Common Scale-Up Factors

The most commonly used scale-up method maintains constant shear rate by increasing the channel depth proportional to the square root of the diameter ratio and by reducing the screw speed by the square root of the diameter ratio [60]. The resulting scaling factors for output, residence time, melting capacity, power consumption, and specific energy consumption are shown in Table 8.5. 

The pumping capacity can be checked by using Eq. 7.291. The drag flow rate can be written as  

If the helix angle cp is constant, W D, H Vd, and N 1 -/D, the drag flow rate ratio becomes  

In order for the pressure flow rate to increase by the same rate as the drag flow, the helical length for pressure build-up has to be  

This means that the axial length of the metering section can be increased by the square root of the diameter ratio. Thus, the L/D of the metering section can be reduced by the square root of the diameter ratio. 

---

The effect of the common scale-up factors on extruder performance is presented in tabular form in Table 8.5. 

Common scale-up factors Scale-up for heat transfer Scale-up for mixing (geometric)... 

Use common chemical engineering scale-up factors to scale-up the design producing lowest-cost... 

In the development of a 3,4-epoxy-l-butene (1) rearrangement process suitable for industrial scale-up, a number of factors were evident. The product (2,5-DHF) and starting material (1) are both liquids with identical boiling points (66°C). No practical method is known by which to separate these isomers. This fact demands that the catalytic process be performed at high conversion for acceptable economics. The common practice of recycling unreacted starting material was not an option for this process. 

Despite the diligent use of predictive studies, compaction simulation, pilot scale work, the state of the art of tablet scale-up still provide opportunities for problems to arise. The issues typically encountered are those that have multiple factors involved, and are difficult to predict and simulate at smaller scale. Of these problems, tablet mixture flow, including weight uniformity and segregation, and sticking and picking of the tablet mixture to the tools and tablet specks, are common occurrences. 

Literature data is almost entirely for small equipment whose capacity and efficiency cannot be scaled up to commercial sizes, although it is of qualitative value. Extraction processes are sensitive because they operate with small density differences that are sensitive to temperature and the amount of solute transfer. They also are affected by interfacial tensions, the large changes in phase flow rates that commonly occur, and even by the direction of mass transfer. For comparison, none of these factors is of major significance in vapor-liquid contacting. 

Various aspects of the effect of process scale-up on the safety of batch reactors have been discussed by Gygax [7], who presents methods to assess thermal runaway. Shukla and Pushpavanam [8] present parametric sensitivy and safety results for three exothermic systems modeled using pseudohomogenous rate expressions from the literature. Caygill et al. [9] identify the common factors that cause a reduction in performance on scale-up. They present results of a survey of pharmaceutical and fine chemicals companies indicating that problems with mixing and heat transfer are commonly experienced with large-scale reactors. 

The above discussion is an oversimplification of the commercialization, but it presents basic factors common to virtually all commercialization problems. In addition, each particular situation has additional criteria and looping of problems (e.g., the need to remove one trace enzyme may unstabilize the desired activity or may remove another trace enzyme important to the action of the primary one). Commercialization, while appearing to be a straightforward simple extension and scale up from fundamental research data, seldom is either simple or straightforward. 

For preliminary evaluation (Gate 1 in Table 16.1), correlations for complete processes scaled up for capacity and for time are commonly used. For a conceptual design (Gate 2), FOB equipment cost correlations based on flow rate are often used and scaled up to BM cost based on L -f M factors. For a preliminary engineering design (Gate 3), the equipment is sized more accurately based on simple rules of thumb, the cost is estimated from FOB cost correlations related to equipment size and scaled up to BM cost based on L + M factors. The process and FOB cost correlations are all of the form... 

---