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Lecture_F11_ECH157_Project

Lecture_F11_ECH157_Project - University of California Davis...

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University of California, Davis Department of Chemical Engineering & Materials Science ECH 157 - Process Dynamics and Control Fall 2011 Term Project: Dynamics and Control of a Solid Oxide Fuel Cell Assigned: Monday, November 7. Due: Friday, December 9 (before 5:00pm). Process Description and Modeling: A solid oxide fuel cell is an electrochemical device that generates electrical energy from chemical reactions. It consists of two porous electrodes, an anode and a cathode in contact with a solid metal oxide electrolyte between them. Hydrogen rich fuel is fed along the surface of the anode where it releases electrons that migrate externally towards the cathode. The electrons combine with oxygen in air that is fed along the surface of the cathode to form oxide ions. These ions diffuse through the electrolyte towards the anode where they combine with the H + ions to form water. The Nernst equation describes the potential difference between the electrodes that drives the reaction and the movement of electrons, and is given by: E = E 0 + RT s 2 F ln p H 2 p (0 . 5) O 2 p H 2 O (1) where E 0 is the standard cell potential given by Δ E 0 ( V ) = 1 . 2586 0 . 000252 T s ( K ) , F is Faraday’s constant and p H 2 , p O 2 , p H 2 O are the partial pressures of hydrogen, oxygen and steam respectively. Typically, a number of these cells are connected in series to form a stack. The overall stack voltage is then given by: V s = N 0 E r 0 exp bracketleftbigg α parenleftbigg 1 T s 1 T 0 parenrightbiggbracketrightbigg I (2) 1
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where N 0 is the number of cells in the stack, r 0 is the internal resistance at T 0 , α is the resistance slope, and I is the load current. In Eq.2, only ohmic losses are included, while activation and concentration losses are neglected. Under standard modeling assumptions, a dynamic model of the following form can be derived for the SOFC stack from material and energy balances: Species balances : ˙ p H 2 = T s τ * H 2 T * K H 2 ( q in H 2 K H 2 p H 2 2 K r I ) ˙ p O 2 = T s τ * O 2 T * K O 2 ( q in O 2 K O 2 p O 2 K r I ) ˙ p H 2 O = T s τ * H 2 O T * K H 2 O ( q in H 2 O K H 2 O p H 2
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