Stirred tanks in series

Operation in several tanks in series will provide narrower size distributions. Equations were developed by Nyvlt (1971) for two main cases. Wilh generation of nuclei in die first stage only, the 

Nyvlt (1971) also develops equations for multistage crystalhzers in which nuclei form at the same rate in all stages. For two such the cumulative distribution is represented by 

As in the operation of chemical reactors, multistaging requires shorter residence time for the same performance. For the same LIG ratio, the relative crystallization times of k stages and one stage to reach the peaks are given by Eq. (16.26) as 

One way to double the output of a stirred tank process is to increase each linear dimension by 2 / = 1.26, but this may lead to heat transfer or mixing limitations. Another way is to add a stirred tank in parallel, but better results and a more flexible process are usually achieved by adding a stirred tank in series. Some polystyrene processes use five stirred-tank and stirred-tube reactors in series. Some polypropylene processes use two or three loop and stirred-tank reactors in series. Modern fluidized-bed processes for polypropylene use two beds in series. 

One advantage of using tanks in series is the improvement in residence time distribution from the exponential distribution of a single stirred tank toward that of piston (plug) flow. The series arrangement leads to higher conversion and thus eases the burden of downstream recovery and recycling. The usual case is for two 

A major advantage of using tanks in series is the ability to have a different reaction environment in the various tanks. This advantage is especially useful in polypropylene processes where the last reactor adds ethylene for impact modification. 

When scaling in parallel, the number of tubes scales directly with the inventory scaleup factor, S. Factors for other forms of scaleup for incompressible fluids are given in Table 10.2. This table includes three geometric scaleup factors. They are for volume, S, radius Sr, and length, Sl. They are related by Eq. (4) so that only two are arbitrarily adjustable. 

Thus the general scaling equation for pressure drop in a single tube in laminar flow can be given in several equivalent forms [Eqs. (5)]. 

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In a single eontinuous flow stirred tank reaetor, a portion of the fresh feed eould exit immediately in the produet stream as soon as the reaetants enter the reaetor. To reduee this bypassing effeet, a numher of stirred tanks in series is frequently used. This reduees the prohahility that a reaetant moleeule entering the reaetor will immediately find its way to the exiting produet stream. The exit stream from the first stirred tank serves as the feed to the seeond, the exit stream from the seeond reaetor serves as the feed to the third, and so on. For eonstant density, the exit eoneentration or eonversion ean he solved hy eonseeutively applying Equation 5-158 to eaeh reaetor. The following derived equations are for a series of tliree stii+ed tanks (Figure 5-23) with eonstant volume Vr. 

N —> This indicates that the behavior of stirred tanks in series... 

The model consists of i -i- 1 stirred tanks in series, i of which have a common volume, and one of which has a smaller volume... 

Computer program PROGS 1 determines the number of tanks, the varianee, dispersion number, and the Peelet number from Hull and von Rosenberg data. The results of the simulation suggest that about three stirred tanks in series are equivalent to the RTD response eurve. Figure 8-44 shows the shows E(6), Fe p(6), and Fjy[gjgi(6) versus 6. 

This chapter develops the techniques needed to analyze multiple and complex reactions in stirred tank reactors. Physical properties may be variable. Also treated is the common industrial practice of using reactor combinations, such as a stirred tank in series with a tubular reactor, to accomplish the overall reaction. 

Example 4.12 used N stirred tanks in series to achieve a 1000-fold reduction in the concentration of a reactant that decomposes by first-order kinetics. Show how much worse the CSTRs would be if the 1000-fold reduction had to be achieved by dimerization i.e., by a second order of the single reactant type. The reaction is irreversible and density is constant. 

Example 4.13 treated the case of a piston flow reactor inside a recycle loop. Replace the PER with two equal-volume stirred tanks in series. The reaction remains first order, irreversible, and at constant density. 

A continuous polymerization train consisting of two stirred tanks in series is used to copolymerize styrene, rx = 0.41, and acrylonitrile, vy = 0.04. The flow rate to the first reactor is 3000 kg/h and a conversion of 40% is expected. Makeup styrene is fed to the second reactor and a conversion of 30% (based on the 3000 kg/h initial feed) is expected there. What should be the feed composition and how much styrene should be fed to the second reactor if a copolymer containing 58 wt% styrene is desired ... 

Real reactors can have 0 < cr < 1, and a model that reflects this possibility consists of a stirred tank in series with a piston flow reactor as indicated in Figure 15.1(a). Other than the mean residence time itself, the model contains only one adjustable parameter. This parameter is called the fractional tubularity, Xp, and is the fraction of the system volume that is occupied by the piston flow element. Figure 15.1(b) shows the washout function for the fractional tubularity model. Its equation is... 

Example 15.14 Solve Zwietering s differential equation for the residence time distribution corresponding to two stirred tanks in series. Use second-order kinetics with ai ki = 5. 

In this case, three time constants in series, X, %2 and X3, determine the form of the final outlet response C3. As the number of tanks is increased, the response curve increasingly approximates the original, step-change, input signal, as shown in Fig. 2.12. The response curves for three stirred tanks in series, combined with chemical reaction are shown in the simulation example CSTR. 

Figure 2.12. Step response of n stirred tanks in series (n=l 2 5 10 20).

Thus the respective rate expressions depend upon the particular concentration and temperature levels, that exist within reactor, n. The rate of production of heat by reaction, rg, was defined in Sec. 1.2.5 and includes all occurring reactions. Simulation examples pertaining to stirred tanks in series are CSTR, CASCSEQ and COOL. 

Setting k = 0, simulate the tracer response (F-curves) for 3 perfectly-stirred tanks in series. 

Figure 5.36 Stirred tanks in series with feeding to accomplish the best performance with this complex reaction.

The Stirred Tanks in Series Model Another model that is frequently used to simulate the behavior of actual reactor networks is a cascade of ideal stirred tank reactors operating in series. The actual reactor is replaced by n identical stirred tank reactors whose total volume is the same as that of the actual reactor. 

The Gain and phase angle will be found for several ideal stirred tanks in series. For such a series of vessels, the overall transfer function is the product of the individual transfer functions, that is,... 

A reactor is modelled as two stirred tanks in series, of which the first is half the size of the other. Derive equations for the time distributions E(tr), F(tr) and A(tr). 

Fig. 2.12 Step response of n equal volume stirred tanks in series (n = 1, 2, 5, 10, 20).

Setting k = 0, simulate the response to a pulse of tracer for 3 perfectly-stirred tanks in series. Repeat this for various numbers of tanks and plot E versus dimensionless time for these on an overlay graph. 

We also notice, from either Eq. (124) or Eq. (126), that j-> as DI->0. This is the basis for the statement that an infinite number of stirred tanks in series is the equivalent to plug flow. 

Injection rate of tracer Number of ideal stirred tanks in series Bessel functions Moment order, see Eq. (65)... 

The other mode of flow reaction employs one or more stirred tanks in series, which is called a continuous stirred tank (CSTR) battery. The rate of reaction in a single tank is... 

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