the full module can be een in the Appendix of thi paper. In two of the homewor aignment, only a problem tatement wa provided. The goal wa to tet the value of providing an example problem and olution. Intitutional Review Board approval wa granted (MTU protocol # M043, Aeing New Learning Module for Fuel Cell Intruction) to ue human ubject in the claroom. A urvey intrument wa developed and ditributed during the final cla meeting.

5 Participation in the urvey wa voluntary. Nineteen tudent participated. The quetion on the urvey and urvey reult, which were very poitive, are ummarized below. 1. I felt that the intructional material helped facilitate my learning. Strongly Agree Agree Ambivalent Diagree Strongly Diagree 9 repone 10 repone 0 repone 0 repone 0 repone. I felt that the homewor problem allowed me to apply my engineering principle to fuel cell and / or fuel cell ytem deign. Strongly Agree Agree Ambivalent Diagree Strongly Diagree 8 repone 11 repone 0 repone 0 repone 0 repone 3. Pleae provide any additional comment you may have on thi coure and/or the intructional module: Sample repone: It wa nice to ee one wored out it conceptualized and gave better bacground. I thought the content and pace of thi coure were ideal for providing an intereting coure which wa not bogged down with an overwhelming amount of courewor. The example problem helped a lot in figuring out how to do each problem. Even when the problem weren t exactly the ame a the aignment the example were till helpful. Wih the material could be more advanced. Future Direction In the future, we aim to develop module for the following coure, with problem decription in italic: Fundamental of Engineering: unit converion, baic engineering calculation, graphing Fundamental of Chemical Engineering: material and energy balance in fuel cell and fuel reformer Tranport / Unit Operation 1 (Fluid Mechanic): preure drop in bipolar plate channel, izing air compreor for fuel cell, izing cooling fan for fuel cell ytem Tranport / Unit Operation (Heat and Ma Tranfer): deign of membrane for ue in fuel cell vehicle, thermal management, ma tranfer through fuel cell electrode, hydrogen leaage through fuel cell bipolar plate, finite element modeling of ma tranfer in fuel cell application Chemical Engineering Thermodynamic: theoretical efficiency of fuel cell, and hydrogen reformer, comparion with internal combution engine

6 Chemical Reaction Engineering: impact of heat and ma tranfer on reactor deign, catalyt for hydrogen proceing, catalyt for fuel cell Chemical Proce Analyi and Deign: deign of alternative energy production facilitie, including hydrogen reforming tation Concluion Thi paper ha decribed module to introduce fuel cell technology into the undergraduate chemical engineering curriculum. Each module contain a problem motivation, example problem tatement, example problem olution, home problem tatement, and home problem olution. Preliminary aement of the module indicate that they are very effective in teaching tudent about fuel cell. It i hoped that thee module can enhance interet in alternative energy technology. New module idea are alo welcome to be included in thi initiative and anyone that would lie to participate in thi CACHE ta force hould contact one of the author. Acnowledgment The CACHE Corporation i acnowledged for partial upport of thi project. JMK i upported by the United State Department of Energy (DE-FG0-04ER6381), National Science Foundation, and the Michigan Space Grant Conortium. DJC i upported by Argonne National Laboratory. HSF and VT are upported by the Vennema and Thurnau Profeorhip at the Univerity of Michigan.

7 Reference 1. Larminie, J.; Dic, A. Fuel Cell Sytem Explained, nd Edition, Wiley, Wet Suex, England, Lo Alamo National Laboratory fuel cell webite, acceed January J. M. Keith, A Student-Driven Enterprie in Fuel Cell and Alternative Fuel, ASEE Conference Proceeding, J. M. Keith, K. C. Opella, M. G. Miller, J. A. King, G. D. Gwaltney, C. A. Green, J. S. Meldrum, and S. A. Bradley, Engineering Education in Alternative Energy, ASEE Conference Proceeding, J. S. Meldrum, C. A. Green, G. D. Gwaltney, S. A. Bradley, J. M. Keith, and T. F. Podlea, Fuel Cell Powered Unmanned Ground Vehicle, SPIE Conference Proceeding, 007, Orlando, FL. 6. J. M. Keith, F. A. Morrion, and J. A. King, Finite Element Method for Enhancing Undergraduate Tranport Coure: Application to Fuel Cell Fundamental, ASEE Conference Proceeding, J. M. Keith, D. J. Chmielewi, H. S. Fogler, and V. Thoma, CACHE Module on Energy in the Curriculum: Fuel Cell, preented at the AIChE Annual Meeting, 007, Salt Lae City, UT. 8. Fuel Cell Curriculum webite, acceed January CACHE webite, acceed January 008.

