36 Influence of the Wall on the Dynamic Behavior of Homogeneous Tubular Reactors with a Highly Exothermic Reaction GERHART EIGENBERGER
1
Downloaded by UNIV LAVAL on July 15, 2014 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch036
Institut fuer Systemdynamik und Regelungstechnik, Universitaet Stuttgart, West Germany The influence of the tube wall on the behavior of tubular reactors with a highly exothermic reaction was studied. The effect of heat accumulation in the wall has a considerable influence upon the transient behavior of the reactor. Because of this influence excess temperatures can occur if the feed temperature is lowered or the flow velocity is raised. For a gas phase reaction the transient behavior is determined almost completely by the heat capacity of the wall. An example of multiple steady states caused by axial heat conduction in the wall is given, and the influence of heat conduction in the wall is compared with that in the reaction mixture.
H
omogeneous tubular reactors are usually described in terms of a plug flow or diffusion model. The temperature of the reactor wall is assumed constant with time of operation. However, only the coolant temperature can be held constant while the wall temperature will be between that of the coolant and the reaction mixture. Thus, the wall temperature is influenced by changes in the reaction temperature, and the wall temperature in turn influences the behavior of the reaction. This wall influence is studied below. A highly exo thermic first-order reaction (A -» products) is considered. The simple reaction mechanism does not restrict the general validity of the results since the impor tant dynamic effects are the result of exothermic acceleration of the reaction. Tubular Reactor with Liquid Phase Reaction Homogeneous liquid phase reactions in tubular reactors are often de scribed by the plug flow model, Equations 1-3: dc S
dT dt
dT dz
_|_ t> —— =
+
*
2
ai
S
-
(i\v
c
rip
dc
/1N
-«»T> -
(i)
(-AH ) —; ρ c R
i ) H
p
r ,T) ic
(2)
p
with r ,T) = k c e~ ' (c
0
E
RT
(3)
Present address: Department of Chemical Engineering, Northwestern Univer sity, Evanston, 111. 60201. 1
477
In Chemical Reaction Engineering—II; Hulburt, H.; Advances in Chemistry; American Chemical Society: Washington, DC, 1975.
478
CHEMICAL REACTION ENGINEERING
Table I. Reaction:
II
Constants of the Liquid Phase Reaction
frequency factor, k = 10 liters/sec activation energy, È = 22000 kcal/kmole reaction enthalpy, (~AHR) = 76000 kcal/kmole feed concentration, c = 1.2 kmoles/m length, I = 10 m inner tube radius, η = 0.01 m outer tube radius, r = 0.02 m flow velocity, ν = 0.4 m/sec heat capacity: of reaction mixture, g c = 1000 kcal/m grad of the reactor wall, p c = 864 kcal/m grad heat transfer coefficient fluid-wall, η Β ) r reaction rate of liquid phase reaction, kmoles/m /sec r* reaction rate of gas phase reaction, 1 /sec r inner tube radius r outer tube radius t time coordinate υ flow velocity ζ space coordinate Ε activation energy M molecular weight of component A M mean molecular weight of feed R gas constant Τ reaction temperature T wall temperature T coolant temperature a heat transfer coefficient fluid-wall a heat transfer coefficient coolant-wall AH reaction enthalpy λ axial heat conductivity in the fluid A axial heat conductivity in the wall ρ density of reaction mixture p density of wall
Downloaded by UNIV LAVAL on July 15, 2014 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch036
p
w
0 x
3
x
2
A
0
w
c
x
2
R
w
w
Subscripts s steady state ο reactor inlet
Literature Cited 1. Widmaier, H., unpublished data. 2. Wicke, E., Vortmeyer, D., Ber. Bunsenges. (1959) 63, 145-52. 3. Padberg, G., Wicke, E., Chem. Eng. Sci. (1967) 22, 1035-51. 4. Wicke, E., Padberg, G., Arens, H., Proc. European Symp. Chem. Reaction 4th, Brusselles, 1968, 425-37. 5. Schuchmann, H., Chem. Ing. Tech. (1969) 47, 868-77. 6. Gilles, Ε. D., Chem. Eng. Sci. (1967) 22, 745-758. 7. van Heerden, C., Chem. Eng. Sci. (1958) 8, 133-145. RECEIVED January 2, 1974.
In Chemical Reaction Engineering—II; Hulburt, H.; Advances in Chemistry; American Chemical Society: Washington, DC, 1975.
