McCabe-Thiele method of distillation: An overview

The composition of the feed determines the boundary between the rectifying and stripping sections of the distillation column, which determines the separation. This has been explained in straightforward language, which you might find difficult to obtain online.

General reading

Heat and Mass transfer in a distillation column

To quickly comprehend this process, let's focus on one stage or tray at a time. The vapor moving from the bottom tray to the top tray is obviously at a higher temperature than the liquid on the top tray. Therefore, when the top tray liquid and bottom vapor make contact, heat will be transferred from the vapor to the liquid. As a result, the temperature of the liquid will increase, and the volatile components in the liquid will become vapor and rise as a result. However, as a result of the heat exchange, the vapor's temperature will drop and become less intense, and less volatile components in the vapor will condense into the liquid. Thus, the vapor and liquid will simultaneously transfer heat and mass, which results in the enrichment of the vapor in more volatile components and the enrichment of the liquid in less volatile components. This was only for one tray. All of the trays go through the same process. Keep in mind that until the equilibrium composition is reached, the aforementioned process will continue and enrichment will take place. Increasing the temperature after the equilibrium composition of the components has been archived won't alter the composition unless and until there is a reflux provision.

Two important aspects of the distillation column [1] Composition of feed and the location of the feed plate.

Effect of composition of feed on the feed plate location:

It is not necessary for the feed will be always liquid

As the image shows it can just be a saturated liquid [4] vertical line an extension of the feed line. It can be partially vaporized feed [3] It can be saturated vapor [2] It can be superheated vapor [1] It can also be subcooled liquid feed [5]. It may be noticed in each case the slope of the feed line is different and its intersection with the rectification operating line is different. Thus, each composition will have a different location in the feed tray.?For example, a saturated liquid will have a feed plate somewhere at the center of the column. A partially vaporized feed will have a feed tray more towards the bottom of the column meaning more rectification trays and fewer stripping trays. If the feed is subcooled liquid there will be more stripping plates and fewer rectification plates.?

Location of feed plate

This is another important aspect of a distillation column

As discussed, the location of the feed tray is an important aspect and this requires a rigorous tray-to-tray calculation to identify a tray where the feed composition is the same as the tray composition.

In short, the definition is an ideal feed location is feeding to a section of the distillation column where column internal liquid traffic composition is similar to feed stream composition. It means, it’s the location of a plate or tray in the distillation column where entering feed can make minimum composition gradient between feed stream and distillation internal fluids and thus don’t break plate to plate equilibrium. ?The optimum location of the feed plate would be the one represented by the triangle that has one corner on the rectifying line and the other corner on the stripping line.

What is McCabe's plot

McCabe-Thiele plot is an easy and condensed graphical tool to understand distillation. It is a technique for estimating the number of theoretical trays needed for the distillation of a binary mixture.

McCabe – Thiele method assumptions

[1] Molal heats of vaporization of the components are roughly the same

[2] Heat effects (heats of solution, heat losses to and from column, etc.) are negligible

[3] For every mole of vapor condensed, 1 mole of liquid is vaporized

[4] It is not used when the relative volatility is less than 1.3 or greater than 5.

[5] It is not used when more than 25 theoretical stages/plates are required, and.

[6] It is not used when the operating reflux ratio is less than 1.1 times the minimum reflux ratio.

[7] It applies to ideal binary mixtures of liquids

[8] 100% tray efficiency. Trays calculated using the McCabe-Thiele method are called "theoretical trays". In practice, fluids do not reach equilibrium on each tray, and so the "tray efficiency" is used to determine the number of actual trays required to make a given separation.

The above-cited assumptions lead to a concept of constant molal vapor flow and constant molal liquid flow in any section of the column (i.e., the molal flow rates of vapor and liquid are constant in any section of the column). In other words, for one mole of liquid vaporized, one mole of vapor is condensed in any section (rectifying or stripping).

What is a theoretical plate?