8 Appendix: Sample Module for Material and Energy Balance Module Title: Material Balance in a Solid Oxide Fuel Cell Module Author: Donald J. Chmielewi Author Affiliation: Center for Electrochemical Science and Engineering Department of Chemical and Biological Engineering Illinoi Intitute of Technology, Chicago, IL Coure: Material and Energy Balance Text Reference: Felder and Roueau (000), Section 4.7 Concept Illutrated: Material balance on a reactive proce with complex geometry; Extenion of balance and toichiometry concept to electron. Problem Motivation: Fuel cell are a promiing alternative energy technology. One type of fuel cell, the Solid Oxide Fuel Cell (SOFC) ue hydrogen a a fuel. The fuel react with oxygen to produce electricity. Fundamental to the deign of an SOFC i an undertanding of the fuel and oxidant utilization a well a the amount of current generated. The SOFC reaction are: Anode: H + O - H O + e - Cathode: O + 4 e - O - Overall: H + 1/O H O e - e - Electron Flow (Current) Electric Load Cell Voltage HO H HO H H H H HO HO O - O - O - O - Figure 1: Reaction within SOFC O O N O O Anode Cathode Electrolyte N N O H In H & H O Out Fuel Cell Ga Anode Ga Chamber Cathode Chamber Air In Air Out Figure : Flow Diagram for SOFC For each mole of hydrogen conumed, two mole of electron are paed through the electric load. To convert electron flow (mole of electron/) to electrical current (coulomb/ or amp), one would ue Faraday contant: F = 96, 485 coulomb / mole of electron. The primary objective of a fuel cell i to deliver energy to the electric load. To calculate the energy delivery rate (alo now a power) one would multiply the current

9 time the cell voltage: Power = Current * Voltage. (Recall the unit converion: coulomb volt = joule and joule / = watt ). Problem Information Example Problem Statement: A SOFC i operated with an inlet flow of 0 g/ of pure hydrogen and an inlet flow of 1450 g/ of air. If the fuel utilization i 50%, then determine the following: 1) The ma flow out of the anode ga chamber. ) The ma flow out of the cathode ga chamber and the oxygen utilization. 3) The current through the electric load. 4) If the cell voltage i 0.8 volt, determine the power delivered to the load. Example Problem Solution: 1) We begin by converting the anode inlet ma flow rate to molar flow: 0 g H fed 1 mole H 10 mole H fed = g H The term utilization i ynonymou with the percent converion, a defined in ection 4.6 of Felder and Roueau (000). Thu, a 50% utilization of hydrogen indicate 0.5 mole H reacted 10 mole H fed 5 mole H = mole of H fed reacted Thu, 5 mole / ec of H will be converted to H O. The remaining 5 mole/ec of H will then exit with the generated team. Converting bac to ma flow, we have: 5 mole H exiting g H 10 g H exiting = 1 mole H 5 mole H O exiting 18 g H O 90 g H O exiting = 1 mole H O for a total of 100 g/ exiting the anode. ) Auming the ma fraction of air i 76.7% N and 3.3% O, we find the cathode inlet molar flow to be: g of of air fed g N g of air air fed 0.33 g O g of air mole N 8 g N mole O 3 g O = mole N g = mole O fed fed

