Dynamic modelling of a proton exchange membrane (PEM) electrolyzer

Transcription

1 Internatonal Journal of Hydrogen Energy (006) Dynamc modellng of a proton exchange membrane (PEM) electrolyzer Haluk Görgün Yldz Techncal Unversty, Electrcal-Electroncs Faculty, Istanbul 8070, Turkey Avalable onlne 6 May 00 Abstract Ths paper descrbes a dynamc model for PEM electrolyzer based on conservaton of mole balance at the anode and the cathode. A further feature of the model s t ncludes water phenomena, electro-osmotc drag and dffuson, through the membrane. The model consders PEM electrolyzer to be composed of four ancllares: anode, cathode, membrane and voltage ancllary. Addtonally, hydrogen storage dynamcs s presented. The developed model s sutable for determnng control strategy that wll ensure effcent and relable operaton of the electrolyzer. Moreover, the dynamc model can be ntegrated wth renewable energy systems models to desgn, analyze and optmze sustanable energy systems. The study llustrates the dynamc nteractons wthn a PEM electrolyzer and shows the necessty of the proposed approach of separate ancllares. 00 Internatonal Assocaton for Hydrogen Energy. Publshed by Elsever Ltd. All rghts reserved.. Introducton Electrolyzers are unque devces to produce pure hydrogen and oxygen. They could be wdely dstrbuted and rated to meet the hydrogen and oxygen requrements of dfferent users such as unts for ndvduals, renewable energy systems, fuellng statons and ndustral applcatons. Among the other types of electrolyzers PEM electrolyzers are very smple and compact. Besdes they ensure hgh purty and effcency at hgh current densty levels. In PEM electrolyzers, the bonds between the hydrogen and oxygen n the H O are broken by electromotve force and the catalytc acton of the platnum when dc voltage s suppled. The membrane separates the H from the O. The hydrogen protons, H, mgrates through the membrane and recombnes at the cathode wth the returnng electrons, e, and form hydrogen, H. PEM electrolyzers offer the potental for low cost n mass producton, f nexpensve membranes are developed. Last but not least, the other notable advantage of PEM electrolyzers s that the PEM electrolyzer can be used as a fuel Tel.: (78); fax: E-mal address: halukgorgun@alum.rp.edu. cell to produce electrcty from hydrogen and oxygen wth small modfcatons. In addton to the cell stack an electrolyzer must have a dc power supply, a water pump, water gas separators as llustrated n Fg.. Although electrolyzers produce both H and O by splttng water electrochemcally only few applcatons uses both products. Most of the tme electrolyzer s consdered as a hydrogen generator. Electrolyzers are categorzed as anode feed system or cathode feed system dependng on where the water enters the unt. When the electrolyzer s used for just hydrogen generator, cathode feed system could be a good opton because the separator whch separates oxygen and water s elmnated at the anode and oxygen s ventlated wth water. The penalty n ths case s that mass transfer lmtatons occurs and only low current denstes can be acheved. In ths study, anode feed electrolyzer modellng s studed snce most of the commercal electrolyzers and mltary unts are anode feed electrolyzers. However, t should be mentoned that modellng of cathode feed electrolyzer can be accomplshed wth couple of changes n water transport phenomena. Applcatons of electrolyzers nclude: O for lfe support, fuel cells, sustanable energy systems, provdng H for /$ Internatonal Assocaton for Hydrogen Energy. Publshed by Elsever Ltd. All rghts reserved. do:0.06/j.jhydene

