The continuous stirred tank reactor

Although continuous stirred-tank reactors (Fig. 3.12) normally operate at steady-state conditions, a derivation of the full dynamic equation for the system, is necessary to cover the instances of plant start up, shut down and the application of reactor control. 

The dynamic total mass balance equation is given by 

Under constant volume and constant density conditions 

Under constant density and constant volume conditions, this may be 

For steady-state conditions to be maintained, the volumetric flow rate F, and inlet concentration, Cao must remain constant and 

I Rate of accumulation t Mass flowA / Massflow l of mass in the reactor j v rate in j rate out 

In a plug-flow reactor, all the volume elements take the same time to pass through the reactor, but in a continuous stirred tank reactor, as a 

Several continuous stirred tank reactors are often operated in series or cascade as shown in Fig. 13. In this way, the disadvantages of the relatively low reactant concentration on the one hand, and by-passing on the other, may be partially off-set. As the number of tanks in series increases, the performance of the complete system approaches that of a plug-flow reactor and, in the limit of an infinite number of tanks, becomes equal to it. 

Since conditions in the tank are uniform, the material balance for A can be performed over the whole reactor. 

When there are appreciable density changes, as for example in reactions involving gases or in some polymerisation reactions, these must be taken into account. In this case, at the reactor inlet, the volumetric flow rate Fi is 

The mass balance for A over the whole tank may be written 

Here we consider the situation where mixing of fluids is sufficiently rapid that the composition does not vary with position in the reactor. This is a stirred-tank or backmix 

The completely mixed limit is in fact rather easy to achieve with ordinary mixing techniques. The approximation can be thought of in terms of mixing time tmix versus residence time r of the fluid in the reactor. If 

Since the reactor is assumed to be uniform in composition everywhere, we can make an integral mass balance on the number of moles Nj of species j in a reactor of volume V. This gives 

It is evident that this equation looks identical to the batch-reactor equation in the 

We can also relate the molar flow rates Fjo and Fj of species j to the concentration by the relationships 

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During the manufacturing process, if the grafting increases during early stages of the reaction, the phase volume will also increase, but the size of the particles will remain constant [146-148]. Furthermore, reactor choice plays a decisive role. If the continuous stirred tank reactor (CSTR) is used, little grafting takes place and the occlusion is poor and, consequently, the rubber efficiency is poor. However, in processes akin to the discontinuous system(e.g., tower/cascade reactors), the dispersed phase contains a large number of big inclusions. 

Reactor Conditions for Experimental Runs. Operating conditions for the continuous, stirred tank reactor runs were chosen to study the effects of mixing speed on the monomer conversion and molecular weight distribution at different values for the number average degree of polymerization of the product polymer. 

Based on the kinetic mechanism and using the parameter values, one can analyze the continuous stirred tank reactor (CSTR) as well as the dispersed plug flow reactor (PFR) in which the reaction between ethylene and cyclopentadiene takes place. The steady state mass balance equations maybe expressed by using the usual notation as follows ... 

Choose the right type of reactor for testing There are quite a number of different reactors. The above-mentioned plug flow reactor and the continuously stirred tank reactor are usually preferred for research laboratory use, but other set-ups may also be of interest for simulating real industrial conditions. 

One of the simplest models for convective mass transfer is the stirred tank model, also called the continuously stirred tank reactor (CSTR) or the mixing tank. The model is shown schematically in Figure 2. As shown in the figure, a fluid stream enters a filled vessel that is stirred with an impeller, then exits the vessel through an outlet port. The stirred tank represents an idealization of mixing behavior in convective systems, in which incoming fluid streams are instantly and completely mixed with the system contents. To illustrate this, consider the case in which the inlet stream contains a water-miscible blue dye and the tank is initially filled with pure water. At time zero, the inlet valve is opened, allowing the dye to enter the... 

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

Let xp and xc represent the space times of the plug flow reactor and the continuous stirred tank reactor respectively. Consider the following reactor combination... 

The classical CRE model for a perfectly macromixed reactor is the continuous stirred tank reactor (CSTR). Thus, to fix our ideas, let us consider a stirred tank with two inlet streams and one outlet stream. The CFD model for this system would compute the flow field inside of the stirred tank given the inlet flow velocities and concentrations, the geometry of the reactor (including baffles and impellers), and the angular velocity of the stirrer. For liquid-phase flow with uniform density, the CFD model for the flow field can be developed independently from the mixing model. For simplicity, we will consider this case. Nevertheless, the SGS models are easily extendable to flows with variable density. 

For the continuous stirred-tank reactor of volume Vc A steady-state balance on reactant A gives ... 

In the continuous stirred tank reactor (CSTR) instant mixing to achieve a homogeneous reaction mixture is assumed so that the composition throughout the reactor is uniform. During the reaction, monomer is fed into the system at the same rate as polymer is withdrawn. The heat problem is somewhat diminished because of the constant removal of heated products and the addition of nonheated reactants. 