10 Since 5 mole/ of H are converted in the anode,.5 mole/ of O mut be conumed in the cathode. Thu, only 8.1 mole/ of O remain, and the oxygen utilization i calculated a: Utilizatio n.5 mole of O reacted = mole of O fed Converting bac to ma flow, we have: = 3.6% 8.1 mole O exiting 3 g O 59 g O = 1 mole O exiting Adding thi to the inert flow of N (111 g/), give a total of 1371 g/ exiting the cahode ga chamber. 3) Looing at the anode toichiometry, we find that mole of electron are ent to the load for every mole of hydrogen conumed. Thu, the electron flow i 10 mole / ec. If we now employ Faraday contant, F = 96, 485 coulomb / mole of electron, for unit converion, we find the current to be 964,850amp (1 amp = 1 coulomb/ec). 4) Application of the relation: Power = Current * Voltage, yield a power of 770,000 J/ or 0.77 mega-watt (MW) Home Problem Statement: A SOFC i operated with an anode exit flow of g/ec and an inlet of pure hydrogen. If the cell i operated at 0.75 volt and deliver 10W of power, determine the following: 1) The ma flow into the anode ga chamber. ) The ma flow into the cathode chamber if a 0% oxygen utilization i deired. Home Problem Solution: Firt, we will need ome preliminary calculation. From the delivered power and operating voltage, we find the current a: 10,000J / Current = = 13,330 amp = 13,330 coulomb / 0.75 volt Uing Faraday contant, thi i equal to 0.14 mole of electron/. Uing the SOFC toichiometry thi tranlate to 0.07 mole of H reacted /, 0.07 mole H O produced / and mole of O reacted /. 1) If we define a control volume around the anode ga chamber, we find the balance:

11 m a, in = m ( m m a, out a, produced a, conumed ) g of H = = 0.88g / 0.07mole of H O 18g H O 0.07mole of mole H O H g H mole H A an additional note, thee number indicate a 15% utilization of the hydrogen feed. ) From the preliminary calculation, mole of O are reacted /. To achieve the deired 0% oxygen utilization the flow oxygen to the cathode i calculated a: mole of O fed mole O reacted mole O = 0. mole O reacted fed Auming the mole fraction of air i 79% N and 1% O, we find that the required inlet flow of N to be: mole O fed 0.79 mole of N mole N = 0.1 mole of O fed Finally, the ma flow into the cathode i calculated a: m c in = m + m O, in N, in, mole of = = 4g / O 3g O mole O mole of + N 8g N mole N A an additional note, the exit flow from the cathode hould be 1.7 g/ec.

12 Appendix: Sample Module for Tranport Phenomena Module Title: Microcopic Energy Balance in Fuel Cell Module Author: Jaon Keith Author Affiliation: Department of Chemical Engineering Michigan Technological Univerity, Houghton, MI Coure: Tranport Phenomena (Heat Tranfer) Text Reference: Bird, Stewart, and Lightfoot ( nd edition) ection 10. Welty, Wic, Wilon, and Rorrer (4 th edition) ection 17. Concept: Solving differential equation to obtain the temperature profile Problem Motivation: Fuel cell are a promiing alternative energy technology. One type of fuel cell, a proton exchange membrane fuel cell react hydrogen and oxygen together to produce electricity. Fundamental to the deign of fuel cell i an undertanding of heat tranfer mechanim within fuel cell. Heat removal from fuel cell i critical to their caleup for large power application. Conider the chematic of a compreed hydrogen tan feeding a proton exchange membrane fuel cell, a een in the figure below. The electricity generated by the fuel cell i ued here to power a laptop computer. In thi module we will olve microcopic equation to determine the temperature profile within one cell of a fuel cell. Computer (Electric Load) H feed line Air in Anode Ga Chamber Cathode Ga Chamber H tan H out Fuel Cell Air / H O out

13 Example Problem Statement: In thi example we will apply principle of microcopic energy balance to the deign of a fuel cell ytem. For implicity, we will conider the rectangular geometry hown below, which decribe flow over and heat conduction through a olid plate, with a heat ource (due to reaction). Flow, h, T Solid,, q Inulated Boundary x The governing equation decribing the thermal energy conervation equation i given by: d T = q (1) Note that in equation 1 there i a uniform heat generation rate q within the olid. Equation 1 i ubject to the boundary condition: and dt = h( T T ), at x = 0 () dt = 0 at x = L (3) It i noted that equation condition can be derived from an energy balance at the ga/olid interface and that equation 3 i due to the inulated boundary. The following parameter are available: q = 48 W/cm 3, L = 0.5 cm, T = 93 K, = 0.0 W/cm-K. Your ta are the following: 1) Integrate the equation to determine T a a function of x. ) Determine the value of the heat tranfer coefficient h (in unit of W/cm -K) needed to eep the maximum temperature in the olid below 358 K. 3) Plot the temperature ditribution T a a function of the patial coordinate x under the condition of part.

