Plug flow reactor single CSTR

Comparison of performance of single CSTR and plug flow reactor for the nth-order reactions... 

Single Reactions—For all reactions of orders above zero, tire CSTR gives a lower production rate than the batch, semi-batch, or kinetically equivalent plug-flow reactor. 

For some purposes it is adequate to assume that a battery of five or so CSTRs is a close enough approximation to a plug flow reactor. The tubular flow reactor is smaller and cheaper than any comparable tank battery, even a single shell arrangement. For a first order reaction the ratio of volumes of an n-stage CSTR and a PFR is represented by... 

The representation of different types of reactor units in the approach proposed by Kokossis and Floudas (1990) is based on the ideal CSTR model, which is an algebraic model, and on the approximation of plug flow reactor, PFR units by a series of equal volume CSTRs. The main advantage of such a representation is that the resulting mathematical model consists of only algebraic constraints. At the same time, however, we need to introduce binary variables to denote the existence or not of the CSTR units either as single units or as a cascade approximating PFR units. As a result, the mathematical model will consist of both continuous and binary variables. 

Note that the uniform conditions in the reactor equal those at the reactor outlet, which implies that the production rate of A is also determined by the outlet conditions. The mass balance for a component in a CSTR is an algebraic equation, in contrast to the case of reactions in a batch or a plug flow reactor. For a single, irreversible first-order reaction and constant density, Eqn. 7.32 becomes ... 

The control system must manipulate heat removal from the reactor, but what should be the measured (and controlled) variable Temperature is a good choice because it is easy to measure and it has a close thermodynamic relation to heat. For a CSTR. temperature control is particularly attractive since there is only one temperature to consider and it is directly related to the heat content of the reactor. However, in a spatially distributed system like a plug-flow reactor the choice of measured variable is not so clear. A single temperature is hardly a unique reflection of the excess heat content in the reactor. We may select a temperature where the heat effects have the most impact on the operation. This could be the hot spot or the exit temperature depending upon the design of the reactor and its normal operating-profile. 

The whole problem has thus been reduced to the solution of Eq. (134), which is a functional equation for the single scalar W. It is, however, a nasty functional equation, not so much for the possible nonlinearity of the functional F[ ] itself, but because the argument function is nonlinear in the unknown W. The warped time technique is again useful, but, contrary to what happens in the single-component case, the solution for the CSTR is more difficult than the one for the plug flow reactor or batch reactor. 

Figure E8.5.1 shows the reaction curve for a cascade of equal-size tanks, and compare them to those of a plug-flow reactor and a single CSTR.

Using our measured rate data and equilibria from Pressman and Lucas, the estimated reactor residence times for 85% conversion with 1 M H2SO4 at 105°C are 14 hours for a batch or plug flow reactor, 85 hours for a single completely stirred tank reactor (CSTR), or 33 hours for two CSTR s in series. If the reaction was carried out at the scrubber site, no additional purification should be required, but there would be a makeup requirement for sulfuric acid. 

We saw that two CSTRs in series gave a smaller total volume than a single CSTR to achieve the same conversion. This case does not hold true for the two plug-flow reactors connected in series shown in Figure 2-7. 

To reduce the disparities in volume or space-time requirements between an individual CSTR and a plug flow reactor, batteries or cascades of stirred-tank reactors are employed. These reactor networks consist of a number of stirred-tank reactors connected in series with the effluent from one reactor serving as the feed to the next. Although the concentfa-tion is uniform within any single reactor, there is a progressive decrease in reactant concentration as one moves from the initial tank to the final tank in the cascade. In effect, there are stepwise variations in composition as one moves from one CSTR to the next. Figure 8.9 illustrates the stepwise variations typical of reactor cascades. In the general nonisothermal case one will also encounter stepwise variations in temperature as one passes from one reactor to the next in the cascade. 

For reactions with positive order, the performance of such a cascade reactor has a specific function between an ideal plug flow reactor and a single CSTR. This can easily be understood comparing the reactant concentration as function of the reactor volume. In a PFR the concentration and, therefore, the transformation rate diminishes with increasing volume from the reactor entrance to the outlet. The low specific performance of a CSTR can be explained by the overall low concentration corresponding to the outlet concentration. In the cascade, the concentration diminishes stepwise from one vessel to the next. This is shown schematically for a series with N=5 vessel in Figure 3.22. With increasing number of equal sized vessels the concentration profile approaches that of a PFR. 

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