Explain the difference between (and solve) binary and multi-component flash calculations

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