Residue curve mapping is a powerful tool to better understand the design and operation of distillation columns, especially when the mixture is azeotropic . A previous article in Chemical Processing  introduced the approach and focused on the feasibility of applications involving mixtures that form two liquid phases. That article showed how to exploit two-liquid-phase behavior to facilitate a desired separation. This article will describe using residue curve maps to check the feasibility of separation of homogeneous mixtures and for developing the conceptual design of towers.
A standard residue curve map is a composition plot of the kettle residue liquid as the mixture is continually boiled with no reflux. As you can imagine, the mixture will get heavier over time, as the lighter components are boiled off. This is important because residue curve maps are an approximation to the liquid composition profile in a distillation column operated at total reflux.
Residue curves can be used to determine what separations are possible with a distillation column independent of how many stages are required and how much energy is consumed. Moreover, compared to stage-to-stage column-composition-profile calculations, residue curves are mathematically much easier to work with and can provide a great amount of insight into the separation of a mixture.
For instance, consider the mixture of methanol, ethanol and n-propanol. This mixture does not form azeotropes and is reasonably ideal. The residue curves for the mixture (Figure 1) have two endpoints: one at the methanol vertex and the other at the n-propanol vertex. If you picked any point along a residue curve as an initial composition for the boiling kettle, then, as the lighter material is boiled off, the kettle composition would stay on the same curve and eventually converge on the n-propanol vertex.
Figure 1. Separation of a mixture of methanol, ethanol and 1-propanol follows the appropriate residue curve. (Click to enlarge)
A stage-to-stage composition map for a column operated at total reflux (Figure 2) has 16 equilibrium stages to produce the indicated bottoms and distillate compositions from the feed. A residue curve passing through one of the equilibrium stages is also shown; it closely resembles the column liquid-composition profile. Generally, as the mixture becomes more difficult to separate, these curves will be more similar.
Figure 2. Producing the overhead and bottoms products indicated requires sixteen equilibrium stages. (Click to enlarge)
Also notice that the feed, distillate and bottoms compositions are all on a line. This is required via mass balance for a single-feed, two-product column. From a mass balance, we know that:
where D is the distillate flow, B is the bottoms flow, ziFis the feed (mass or mole) fraction, ziB is the bottoms fraction and ziD is the distillate fraction of a given component in the mixture. This equation provides the co-linear relationship previously described and also is an excellent way to check mass balances from plant samples. Plugging into the equation the results of a feed, distillate and bottoms composition analysis for every component in the mixture should result in the same D/B ratio. This equation also can be used to verify the results of flow meters.
A column mass balance and residue curve maps can significantly help determine what separations are possible. For example, consider a mixture of acetone, isopropanol and water. This mixture forms a single homogeneous azeotrope between isopropanol and water.
The residue curve map for this mixture shows all of the curves starting at acetone but some ending at isopropanol and some at water (Figure 3). So, depending on the initial starting concentration in the pot, the last drop of liquid in the kettle will be water or isopropanol. This is the effect of the azeotrope between water and isopropanol. The mixture is split into two zones or distillation regions by a curve between acetone and the isopropanol/water azeotrope. This curve is termed a distillation boundary as it separates the two distillation regions. The distillation boundary indicates that if the feed composition to the column is in one distillation region, then a column operating at total reflux would be unable to separate the mixture into the three distinct compounds. It also shows that water, although a potential pure product from a mixture lying in the lower region, cannot be completely recovered from isopropanol and acetone.
Figure 3. Acetone/isopropanol/water mixture can form an isopropanol/water azeotrope. (Click to enlarge)
Column at less-than-total reflux
Engineers use the well-known McCabe-Thiele diagram to evaluate distillation designs for mixtures with two key components when the feed composition, feed quality (liquid, vapor, degree of superheat, etc.) and desired product compositions are known. Stepping off stages between the operating line and the equilibrium curve gives the number of equilibrium stages necessary. Contrast this to how simulations are performed in a standard process simulator: the number of stages is guessed and the column compositions are iteratively solved and the stage count updated until the desired solution is found. McCabe-Thiele diagrams are particularly useful because they provide instant visual feedback you can quickly determine if the reflux ratio is too low, if a pinch-point arises or if there is an infeasible set of specifications due to the presence of an azeotrope.