2 0 H. Görgün / Internatonal Journal of Hydrogen Energy (006) 9 8 DC Power Supply H O n - Seperator H Water Pump A C O Seperator PEM Electrolyzer H Bottle Fg.. PEM electrolyzer. corroson control, gas chromatograph sensors, metal formng and weldng. Electrolyzers are currently beng studed by several researchers from ndustry, academa and mltary and research results are beng publshed at an ncreasng rate. There are several studes to model electrolyzers and renewable energy systems. Among them, Onda [] has developed a two dmensonal mathematcal model to analyze PEM electrolyzer. Ulleberg [] has shown a model for alkalne electrolyzers based on thermodynamcs and heat transfer theory. More recently on renewable energy systems, Kélouwan et al. [] have demonstrated stand alone renewable energy system wth hydrogen storage. Khan et al. [] have presented modellng of a small wnd fuel cell hybrd energy system. In an earler study, Busquet et al. [] have establshed an emprcal approach to model a electrolyzer or a regeneratve fuel cell. In general, electrolyzer, renewable energy or regeneratve fuel cell studes have been formulated electrolyzers wth just Faraday s Law. There s a need for an electrolyzer model whch explans ts dynamcs n detal and s sutable for dynamc smulaton together wth renewable energy systems. Ths paper gves a detaled control orented model for a PEM electrolyzer based on mole balance n the anode and the cathode subsystems. The model s capable of characterzng PEM electrolyzer and essental for determnng control strategy that wll ensure effcent and relable operaton of the electrolyzer. Besdes, the PEM electrolyzer dynamc model can be employed n the optmzaton of sustanable energy systems. Ths paper s organzed as follows: model detals are presented n Secton. Smulaton studes demonstrated n Secton. Fnally, conclusons are gven n Secton.. Modellng To clearly quantfy the dynamc nteractons, the PEM electrolyzer s consdered to have four ancllares: anode, cathode, membrane and voltage ancllary. Each ancllares dynamcs and nteracton between them are contemplated. Voltage ancllary calculates electrolyzer appled voltage level by usng Nernst Equaton, ohmc polarzaton and actvaton polarzaton. Membrane ancllary computes water content, electro-osmotc drag, water dffuson and conductvty of the membrane. The anode ancllary dynamcally calculates oxygen and water flows and partal pressures. Smlarly, hydrogen and water partal pressures and ther flows are obtaned n the cathode subsystem. Storage ancllary shows storage dynamcs of the generated hydrogen n a bottle by takng account the ntal hydrogen level n t and compressblty of the hydrogen. The Smulnk Model of the electrolyzer s shown n Fg. and n the followng subsectons, the model s explaned n detal... Anode ancllary Electrochemcally, all electron transfer reactons are consdered oxdaton and reducton. The substance ganng electrons s oxdzng the substance that s losng electrons. The anode electrode s the electrode where the oxdaton occurs n electrolyzers by defnton. In ths sde of the electrolyzer the states are oxygen, and water molar hold-ups. The dynamcs n the model are: Ṅ O = F O a F O ao O g, Ṅ H O a = F H O a F H O ao F H O eod F H O d, () where, F O a, F O ao, F H Oa, F H Oao (mol/s) are cathode nlet and outlet molar flows of oxygen and water, respectvely. One should note that F O a s zero because only nput s the water, ths term s wrtten to show the general complete mole balance dynamcs. F H Oeod and F H O d are electro-osmatc drag and dffuson flows. O g s the rate of oxygen generated at the anode. The partal pressures of the oxygen and water at the anode are p O = N O RT el V a and p H O a = N H O a RT el V a, ()

3 H. Görgün / Internatonal Journal of Hydrogen Energy (006) 9 8 Current 0 Electrolyzer pressure pelec P0 px TSTACK Tel Fef Faraday Effcency Faref FH0n Fa Fa H C Water n Cathode Ancllary Tc Vel Vel L t Clock FH0m FH0m t Ourrent Ph Fa Current /A Curd Current Densty Cu pelec Tel Fc Fc Fc Tst lamn lamn landern Voltage Ancllary Faef Membrane Ancllary FH FH0n Cathode Ancllary H Flow pb Pb Bottle Pressure Storage Ancllary Fg.. PEM electrolyzer smulnk dagram. where V a (m ) s the anode volume, and the total anode pressure, P a,s P a = p O p H O a. () Oxygen mole fracton at the anode outlet s as follows: y O = p O, () P a and the flows are computed as F ao = F O ao F H Oao, F O ao = y O F ao, F H O ao = ( y O )F ao, () where the anode total out-flow, F co, s obtaned by F ao = k ao (P a P a0 ), (6) where k co s the cathode outlet flow coeffcent. Fnally, the rate of oxygen generated s O g = ni F η F, (7) where n s the number of the electrolyzer cells, I s the electrolyzer current, F s the Faraday constant and η F s Faraday effcency whch s gven as [6,7], η F = Loss, (8) where Loss s nternal current and hydrogen loss that could be result of oxygen travel from anode to cathode or hydrogen travel from cathode to anode n general Loss s less than % of the operatng current densty... Cathode ancllary Cathode s the electrode where the reducton takes place n electrolyzers by defnton. The states of the cathode sde of the electrolyzer are hydrogen and water molar hold-ups, N H and N H O c, respectvely, Ṅ H = F H c F H co H g, Ṅ H O c = F H O c F H O co F H O eod F H O d, (9) where F H c and F H O c (mol/s) are cathode electrode hydrogen and water nlet molar flows and they are equal to zero snce there s no n flows. F H co are F H O co (mol/s)

