Scaling Up Tubular Reactors

Convective heat transfer to fluid inside circular tubes depends on three dimensionless groups the Reynolds number. Re = pdtu/ii, the Prandtl number, Pr = Cpiilk where k is the thermal conductivity, and the length-to-diameter ratio, L/D. These groups can be combined into the Graetz number, Gz = RePr4/L. The most commonly used correlations for the inside heat transfer coefficient are 

TABLE 5.1 Scaleup Factors for Liquid-Phase Tubular Reactors. 

Flow regime General scaleup factors Series scaleup Geometric similarity Constant pressure scaleup 

Example 5.10 A liquid-phase, pilot-plant reactor uses a 12-ft tube with a 1.049-in i.d. The working fluid has a density of 860 kg/m, the residence time in the reactor is 10.2 s, and the Reynolds number is 8500. The pressure drop in the pilot plant has not been accurately measured, but is known to be less than 1 psi. The entering feed is preheated and premixed. The inlet temperature is 60°C and the outlet temperature is 64°C. Tempered water at 55°C is used for cooling. Management loves the product and wants you to design a plant that is a factor of 128 scaleup over the pilot plant. Propose scaleup alternatives and explore their thermal consequences. 

Solution Table 5.1 provides the scaling relationships, throughput and volume scaling factor is A = 128. 

Heat transfer area, Aext SrSl s s2/3 s059 

These equations apply to ordinary fluids (not liquid metals) and ignore radiative transfer. Equation 5.35 is rarely used and applies to very low Re or very long mbes. No correlation is available for the transition region, but Equation 5.36 should provide a lower limit on hdt/K in the transition region. The dimensionless number, hdt /k, is the Nusselt number, Nu. 

The reader is reminded of the usual caveat detailed calculations are needed to confirm any design. The scaling exponents are approximate. They are used for 

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Although fluidized sand or alumina can also be used in the jacket of these somewhat larger reactors, the size makes the jacket design a problem in itself, hence these reactors are seldom used. An advantage of the jacketed reactor is that several—usually four—parallel tubes can be placed in the same jacket. These must be operated at the same temperature, but otherwise all four tubes can have different conditions if needed. This type of arrangement saves time and space in long-lasting catalyst life studies. Jacketed tubular reactors come close, but still cannot reproduce industrial conditions as needed for reliable scale-up. Thermosiphon reactors can be used on all but the most exothermic and fast reactions. 

The effective reactor volume was 1000 cm3. The initial concentration of A was the same in all runs and equal to the solubility limit of species A in water. No R or S is present in the feed. You have been asked to scale up this reactor to produce significantly larger quantities of R. It has been suggested that you use a tubular flow reactor with an inside diameter of 2 cm and that your feed be a saturated solution of species A. No R or S is present in the feed. 

This section has based scaleups on pressure drops and temperature driving forces. Any consideration of mixing, and particularly the closeness of approach to piston flow, has been ignored. Scaleup factors for the extent of mixing in a tubular reactor are discussed in Chapters 8 and 9. If the flow is turbulent and if the Reynolds number increases upon scaleup (as is normal), and if the length-to-diameter ratio does not decrease upon scaleup, then the reactor will approach piston flow more closely upon scaleup. Substantiation for this statement can be found by applying the axial dispersion model discussed in Section 9.3. All the scaleups discussed in Examples 5.10-5.13 should be reasonable from a mixing viewpoint since the scaled-up reactors will approach piston flow more closely. 

We will consider only the batch reactor in this chapter. This is a type of reactor that does not scale up well at all, and continuous reactors dominate the chemical industry. However, students are usually introduced to reactions and kinetics in physical chemistry courses through the batch reactor (one might conclude fi om chemistry courses that the batch reactor is the only one possible) so we wiU quickly summarize it here. As we vrill see in the next chapter, the equations and their solutions for the batch reactor are in fact identical to the plug flow tubular reactor, which is one of our favorite continuous reactors so we will not need to repeat all these definitions and derivations in the section on the plug flow tubular reactor. 

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. 

Donnet, M., Bowen, P., Jongen, N., Lemaitre, J., Hofmann, H., Schreiner, A., Jones, A. G., Schenk, R., Hofmann, C., Successful scale-up from millilitre batch optimization to a small scale continuous production using the segmented flow tubular reactor example of calcium carbonate precipitation, Chem. Eng. Trans. 2002, 1,1353-1358. 

In dealing with chemical process engineering, conducting chemical reactions in a tubular reactor and in a packed bed reactor (solid-catalyzed reactions) is discussed. In consecutive-competitive reactions between two liquid partners, a maximum possible selectivity is only achievable in a tubular reactor under the condition that back-mixing of educts and products is completely prevented. The scale-up for such a process is presented. Finally, the dimensional-analytical framework is presented for the reaction rate of a fast chemical reaction in the gas/liquid system, which is to a certain degree limited by mass transfer. 

If scale-up of the tubular reactor of the given geometry (L/d = idem) is performed at T0 and AT/T0 = idem, taking account of these restrictions, the kinetic and material numbers E/RT0, Da, Sc, Pr remain unchanged. Therefore, to attain a specified degree of conversion col,iyCin = idem, it is only necessary to ensure that the other two numbers Re = v d p/p and kot = ko L/v are adjusted in such a way that they remain idem. However, it is immediately dear that this is an impossibility in the case of L/d = idem because... 

In the scale-up of a tubular reactor, the problem is to increase the flowrate q v d2 by a factor n (not to be confused with the scale p ) while retaining the chemical efficiency (yield, conversion, selectivity, etc.) ... 

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. 

G. Damkohler bases his analysis of the scale-up problem relating to the catalytic tubular reactor on the following pi-set (D and hence number combination II are irrelevant) ... 

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