In contrast to the design equations for batch and plug-flow reactors, eqns. (5) and (62), the design equation for the continuous stirred tank reactor does not contain an integral sign. Figure 14 shows [ A]o/r plotted... 

Chapter 1 reviews the concepts necessary for treating the problems associated with the design of industrial reactions. These include the essentials of kinetics, thermodynamics, and basic mass, heat and momentum transfer. Ideal reactor types are treated in Chapter 2 and the most important of these are the batch reactor, the tubular reactor and the continuous stirred tank. Reactor stability is considered. Chapter 3 describes the effect of complex homogeneous kinetics on reactor performance. The special case of gas—solid reactions is discussed in Chapter 4 and Chapter 5 deals with other heterogeneous systems namely those involving gas—liquid, liquid—solid and liquid—liquid interfaces. Finally, Chapter 6 considers how real reactors may differ from the ideal reactors considered in earlier chapters. 

The chemical reactor is the unif in which chemical reactions occur. Reactors can be operated in batch (no mass flow into or out of the reactor) or flow modes. Flow reactors operate between hmits of completely unmixed contents (the plug-flow tubular reactor or PFTR) and completely mixed contents (the continuous stirred tank reactor or CSTR). A flow reactor may be operated in steady state (no variables vary with time) or transient modes. The properties of continuous flow reactors wiU be the main subject of this course, and an alternate title of this book could be Continuous Chemical Reactors. The next two chapters will deal with the characteristics of these reactors operated isothermaUy. We can categorize chemical reactors as shown in Figure 2-8. 

Figure 3-1 The continuous stirred tank reactor (CSTR) of volume V with inlet molar flow rate Fja and outlet molar flow rate F ...

Many reviews and several books [61,62] have appeared on the theoretical and experimental aspects of the continuous, stirred tank reactor - the so-called chemostat. Properties of the chemostat are not discussed here. The concentrations of the reagents and products can not be calculated by the algebraic equations obtained for steady-state conditions, when ji = D (the left-hand sides of Eqs. 27-29 are equal to zero), because of the double-substrate-limitation model (Eq. 26) used. These values were obtained from the time course of the concentrations obtained by simulation of the fermentation. It was assumed that the dispersed organic phase remains in the reactor and the dispersed phase holdup does not change during the process. The inlet liquid phase does not contain either organic phase or biomass. 

A continuous bulk polymerization process with three reaction zones in series has been developed. The degree of polymerization increases from the first reactor to the third reactor. Examples of suitable reactors include continuous stirred tank reactors, stirred tower reactors, axially segregated horizontal reactors, and pipe reactors with static mixers. The continuous stirred tank reactor type is advantageous, because it allows for precise independent control of the residence time in a given reactor by adjusting the level in a given reactor. Thus, the residence time of the polymer mixtures can be independently adjusted and optimized in each of the reactors in series (8). 

The Continuously Stirred Tank Reactor There are differences in the detailed construction of the continuous stirred tank reactors (or well-stirred reactors) used for high temperature chemistry, but in principle they are all modifications of the original Longwell-Weiss reactor [249]. A schematic diagram of a reactor with a hemispherical geometry is shown in Fig. 13.9. 

One of the advantages of the continuous stirred-tank reactor is the fact that it is ideally suited to autothermal operation. Feed-back of the reaction heat from products to reactants is indeed a feature inherent in the operation of a continuous stirred-tank reactor consisting of a single tank only, because fresh reactants are mixed directly into the products. An important, but less obvious, point about autothermal operation is the existence of two possible stable operating conditions. 

General conclusions In series reactions, as the concentration of the desired intermediate P builds up, so the rate of degradation to the second product Q increases. The best course would be to remove P continuously as soon as it was formed by distillation, extraction or a similar operation. If continuous removal is not feasible, the conversion attained in the reactor should be low if a high relative yield is required. As the results for the continuous stirred-tank reactor show, backmixing of a partially reacted mixture with fresh reactants should be avoided. 

This expression enhances the fact that the heat release rate is a function of the conversion and will therefore vary with time in discontinuous reactors or during storage. In a batch reaction, there is no steady state. It is constant in the Continuous Stirred Tank Reactor (CSTR) and is a function of the location in the tubular reactor (see Chapter 8). The heat release rate is... 

Yet who would have thought the old man to have had so much hlood in him This title, given by Prof. Rutherford Aris and his collaborator W.W. Farr to their recent paper [Chem. Eng. Sci., 41 (1986) 1385], is a phrase used by Lady Macbeth (Macbeth, V, 1, 42-44). Fierce, isn t it Apparently, they mean it to imply that traditional theoretical problems in the dynamics of chemical reactions, in particular the known problem of the dynamics of the continuous stirred tank reactor (CSTR), are far from being exhausted. Novel mathematical approaches provide new results oriented to physico-chemical comprehension. This current trend is confirmed by the present volume. 

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