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A Concise Model for Evaluating Water Electrolysis

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international journal of hydrogen energy 36 (2011) 14335e14341 Available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/he A concise model for evaluating water electrolysis Muzhong Shen a,*, Nick Bennett a, Yulong Ding b, Keith Scott c a Department of Mechanical & Design Engineering, University of Portsmouth, Portsmouth PO1 3DJ, UK b School of Process, Environmental and Materials Engineering, University of Leeds, Leeds LS2 9JT, UK c School of Chemical Engineering and Advanced Materials, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, UK article info abstract Article history: To evaluate water electrolysis in hydrogen production, a concise model was developed to Received 30 July 2010 analyze the currentevoltage characteristics of an electrolytic cell. This model describes the Received in revised form water electrolysis capability by means of incorporating thermodynamic, kinetic and elec- 2 December 2010 trical resistance effects. These three effects are quantitatively expressed with three main Accepted 7 December 2010 parameters; the thermodynamic parameter which is the water dissociation potential; the Available online 15 September 2011 kinetic parameter which reflects the overall electrochemical kinetic effect of both elec- trodes in the electrolytic cell, and the ohmic parameter which reflects the total resistance Keywords: of the electrolytic cell. Using the model, different electrolytic cells with various operating Water electrolysis conditions can be conveniently compared with each other. The modeling results are found Hydrogen production to agree well with experimental data and previous published work. Electrochemical kinetics Copyright ª 2010, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights Concise model reserved. ButlereVolmer equation 1. Introduction The water electrolysis performance is normally evaluated with the currentevoltage characteristics of an electrolytic cell Hydrogen is a clean fuel for fuel cell applications. Combined as shown in Fig. 1. Several models [11e13] have been devel- with solar cell systems or wind power systems, hydrogen oped to try to simply and effectively simulate the cur- produced with water electrolysis will play an important role as rentevoltage characteristics of PEM electrolysis for hydrogen an energy carrier for sustainable development in future [1]. production. With present models, the cell voltage is basically For reducing operating costs and increasing energy efficiency, described as the sum of Nernst voltage, resistive voltage drop, there are many techniques and research works [2e9] concerning and anode and cathode overpotentials [14]. The anode and the water electrolysis process. Compared with traditional alka- cathode overpotentials are usually obtained via the Butler- line electrolysis [4], in which corrosive potassium hydroxide eVolmer kinetic equation. To solve the ButlereVolmer equa- (KOH) solution is used as the electrolyte, proton exchange tion, two parameters of exchange current density for the membrane (PEM) electrolysis has acquired a lot of attention for anode and the cathode are required to describe the electrode its advantages of ecological cleanliness, high degree of hydrogen activities. Additionally, the symmetrical factors of the equa- purity, and easy maintenance [10]. In general, all these research tion also need to be assumed as a specific number [15]. The works try to improve the electrolysis performance from two exchange current density depends on the temperature and aspects; to increase electrochemical activity of electrodes and to the roughness of the electrode surface [13]. In most case, the reduce the total resistance of the electrolytic cell. values of exchange current density for anode and cathode are * Corresponding author. E-mail address: [email protected] (M. Shen). 0360-3199/$ e see front matter Copyright ª 2010, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.12.029 14336 international journal of hydrogen energy 36 (2011) 14335e14341 ref Nomenclature Ji the pre-exponential factor E the activation energy PEM proton exchange membrane act,i a, c anode, cathode KOH potassium hydroxide 2 0 A: surface area, cm Eanode reversible anode potential À1 0 N: H2 hydrogen producing rate, mol s Ecathode reversible cathode potential À1 0 N O2 oxygen producing rates, mol s Ecell reversible cell potential À À I cell current, A R gas constant, 8.3145 J mol 1 K 1 À r cell resistance, U F Faraday constant, 96,485 C mol 1 V cell potential, V T the absolute temperature, K P electrical power consumed in the electrochemical p pressure, Pa À process, W J the current density, A cm 2 E0 water dissociation potential, V h the activation overpotential À act,i K power conversion coefficient, U 1 J0,i exchange current density different to each other [11,12]. All these make it difficult to At cathode: predict the water electrolysis performance