Separation Processes 1

In many mixtures (binary, ternary, etc.), we encounter **azeotropes**. In this water-isopropanol system, the azeotrope is clear to discern and we might be able to use pressure swing distillation effectively.

TXY diagram for ethanol-water mixtures at 1 atm.

In many azeotropic systems, pressure swing distillation is ineffective.
For example, in the ethanol-water system above, the relative volatility for the high concentrations of ethanol is close to $\alpha\approx1$ !
What other methods are available for breaking azeotropes?

To break this azeotrope, we must either:
- Modify the VLE behaviour of the mixture using another component.
- Use an alternative separation technique.
Alternative separation techniques may be used to just to completely separate the azeotropic mixture, or just to help distillation get past the azeotrope.

$xy$ diagram for ethanol-water at 1 atm.

In azeotropic distillation, an entrainer is added which is volatile and exits the column in the top-product.
This method is called azeotropic distillation as a new ternary azeotrope is often formed, but this azeotrope will be at lower concentrations than the binary azeotrope.
The distillation can then be continued up to high purities, but a recovery strategy must be devised to recover the entrainer.
This technique is quite popular for the dehydration of ethanol…

$x$ - $y$ diagram of ethanol-water mixtures at 1 atm.

In multi-stage absorbtion, we have an of the following form. $\begin{align} L'\frac{x_{A,i}}{1-x_{A,i}}+V'\frac{y_{A,j+1}}{1-y_{A,j+1}}&=L'\frac{x_{A,j}}{1-x_{A,j}} + V'\frac{y_{A,i+1}}{1-y_{A,i+1}} \end{align}$
We also have some , which at typical absorber concentrations can described by Henry's law $\begin{align*} y = \mathcal{H} x \end{align*}$
The solution of these equations is just the same as for multi-stage distillation. We draw the operating line and the equilibrium line and step between the two.

$\begin{align} L'\frac{x_{A,i}}{1-x_{A,i}}+V'\frac{y_{A,j+1}}{1-y_{A,j+1}}&=L'\frac{x_{A,j}}{1-x_{A,j}} + V'\frac{y_{A,i+1}}{1-y_{A,i+1}} \end{align}$

One of the biggest difficulties of absorber design is that you have to alter the operating line a lot.
In distillation, the operating line is straight due to the assumption of constant molar overflow.
But in absorption, we must plot several points to capture its curvature (see right).
Can we make the operating line straight using a change of variables?

$\begin{align} L'\frac{x_{A,i}}{1-x_{A,i}}+V'\frac{y_{A,j+1}}{1-y_{A,j+1}}&=L'\frac{x_{A,j}}{1-x_{A,j}} + V'\frac{y_{A,i+1}}{1-y_{A,i+1}} \end{align}$

Defining two new variables: $\begin{align*} X&=\frac{x}{1-x} & Y&=\frac{y}{1-y} \end{align*}$
We can rewrite the in terms of these variables. $\begin{align} L' X_i+V' Y_{j+1}&=L' X_j + V' Y_{i+1} \end{align}$
Rearranging then gives us a convenient linear form: $\begin{align*} Y_{A,j+1}&=\frac{L'}{V'}\left(X_{A,j}-X_{A,i}\right)+ Y_{A,i} \end{align*}$

$\begin{align*} Y_{A,j+1}&=\frac{L'}{V'}\left(X_{A,j}-X_{A,i}\right)+ Y_{A,i} \end{align*}$

This form is much more convenient to plot, as it is a straight line on a XY plot.
It is also very easy to convert from $x\to X$ or $y\to Y$ .
The only difficulty is that the is no longer straight. $\begin{align*} y &= \mathcal{H} x & Y &= \frac{\mathcal{H} x}{1+\mathcal{H} x} \end{align*}$
However, if XY graphs for the equilibrium data have been prepared once, it is much more convenient to perform the design in these variables.

Breaking Azeotropes and Absorption Tricks