Ideal Stirred-tank Reactors Flow

One final point is of significance. As conditions have been attained for the maximum yield of X, the reactor has become relatively large. At 5°C the reaction rate will be low and the total conversion is approaching 100%. Whether it is advisable to operate at these conditions for maximum conversion of Xdepends on the economics of reactor costs, separation costs, and price of product X. 

The ideal stirred-tank reactor operates isothermally and hence at a constant rate. However, an energy balance is needed to predict the constant temperature when the heat of reaction is sufficient (or the heat exchange between the surroundings and reactor is insufficient) to cause a difference between 

A stirred tank may give better or worse selectivities than a tubular-flow unit in multiple-reaction systems. As usual, the key point is the relative values of the activation energies for the reactions. In particular, for a set of parallel reactions, where the desired product is formed by the reaction with the higher activation energy, the stirred tank is advantageous. The production of allyl chloride considered in Example 5-2 is a case in point. The performance of a stirred-tank reactor for this system is discussed next, and the results are compared with the performance of the tubular-flow reactor. 

Example 5-3 Consider the design of a continuous stirred-tank reactor for the production of allyl chloride from propylene, using the reaction-rate data given in Example 5-2. So that we may compare the two types of reactors, the same feed condition will be employed  

The operation is adiabatic. Also, suitable baffles and entrance nozzles will be used so that, although the contents of the reactor are gaseous, they will be of uniform temperature, pressure, and composition. 

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SECTIDN 5-3 IDEAL STIRRED-TANK REACTORS (FLOW)... 

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

The other ideal steady-state flow reactor is called the mixed reactor, the backmix reactor, the ideal stirred tank reactor, the C " (meaning C-star), CSTR, or the CFSTR (constant flow stirred tank reactor), and, as its names suggest, it is a reactor in which the contents are well stirred and uniform throughout. Thus, the exit stream from this reactor has the same composition as the fluid within the reactor. We refer to this type of flow as mixed flow, and the corresponding reactor the mixed flow reactor, or MFR. 

We have a first-order homogeneous reaction, taking place in an ideal stirred tank reactor. The volume of the reactor is 20 X 10 3 m3. The reaction takes place in the liquid phase. The concentration of the reactant in the feed flow is 3.1 kmol/m3 and the volumetric flow rate of the feed is 58 X 10 m3/s. The density and specific heat of the reaction mixture are constant at 1000 kg/m3 and 4.184kJ/(kg K). The reactor operates at adiabatic conditions. If the feed flow is at 298 K, investigate the possibility of multiple solutions for conversion at various temperatures in the product stream. The heat of reaction and the rate of reaction are... 

Fig. 3-1 Ideal stirred-tank reactors classified according to method of operation (a) flow (steady-state), (b) batch, (c) semibatch (non-steady-flow)...

Semibatch Operation In semibatch operation the rates of mass flow into and out of the system are unequal (see Fig. 3-1 c). For example, benzene may be chlorinated in a stirred-tank reactor by first adding the charge of liquid benzene and catalyst and then continuously adding chlorine gas until the required ratio of chlorine to benzene has been obtained. Operation of this kind is. batch from the standpoint that the composition of the reaction mixture changes with time. However, from a process standpoint the chlorine is added continuously. The system is still an ideal stirred-tank reactor if the... 

It was possible to solve this polymerization problem in closed form because we were dealing with algebraic equations, that is, with an ideal stirred-tank reactor. The same problem in a tubular-flow reactor would require the solution of a series of integral equations, which is possible only by numerical methods. 

We shall consider three methods of estimating deviations from ideal reactor performance. The first method is to determine the actual RTD from experimental response data and then calculate the conversion by assuming the flow to be wholly segregated (Sec. 6-8). This model should be a good approximation, for example, for a tubular-flow reactor, where the flow is streamline. It would not describe a nearly ideal stirred-tank reactor, for here the fluid is nearly completely mixed when it enters the reactor. In this case no error is introduced by an approximation of the RTD, since the actual... 

For reactors with known mixing characteristics the response curve and the RTD can be predicted no experiments are necessary. As an illustration let us deyelop the RTD for the plug-flow reactor, a single ideal stirred-tank reactor, and a tubular reactor with laminar flow. 

Figure 6-lOh is a plot of Eq. (6-33) for various values of n. The similarity between Figs. 6-8 and 6-10 indicates that the axial-dispersion and series-of-stirred-tanks models give the same general shape of response curve. The analogy is exact for = 1, for this curve in Fig. 6-1 Oh agrees exactly with that in Fig. 6-8 for infinite dispersion, DJuL = oo both represent the behavior of an ideal stirred-tank reactor. Agreement is exact also at the other extreme, the plug-flow reactor ( = oo in Fig. 6-1 Oh and DjuL = 0 in Fig. 6-8). The shapes of the curves for the two models are more nearly the same the larger the value of n.

In contrast, suppose complete micromixing is assumed. Then, for the same RTD, an ideal stirred-tank reactor results. The conversion for a first-order reaction in this case is given by Eq. (4-7), which is identical to the above expression for segregated flow. This verifies the conclusion of Eq. (6-36) that the extent of micromixing does not affect conversion for first-order kinetics (as long as the correct RTD is used). The same develop-... 

