Tubular reactor sensitivity

J. Coste, N. R. Amundson, and R. Aris, Tubular Reactor Sensitivity, ... 

The study of the peak temperature sensitivity to the reactor operating parameters and the construction of sensitivity boundary curves for stable reactor operation were previously reported ( l). This paper presents a computer study on conceptual relationships between the conversion-product properties and the reactor operating parameters in a plug flow tubular reactor of free radical polymerization. In particular, a contour map of conversion-molecular weight relationships in a reactor of fixed size is presented and the sensitivity of its relationship to the choice of initiator system, solvent system and heat transfer system are discussed. 

The ability to manipulate reactor temperature profile in the polymerization tubular reactor is very important since it directly relates to conversion and resin product properties. This is often done by using different initiators at various concentrations and at different reactor jacket temperature. The reactor temperature response in terms of the difference between the jacket temperature and the peak temperature (0=Tp-Tj) is plotted in Figure 2 as a function of the jacket temperature for various inlet initiator concentrations. The temperature response not only depends on the jacket temperature but also, for certain combinations of the variables, it is very sensitive to the jacket temperature. 

In order to implement the PDF equations into a LES context, a filtered version of the PDF equation is required, usually denoted as filtered density function (FDF). Although the LES filtering operation implies that SGS modeling has to be taken into account in order to capture micromixing effects, the reaction term remains closed in the FDF formulation. Van Vliet et al. (2001) showed that the sensitivity to the Damkohler number of the yield of competitive parallel reactions in isotropic homogeneous turbulence is qualitatively well predicted by FDF/LES. They applied the method for calculating the selectivity for a set of competing reactions in a tubular reactor at Re = 4,000. 

The maximum reactor temperature is mueh more sensitive to feed temperature for feed-eooled tubular reaetors than for tubular reactors with a separate eooling stream. Why ... 

Precolumn derivatization is often inadequate for dirty samples. In these cases, application of a postcolumn reaction detection system will often suffice. Deelder et al. (44) and van der Wal (45) have examined different configurations for postcolumn reactors and defined optimal selections on the basis of reaction time and type and effect on resolution and sensitivity. Both studies preferred the packed-bed reactor to the open tubular reactors when conventional column geometries were employed for separation, that is, 4.6 mm i.d. X 15 or 25 cm. 

To illustrate the problem of thermal sensitivity we will analyse the simple one-dimensional model of the countercurrent cooled packed tubular reactor described earlier and illustrated in Fig. 3.25. We have already seen that the mass and heat balance equations for the system may be written ... 

The effect of reactor inlet temperature is shown in Figure 5.3. For an inlet temperature of 446 K, the reaction rate is small. Therefore there is only a small increase in temperature and little consumption of the reactants (low conversion). However, a quite small increase in inlet temperature to 448 K results in very rapid increases in temperature and conversion. With an inlet temperature of 450 K, the reactants are essentially completely consumed. The adiabatic temperature rise is about 330 K This example illustrates one of the difficult problems associated with tubular reactors. They can be very sensitive to reactor inlet temperature. The problem is analogous to that seen in earlier chapters in CSTRs that are designed for low conversions. The reactor inlet stream contains high concentrations of both reactants, so there is plenty of fuel to generate a runaway reaction. If the maximum temperature limitation in the system is 550 K, this runaway could do real damage to the catalyst or result in a vessel meltdown. 

Bilous and Amundson [1] were the first to describe the phenomenon of parametric sensitivity in cooled tubular reactors. This parametric sensitivity was used by Barkelew [2] to develop design criteria for cooled tubular reactors in which first order, second order and product- inhibited reactions take place. He presented diagrams from which for a certain tube diameter dt the required combination of CAO and Tc can be derived to avoid runaway or vice versa. Later van Welsenaere and Froment [3] did the same for first order reactions, but they also used the inflexion points in the reactor temperature T versus relative conversion XA trajectories, which describe the course of the reaction in the tubular reactor. With these trajectories they derived a less conservative criterion. Morbidelli and Varma [4] recently devised a method for single order reactions based on the isoclines in a temperature conversion plot as proposed by Oroskar and Stern [5]. 

Bilous, 0. and Amundson. N. R. Chemical Reactor Stability and Sensitivity II. Effect of Parameters on Sensitivity of Empty Tubular Reactors. AIChE J.,2,117-126 (1956). 

In critical cases it may well be worthwhile to make a complete analysis of stability. In many cases, however, enough can be learned by studying what Bilous and Amundson (B7) called parametric sensitivity. These authors derived formulas for calculating the amplification or attenuation of disturbances imposed on an unpacked tubular reactor originally in a steady state, with the idea that if the disturbances grow unduly the performance of the reactor is too sensitive to the conditions imposed on it, that is, to the parameters of the system. The effect of feedback from a control system was not considered. As pointed out by the authors, it would be a much more complicated task to apply their procedure to a packed reactor, but it still would entail far less computation than a study of the transient response. 

To provide an example of how the sensitivity may be elucidated, consider a tubular reactor accomplishing an exothermic reaction and operating at nonisothermal conditions. As described in Example 9.4.3, hot spots in the reactor temperature pro-... 

Coste, J. 1959. Chemical tubular reactor studies. Sensitivity and diffusion. Ph.D. Thesis. Department of Chemical Engineering, University of Minnesota, Minneapolis, Minnesota. 

In all these cases, the correct design must grow from the equations of mass, energy, and momentum balance to which we now turn in the next few sections. From these we proceed to the design problem (Sec. 9.5) and hence to elementary considerations of optimal design (Sec. 9.6). The stability and sensitivity of a tubular reactor is a vast and fascinating subject. Since the steady state equations are ordinary differential equations, the equations describing the transient behavior are partial differential equations. This... 

We now turn to a more general description of the sensitivities and stability of the tubular reactor. 

Still be very sensitive to a particular variable. On the other hand, an unstable condition is such that the least perturbation will lead to a finite change and such a condition may be regarded as infinitely sensitive to any operating variable. Sensitivity can be fully explored in terms of steady state solutions. A complete discussion of stability really requires the study of the transient equations. For the stirred tank this was possible since we had only to deal with ordinary differential equations for the tubular reactor the full treatment of the partial differential equations is beyond our scope here. Nevertheless, just as much could be learned about the stability of a stirred tank from the heat generation and removal diagram, so here something may be learned about stability from features of the steady state solution. 

Figure 4-1 Sensitivity of reactant conversion to changes in the wall temperature for nonisothermal plug-flow tubular reactors with exothermic chemical reaction. The reactive fluid enters at 340 K.

Figure 4-7 Sensitivity of cooling fluid temperature to changes in flow rate ratio for nonisothermal plug-flow tubular reactors with exothermic chanical reaction and cocurrent cooling in a concentric double-pipe conflguration with radius ratio c = 0.5. The inlet temperatures are 340 K for the reactive fluid and 335 K for the cooling fluid.

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