{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
Please cite us if you use the software
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Amphlett Static Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Version 1.4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "The Amphlett static model has been used to predict the performance of proton exchange membrane fuel cell. Key concepts in Amphlett static model are Nernst voltage, activation polarization loss, ohmic polarization loss and concentration polarization loss. Amphlett static model has a mechanistic and empirical approach to describe the performance of proton exchange membrane fuel cell. The ideal standard potential of an H2/O2 fuel cell is 1.229 V with liquid water product. The actual cell potential is decreased from its reference potential because of irreversible losses.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fig1. Graphical Abstract of Static Models
\n", "$$Parameter$$ | \n", "$$Description$$ | \n", "$$Unit$$ | \n", "
$$V_0$$ | \n", "Intercept of the curve obtained by linear approximation | \n", "$$V$$ | \n", "
$$k$$ | \n", "Slope of the curve obtained by linear approximation | \n", "$$A^{-1}$$ | \n", "
$$P_{max}$$ | \n", "Maximum power obtained by linear approximation | \n", "$$W$$ | \n", "
$$V_{FC}|P_{max}$$ | \n", "Cell voltage at maximum power obtained by linear approximation | \n", "$$V$$ | \n", "
$$Parameter$$ | \n", "$$Description$$ | \n", "$$Unit$$ | \n", "
$$\\eta|P_{Max}$$ | \n", "Cell efficiency at maximum power | \n", "$$--$$ | \n", "
$$P_{Max}$$ | \n", "Maximum power | \n", "$$W$$ | \n", "
$$P_{Elec} $$ | \n", "Total electrical power | \n", "$$W$$ | \n", "
$$P_{Thermal} $$ | \n", "Total thermal power | \n", "$$W$$ | \n", "
$$V_{FC}|P_{Max}$$ | \n", "Cell voltage at maximum power | \n", "$$V$$ | \n", "
$$Parameter$$ | \n", "$$Description$$ | \n", "$$Unit$$ | \n", "$$Value$$ | \n", "
$$P_{H2}$$ | \n", "Partial pressure | \n", "$$atm$$ | \n", "$$User$$ | \n", "
$$P_{O2}$$ | \n", "Partial pressure | \n", "$$atm$$ | \n", "$$User$$ | \n", "
$$T$$ | \n", "Cell operation temperature | \n", "$$K$$ | \n", "$$User$$ | \n", "
$$l$$ | \n", "Membrane thickness | \n", "$$cm$$ | \n", "$$User$$ | \n", "
$$A$$ | \n", "Active area | \n", "$$cm^2$$ | \n", "$$User$$ | \n", "
$$\\lambda$$ | \n", "An adjustable parameter with a possible minimum value of 14 and a maximum value of 23 | \n", "$$--$$ | \n", "$$User$$ | \n", "
$$J_{Max}$$ | \n", "Maximum current density of the cell | \n", "$$Acm^{-2}$$ | \n", "$$User$$ | \n", "
$$N$$ | \n", "Number of single cells | \n", "$$--$$ | \n", "$$User$$ | \n", "
$$R_{electronic}$$ | \n", "R-Electronic | \n", "$$\\Omega$$ | \n", "$$User$$ | \n", "
$$i_{start}$$ | \n", "Cell operating current start point | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$i_{step}$$ | \n", "Cell operating current step | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$i_{stop}$$ | \n", "Cell operating current end point | \n", "$$A$$ | \n", "$$User$$ | \n", "
$$B$$ | \n", "Constant in the mass transfer term | \n", "$$V$$ | \n", "$$System$$ | \n", "
$$\\rho$$ | \n", "Membrane specific resistivity | \n", "$$\\Omega cm$$ | \n", "$$System$$ | \n", "
$$J$$ | \n", "Actual current density of the cell | \n", "$$Acm^{-2}$$ | \n", "$$System$$ | \n", "
$$C_{O_2}$$ | \n", "Concentration of oxygen in the catalytic interface of the cathode | \n", "$$molcm^{-3}$$ | \n", "$$System$$ | \n", "
$$C_{H_2}$$ | \n", "Concentration of hydrogen in the catalytic interface of the anode | \n", "$$molcm^{-3}$$ | \n", "$$System$$ | \n", "
$$R_{Proton}$$ | \n", "Resistance to proton flow | \n", "$$\\Omega$$ | \n", "$$System$$ | \n", "
$$\\xi_2$$ | \n", "Parametric coefficients for cell model | \n", "$$--$$ | \n", "$$System$$ | \n", "
$$\\xi_1$$ | \n", "Parametric coefficients for cell model | \n", "$$--$$ | \n", "$$-0.948$$ | \n", "
$$\\xi_3$$ | \n", "Parametric coefficients for cell model | \n", "$$--$$ | \n", "$$7.6\\times10^{-5}$$ | \n", "
$$\\xi_4$$ | \n", "Parametric coefficients for cell model | \n", "$$--$$ | \n", "$$-1.93\\times10^{-4}$$ | \n", "
$$R$$ | \n", "Universal gas constant | \n", "$$J.kmol^{-1}.K^{-1}$$ | \n", "$$8314.47$$ | \n", "
$$F$$ | \n", "Faraday’s constant | \n", "$$C.kmol^{-1}$$ | \n", "$$96484600$$ | \n", "
$$n$$ | \n", "Number of moles of electrons transferred in the balanced equation occurring in the fuel cell | \n", "$$--$$ | \n", "$$2$$ | \n", "
$$\\mu_F$$ | \n", "The fuel utilization | \n", "$$--$$ | \n", "$$0.95$$ | \n", "
$$HHV$$ | \n", "Higher heating value potential | \n", "$$V$$ | \n", "$$1.482$$ | \n", "
$$E_{th}$$ | \n", "Theoretical potential | \n", "$$V$$ | \n", "$$1.23$$ | \n", "
\n", "1-J. C. Amphlett, R. M. Baumert, R. F. Mann, B. A. Peppley, and P. R. Roberge. 1995. \"Performance Modeling of the Ballard Mark IV Solid Polymer Electrolyte Fuel Cell.\" J. Electrochem. Soc. (The Electrochemical Society, Inc.) 142 (1): 9-15. doi: 10.1149/1.2043959.\n", "\n", "
\n", "2-Jeferson M. Correa, Felix A. Farret, Vladimir A. Popov, Marcelo G. Simoes. 2005. \"Sensitivity Analysis of the Modeling Parameters Used in Simulation of Proton Exchange Membrane Fuel Cells.\" IEEE Transactions on Energy Conversion (IEEE) 20 (1): 211-218. doi:10.1109/TEC.2004.842382.\n", "\n", "
\n", "3-Larminie, J., Dicks, A., & McDonald, M. S. 2003. Fuel cell systems explained (Vol. 2, pp. 207-225). Chichester, UK: J. Wiley. doi: 10.1002/9781118706992.\n", "\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": false, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "OPEM", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }