The liquid and vapor mole fractions of the two product streams (i.e. one vapor and one liquid stream leaving each flash vessel) are solutions of the mass balance and equilibrium relationship given by:

,

.

A simple algebraic manipulation using these equations gives the following quadratic equation, which can be solved for :

;

here is the vapor fraction of the feed.

This Demonstration shows the graphical solution of the cascade of flash drums. As you increase the number of flash vessels, the exit composition approaches that of the pure heavy component. This component is obtained more rapidly for larger values of the relative volatility.