First-order reactions CSTR design

It is readily apparent that equation 8.3.21 reduces to the basic design equation (equation 8.3.7) when steady-state conditions prevail. Under the presumptions that CA in undergoes a step change at time zero and that the system is isothermal, equation 8.3.21 has been solved for various reaction rate expressions. In the case of first-order reactions, solutions are available for both multiple identical CSTR s in series and individual CSTR s (12). In the case of a first-order irreversible reaction in a single CSTR, equation 8.3.21 becomes... 

Thus, for known kinetics and a specified residence time distribution, we can predict the fractional conversion of reactant which the system of Fig. 9 would achieve. Recall, however, that this performance is also expected from any other system with the same E(t) no matter what detailed mixing process gave rise to that RTD. Equation (34) therefore applies to all reactor systems when first-order reactions take place therein. In the following example, we apply this equation to the design of the ideal CSTR and PFR reactors discussed in Chap. 2. The predicted conversion is, of course, identical to that which would be derived from conventional mass balance equations. 

CSTRs in series. The latter is often normalised by dividing by the volume of an ideal PFR required to perform the same duty. Different charts are required for each reaction rate expression. Figure 12 refers specifically to first-order kinetics, but other charts are available in, for instance refs. 17, 18 and 26. Figure 12 re-emphasises many of the points we have made already. In particular, the performance of the N CSTRs in series tends to that of a PFR of the same total volume as N becomes large and the PFR volume required to achieve a certain conversion for a first-order reaction is always smaller than the total volume of any array of CSTRs which perform the same duty. Charts in the form of Fig. 12 are particularly useful when performing approximate design calculations. 

Derive the equation of a first-order reaction using the segregation model when the RTD is equivalent to (a) an ideal PFR, and (b) an ideal CSTR. Compare these conversions with those obtained from the design equation. 

Consider a liquid-phase, first-order reaction of the form A P + R in an isothermal cascade of CSTRs where only reactant A is fed to the system. Taking the inlet stream to the cascade as the reference stream and since only reactant A is fed, y o = 1- Using Eq. 8.2.3, the design equation for the nth CSTR is... 

The analysis of the effects of catalyst deactivation on CSTR performance is straightforward and there is really not too much to write about however, this can be of considerable importance in the design of slurry reactors, which will be discussed in Chapter 8. We can start with the familiar relationship for a first-order reaction given in equation (4-68)... 

As a designer, you are confronted with the following dilemma. You have available N CSTR of equal individual volume V. These are to be used under isothermal conditions (same temperature in each vessel) to carry out an irreversible first-order reaction with rate constant k. You wish to process the maximum volume per time of feed, Fj, and would like to decide whether the N reactors should be placed N in parallel, or in m parallel processing lines, each with n reactors (i.e., N = mri). A specified fractional conversion, x, of reactant is always required. Show that the allowable feed rate is given by... 

Equation (32) predicts conversions lower than that in a CSTR when Qg > 1. At = 1, CSTR performance is recovered. Figure 8 gives the conversion for a first-order process as a function of Damkohler number as predicted by eqs. (27), (28) and (32). Clearly, only the upper bound on performance can be established in absence of information on the RTD or at least on its variance. This is not of great help to the designer. Thus, we conclude that knowledge of RTDs is essential for predicting reactor performance for first-order reaction systems. 

Adams et al. (/. Catalysis 3, 379, 1964) investigated these reactions and expressed the rate of each as second order (first order with respect to each reactant). Formulate the dimensionless, reaction-based design equations for an ideal batch reactor, plug-flow reactor, and a CSTR. 

It is desired to design a CSTR to produce 200 million pounds of ethylene glycol year by hydrolyzing ethylene oxide. However, before the design can be carried c it is necessary to perform and analyze a batch reactor experiment to determine specific reaction rate constant, k. Because the reaction will be carried out isoth mally, the specific reaction rate will need to be determined only at the reaction tc perature of the CSTR. At high temperatures there is a. significant by-prod formation, while at temperatures below 40 C the reaction does not proceed at a s nificant rate consequently, a temperature of 55°C has been chosen. Because water is usually present in excess, its concentration may be considered constant d ing the course of the reaction. Tlie reaction is first-order in ethylene oxide. 

