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Steady state multiplicity of chemically reacting systems. The method of computation
Affiliation:1. Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, PR China;2. Applied Optics and Instrumentation Laboratory, Department of Physics, National Institute of Technology Calicut, Calicut 673601, Kerala, India;3. Optind Solutions Private Limited, Unit No. 11, Technology Business Incubator, National Institute of Technology Calicut, Calicut 673601, Kerala, India;1. University of Rome “Tor Vergata”, Dept. Electronics Engineering, Via del Politecnico 1, 00133 Rome, Italy;2. TU Hamburg, Institut für Mathematik, Am Schwarzenberg-Campus 3, 21073 Hamburg, Germany;3. Weierstrass Institute (WIAS), Mohrenstr. 39, 10117 Berlin, Germany;1. Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore;2. Chu Kochen Honors College, Zhejiang University, Hangzhou, China;3. School of Control Science and Engineering, Zhejiang University, Hangzhou, China;4. School of Materials Science and Engineering, Zhejiang University, Hangzhou, China;5. Department of Electrical and Computer Engineering, University of California Santa Barbara, Santa Barbara, CA 93106, USA;1. School of Chemical Engineering and Technology, Tianjin University, Tianjin, PR China;2. School of Electrical and Information Engineering, Tianjin University, Tianjin, PR China
Abstract:To analyse the steady state multiplicity of chemically reacting systems of different types it is necessary to find all roots of systems of non-linear equations describing steady states of the systems. This can be solved rather simply in the case of a reducible system to a single equation. We present a numerical method of nonlocal solution for systems of non-linear equations which does not require computing with the Jacobian matrix. The method is illustrated by joint equilibrium absorption of two species for a semi-empirical model of induced inhomogeneity of the catalyst surface and by computation of the steady states of the stirred tank reactor in which the reaction ABC occurs.
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