A theoretical plate in a distillation column is a plate in which two phases, such as the liquid and vapor phases of a substance, establish an equilibrium with each other. In other words, the average composition of vapor rising up and the average composition of liquid leaving the plate are in equilibrium. Such equilibrium stages are also referred to as an equilibrium stage, ideal stage, or theoretical tray.

An actual, physical plate can never be a 100% efficient equilibrium stage, the number of actual plates is more than the required theoretical plates.

Na = Nt/E

Na is a number of actual plates, Nt is a number of theoretical plates E is the plate or tray efficiency. Typical values for tray efficiency range from 0.5 to 0.7 and depends on a number of factors, such as the type of trays being used, and internal liquid and vapor flow conditions. Sometimes, additional trays are added (up to 10%) to accommodate the possibility that the column may be under-designed.

Construction of McCabe – Thiele diagram step by step

Step 1 is to draw equal-sized vertical and horizontal axes of a graph. The horizontal axis will be for the mole fraction (denoted by x) of the lower-boiling feed component in the liquid phase. The vertical axis will be for the mole fraction (denoted by y) of the lower-boiling feed component in the vapor phase.

Step2 is to draw a straight line from the origin of the graph to the point where x and y both equal 1.0, which is the x = y line. This 45-degree line is used simply as a graphical aid for drawing the remaining lines.

Step3 is to draw the equilibrium line using the VLE [vapor liquid equilibrium] data points of the lower boiling component, representing the equilibrium vapor phase compositions for each value of liquid phase composition.

What is the equilibrium line?

It is a curved line that describes the compositions of the liquid and vapor in equilibrium at some fixed pressure. For example, the Benzene-toluene VLE plot shows a binary mixture that has a uniform vapor-liquid equilibrium and it is relatively easy to separate.

The table above is showing equilibrium data for benzene-toluene at 101.3kPa

Step 4, Choose Product Compositions

Mark the composition of the feed, top, and bottom products on the x-axis. Then plot a vertical line from each of these points to the 45° line as shown below.

Step 5, extend XB [bottom] XF [feed], XT[Top] to diagonal line in the image.

Step 6, draw feed line. Where the feed is saturated liquid, the line is vertical. Where the feed is a saturated vapor, the line is horizontal.

Depending on the state of the feed, the slope of the feed line on x=y line called q line will be different.?

Where the feed is saturated liquid, the line is vertical. Where the feed is a saturated vapor, the line is horizontal. This has been discussed on page 1.

For feeds lying between a saturated vapor and a saturated liquid we can use a simple formula to determine the slope of the feed condition line:

m = q / q-1

Where q is the mole fraction of liquid in the feed.

Once the slope of the line feed condition line is calculated it can be drawn on the McCabe-Thiele plot from the point where the feed line meets the 45° line until it intersects the VLE curve. For a saturated liquid-like binary mixture of benzene-toluene q is a. straight line.

Step 7 is to plot the operating line or rectifying part of the column. The intercept of the operating line on the y-axis is given XD/[R+1]. Draw an upper operating line from the intersection of XD with x = y diagonal line such that its intercept is XD/[R+1] on Y-axis. This is a rectification operating line.

What is rectifying section of the distillation column?

The rectification section of a distillation column is the portion of the column above the feed plate where volatiles are stripped from vapor.

Step 8, the next step is joining the intersection of the upper operating line with q line with XB [ bottom]. This line is an operating line for the stripping section.

What is the stripping section of the distillation column?

The stripping section of a distillation column is the portion of the column below the feed plate where volatiles are stripped from the liquid.

The feed plate triangle is located with its base both in the rectification and stripping sections.

Step 9, the final step is to draw triangular steps between two operating lines and the equilibrium diagram. By counting the triangular steps, you can see between 11 to 12 perfect plates are required for the desired separation in the above image with feed on the 6th plate from the top of the column. If the reboiler can be considered as a perfect plate, between 10-11 perfect plates are required in the column.

Credit: Google