The Continuous-Flow Stirred Tank Reactor

3 The Continuous-Flow Stirred Tank Reactor 4.4.3.1 Physical Description 

A consequence of the perfect mixing assumption is that the concentration of the effluent stream of a CSTR must be identical to the concentration found in the bulk fluid inside the tank. Knowledge of the effluent concentration provides insight into the conditions inside of the reactor, and vice versa. Only one product concentration is produced in a CSTR as a result. This is significantly different from the PFR, where concentration is assumed to change continuously down the length of the reactor. 

For every element of feed that enters a CSTR, the perfect mixing assumption implies that the entering element is instantaneously converted to the concentration of the bulk volume. Conversion of reactants might then be viewed to occur as a result of mixing and dilution rather than from reaction alone. 

Residence Time A measure of the average reaction time of a fluid element inside a CSTR is often interpreted in an analogous way to that of the residence time of a fluid element inside a PFR. We hence define the CSTR residence time t as follows  

Q is the volumetric flow rate of the CSTR effluent stream, whereas Vcstr is the volume of the CSTR vessel. 

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Specific reactor characteristics depend on the particular use of the reactor as a laboratory, pilot plant, or industrial unit. AH reactors have in common selected characteristics of four basic reactor types the weH-stirred batch reactor, the semibatch reactor, the continuous-flow stirred-tank reactor, and the tubular reactor (Fig. 1). A reactor may be represented by or modeled after one or a combination of these. SuitabHity of a model depends on the extent to which the impacts of the reactions, and thermal and transport processes, are predicted for conditions outside of the database used in developing the model (1-4). 

There are two important types of ideal, continuous-flow reactors the piston flow reactor or PFR, and the continuous-flow stirred tank reactor or CSTR. They behave very diflerently with respect to conversion and selectivity. The piston flow reactor behaves exactly like a batch reactor. It is usually visualized as a long tube as illustrated in Figure 1.3. Suppose a small clump of material enters the reactor at time t = 0 and flows from the inlet to the outlet. We suppose that there is no mixing between this particular clump and other clumps that entered at different times. The clump stays together and ages and reacts as it flows down the tube. After it has been in the piston flow reactor for t seconds, the clump will have the same composition as if it had been in a batch reactor for t seconds. The composition of a batch reactor varies with time. The composition of a small clump flowing through a piston flow reactor varies with time in the same way. It also varies with position down the tube. The relationship between time and position is... 

Continuous Flow Reactors—Stirred Tanks. The continuous flow stirred tank reactor is used extensively in chemical process industries. Both single tanks and batteries of tanks connected in series are used. In many respects the mechanical and heat transfer aspects of these reactors closely resemble the stirred tank batch reactors treated in the previous subsection. However, in the present case, one must also provide for continuous addition of reactants and continuous withdrawal of the product stream. 

THE CONTINUOUS FLOW STIRRED TANK REACTOR (CSTR)... 

We first consider the continuous flow stirred tank reactor (CFSTR). A schematic presentation of the continuous flow stirred tank reactor is given in Figure 1. It is assumed that no mass transfer limitations exist regarding the supply of ozone. The accuracy of this assumption depends on the way ozone is supplied to the system and the reaction rate constants of the components involved. 

The bioreactor has been introduced in general terms in the previous section. In this section the basic bioreactor concepts, i.e., the batch, the fed-batch, the continuous-flow stirred-tank reactor (CSTR), the cascade of CSTRs and the plug-flow reactor, will be described. 

Heinrichs, M. and Schneider, F. W. (1981). Relaxation kinetics of steady-states in the continuous flow stirred tank reactor. Response to small and large perturbations critical slowing down. J. Phys. Chem., 85, 2112-16. 

P. Aroca, Jr., and R. Aroca, Chemical Oscillations A Microcomputer-Controlled Experiment, J. Chem. Ed. 1987,64, 1017 J. Amrehn, P. Resch, and F. W. Schneider, Oscillating Chemiluminescence with Luminol in the Continuous Flow Stirred Tank Reactor, J. Phys. Chem. 1988,92, 3318 D. Avnir, Chemically Induced Pulsations of Interfaces The Mercury Beating Heart, ... 

Figure 5-21. The continuous flow stirred tank reactor (CFSTR).

When the reactant ratio is unity (i.e., 0A= 1), the mass balance for component A in the continuous flow stirred tank reactor is... 

The various types of reactors employed in the processing of fluids in the chemical process industries (CPI) were reviewed in Chapter 4. Design equations were also derived (Chapters 5 and 6) for ideal reactors, namely the continuous flow stirred tank reactor (CFSTR), batch, and plug flow under isothermal and non-isothermal conditions, which established equilibrium conversions for reversible reactions and optimum temperature progressions of industrial reactions. 

Various laboratory reactors have been described in the literature [3, 11-13]. The most simple one is the packed bed tubular reactor where an amount of catalyst is held between plugs of quartz wool or wire mesh screens which the reactants pass through, preferably in plug flow . For low conversions this reactor is operated in the differential mode, for high conversions over the catalyst bed in the integral mode. By recirculation of the reactor exit flow one can approach a well mixed reactor system, the continuous flow stirred tank reactor (CSTR). This can be done either externally or internally [11, 12]. Without inlet and outlet feed, this reactor becomes a batch reactor, where the composition changes as a function of time (transient operation), in contrast with the steady state operation of the continuous flow reactors. 

Another type of continuous flow reactor is found in industry the continuous flow stirred tank reactor (CSTR), Fig. 7.2. Stirring of the reactor content might be necessary to increase the heat exchange with the surroundings or to maintain a heterogeneous catalyst in suspension. If more than one fluid phase is present in the reactor, stirring increases the contact surface area and, hence, the rate of mass transfer between these phases. 

A first-law energy balance on the continuous-flow stirred-tank reactor gives the expression... 

Solve for reactor volume using the material-balance expression. The material balance for the continuous-flow stirred-tank reactor may now be used to calculate the reactor volume required for the isomerization. Inserting the first-order rate expression into the material balance,... 

We turn now to consider the principal types of reactors and derive a set of equations for each that will describe the transformation 5 of the state of the feed into the state of the product. The continuous flow stirred tank reactor is one of the simplest in basic design and is widely used in chemical industry. Basically it consists in a vessel of volume V furnished with one or more inlets, an outlet, a means of cooling and a stirrer which keeps its composition and temperature essentially uniform. We shall assume that there is complete mixing on the molecular scale. It would be possible to treat of other cases following the work of Danckwerts (1958) and Zweitering (1959), but the corresponding transformation is much less wieldy. If the reactants flow in and out at a constant rate q, the mean residence time T/g is known as the holding time of the reactor. 

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