14 Example Problem Solution: We begin by doing ome mathematical manipulation and then olve the ordinary differential equation of equation 1. For more information, pleae conult a differential equation text. Part 1) Step 1) Manipulation. We divide both ide of equation 1 by and write the econd derivative a the derivative of the firt derivative to obtain: d dt = q (4) Step ) Integration. We can then multiply both ide by, and integrate to obtain: dt = q x + c (5) where c i an integration contant. Step 3) Boundary condition. Applying the no-flux boundary condition at x = L we can olve to how that: ql c = (6) dt ql We alo note that at x = 0 the derivative = or ued later in the other boundary condition. dt = ql. Thi will be Step 4) Another integration. Since the derivative dt/ i already iolated, we can integrate equation 5 to olve for the temperature ditribution: q x T = Lx + d (7) where d i an integration contant. We note that at x = 0, T = d. Step 5) Other boundary condition. Applying the mixed boundary condition at x = 0 we dt can how that = h( T T ) can be manipulated to give: ql = h( T d) (8)

15 ql and upon olving for d = T + we can write down the temperature ditribution a: h q x ql T = T Lx + h (9) Part ) Step 1) Manipulation. We firt note that the maximum temperature T max will occur at the inulated boundary, where x = L. Performing thi ubtitution into equation 9 give: ql ql T max = T + + (10) h Step ) Algebra. Solving equation 10 for h we obtain: h = T max ql ql T (11) Step 3) Calculation. We can now ubtitute the nown parameter to determine the value of the heat tranfer coefficient. Equation 11 become: W cm 3 W h = cm = (1) W cm K 48 (0.5cm) 3 358K 93K cm 0.W cmk Part 3) The following i a plot of equation 9, howing T a a function of x. Note that the hape of the graph i parabolic. Thi mae ene ince the econd derivative i equal to a contant. The lope of the graph at x = L i zero a it i expected to be for an inulated boundary.

16 Home Problem Statement: In thi example we will apply principle of microcopic energy balance to the deign of a fuel cell ytem. For implicity, we will conider the rectangular geometry hown below: Flow, h, T Solid,, q Inulated Boundary x Let u aume a nonuniform ource, with more reaction near the inulated boundary, uch that equation 1 of the example problem can be modified a: d T = qx (13)

17 Equation 13 i ubject to the boundary condition and dt = h( T T ), at x = 0 (14) dt = 0 at x = L (15) The following parameter are available: q = 100 W/cm 4, L = 0.5 cm, T = 93 K, = 0.0 W/cmK, and h = 1 W/cm K. Your ta are the following: 1) Integrate the equation to determine T a a function of x. ) Determine the maximum temperature in the olid. 3) Plot the temperature ditribution T a a function of the patial coordinate x Home Problem Solution: Part 1) Step 1) Manipulation. We divide both ide of equation 1 by and write the econd derivative a the derivative of the firt derivative to obtain: d dt = q x (16) Step ) Integration. We can then multiply both ide by, and integrate to obtain: dt = q x + c (17) where c i an integration contant. Step 3) Boundary condition. Applying the no-flux boundary condition at x = L we can olve to how that: ql c = (18) dt We alo note that at x = 0 the derivative ued later in the other boundary condition. = ql or dt ql =. Thi will be Step 4) Another integration. Since the derivative dt/ i already iolated, we can integrate equation 17 to olve for the temperature ditribution:

18 3 q x T = L x + d 3 (19) where d i an integration contant. We note that at x = 0, T = d. Step 5) Other boundary condition. Applying the mixed boundary condition at x = 0 we dt can how that = h( T T ) can be manipulated to give: ql = h( T d) (0) and upon olving for d ql = T + we can write down the temperature ditribution a: h T 3 q x L ql = T x + 6 (1) h Part ) Step 1) Manipulation. We firt note that the maximum temperature T max will occur at the inulated boundary, where x = L. Performing thi ubtitution into equation 1 give: T 3 ql ql = T + () 3 h max + Step ) Calculation. We can now ubtitute the nown parameter to determine the value of the heat tranfer coefficient. Equation become: W 3 W 100 (0.5cm) 100 (0.5cm) 4 4 T cm cm max = 93K + + = 36K (3) 0.W 1W 3 cmk cm K Part 3) The following i a plot of equation 1, howing T a a function of x. Note that the hape of the graph i cubic, but till retain a zero lope at x = L for the inulated boundary.

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