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Optimization by distributed control of reactors with decaying catalyst Part I: Non‐linear catalyst deactivation
Author(s) -
Therien N.,
Crowe C. M.
Publication year - 1974
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450520619
Subject(s) - catalysis , rate equation , order of reaction , product (mathematics) , activation energy , reaction rate , optimal control , chemistry , upper and lower bounds , order (exchange) , mathematics , thermodynamics , control theory (sociology) , kinetics , physics , control (management) , mathematical analysis , mathematical optimization , computer science , reaction rate constant , quantum mechanics , organic chemistry , finance , economics , geometry , artificial intelligence
Abstract The quasi‐steady state optimization of a single tubular fixed bed reactor with a slowly decaying catalyst is considered. The optimal choice of temperature T(z, t) distributed in both the space of the reactor and in chronological time is sought so as to maximize the total amount of reaction in a fixed given period of time. A single irreversible reaction is considered with a rate expressible as a product of separate functions of temperature, activity and conversion. The rate of catalyst decay is also a product of separate functions of temperature and activity but independent of conversion. Upper and lower bounds are placed on the permitted temperature. Theoretical characterization of the optimal policy is obtained using Sirazetdinov and Degtyarev's maximum principle derived for first‐order partial differential equations and the influence of the ratio of reaction activation energy to catalyst deactivation energy on the derived optimal policy is indicated. Numerical calculations are presented to illustrate the optimal policies.