Mixing Times and Scaleup

Suppose a homogeneous reaction is conducted in a pilot plant reactor that is equipped with a variable-speed agitator. Does changing the agitator speed (say by 20%) change the outcome of the reaction Does varying the addition rate of reactants change the selectivity If so, there is a potential scaleup problem. The reaction is sensitive 

This requirement applies to batch reactors and to CSTRs. (For PFRs, we assume that the components are perfectly mixed when they enter the reactor.) When Equation 1.54 is satisfied, the conversion in the reactor will be limited by the reaction kinetics, not by the mixing rate. The assumption of perfect mixing is probably reasonable when fi/2 is 8 times larger than f ix. 

What happens to fmx upon scaleup Mixing times in mechanically agitated vessels typically range from a few seconds in laboratory glassware to a few minutes in large industrial reactors. As the size of the vessel increases, will increase, and the increase will eventually limit the size at which the reactor is operable. No process is infinitely scaleable. Sooner or later, additional scaleup becomes impossible, and further increases in production cannot be achieved in single-train plants but must use units in parallel. Fortunately for the economics of the chemical industry, this size limit is often very large. 

Plant sizes are usually characterized by their production capacity or throughput. Define the throughput scaleup factor as 

Assume that the pilot-scale and full-scale vessels operate with the same inlet density. Then p cancels in Equation 1.55 and 

Mixing times in mechanically agitated vessels typically range from a few seconds in laboratory glassware to a few minutes in large industrial reactors. The classic correlation by Norwood and Metzner for turbine impellers in baffled vessels can be used for order of magnitude estimates of 

In a batch vessel, the question of good mixing will arise at the start of the batch and whenever an ingredient is added to the batch. The component balance, Equation (1.21), assumes that uniform mixing is achieved before any appreciable reaction occurs. This will be true if Equation (1.55) is satisfied. Consider the same vessel being used as a flow reactor. Now, the mixing time must be short compared with the mean residence time, else newly charged 

In practice, Equation (1.56) will be satisfied if Equation (1.55) is satisfied since a CSTR will normally operate with t j2 t. 

The net flow though the reactor will be small compared with the circulating flow caused by the agitator. The existence of the throughput has little influence on the mixing time so that mixing time correlations for batch vessels can be used for CSTRs as well. 

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Example 4.7 A fully turbulent, baffled vessel is to be scaled up by a factor of 512 in volume while maintaining constant power per unit volume. Determine the effects of the scaleup on the impeller speed, the mixing time, and the internal circulation rate. 

A volumetric scaleup by a factor of 512 is quite large, and the question arises as to whether the large vessel wiU behave as a CSTR. The concern is due to the factor of 4 increase in mixing time. Does it remain true that tmix h/i and tmix t If so, the assumption that the large vessel wiU behave as a CSTR is probably justified. The ratio of internal circulation to net throughput—which is the internal recycle ratio—scales as the inverse of the mixing time and will thus decrease by a factor of 4. The decrease may appear worrisome, but if the increase in mixing time can be tolerated, then it is likely that the decrease in internal recycle ratio is also acceptable. 

Section 1.5 described one basic problem of scaling batch reactors namely, it is impossible to maintain a constant mixing time if the scaleup ratio is large. However, this is a problem for fed-batch reactors and does not pose a limitation if the reactants are premixed. A single-phase, isothermal (or adiabatic) reaction in batch can be scaled indefinitely if the reactants are premixed and preheated before being charged. The restriction to single-phase systems avoids mass... 

Copolymerizations. The uniform chemical environment of a CSTR makes it ideally suited for the production of copolymers. If the assumption of perfect mixing is justified, there will be no macroscopic composition distribution due to monomer drift, but the mixing time must remain short upon scaleup. See Sections 1.5 and 4.4. A real stirred tank or loop reactor will more closely... 

Solution If power scales as NjDj, then power per unit volume scales as NjDj. To maintain constant power per unit volume, IV/ must decrease upon scaleup. Specifically, Nj- must scale as DJ2 3. When impeller speed is scaled in this manner, the mixing time scales as D2J3and the impeller pumping rate scales as D7/3. To maintain a constant value for t, the throughput Q scales as Dj = S. Results for these and other design and operating variables are shown in Table 4.1. 

Belter and co-workers developed a periodic countercurrent process for treating a fermentation broth to recover novobiocin. They found that they were able to scaleup the laboratory results to production operations if the two systems have similar mixing patterns and the same distribution of residence times in the respective columns. The mixing patterns are the same when the space velocity (F/%) and the volume ration (f /c) are the same. This is shown in Fig. 22 for the effluent concentration of novobiocin from laboratory and production columns. 

A volumetric scaleup by a factor of 512 is quite large, and the question arises as to whether the large vessel will remain well mixed on the large scale. The concern is the fact that the mixing time increases by a factor of 4. Does it remain true that [Pg.144]

Stirred reactors are sometimes scaled up keeping the power per unit volume constant but in other cases, constant mixing time or constant maximum shear rate is recommended. It is impossible to keep all these parameters constant on scaleup and maintain geometric similarity, so tests are... 

A theoretical justification for using the blending time as a scaleup criterion is that is usually proportional to t and is the critical mixing time if most of the extra byproduct formation occurs in or near the feed plume. If the ratio dg/D is kept the same, with d = aD, and the average rate of energy dissipation is e = then Eq. (6.7) becomes... 

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