The results of Examples 6-6 and 6-7 are for one case, but they are representative of the situation for many reactors. We saw in Secs. 6-7 and 6-8 that extremes of RTD can have large effects on the conversion, particularly at high conversion levels. However, with relatively simple models to estimate the RTD, little error need be involved. Put differently, if an engineer were to use an ideal stirred-tank reactor to simulate a nearly ideal tubular-flow unit, the pr cted conversion would be seriously in error. However, if the measured RTD or a reasonable model were employed, the result would be approximately correct. The residual error will be due to uncertainty in the extent of micromixing. 

An ideal stirred-tank reactor followed by a plug-flow reactor is proposed as a model for the RTD of the reactor system in Prob. 6-1. The volumetric flow rate and combined volume of the two reactors will be the same as in Prob. 6-1. What ratio of the volume of the plug-flow and stirred-tank vessels would best represent the RTD Comment on the suitability of the model. 

Most large reactors do not fit the foregoing criteria, but in many cases the deviations from ideal reactors are small, and the equations for ideal reactors can be used for approximate design calculations and sometimes for determining optimum reaction conditions. In this chapter, ideal stirred-tank reactors are considered first and then plug-flow reactors are discussed. The effects of heat transfer, mass transfer, and partial mixing in real reactors are treated in later chapters. 

Finally, several alternate names have been used for what here is called the perfectly mixed flow reactor. One of the earliest was continuous stirred tank-reactor, or CSTR, which some have modified to continuous flow stirred tank reactor, or CFSTR. Other names are backmix reactor, mixed flow reactor, and ideal stirred tank reactor. All of these terms appear in the literature, and must be recognized. 

Continuous flow stirred-tank reactors are normally just what the name implies tanks into which reactants flow and from which a product stream is removed on a continuous basis. CFSTRs, CSTRs, C-star reactors, and backmix reactors are only a few of the names applied to the idealized stirred-tank flow reactor model. We will use the letters CSTR in this book. The virtues of a stirred-tank reactor lie in its simplicity of construction and the relative ease with which it may be controlled. These reactors are used primarily for carrying out liquid phase reactions in the organic chemicals industry, particularly for systems that are characterized by relatively slow reaction rates. If it is imperative that a gas phase reaction be carried out under efficient mixing conditions similar to those found in a stirred-tank reactor, one may employ a tubular reactor containing a recycle loop. At sufficiently high recycle rates, such systems approximate the behavior of stirred tanks. In this section we are concerned with the development of design equations that are appropriate for use with the idealized stirred-tank reactor model. 

In Chapter 2, the design of the so-called ideal reactors was discussed. The reactor ideahty was based on defined hydrodynamic behavior. We had assumedtwo flow patterns plug flow (piston type) where axial dispersion is excluded and completely mixed flow achieved in ideal stirred tank reactors. These flow patterns are often used for reactor design because the mass and heat balances are relatively simple to treat. But real equipment often deviates from that of the ideal flow pattern. In tubular reactors radial velocity and concentration profiles may develop in laminar flow. In turbulent flow, velocity fluctuations can lead to an axial dispersion. In catalytic packed bed reactors, irregular flow with the formation of channels may occur while stagnant fluid zones (dead zones) may develop in other parts of the reactor. Incompletely mixed zones and thus inhomogeneity can also be observed in CSTR, especially in the cases of viscous media. 

Other models to characterize residence time distributions are based on fitting the measured distribution to models for a plug flow with axial dispersion or for series of continuously ideally stirred tank reactors in series. For the first model the Peclet number is the characteristic parameter, for the second model the number of ideally stirred tank reactors needed to fit the residence time distribution typifies the distribution. However, these models should be used with care because they assume a standard distribution in residence times. Most distributions in extruders show a distinct scewness, which could lead to erroneous results at very short and very long residence times. The only exception is the co-kneader the high amount of back mixing in this type of machine leads to a nearly perfect normal distribution. 

Experimental kinetic data always should be taken in a reactor that behaves as one of tiie tiiree ideal reactors. It is relatively straightforward to analyze the data from an ideal batch reactor, an ideal plug-flow reactor, or an ideal stirred-tank reactor. This is not the case if the reactor is nonideal, e.g., somewhere between a PFR and a CSTR. Characterizing the behavior of nonideal reactors is difficult and imprecise, as we shall see in Chapter 10. This can lead to major uncertainties in the analysis of data taken in nonideal reactors. 

Continuous-Flow Stirred-Tank Reactor. In a continuous-flow stirred-tank reactor (CSTR), reactants and products are continuously added and withdrawn. In practice, mechanical or hydrauHc agitation is required to achieve uniform composition and temperature, a choice strongly influenced by process considerations, ie, multiple specialty product requirements and mechanical seal pressure limitations. The CSTR is the idealized opposite of the weU-stirred batch and tubular plug-flow reactors. Analysis of selected combinations of these reactor types can be useful in quantitatively evaluating more complex gas-, Hquid-, and soHd-flow behaviors. 

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