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Nonlinear Dynamics of Fuel Cells: A Prototype Model


Hanke-Rauschenbach,  Richard
Process Systems Engineering, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;
Otto-von-Guericke-Universität Magdeburg, External Organizations;

Sundmacher,  Kai
Process Systems Engineering, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;
Otto-von-Guericke-Universität Magdeburg, External Organizations;

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Hanke-Rauschenbach, R., Mangold, M., & Sundmacher, K. (2011). Nonlinear Dynamics of Fuel Cells: A Prototype Model. Talk presented at 220th ECS Meeting. Boston/Massachusetts. 2011-10-09 - 2011-10-14.

A meaningful design and an efficient operation of fuel cells require a comprehensive understanding of the un­der­lying physico-chemical processes. Intensive fuel cell re­search carried out over the last decades led to the develop­ment of fundamental concepts which in the meantime have found entry into text books and standard works. How­ever, special attention needs to be paid, when the sys­tem under consideration exhibits nonlinear operating be­havior. The fuel cell literature con­tains va­rious relevant experimental reports and theoretical pre­dic­tions on non­li­near phenomena in fuel cells. Among them are several ins­tances of bistability, observed e.g. in pro­ton-exchange mem­brane (PEM) fuel cells or high-tem­perature fuel cells (e.g. [1-3]). Further­more, os­cil­latory conditions and pat­tern formation have been re­por­ted especially in PEM fuel cells (e.g. [4,5]). A careful ana­lysis of these studies re­veals that the understanding of non­linear effects in fuel cells is not only of academic in­te­rest, but is crucial for improved operation and process de­sign. Within the present contribution a prototype mo­del is suggested [6], which allows for a systematic dis­cus­sion of the findings on nonlinear operating behavior of fuel cells, mentioned above. The model consists of Kirch­hoff’s loop law for the determination of the cell voltage, a ge­ne­ric charge balance and a generic mass and energy ba­lance. The model is used to illustrate that nonlinear ope­ra­ting be­havior, such as bistability or oscillations, can be traced back to a branch of the current-voltage-curve ex­hi­bi­ting a negative differential resistance (NDR) [7]. Two diffe­rent types of such an NDR-branch can be dis­tin­guished. An N-type NDR-branch ends in two ver­ti­cal tangents in the iU-phase-plane. Systems possessing such an NDR-branch can exhibit bistability under gal­va­no­static control but not under potentiostatic control. A S-type NDR-branch ends in two horizontal tangents in the iU-phase-plane. Such systems can exhibit bistability under potentionstatic control but not under galvanostatic con­ditions. A careful analysis of the prototype model reveals the exis­tence of three main classes of system properties lea­ding to a NDR-branch. The first class of phenomena ori­gi­nates from the ion transport trough the electrolyte ma­terial. In order to create a negative differential resis­tance, a state-dependent electrolyte resis­tance is required. Clear examples for such a behavior can be found in PEM fuel cells operated under reduced feed stream humi­di­fi­ca­tion at constant flow rate, as well as in high-tem­pe­ra­ture fuel cells. In both cases, a product of the electro­che­mi­cal reac­tion – product water in case of the PEM fuel cell and ther­mal energy released in the elec­tro­che­mical reaction in case of the high-temperature fuel cell – leads to a decrease of the electrolyte resistance. Bistable iU-curves of the S-type have been observed or predicted under such con­di­tions. The second class of phenomena originates from nonlinear electrochemical surface kinetics at one of the elec­trodes of the fuel cell. In order to create a negative diffe­rential resistance, a potential dependent transport step is required. The PEM fuel cell exposed to H2/CO-mix­tures gives a clear example for this class. Here, the sur­face coverage of hydrogen, which is the reactant of the main Faradaic reaction at the anode, is influenced at ele­va­ted electrode potentials by the dissociation of water to­wards the catalyst surface. As a consequence a N-type NDR-branch is formed, which however gets hidden under steady-state conditions by the CO electro-oxidation. Due to an interaction of the fast N-NDR system with the slower dynamics of the CO, oscillations occur under gal­va­nostatic control. The third class of phenomena originates from nonlinearities other than ion transport in the membrane or electrochemical surface kinetics. So far, one example for this last class can be identified in the relevant literature. The self-inhibition of the transport of product water within the porous structures was found to lead to bi­sta­bi­li­ty. As the oxygen transport towards the cathode catalyst layer gets affected by the presence of the product water, this non-electrochemical nonlinearity projects a N-type NDR-branch into the iU-curve of the cell. Furthermore, the present contribution places some remarks on the technical relevance of the reviewed fin­dings. In general, it can be stated that the knowledge and the understanding of nonlinear effects in fuel cells are es­sential for preventing them, for mastering them or for ex­ploiting them systematically in order to ensure a rea­son­able and efficient operation of fuel cells. [1]Moxley et al., Chem. Eng. Sci. 58, 4705 (2003) [2]Hanke-Rauschenbach et al., J. Electrochem. Soc. 155, B97 (2008) [3]Katsaounis et al., Solid State Ionics 177, 2397 (2006) [4]Zhang and Datta, J. Electrochem. Soc. 149, A1423 (2002) [5]Hanke-Rauschenbach et al., J. Electrochem. Soc. 157, B1521 (2010) [6]Hanke-Rauschenbach et al., Rev. Chem. Eng. (2011), submitted [7]K. Krischer , Adv. in Electrochem. Sci. and Eng. 8, p. 89 (2003)