directly. þ þ 5 0 ð + Þ ¼ In this paper, a new model is proposed to simulate the cur- 2H 2e H2 Ecathode 25 C 0 V (2) rentevoltage characteristics of water electrolysis. The water electrolysis capability of an electrolytic cell was expressed The net reaction in the electrolytic cell is: through three main parameters which reflect the thermody- namic effect, the overall electrochemical kinetic effect and the ð Þ5 þ 1 0 ð + Þ¼ : H2O l H2 O2 Ecell 25 C 1 23 V (3) total resistance of the electrolytic cell. With these parameters, 2 different electrolytic cells in various operating conditions can The reversible potential reflects the thermodynamic effect be conveniently compared with each other. An experiment of electrochemical reaction. The Nernst equation of water was designed to investigate the water electrolysis process electrolysis is shown as equation (4) [16]. with different electrode materials and cell resistances. The ! 2 $ RT p pO modeling results are compared and validated with the experi- 0 ¼ : À : Â À3ð À Þ þ H2 2 Ecell 1 23 0 9 10 T 298 ln (4) mental data and with previously published work. 4F pH2O where pH2 , pO2 and pH2O are the partial pressures of hydrogen, oxygen and water vapor respectively. Although the reversible 2. Model description potential of water electrolysis at 25 C is 1.23 V, the water dissociation potential is influenced by the catalyst activity of 2.1. The fundamentals of water electrolysis electrodes. When platinum is used as the anode and cathode, the dissociation potential is 1.68 V [9]. The dissociation Water electrolysis is the process of dissociating water mole- potential can be reduced to 1.4 V when platinum and iridium cules into hydrogen and oxygen gas using electrical power. are used as electrocatalysts [2,6,9,17]. The electrochemical The electrochemical reaction happens on both anode and properties of electrodes not only influence the kinetic effects cathode. of water electrolysis, but also influence the mechanism of At the anode: electrochemical reaction which decides the value of water ð Þ5 þ þ 1 þ 0 ð + Þ¼ : dissociation potential. H2O l 2H O2 2e Eanode 25 C 1 23 V (1) 2 The kinetic effect of water electrolysis is conventionally expressed with the ButlereVolmer equation via the activation A overpotential of both electrodes which can be expressed as equation (5) [12]. " # sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 h ¼ RT À1 J ¼ RT J þ J þ ; ¼ ; act;i sinh ln 1 i a c (5) F 2J0;i F 2J0;i 2J0;i Current ( I ) h where act,i is the activation overpotential and subscripts a and c represent anode and cathode respectively; J is the D B operating current density; J0,i is the exchange current density. The exchange current density can be expressed as O C equation (6). Voltage (V) e ; Fig. 1 The relationship between the current versus ¼ ref Eact i ; ¼ ; J0;i Ji exp i a c (6) potential of water electrolysis. RT international journal of hydrogen energy 36 (2011) 14335e14341 14337 In the water electrolysis process, the activation over- 3.5 potentials of anode and cathode are normally different to 3 each other [12] which reflect their different catalytic activi- ties. However the ratio of electrochemical reaction rate on 2.5 cathode to anode is not decided by their catalytic activities, 2 but only by the stoichometric ratio, because the electric current passing through the cathode always equals the 1.5 Current / A current pass through the anode in electrolysis process. The 1 hydrogen and oxygen producing rates are expressed with eqs. 0.5 (7) and (8) respectively [13]. 0 : ¼ JA 0123456 N H2 (7) 2F Voltage / V r=0.01 r=0.1 r=0.2 r=0.4 r=1.0 : JA N O ¼ (8) 2 4F Fig. 2 e The electrolysis curve of equation (13) with different resistances. 2.2. An assumption and model expression The water electrolysis process and the fuel cell process are From equation (12), the relationship between the potential similar, but working in the opposite direction [18].Our versus current can be expressed with equation (13). pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi previous work [19] has investigated the fuel cell performance 2 V þ 2KrðV À E0Þ V þ 4KrE0ðV À E0Þ from the viewpoint of power conservation. Same as the fuel I ¼ (13) 2rð1 þ KrÞ cell performance, we assume the power consumed in the water electrolysis process is proportional to the square of the 2.3. Characteristics of the mathematical model potential difference between the cell and the water dissoci- ation potentials. This assumption can be expressed as Equation (13) expresses the performance of an electrolytic cell. equation (9). The three parameters, E0, r and K, influence the performance of an electrolytic cell respectively. When E0 equals 1.0 V, Fig. 2 PfðV À E Þ2 (9) 0 shows the relationship between current versus potential of where P is the power consumed in the water electrolysis equation (13) with different resistances if the power conversion À1 process; V is cell potential and E0 is the water dissociation coefficient K is 1.0 U .
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