4 H. Görgün / Internatonal Journal of Hydrogen Energy (006) 9 8 are cathode outlet molar flows of hydrogen and water, respectvely, F H O eod (mol/s) and F H O d (mol/s) are electro-osmotc drag and dffuson from anode electrode through the membrane, and H g s the rate of hydrogen generated. The partal pressures of hydrogen and water n the cathode are obtaned from the deal gas law as n the anode, p H O c = N H O c RT el V c and p H = N H RT el V c, (0) where V c (m ) s the cathode volume, and the total cathode pressure s P c = p H p H O c. () Smlar to the anode, hydrogen and water molar flows at the cathode are computed from cathode out total flow and mole fractons. y H = p H P c () and the flows are F co = F H co F H O co, F H co = y H F co, F H O co = ( y H )F co, () where the cathode subsystem out-flow, F co,s F co = k co (P c P 0 ), () where k co s flow coeffcent and P 0 s the cathode out pressure. The rate of hydrogen reacted s calculated as H g = ni F η F. ().. Membrane ancllary Membrane ancllary s of mportance to understand the water transport phenomena n electrolyzers. There are two man water flows occurrng through the membrane: Electroosmatc drag and dffuson. Both of them are functon of the water content of the membrane. When the H protons moves through the membrane, water molecules accompany them. Ths phenomenon s wellknown as electro-osmotc drag and ths water transportaton s expressed by F H O eod = n d F M H OAn, (6) where M H O s molecular weght of water, A s the area of the cell and n d s the electro-osmotc drag coeffcent whch s gven as n d = 0.009λ m 0.0λ m. 0 9, (7) where λ m s the arthmetc mean of both λ s for the anode and the cathode whch are calculated by ther own water actvtes by (8). Membrane water content, λ s gven as n [8] λ = a a 9.8aa 6a a, 0 <a a, λ =.(a a ), <a a. (8) Volt (Volts) (ma/cm ) Fg.. Electrolyzer polarzaton.

