(82a) A Better(?) Way to Calculate the Slope of the Equilibrium Line

The calculation of tray efficiencies or the HETP of packed columns requires, among other things, the slope of the equilibrium line. For binary systems the slope is unambiguously defined (although not always rigorously calculated). However, there is no easy way to use a definition of the slope for multicomponent systems because the vapor liquid equilibrium is represented by a surface (in hyperspace if there are more than 3 compounds).

Thus, for multicomponent systems any pseudo-binary method for estimating tray efficiencies and HETP must rely, in part, on an approximate method of estimating the slope. Particularly, information regarding thermodynamic interactions is lost using pseudo-binaries and the slope of the equilibrium line may, therefore, have very limited meaning for a multicomponent system.

In a presentation given at the 2015 National Spring Meeting of the AIChE we looked at four different methods for approximating the slope of the equilibrium line for multicomponent systems. It was shown that these different methods could lead to dramatically different estimates of the equilibrium slope.

Our purpose here is to take further our earlier work and propose a different and, we believe, definitive way to approximate the slope.

The method requires us to define a design component, one per section of the column. The design component can be defined as that which is to be removed from a designated column section. For example: in a distillation to separate the four component mixture ABCD into the AB and CD fractions then the design component for the top section is C and the design component section for the bottom section is B. (In this example these design components are like the heavy and light keys respectively, but that is not always the case, e.g. for column configurations involving side streams.)

The slope then is estimated from two similar flash calculations in which only the design component has its molar amount altered (slightly). This methodology allows proper consideration of thermodynamic interactions and thereby avoids the short comings of adopting a pseudo-binary approach.

We will show that for binary systems this method is exactly equivalent to the rigorous definition of the slope. We will further demonstrate that this method provides a sensible approximation in cases when other published methods have the potential to lead one astray.