Short note on McCabe-Thiele distillation trays and feed plate

Basics

Distillation is used to separate components from a liquid mixture based on the differences in boiling points of the individual components. Furthermore, the boiling point characteristics of the liquid mixture will vary depending on the concentrations of the components present. As a result, distillation processes are influenced by the vapor pressure properties of liquid mixtures.

Concept of trays: Theoretical stages in a distillation column

The number of trays or plates in a distillation column is one of the most important aspects of distillation. This determines the separation process's efficiency and the final product's quality. The McCabe-Thiele method is a graphical method for calculating the number of theoretical plates in a distillation column (or the number of trays). It is based on the equilibrium between the vapor and liquid phases at each tray in the column. The method entails plotting the operating and equilibrium lines on a McCabe-Thiele diagram and calculating the number of trays needed to achieve the desired degree of separation. The number of theoretical trays can be determined by counting the number of times the horizontal ‘steps’ of the triangles touch the VLE curve (including the line that passes the bottom's product line). These trays are counted starting at the top right and moving to the bottom left. The base of each triangle represents the mass transfer between liquid and vapor. The larger the base of the triangles the larger the mass transfer. ?

In many separation processes, a theoretical plate is a hypothetical zone or stage in which two phases, such as the liquid and vapor phases of a substance, establish equilibrium with each other. Equilibrium stages are also known as an equilibrium stage, ideal stage, or theoretical tray. Having more theoretical plates improves the efficiency of the separation process, whether it is distillation, absorption, chromatography, adsorption, or another similar process. Because an actual, physical plate can never be in a completely efficient equilibrium stage, the number of actual plates is greater than the number of theoretical plates required.

Na = Nt/E

The actual number of plates is Na, the theoretical number of plates is Nt, and the plate efficiency is E.

Concept of feed plate

Position of the feed tray in the distillation column

The optimum feed tray location for a given number of trays in a column with a given feed temperature, product specifications, and operating pressure is the one with the lowest reboiler duty. Although, for some columns, the optimal tray is the middle tray.

What is a feed plate in the McCabe diagram?

The feed plate is the only place where both rectification and stripping take place.?The feed plate is the tray where maximum mass transfer takes place because on this plate the ratio of volatiles / non-volatiles is the maximum.

Effect of the number of trays on the degree of separation

Example

Consider as a base case, a 10-stage column. The feed is a binary mixture that has a composition of 0.5-mole fraction in terms of the more volatile component and is introduced at stage 5. The steady-state terminal compositions of about 0.65 at the top (stage 1) and 0.1 at the bottom (stage 10) are shown below:

Composition Profile: 10 stages, feed at stage 5

Suppose we decrease the number of stages to 8, and keep the feed at the middle stage, i.e., stage 4. The resulting composition profile is:

Composition Profile: 8 stages, feed at stage 4

We can see that the top composition has decreased. [ it is a marginal decrease. See the graph carefully] while the bottom composition has increased. The bottom has almost 16% volatiles. ?That is, the separation is poorer.

Now, if we increase the number of stages to 12, and again introduce the feed at mid-column, i.e., stage 6, the composition profile we get is:

Composition Profile: 12 stages, feed at stage 6

Again, the composition has changed. This time the distillate is much richer in the more volatile component, while the bottoms have less than 1% volatile component. indicating better separation.

Location of feed plate

The optimum location for a feed plate is one represented by the triangle that has one corner on the rectifying line and the other corner on the stripping line. The feed plate is one where the relative volatility is maximum and therefore the mass transfer is maximum. The feed plate is the only place where both rectification and stripping take place.?The feed plate is the tray where maximum mass transfer takes place because on this plate the ratio of volatiles / non-volatiles is the maximum.

In transferring from the rectifying section to the stripping section, the steps on the diagram should be kept as large as possible, and the transition is made at the first opportunity after passing the intersection point. This depends on two things [1] the slope of the rectification operating line and [2] the state of the feed or the slope of the q line.

Why feed plate location is so important?

In short, the location of a feed plate can impact the utility costs by either condenser load or reboiler heating. If you change the location of the feed plate, the reflux ratio, column pressure, and top and bottom temperature may change. As the feed stage is moved lower down the column, the top composition becomes less rich in the more volatile component while the bottom contains more of the more volatile component.

Example

Suppose we have a 20-stage column, again separating a binary mixture that has a composition of 0.5-mole fraction in terms of the more volatile component. The terminal compositions obtained when the feed is introduced at stages 5, 10, and 15 (at fixed reflux and reboil rates) are shown in the following plots.

Composition profile: 20 stages, feed at stage 5

Composition profile: 20 stages, feed at stage 10

Composition profile: 20 stages, feed at stage 15

The top composition becomes less rich in the more volatile component as the feed stage is moved lower down the column, while the bottoms contain more of the more volatile component. However, the changes in top composition are not as pronounced as the changes in the bottom composition.

Summary

Finally, to summarize, each triangle represents a mass transfer step. Larger the size of the triangle, the larger the driving force for mass transfer.

q line decides the size of rectification and striping sections of a distillation column. If q equals 0, we have saturated vapor meaning we're right at the dew point and if q is one it's saturated liquid right at the bubble point and then q between zero and one means we have a mixture.

Credit: Google