5 H. Görgün / Internatonal Journal of Hydrogen Energy (006) 9 8 The water dffuson coeffcent s computed as ( D w = D λ exp 6 where ( 0 T fc )), (9) D λ = 0 0, λ < ; D λ = 0 0 ( (λ m )), λ m ; D λ = 0 0 (.67(λ m )), λ m.; D λ =. 0 0, λ m.. (0) Water dffuson through the membrane s gven from Fck s frst law of dffuson as follows: (C wc C wa ) F H O d = D w M H OAn, () t m where t m s the thckness of the membrane and C wc and C wa are water concentraton for the cathode and anode surface of the membrane, respectvely, and they are expressed as C wa = ρ m,dry M m,dry λ a,.. Voltage ancllary C wc = ρ m,dry M m,dry λ c. () Electrolyzers operates n ether current mode or voltage mode. When they are run n voltage mode, voltage s appled to the electrolyzer and dependng on the operatng condtons the electrolyzer draws the current from the source and after a couple of transent cycles t has ts steady state value. Ths mode s sutable for when photovoltac source s used for an electrolyzer. However, most of the commercally avalable electrolyzers run n current mode and operatng voltage of an electrolyzer s gven as V el = E V act V ohm, () where E s open crcut voltage, V act s actvaton polarzaton, V ohm s ohmc polarzaton. Open crcut voltage, E, s defned as Nernst Equaton [9] E = E 0 RT el F ln p H p / O, () a H O where E 0 s the standard potental, R s the unversal gas constant, T el s the cell temperature and a H O s water actvty between anode and electrolyte for smplcty t s assumed here to be. Standard voltage E 0 s E 0 = ΔG f F, () where ΔG f s Gbbs free energy of formaton. The actvaton polarzaton s obtaned by ( V act = RT el αf ln 0 ), (6) Effcency (ma/cm ) Fg.. Electrolyzer effcency. where α s charge transfer coeffcent, s the current densty and 0 s the exchange current densty. The ohmc polarzaton s calculated by V ohm = R ohm, (7) where the membrane resstance, R ohm,s R ohm = t m σ m, (8) where σ m s the conductvty of the membrane whch s calculated from water content of the membrane, λ m, and the electrolyzer temperature, T el, as follows [0]: ( ( σ m = (0.00λ m 0.006) exp 68 0 )). T el (9).. Storage ancllary Produced H by electrolyzer s stored n H bottle. Constant H flow flls up the bottle untl ts pressure reaches up the electrolyzer cathode pressure. The dynamcs of the storage s obtaned as follows: P b P b = z N H RT b M H V b, (0) where P b s the ntal H pressure n the bottle, z s the compressblty factor of the hydrogen. The compressblty factor s a functon of temperature and pressure, t s equal to when the pressure s below 000 ps at room temperature but t s hgher than when the pressure s above

6 H. Görgün / Internatonal Journal of Hydrogen Energy (006) x 0 8 Bottle Pressure (Pascal) tme (secs) Fg.. Bottle pressure. 00 Current(A) 80 I (Amper) 60 0 Hydrogen Flow (mole/secs) tme (secs) x 0 Hydrogen Flow tme(secs) Fg. 6. Electrolyzer current transents.

7 H. Görgün / Internatonal Journal of Hydrogen Energy (006) 9 8 R Og Current faref n*u[]/(*f) s NO po po Pa 6 Water n s phoa yo FHOm Fa Tel Psata Peleo 0.9 Fao x FOa0 x FHOa0 Fg. 7. PEM electrolyzer anode ancllary smulnk dagram. /Vc u[]*u[] R Hg Current n*u[]/(*f) s NH ph ph faref Pc FHOm s NHOc phoc (u[]/u[]) yh Fc Tel f(u) P satc P elec 0. Fco x FHCo FH x FHOco Fg. 8. PEM electrolyzer cathode ancllary smulnk dagram.