Consider a train of five CSTRs in series that have the same volume and operate at the same temperature. One first-order irreversible chemical reaction occurs in each CSTR where reactant A decomposes to products. Two mass-transfer-rate processes are operative in each reactor. The time constant for convective mass transfer across the inlet and outlet planes of each CSTR is designated by the residence time x = Vjq. The time constant for a first-order irreversible chemical reaction is given >y X = l/k. The ratio of these two time constants,... 

Design a two-phase gas-liquid CSTR that operates at 55°C to accomplish the liquid-phase chlorination of benzene. Benzene enters as a liquid, possibly diluted by an inert solvent, and chlorine gas is bubbled through the liquid mixture. It is only necessary to consider the first chlorination reaction because the kinetic rate constant for the second reaction is a factor of 8 smaller than the kinetic rate constant for the first reaction at 55°C. Furthermore, the kinetic rate constant for the third reaction is a factor of 243 smaller than the kinetic rate constant for the first reaction at 55°C. The extents of reaction for the second and third chlorination steps ( 2 and 3) are much smaller than the value of for any simulation (i.e., see Section 1-2.2). Chlorine gas must diffuse across the gas-liquid interface before the reaction can occur. The total gas-phase volume within the CSTR depends directly on the inlet flow rate ratio of gaseous chlorine to hquid benzene, and the impeller speed-gas sparger combination produces gas bubbles that are 2 mm in diameter. Hence, interphase mass transfer must be considered via mass transfer coefficients. The chemical reaction occurs predominantly in the liquid phase. In this respect, it is necessary to introduce a chemical reaction enhancement factor to correct liquid-phase mass transfer coefficients, as given by equation (13-18). This is accomplished via the dimensionless correlation for one-dimensional diffusion and pseudo-first-order irreversible chemical reaction ... 

Program to calculate conversion in a sequence of reactors (both CSTR and PFR) Program to design polymerisation reactor used for chain polymerisation reaction Program to design batch reactor/CSTR/PFR for first-order exothermic reversible reaction following optimal temperature progression policy... 

Program to design batch reactor/CSTR/PFR for first-order exothermic irreversible reaction operating at adiabatic condition... 

Now, this is not a mass balance equation it is actually a design equation which can be used for the design of a lumped system (e.g., an isothermal CSTR). Let us illustrate this for a very simple case of a first-order irreversible liquid-phase reaction, where... 

An exothermic first-order reactive system in a sequence of jacketed CSTRs is considered. Several alternative process designs are constructed and studied with respect to their static and dynamic controllability properties to multiple and simultaneous process disturbances. The same system has been studied by numerous researchers (Ref 14, 15, 44) and served as an illustrative example of process design and control interactions. The reaction is carried out in either a single reactor or two reactors in series (Fig. 1). The dynamic model (see Ref 14, 15) contains four state variables per reactor namely the reactor s volume, concentration and temperature and the jacket temperature. Model parameters for the system are shown in Table... 

ILLUSTRATIVE EXAMPLE 11.1 Your company has two reactors of equal volume which it would like to use in the production of a specified product formed by a first order irreversible liquid reaction. One reactor is a CSTR and the other is a TF reactor. How should these reactors be hooked up to achieve maximum conversion (see Figure 11.11) Justify your answer using concentration (not conversion) terms in the design equations. 

Table 12-3 shows three ways to specify the design of a CSTR. This procedure for non-iscMhermal CSTR design can be illustrated by considering a first-order irreversible liquid-phase reaction. The algorithm for woridng through either cases A ()f specified), B (7 specified), cw C (V. specified) is shown in Table 12-3. Its application is illustrated in Example 12-3.

The specific models we will analyse in this section are an isothermal autocatalytic scheme due to Hudson and Rossler (1984), a non-isothermal CSTR in which two exothermic reactions are taking place, and, briefly, an extension of the model of chapter 2, in which autocatalysis and temperature effects contribute together. In the first of these, chaotic behaviour has been designed in much the same way that oscillations were obtained from multiplicity with the heterogeneous catalysis model of 12.5.2. In the second, the analysis is firmly based on the critical Floquet multiplier as described above, and complex periodic and aperiodic responses are observed about a unique (and unstable) stationary state. The third scheme has coexisting multiple stationary states and higher-order periodicities. 

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