Assuming that we choose a basis of the feed flowrate, we have 5 unknowns (the outlet flows: V, L; and the compositions: x, y, z).

We can clearly write two material balances:

F = V + L

zF = yV + xL

We can also use K values (or a similar VLE method, like Raoult's Law) in order to relate our outlet compositions:

y = Kx

In addition to these three relations, we are often given the inlet composition, or the fraction of material vaporized (V/F). Therefore, the relations can be closed (i.e., the degrees of freedom goes to zero), if we are given more than one of these additional bits of information or if we have an adiabatic flash drum, so that we can use an energy balance as our last relation:

$zF\hat H_{1_F} + (1-z)F\hat H_{2_F} = yV\hat H_{1_V} + (1-y)V\hat H_{2_V} + xL\hat H_{1_L} + (1-x)L\hat H_{2_L}$

Analytically solve binary flash distillation problems