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Industrial & Engineering Chemistry Research
30 (4) (April 1991), pp 654 - 661

Abstract

Fundamental consistency relationships exist between the effect of changes in extensive variables under steady-state conditions.

sum_i dlny / dlnui = sum_i (dy/y) / (dui/ui) = 1 or 0 (28) (29)
(1 when y is extensive, 0 when intensive, ui=independent extensive variables

These relationships are derived by use of physical insight about scaling of extensive variables, and the assumption is that intensive variables remain constant when all the extensive variables are increased proportionally. Essentially, this assumes that the efficiency of the system is independent of the load (feedrate).

The relationships may be used to obtain data for or to check consistency of linear steady-state models used in process control and design. The derivation and use of these relationships is very similar to that of the Gibbs-Duhem equation of thermodynamics. Surprisingly, these scaling consistency relationships seem be unknown in the chemical engineering community and examples demonstrate inconsistency in some widely used published models.