Modeling of chemical reactors — XVI Steady state axial heat and mass transfer in tubular reactors An analysis of the uniqueness of solutions
TL;DR: In this article, a new technique is presented which, for the parameter study of a problem, enables one to transform the boundary value problem to the initial value problem and different criteria for testing of uniqueness and multiplicity respectively are discussed.
About: This article is published in Chemical Engineering Science.The article was published on 1970-01-01. It has received 103 citations till now. The article focuses on the topics: Initial value problem & Boundary value problem.
Citations
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TL;DR: In this paper, the bifurcation behavior of a tubular reaction with axial dispersion is analyzed and the influence of the Lewis and Peclet numbers is investigated. But it is shown that oscillations due to interaction of dispersion and reaction effects should not exist in fixed bed reactors and moreover, should only occur in very short “empty” tubular reactors.
166 citations
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TL;DR: In this article, the heat and mass transfer in a monolithic honeycomb catalyst is described. But the authors focus on the control of automobile emissions and exhaust gases from some industrial processes.
93 citations
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TL;DR: In this paper, the authors present numerical procedures for computing the Hopf bifurcation formulas which can determine the stability and location of the oscillation without integrating the parabolic partial differential equations.
90 citations
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TL;DR: In this article, a globally stabilizing boundary feedback control law for an arbitrarily fine discretization of a nonlinear PDE model of a chemical tubular reactor is presented, where the goal is to stabilize an unstable steady state of the system using boundary control on the inlet side of the reactor.
84 citations
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TL;DR: In this article, the existence and uniqueness of the state trajectories (temperature and reactant concentration) for nonisothermal plug flow and axial dispersion tubular reactor models are analyzed.
82 citations
References
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TL;DR: In this paper, the analogy between the stirred tank reactor and the catalyst particle is used to introduce some of the recent techniques of stability analysis in as simple a way as possible, and the relationship between various classes of criteria for uniqueness and stability is developed and interpretations of the less obvious criteria are given.
105 citations
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TL;DR: In this paper, it was shown that the value of the F•K criticality criterion is a slowly varying function of E/RT0 in the range from infinity to 30 but becomes a sensitive function for values of E /RT0 less than 30.
Abstract: In 1939 D. A. Frank‐Kamenetsky proposed a criticality criterion that is a dimensionless constant that varies only with configuration of the self‐heating chemical. In his studies of the equation equating power production as a function of temperature by the formula of Arrhenius and the power loss by conduction alone, he made a simplifying assumption. A Pace analog computer and an IBM 704 have been used to study the exact equation and it was found that the value of the F‐K criticality criterion is a slowly varying function of E/RT0 in the range from infinity to 30 but becomes a sensitive function for values of E/RT0 less than 30.
89 citations
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TL;DR: This paper gives examples and discusses the finite difference method for nonlinear two-point boundary-value problems and the easiest method of attacking these problems, shooting techniques.
Abstract: Solution of nonlinear two-point boundary-value problems is often an extremely difficult task. Quite apart from questions of reality and uniqueness, there is no established numerical technique for this problem. At present, shooting techniques are the easiest method of attacking these problems. When these fail, the more difficult method of finite differences can often be used to obtain a solution. This paper gives examples and discusses the finite difference method for nonlinear two-point boundary-value problems.
83 citations
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TL;DR: In this article, the theoretischen Ansaatze zur behandlung des Stabilitatsproblems bei exothermen reaktionen in Stromungsrohen konnen als Einzelpartikel-Theorie and als Ruckvermischungstheorie gekennzeichnet werden.
81 citations
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TL;DR: In this paper, it was shown that for any reaction mixture the possibility of multiple steady states can usually be eliminated by use of small catalyst particles, or a dilute mixture, and that in this case one can usually guarantee a unique steady state by using either a small reaction mixture or a short reactor.
69 citations