8 6 H. Görgün / Internatonal Journal of Hydrogen Energy (006) 9 8 (u[]*u[])f FH0eod u[]*mho*a*n FH0m 009*u[] 0.0*u[]-.e-9 nd FHOm lamm Damm Dlam am lamm lamm Tst u[]*expt(6*((/0)-(/u[]))) DW Fa Gan am u[]*(u[]-u[])tm FHOd Fc CVC aca lamc larnc CVa u[]*romd/mmd aen lama lama u[]*romd/mmd Fg. 9. PEM electrolyzer membrane ancllary smulnk dagram. 000 ps []: At hgher pressure values t affects the bottle pressure dynamcs remarkably. T b and V b are the bottle temperature and volume, respectvely. It s assumed that the bottle temperature s constant through the storng process snce the process s slow. down from 0 to 0A, and agan t s ncreased to 70A at t = 00 s. These fgures exhbt that the model can capture the transent dynamc behavor of the PEM electrolyzer (Fgs. 7 ).. Smulaton results Ths secton presents smulaton results for a PEM electrolyzer. For the smulatons we mplement the model derved n Secton n Matlab-Smulnk. Smulaton studes are pursued assumng PEM electrolyzer stack conssts of n= cells, wth A m =0 cm actve area each, and wth t m = 0.00 cm thckness. Electrolyzer operatng temperature and pressure are chosen as T =00 K and P =0 Pa. Fgs. and shows polarzaton and effcency of the stack, respectvely. Fg. llustrates hydrogen bottle pressure changes. The bottle pressure can be set one value so that when t s reached, current flow s stopped. In Fg. 6, current transents are ntroduced and respondng hydrogen partal pressure are presented. At t = 00 s operatng current s stepped up from 0 to 0A, and at t = 00 s the current s stepped. Concluson A dynamc PEM electrolyzer model has been developed by explotng conservaton of mole balance. Specal attenton has been gven to the modellng of subsystems to clearly quantfy the dynamc nteractons of a PEM electrolyzer. The ntegrated model s mplemented by usng Matlab-Smulnk. Smulaton studes demonstrated that the model can capture the transent dynamc behavor of the PEM electrolyzer. Ths model s essental for determnng control strategy that wll ensure effcent and relable operaton of the electrolyzer. Furthermore, the PEM electrolyzer dynamc model can be ntegrated wth renewable energy systems models to desgn, analyze and optmze sustanable energy systems. The extenson of ths study wll be to fully valdate the model wth PEM electrolyzers n Connectcut Global Fuel Cell Center.

9 H. Görgün / Internatonal Journal of Hydrogen Energy (006) ph ph po po Ε Tfc Stack Tem p OCV Vohm n number of stack Vel Tfc Rmohm lam dam Rmohm lamdam Vohm.8 Elf 0 Lmtng Current o Tfc Va v 0. Fg. 0. PEM electrolyzer voltage ancllary smulnk dagram. R Ideal Gas Constant 00 Room Temp H Flow -c- S pb Compresblty Factor -c- -c- Bottle ntal pressure Bottle Volume MH H Molecular Mass Fg.. PEM electrolyzer storage ancllary smulnk dagram. Acknowledgements The author would lke to acknowledge Dr. Frano Barbr and Mr. Trent Molter of Connectcut Global Fuel Cell Center for very useful dscussons and suggestons that contrbuted ths paper. References [] Onda K, Murakam T, Hkosaka T, Kobayash M, Notu R, Ito K. Performance analyss of polymer electrolyte water electrolyss cell at a small-unt test cell and performance predcton of large stacked cell. J Electrochem Soc 00;9: [] Ulleberg ]. Modelng of advanced alkalne electrolyzers: A system smulaton approach. Int J Hydrogen Energ 00;8:. [] Kélouwan S, Agbossou K, Chahne R. Model for energy converson n renewable energy system wth hydrogen storage. J Power Sources 00;0:9 9. [] Khan MJ, Iqbal MT. Dynamc modelng and smulaton of a small wnd fuel cell hybrd energy system. Renewable Energy 00;0: 9.

10 8 H. Görgün / Internatonal Journal of Hydrogen Energy (006) 9 8 [] Busquet S, Hubert CE, Labbé J, Mayer D, Metkemejer R. A new approach to emprcal electrcal modellng of a fuel cell, an electrolyser or a regeneratve fuel cell. J Power Sources 00;: 8. [6] Barbr F. Pem electrolyss for producton of hydrogen from renewable energy sources. Solar Energy 00,;78:66 9. [7] Barbr F, Molter T, Dalton L. Effcency and weght tradeoff analyss of regeneratve fuel cells as energy storage for aerospace applcatons. Int J Hydrogen Energy 00, n press. [8] Dutta S, Shmpalaee S, Zee JWV. Numercal predcton of mass-exchange between cathode and anode channels n pem fuel cell. Int J Heat Mass Transfer 00;:09. [9] Larmne J, Dcks A. Fuel cell systems explaned. New York: Wley; 000. [0] Sprnger TE, Zawodznsk TA, Gottesfeld S. Polymer electrolyte fuel cell model. J Electrochem Soc 99; 8:. [] McCarty RD, Hord J, Roder HM. Selected propertes of hydrogen. US Department of Commerce; 98.