Wrong‐way behavior of packed‐bed reactors: 1. The pseudo‐homogeneous model

Abstract

A sudden reduction in the feed temperature to a packed-bed reactor leads to a transient temperature rise, which is referred to as the wrong-way behavior. A pseudo-homogeneous plug-flow model is used to analyze the structure of this transient behavior. The key parameters which determine the magnitude of this response are the dimensionless adiabatic temperature rise, activation energy, heat transfer capacity, coolant temperature, magnitude of temperature drop and length of the reactor. A simple expression is derived for predicing the maximum transient temperature rise. SCOPEWhen the temperature of the feed to a packed-bed reactor is suddenly decreased a transient temperature rise may occur. This surprising dynamic feature is caused by the difference in the speed of propagation of the concentration and temperature disturbances and is referred to as the wrong-way behavior. This response was predicted originally by Boreskov and Slinko (1965) and Crider and Foss (1966), and was observed by many investigators (Hoiberg et al., 1971; Van Doesberg and DeJong, 1976a, 1976b; Hansen and Jorgensen, 1977;Sharma and Hughes, 1979).The wrong-way behavior may damage the catalyst and initiate undesired side reactions. The need to avoid it complicates the control policies and start-up and shut-down procedures of packed-bed reactors. At present lengthy numerical simulations are required to determine when this behavior may be encountered and its magnitude.The purpose of this work is to identify the key rate processes and parameters which cause this behavior and to develop a simple technique for a priori prediction of the highest transient temperature without solving the transient equations. This is accomplished by analyzing the dynamic response of a plug-flow pseudo-homogeneous model of a packed-bed reactor using the method of characteristics. First, we determine the structure of the solution and the conditions for which a wrong-way behavior occurs for a zeroth-order reaction in either a cooled or an adiabatic reactor. We examine then how this behavior is modified by a rate expression for which the reactants are not completely consumed and by intraparticle diffusional resistances. CONCLUSIONS AND SIGNIFICANCEThe analysis indicates that for a zeroth-order reaction the wrong-way behavior occurs only if the reactor is longer than a critical length of z,i. The highest transient temperature increases with reactor length until the reactor is of length z~,~. For 1981.downstream of zrfl.any reactor shorter than z,,, and longer than zri the highest transient temperature is encountered at the exit of the reactor. For a cooled reactor longer than zc.fl the limiting transient-peak temperature occurs at z,,,. For an adiabatic reactor the limiting transient-peak temperature is encountered at all points

Wrong‐way behavior of packed‐bed reactors: II. Impact of thermal dispersion

“…When the axial dispersion of heat is very small, the maximal transient peak temperature may be very large due to the high Peclet number for heat transfer. This is consistent with the earlier predictions by Mehta et al (1981).…”

“…This slowly moving temperature peak may damage the catalyst or the reactor, and may initiate undesired side reactions. The slow movement of this temperature wave is a new feature not predicted by the limiting model of Mehta et al (1981) and is due to the axial heat conduction. When the new feed temperature is higher than the extinction point, a suddent reduction in the feed temperature can lead to two different behaviors.…”

“…The limiting model used by Mehta et al (1981) predicts that the maximal transient temperature rise increases monotonically with an increase in either the adiabatic temperature rise or the activation energy. The axial dispersion model predicts, on the other hand, that for a fixed Da the maximal transient temperature rise occurs for some intermediate value of (?, Figure 8, which is proportional to the feed concentration of the reactant, i.e., the heat generated by the complete conversion of the reactant.…”

“…Such a disturbance may be caused, for example, by the failure of a furnace to preheat a recycle or feed stream. Mehta et al (1981) studied the wrong-way behavior using a pseudohomogeneous, single-phase, one-dimensional model, in which a single reaction occurs. The analysis resulted in a simple algebraic expression which predicts the maximal transient temperature rise.…”

Start-up and wrong-way behavior in a tubular reactor: dilution effect of the catalytic bed

“…McGreavy and Naim (1977) and Windes et al (1989) studied this subject through one and two-dimensional mathematical models. Metha, Sams and Luss (1981) found analytical criteria to predict that behavior, for zero-order reactions. Pinjala, Chen and Luss (1988) analyzed the importance of the thermal dispersion on the transient response, and concluded that the ignition of the reactor during the transient period is possible to occur.…”