Scaleup Factors

Also assume that the pilot- and full-scale vessels will operate at the same temperature. This means that A(o-out,bout, . )and/i/2 will be the same for the two vessels and that Equation (1.49) will have the same solution for provided that 7 is held constant during scaleup. Scaling with a constant value for the mean residence time is standard practice for reactors. If the scaleup succeeds in maintaining the CSTR-like environment, the large and small reactors will behave identically with respect to the reaction. Constant residence time means that the system inventory, pV, should also scale as S. The inventory scaleup factor is defined as... 

So, in the constant-density case, the inventory scaleup factor is the same as the volumetric scaleup factor. 

Unless explicitly stated otherwise, the throughput and inventory scaleup factors will be identical since this means that the mean residence time will be constant upon scaleup ... 

These usually identical scaleup factors will be denoted as S. 

If the pilot reactor is turbulent and closely approximates piston flow, the larger unit will as well. In isothermal piston flow, reactor performance is determined by the feed composition, feed temperature, and the mean residence time in the reactor. Even when piston flow is a poor approximation, these parameters are rarely, if ever, varied in the scaleup of a tubular reactor. The scaleup factor for throughput is S. To keep t constant, the inventory of mass in the system must also scale as S. When the fluid is incompressible, the volume scales with S. The general case allows the number of tubes, the tube radius, and the tube length to be changed upon scaleup ... 

Solution The approach is similar to that in Example 3.7. The unknowns are Sl and (Em)2. Set (Poudi = (Pout) - Equation (3.40) is used to calculate iPm)2 nd Equation (3.41) is used to calculate Sl- Results are given in Table 3.2. The results are qualitatively similar to those for the turbulent flow of a gas, but the scaled reactors are longer and the pressure drops are lower. In both cases, the reader should recall that the ideal gas law was assumed. This may become unrealistic for higher pressures. In Table 3.2 we make the additional assumption of laminar flow in both the large and small reactors. This assumption will be violated if the scaleup factor is large. 

TABLE 4.1 Scaleup Factors for Geometrically Similar Stirred Tanks... 

Table 4.1 includes scaleup factors for heat transfer. They are discussed in Chapter 5. 

TABLE 5.1 Scaleup Factors for Liquid-Phase Tubular Reactors. 

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

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. 

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