# Multi-Component Flash Distillation

If there are more than two components in the flash apparatus, a graphical procedure is no longer possible.

In order to perform our multi-component analysis for N components, we can write N balance equations. A total:

F = V + L

and N-1 component balances:

ziF = yiV + xiL

We also have N equilibrium equations (using K values):

yi = Kixi

In addition to the possibility of using an energy balance equation, we need to also use the physical constraints:

$\sum_i^N y_i = 1$

$\sum_i^N x_i = 1$

An efficient way of solving these equations is to first combine the total mass balance with the component equations to yield (N-1) equations of the form:

$y_i = \frac{f-1}{f}x_i + \frac{z_i}{f}$

we then eliminate xi using the Ki value expressions to give:

$y_i = \frac{K_iz_i}{K_if-f+1}$

the same approach can be used to get a set of equations for xi:

$x_i = \frac{z_i}{K_if-f+1}$

It turns out that neither of these equations, when plugged into the physical laws, yields particularly stable iterative solutions. Therefore, it is often the case that they are combined in such a way as to yield a more numerically-friendly equation

##### DEFINITION

The Rachford-Rice Equation combines these two equations and has much nice convergence than either individually:

$\sum_i^N \frac{z_i(K_i-1)}{K_if-f+1}=0$

##### NOTE:

This expression can be used to solve for the fraction vaporized, f. Similarly, we could have written our material balances in terms of the fraction remaining liquid, typically denoted q.

##### OUTCOMES:

Explain the difference between binary and multi-component flash calculations

##### OUTCOMES:

Solve both sequential and simultaneous binary flash
distillation problems