Operating line

Basically an operating line is a tool which can be used for example in a Mc-Cabe Thiele diagram to determine parameters such as reflux ratio, reboiler ratio and so forth.

Therefore knowing how to derive and then draw it on that diagram is necessary. Otherwise you cannot gain much from that Mc-Cabe Thiele diagram. It is a very useful diagram although it is only valid in a certain case. One important assumption that enables us to work with it is that the evaporation enthalpy of each species is all equal where this is of course not the case in reality.

Let us look at this diagram once again and derive the equation we need:

Total mass (flow) balance:

What goes in = what comes out

hence:

G = L + D

Mass balance for one component ( the more volatile one):

G*y = L*x + D*xd

and then we know that reflux ratio is defined:

v = L/D

Combining all these three equations and do some re-arrangement, you will get this equation looking like this:

y = (v/v+1)x + xd/(v+1)

This is a linear equation and a straight line with the slope v/v+1 and the y-intercept xd/v+1 is to be expected. This is however valid for a rectifying section ( column's part above the feed).