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:

z_{i}F = y_{i}V + x_{i}L

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

y_{i} = K_{i}x_{i}

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 x_{i} using the K_{i} 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
x_{i}:

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

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

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

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

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.

Explain the difference between binary and multi-component flash calculations

Solve both sequential and simultaneous binary flash

distillation problems