An analytic solution for the dynamics of a packed adiabatic chemical reactor

Abstract

L o c a l l y linearized equations for dynamic disturbances from a steady state have been solved analytically for a n adiabatic chemical reactor with chemically inert packing and a homogeneous chemical reaction. T h e solutions, in the form of transfer functions, include the effects of heat capacity of the packing and heat transfer between the packing and the fluid, as well as the coupling effects of chemical reaction and the associated h e a t generation.Several limiting cases o f the transfer functions are discussed and the tronsfer functions are simplified by on approximation of the temperature dependence of the reaction rate. Frequency responses and step responses of the reactor are calculated from the transfer functions.T h e first mathematical analyses of thermal dynamics in a packed bed (heat regenerator) were made by Anzelius (3) and Nusselt ( 1 4 ) and independently by Schumann ( 1 7 ) . Their results were confirmed experimentally by Furnas (11) and extended mathematically by Brinkley ( 6 ) to a packed catalytic reactor in which the rate of heat generation i n the packing i s a linear function of packing temperature.Amundson (2) expanded Brinkley's solution to account for radial gradients within the bed.T h e s e analyses do not include, however, an important feature of many chemical reactors: the interaction of temperature and reactant concentration. For most chemical reactions, the reaction rate depends upon both temperature and reactant concentration, and the rate of heat generation does also. T h e s e dependences are usually nonlinear.This temperature and concentration interaction has, however, been included in a study of the dynamics of unpacked reactors by Bilous and Amundson (5). Furthermore, Douglas and Eagleton (10) have given analytic solutions for the dynamics of adiabatic unpacked reactors. T h e s e results for unpacked reactors cannot b e readily extended, however, t o packed reactors, because it h a s been shown that the exchange of heat between the fluid and the packing h a s important effects upon the dynamics of packed reactors In the present paper, an approximate analytic solution to the dynamics of an adiabatic packed reactor i s presented. This solution shows the dynamic effects of packing heat (19,20,9).J . E. Crider is with Shell Development Company, Houston, Texas.capacity, heat transfer between the packing and the fluid, and interaction of concentration and temperature through the chemical reaction and associated heat generation. This analytic solution applies only to small disturbances from steady s t a t e operating conditions.The reactor considered here is not a catalytic reactor, however; it i s a reactor that contains chemically inert packing and a homogeneous chemical reaction occurring in the fluid phase, which i s here a liquid. Such reactors, which have recently been studied experimentally (20, 1 9 ,

Analysis of instability in an industrial ammonia reactor

“…General work on reactor stability, modeling, and control is abundant. Crider and Foss (1968) refer to Nusselt in 1927 and independently Schuman in 1929 as the first to present a thermal analysis of packed beds. van Heerden (1953) and Aris and Amundson (1958) analyzed the stability of the steady states of autothermal reactors.…”

Effect of design on the stability and control of fixed bed catalytic reactors with heat feedback. 1. Concepts

“…Two simple models for adiabatic fixed bed reactors have been proposed in the literature, that of Liu and Amundson (1962) and that of Crider and Foss (1968) and others. Two simple models for adiabatic fixed bed reactors have been proposed in the literature, that of Liu and Amundson (1962) and that of Crider and Foss (1968) and others.…”

“…As shown by Crider andFoss (1966,1968) and Sinai and Foss (1970), an important feature of catalytic fixed bed reactor behavior is that there are two independent waves, a concentration wave and a temperature wave, which travel and the catalyst. These waves of differing velocities are produced primarily because of the large thermal holdup in the solid phase.…”

“…Since the two models are similar in their overall nonlinear behavior we can for the present consider only one of them (Crider and Foss, 1968). Both models have one important property.…”

Theoretische Und Experimentelle Unter-Suchungen Zur Dynamik Heterogen Katalytischer Festbettreaktoren. Dargestellt Am Beispiel Der Co-Konvertierung

“…Sinai und Foss [9] und Crider und Foss (24] haben die Übertragungs funktionen eines Festbettreaktors für ein Propfenströmungsmodell mit einem linearisierten Reaktionsterm studiert .Die letzteren Autoren haben sogar eine analytische Lösung für das dynamische Verhalten eines solchen Systems ermittelt , nur ist diese Lösung recht unübersichtlich . Chen und Friedly [12] behandeln das selbe Thema und erhalten eine Approximation der Ubertragungsfunktior wobei sie zeigen , daß die zwei Charakteristiken des ursprünglichen hyperbolischen Systems von Dgln.…”