Scaleup in series

An integral form of Equation (3.15) was used to derive the pressure ratio for scaleup in series of a turbulent liquid-phase reactor, Equation (3.34). The integration apparently requires ji to be constant. Consider the case where ii varies down the length of the reactor. Define an average viscosity... 

Everything is known in this equation but Sl- Note that Equations (3.38) and (3.39) contain Sr as a parameter. When scaling in series, Sr=, but the same equations can be applied to other scaleup strategies. 

Table 3.1 suggests that scaling in series could make sense for an adiabatic, gas-phase reaction with no change in the number of moles upon reaction. It would also make sense when the number of moles decreases upon reaction, since the high pressures caused by this form of scaleup will favor the forward reaction. Chapter 5 gives the design equations for nonisothermal reactions and discusses the thermal aspects of scaleup. 

This equation has the same functional dependence on p (namely none) and m as the Poiseuille equation that governs laminar flow in an empty tube. Thus, laminar flow packed beds scale in series exactly like laminar flow in empty tubes. See the previous sections on series scaleup of liquids and gases in laminar flow. 

Geometrically Similar Scaleups for Packed Beds. As was the case for scaling packed beds in series, the way they scale with geometric similarity depends on the particle Reynolds number. The results are somewhat different than those for empty tubes because the bed radius does not appear in the Ergun equation. The asymptotic behavior for the incompressible case is... 

The temperature counterpart of Q>aVR ccj-F/R and if ccj-F/R is low enough, then the reactor will be adiabatic. Since aj 3>a, the situation of an adiabatic, laminar flow reactor is rare. Should it occur, then T i, will be the same in the small and large reactors, and blind scaleup is possible. More commonly, ari/R wiU be so large that radial diffusion of heat will be significant in the small reactor. The extent of radial diffusion will lessen upon scaleup, leading to the possibility of thermal runaway. If model-based scaleup predicts a reasonable outcome, go for it. Otherwise, consider scaling in series or parallel. 

In the Pharmacia approach, the fluid input is split and distributed through six ports on the column end plates.At the entrance of each stream, an anti-jetting device spread the liquid over a fine mesh net. A coarse net between the net and the end plate acts as both a support and a spacer. For the soft Sephadex gels G-50 to G-200, the maximum feasible bed height is 15 cm. Scaleup operations have used as many as six such squat columns in series.The drawbacks of this approach are the cumbersome adsorbent in the column. 

These results, based on single-element filters, provide an indication of the region of performance that might be expected for the process on a commercial scale. However, commercial filters are multi-element modules normally operated in series. Consequently, these results are not directly suitable for scaleup. 

The general scaleup relationships in Tables 3.1-3.3 are made specific for scaling in series by setting = 1 and Sl = S. The results are Srs = S for Reynolds number, Sap = for a turbulent pressure drop, and Sap = for a laminar pressure drop. 

There are many ways of increasing the capacity of a chemical reactor. The simplest methods are scaling in parallel or scaling in series. When applied to a tubular reactor, the tube diameter is held constant, and capacity is increased by adding tubes in parallel or in series. There are several scaleup possibilities ... 

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