Page 188 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

Example 7.4

Compare the error for the scale-up of a reciprocating compressor by a factor of 5 using the six-tenths rule
in place of the cost exponent given in Table 7.3.

Using Equation 7.1,
Cost ratio using six-tenths rule (i.e., n = 0.60) = 5.0 0.60 = 2.63
Cost ratio using (n = 0.84) from Table 7.3 = 5.0 0.84 = 3.86
% Error = ((2.63 – 3.86)/3.86)(100) = –32 %

Another way to think of the economy of scale is to consider the purchased cost of equipment per unit
capacity. Equation 7.2 can be rearranged to give the following relationship:

(7.3)

If Equation 7.3 is plotted on log-log coordinates, the resulting curve will have a negative slope, as shown
in Figure 7.2. The meaning of the negative slope is that as the capacity of a piece of equipment increases,
the cost per unit of capacity decreases. This, of course, is a consequence of n < 1 but also shows clearly
how the economy of scale works. As cost curves for equipment are introduced in the text, they will be

presented in terms of cost per unit capacity as a function of capacity to illustrate better the idea of
economy of scale. For many equipment types, the simple relationship in Equation 7.1 is not very accurate,
and an equation that is second order in the attribute is used.

Figure 7.2 Purchased Cost per Unit of Flowrate of a Centrifugal Air Blower (Adapted from Reference
[3])