Scale reaction, geometric similarity

As shown in the previous section, scaling with geometric similarity, Sr = Sl = gives constant pressure drop when the flow is laminar and remains laminar upon scaleup. This is true for both liquids and gases. The Reynolds number and the external area increase as. Piston flow is a poor assumption for laminar flow in anyfhing but small tubes. Conversion and selectivity of the reaction is likely to worsen upon scaleup unless the pilot reactor is already so large that molecular and thermal diffusion are negligible on the pilot scale. Ways to avoid unpleasant surprises are discussed in Chapter 8... 

Scaling in parallel or series is preferred when heat transfer is a dominant consideration. The third method, scaling with geometric similarity, is cheaper for reactions that permit adiabatic operation. 

Depart from Geometric Similarity. Adding length to a tubular reactor while keeping the diameter constant allows both volume and external area to scale as S if the liquid is incompressible. Scaling in this manner gives poor results for gas-phase reactions. The quantitative aspects of such scaleups are discussed... 

All chemical processes regardless of type involve various mechanisms in addition to the desired chemical conversion, such as chemical reactions, thermodynamic, physical, and chemical equilibria, heat transfer, and mass transfer, which are not independent from one another, thus making it difficult to study their interactions. For example, transfer phenomena essentially depend on fluid flow. In other words, the scale or size of the equipment in which the process takes place has a different effect depending on the mechanism concerned. Extrapolation using geometric similarity can be proved extremely useful in determining the effect of size on a number of characteristic magnitudes of the system. This is shown in Table 6.2. 

In the normal case of a geometrically similar scale-up, it can be readily shown that the surface area per unit volume varies inversely with the vessel diameter. Thus larger vessels are more difficult to cool, since the heat generated by a reaction in a potential runaway situation is proportional to the vessel volume, whereas the surface area available to dissipate a given heat output is decreased. Vigorous reactions may require the reactor to be detuned by operating with more dilute feedstock in order to reduce the full-scale reaction intensity. This... 

In Damkohler s analysis, which applied to a continuous chemical reaction process in a tubular reactor, he solved these dilemmas by completely abandoning geometric similarity and fluid dynamic similarity. In other words, L/D idem and assuming that the Reynolds number is irrelevant in the scaling. Hence, his scale-up depends exclusively on thermal and reaction similarity. In our case it is even easier to see that the Reynolds number is very small and does not play a role in the process. By allowing to adjust L/D accordingly, there is more flexibility in the scaling problem. 

Since the diameter of the catalyst grain has a considerable influence on the reaction rate, its variation will not be permitted during scale-up this means that the geometrical similarity will inevitably be violated by dp/d / idem. Therefore, scale-up of the tubular reactor filled with catalyst is, at best, possible through adherence to partial similarity whereby it is necessary to check whether violation of geometric similarity alone is enough to guarantee scale-up. 

He knows that he may not vary the temperature T0 and dp if he does not want to risk influencing the chemical course of the reaction. Consequently, as already mentioned, geometric similarity is inevitably violated during scale-up on account of dp/d Z idem. Damkohler is therefore prepared to waive adherence to L/d = idem as well. However, he points out that this will necessarily lead to consequences for heat transfer behaviour. In this case, he uses the hypothesis that thermal similarity is guaranteed if the ratio of IV to III (heat conduction through the tube wall to heat removal by convection) is kept equal ... 

Although it is basically possible to apply the theory of similarity to chemical processes and to scale up one of these processes in such a way that geometric, fluid dynamic, thermal and reaction-kinetic similarity is retained to a greater or lesser extent, these transformation processes are only of limited importance. They may be quite useful for increasing equipment performance two to five-fold but hardly to much larger amounts. This circumstance is of importance since it is more or less equivalent to practical failure of the theory of similarity. This, however, was not to be expected from the beginning, especially in view of the fact that the theory of simila-... 

Consistent performance of the ACR during scale-up depends upon thermal and kinematic similarity throughout, but with a dynamic influence on kinematic similarity in the throat and chemical similarity in the diffuser. As a result of the above considerations, it was felt that the ACR process could be scaled in a geometrically similar reactor based on matching Mach numbers, S F ratio, and residence time in the reaction section, provided two critical conditions could be met. When scaled, the sprayed particle size distributions would have to be approximately equal (i.e., equality of Sauter mean diameter) while a kinematically similar oil-particle trajectory also would be required. 

With geometric similarity, equal tip speed means that velocity gradients are reduced and blend times become longer. However, power per volume is also reduced, and viscous heating problems are likely to be more controllable. With any geometric scale-up, the surface-to-volume ratio is reduced, which means that any internal heating, whether by viscous dissipation or chemical reaction, becomes more difficult to remove through the surface of the vessel. 

As soon as the functional relationships between the Nusselt, Reynolds and Prandtl numbers or the Sherwood, Reynolds and Schmidt numbers have been found, be it by measurement or calculation, the heat and mass transfer laws worked out from this hold for all fluids, velocities and length scales. It is also valid for all geometrically similar bodies. This is presuming that the assumptions which lead to the boundary layer equations apply, namely negligible viscous dissipation and body forces and no chemical reactions. As the differential equations (3.123) and (3.124) basically agree with each other, the solutions must also be in agreement, presuming that the boundary conditions are of the same kind. The functions (3.126) and (3.128) as well as (3.127) and (3.129) are therefore of the same type. So, it holds that... 

Fig. 8 The effect of heterogeneous energy dissipation on the progress of the coagulation reaction in geometrically similar systems of different scale the reaction progress is different even if the (microscopically determined) overall energy dissipation is identical (after [8]). There are no numbers given since they depend exclusively on the experimental boundary conditions...

Example 2-4b Scale-up with Exact Geometric Similarity. In this example we consider the relationship between the spectrum of velocity fluctuations and the micromixing scales. At the lab scale, a T = 0.25 m vessel is used to formulate a homogeneous reaction in an aqueous phase. The fully baffled vessel is equipped with a Rushton turbine impeller of D = T/2 at C = T/3 with Np = 5.0. The... 

The laboratory stirred vessel was acmally never used for reaction experiments. It was simply a scaled-down version of the conunercial autoclave geometry and operating conditions. Scale-up/scale-down was accomplished using constant PA and geometric similarity. Reactions in the conunercial reactor proved to be identical to results obtained in the rocking bomb autoclave. 

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