Adiabatic operations CSTRs

Example 5.7 A CSTR is commonly used for the bulk pol5anerization of styrene. Assume a mean residence time of 2 h, cold monomer feed (300 K), adiabatic operation UAgxt = ), and a pseudo-first-order reaction with rate constant... 

The above computation is quite fast. Results for the three ideal reactor t5T)es are shown in Table 6.3. The CSTR is clearly out of the running, but the difference between the isothermal and adiabatic PFR is quite small. Any reasonable shell-and-tube design would work. A few large-diameter tubes in parallel would be fine, and the limiting case of one tube would be the best. The results show that a close approach to adiabatic operation would reduce cost. The cost reduction is probably real since the comparison is nearly apples-to-apples. ... 

Consider the possibility of carrying out the reaction used as the basis for Illustrations 10.1 and 10.2 under adiabatic operating conditions. How much B will it be possible to produce from 2.1 million lb/yr of species A using a pair of 1000-gal CSTR s operating in series Assume that you will be able to operate 7000 hr/yr. Use the data from Illustration 10.2. 

An unusual feature of a CSTR is the possibility of multiple stationary states for a reaction with certain nonlinear kinetics (rate law) in operation at a specified T, or for an exothermic reaction which produces a difference in temperature between the inlet and outlet of the reactor, including adiabatic operation. We treat these in turn in the next two sections. 

Figure 14.6 Illustration of range of feed temperatures (T 0 to T ) for multiple stationary-states in CSTR for adiabatic operation (autothermal behavior occurs for T0 > T )...

For exothermic, reversible reactions, the existence of a locus of maximum rates, as shown in Section 5.3.4, and illustrated in Figures 5.2(a) and 18.3, introduces the opportunity to optimize (minimize) the reactor volume or mean residence time for a specified throughput and fractional conversion of reactant. This is done by choice of an appropriate T (for a CSTR) or T profile (for a PFR) so that the rate is a maximum at each point. The mode of operation (e.g., adiabatic operation for a PFR) may not allow a faithful interpretation of this requirement. For illustration, we consider the optimization of both a CSTR and a PFR for the model reaction... 

Case (2) CSTR T0 for Vmin with adiabatic operation and specified fA, FAo and q The result given by 18.4-4 requires only that the operating temperature within the CSTR be Topt, and implies nothing about the mode of operation to obtain this, that is, nothing about the feed temperature (TJ, or heat transfer either within the reactor or upstream of it. If the CSTR is operated adiabatically without internal heat transfer, T0 must be adjusted accordingly to a value obtained from the energy balance, which, in its simplest integrated form, is, from equation 14.3-10,... 

The primary reason for choosing a particular reactor type is the influence of mixing on the reaction rates. Since the rates affect conversion, yield, and selectivity we can select a reactor that optimizes the steady-state economics of the process. For example, the plug-flow reactor has a smaller volume than the CSTR for the same production rate under isothermal conditions and kinetics dominated by the reactant concentrations. The opposite may be true for adiabatic operation or autocata-lytic reactions. For those situations, the CSTR would have the smaller volume since it could operate at the exit conditions of a plug-flow reactor and thus achieve a higher overall rate of reaction. 

Spontaneous ignition and associated features of organic gases and vapours are a consequence of the exothermic oxidation chemistry discussed in Chapter 1, but the way in which events unfold is determined by the physical environment within which reaction takes place. The heat transfer characteristics are probably most important, as may be illustrated with respect to the different consequences of adiabatic and non-adiabatic operation in a CSTR (Section 5) [117]. The notion of adiabatic operation may seem remote from any practical application, but this idealized condition may be approached if the chemical time-scale is considerably shorter than the time-scale for heat losses. 

For comparison, for adiabatic plug-flow reactor (R = 0) of the same volume, the outlet extent is Zout — 0.742, and 9out =1.135. The production rate of product B is 1,131 mol/min. For adiabatic CSTR R = oo) of the same volume, the outlet extent is Zout = 0.841, and 9out= 1.132. The production rate of product B is 1260 mol/min. Note that for both isothermal and adiabatic operation, a recycle reactor provides a higher production rate of product B than a corresponding plug-flow reactor and a CSTR. 

For adiabatic operation of a PFR. PBR, CSTR. or batch reactor, the temperature conversion relationship is... 

The combined mass and energy balance for the CSTR given in equation (6-4) can be written for adiabatic operation as... 

For an exothermic reaction, adiabatic operation gives an increase in temperature with increasing conversion. However, the optimum temperature profile is one in which the temperature declines with increasing conversion. Severe heat transfer requirements may be needed to make the actual temperature profile approach the ideal desired. Two ways in which this may be achieved are indicated in Figure 10.7. Illustration 10.8 indicates how one determines the optimum temperature at which a single CSTR should be operated. 

Conduct analyses that permit you to determine steady-state (and adiabatic) operating conditions (temperature and fraction conversion) for a single CSTR with a volumes of (1) 500 L, (2) 750 L, and (3) 1000 L. 

Equation 4.77 for a nonisothermal CSTR establishes the temperature at which a stirred reactor operates for a given set of parameter values. This is also true for adiabatic operation. The only difference is that the heat exchange term UA T - T ) vanishes. In either case, the equation is transcendental and not amenable to extension to a CSTR sequence as a single generalized equation for N reactors. On the other hand, for a first-order reaction, a general recursion formula can be written for N reactors in series. This requires that the temperature of each stage is known to enable calculation of the rate constant. 

Adiabatic Operation of a CSTR For adiabatic operation, we have no cooling term, and Eqs. (4.10.59)-(4.10.61) yield ... 

Optimum Operation Line for Adiabatic Operation The relations between conversion, temperature, and rate of reversible reactions in an adiabatic PFR and a CSTR are given schematically in Figure 4.10.36. For a constant value of Cp, we obtain ... 

Figure 4.10.36 Calculation of reactor size for adiabatic operation of a PFR and a CSTR. Adapted from Levenspiel (1999).

The best adiabatic operation of a PFR is found by shifting the operation line to the inlet temperature where the mean rate has the highest value. For endothermic reactions, we start at the highest allowable temperature (Figure 4.10.36a). For exothermic reactions a trial and error search is needed to find the optimal inlet temperature that minimizes the term VR/itA m, as shown schematically in Figure 4.10.37a. A CSTR with a uniform reaction temperature should be always operated on the locus of the maximum rates (Figure 4.10.37b). 

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