Calculating Reactor Performance

Procedures for calculating tiie petfotmance of a series of CSTRs were developed in Chapter 4. However, there are three questions that can arise when using the CIS model  

However, the fluid leaving the first CSTR may not become mixed on a molecular level before it enters the second reactor. In the limit, the fluid elements in this stream may remain completely segregated between the two reactors. For this situation, the procedure described in the preceding paragraph is not appropriate because the stream entering the second CSTR is not uniform on a molecular level. Rather, the feed to the second CSTR consists of packets of fluid with different compositions. In this case, the macrofluid model must be used, with the measured RTD for the whole reactor, i.e., the reactor that was being modeled as a series of equal-volume CSTRs. In the case of a fluid that remains as a macrofluid, there is no need to fit the CIS model to the measured RTD. The macrofluid model must be applied directly. 

The second-order, liquid-phase reaction 2A — B takes place in an isothermal, nonideal reactor with a total volume of 1000 1. The volumetric flow rate through the reactor is 100 lAmin and the concentration of A in the feed, Cao, is 4.0 mol/1. The rate constant at the temperature of operation is 0.25 1/mol-min. 

Tracer tests have been performed to determine the nature of mixing in the reactor. These tests showed that t - 10 min and that Acr = 40min.  

Use the CIS model to estimate the conversion of A in the stream leaving the reactor. Assume that the fluid becomes micromixed between reactors. 

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The complexity and importance of combustion reactions have resulted in active research in computational chemistry. It is now possible to determine reaction rate coefficients from quantum mechanics and statistical mechanics using the ideas of reaction mechanisms as discussed in Chapter 4. These rate coefficient data are then used in large computer programs that calculate reactor performance in complex chain reaction systems. These computations can sometimes be done more economically than to carry out the relevant experiments. This is especially important for reactions that may be dangerous to carry out experimentally, because no one is hurt if a computer program blows up. On the other hand, errors in calculations can lead to inaccurate predictions, which can also be dangerous. 

Model structure is shown in Figure 5. Process variables, unit constants (such as heat transfer coefficients), and feed streams are described on input or as selected by the optimization routine. Then, heat and material balances are performed using an assumed alkylate yield and isobutane consunq>tion. These results form a set of reaction conditions irtiich are used in correlations to calculate reactor performance. The heat and material balance calculations are repeated if reactor performance differs significantly from that used in the previous calculation. Operating incentives are then conqmted and may be used in the optimization routine to select new values of the optimization variables. 

Since the RTD of a particular reactor type does not describe its performance uniquely for nonlinear reactions, it is customary to develop flow models for the reactor. The parameters of the model are then determined from tracer studies and the structure of the model is used to calculate reactor performance. 

Of course, the residence time distribution of the liquid phase is of importance for calculating reactor performance in the slow reaction regime. In the matrix of Fig. 3 the models <11> through <33> are thinkable in this regime. However, for reasons given before only models <11>, <12>, <13>, <22>, and <23> will be considered in what follows. 

Figure 10-11 shows the shape of the E(t) curves that result from various combinations of CSTRs and PFRs in parallel. The conunents beside each figure indicate how the values of Ti and T2 that are required to quantify the model and to calculate reactor performance can be extracted from the E(t) curves. 

Because there are two feeds to this process, the reactor performance can be calculated with respect to both feeds. However, the principal concern is performance with respect to toluene, since it is much more expensive than hydrogen. 

In using a spreadsheet for process modeling, the engineer usually finds it preferable to use constant physical properties, to express reactor performance as a constant "conversion per pass," and to use constant relative volatiHties for distillation calculations such simplifications do not affect observed trends in parametric studies and permit the user quickly to obtain useful insights into the process being modeled (74,75). 

Another view is given in Figure 3.1.2 (Berty 1979), to understand the inner workings of recycle reactors. Here the recycle reactor is represented as an ideal, isothermal, plug-flow, tubular reactor with external recycle. This view justifies the frequently used name loop reactor. As is customary for the calculation of performance for tubular reactors, the rate equations are integrated from initial to final conditions within the inner balance limit. This calculation represents an implicit problem since the initial conditions depend on the result because of the recycle stream. Therefore, repeated trial and error calculations are needed for recycle... 

The basic problem of design was solved mathematically before any reliable kinetic model was available. As mentioned at start, the existence of solutions—that is, the integration method for reactor performance calculation—gave the first motivation to generate better experimental kinetic results and the models derived from them. 

The ODE for the inerts was used to calculate Qg t in Example 4.6. How would you work the problem if there were no inerts Use your method to predict reactor performance for the case where the feed contains 67% SO2 and 33% O2 by volume. 

The method of lines formulation for solving Equation (8.52) does not require that T aii be constant, but allows T aiiiz) to be an arbitrary function of axial position. A new value of T aii may be used at each step in the calculations, just as a new may be assigned at each step (subject to the stability criterion). The design engineer is thus free to pick a T au z) that optimizes reactor performance. 

Optimization requires that a-rtjl have some reasonably high value so that the wall temperature has a significant influence on reactor performance. There is no requirement that 3>AtlR be large. Thus, the method can be used for polymer systems that have thermal diffusivities typical of organic liquids but low molecular diffusivities. The calculations needed to solve the optimization are much longer than those needed to solve the ODEs of Chapter 6, but they are still feasible on small computers. 

When the residence time distribution is known, the uncertainty about reactor performance is greatly reduced. A real system must lie somewhere along a vertical line in Figure 15.14. The upper point on this line corresponds to maximum mixedness and usually provides one bound limit on reactor performance. Whether it is an upper or lower bound depends on the reaction mechanism. The lower point on the line corresponds to complete segregation and provides the opposite bound on reactor performance. The complete segregation limit can be calculated from Equation (15.48). The maximum mixedness limit is found by solving Zwietering s differential equation. ... 

A system of N continuous stirred-tank reactors is used to carry out a first-order isothermal reaction. A simulated pulse tracer experiment can be made on the reactor system, and the results can be used to evaluate the steady state conversion from the residence time distribution function (E-curve). A comparison can be made between reactor performance and that calculated from the simulated tracer data. 

Compare the batch reactor performance at constant cp with that for variable cp. Do this by setting both cp values constant at a temperature Ti and calculating cpii = a + b Ti for particular values of aA = cpAi, aB = cpBi, bA = 0 and bB = 0. 

Nevertheless, these modeling efforts are of little value when the practical implementation does not corroborate the above-calculated results. Ensuring the constancy of any parameter in the catalytic testing workflow, the reactor performance with regard to temperature distribution, gas distribution, constant feed... 

Figure 4.17 Performance of the basic system when operated as a CSTR (n = 1). Concentrations of all the reactants are indicated for the reactor outlet. Calculations were performed with 2 = 6 mL/h. The values used for all other parameters are given in Table 4.1, set I.

So far, all of the material presented has been discussed in the absence of any numerical examples. At this point, we introduce such an example the initial calculations will be used subsequently as a basis for further examples and, in this way, it will be possible to see how raw tracer data can be processed. Eventually, predictions will be made of what conversion can be expected when a reaction with known kinetics takes place in the system from which the tracer information was gathered. In the examples which involve tracer data, it should be emphasised that only in the most carefully engineered equipment could data of the accuracy quoted be obtained. In real situations, tracer mass balances may close inadequately and predictions of reactor performance must be treated with appropriate caution. 

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