# Distillation Column Efficiency Experiment

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The main objective of this experiment was to find the number of theoretical stages and column efficiency of a distillation column with 8 sieve trays and a partial reboiler at total reflux and finite reflux (with a reflux ratio of 2).

The liquid condensate flowrate were measured and the feed flowrate was found at finite reflux. Samples were taken from the bottom product and the distillate when steady steady was reached inside the column. The densities of these samples were found and using graphs, the composition of methanol was found. The McCabe-Thiele method was then used to find the number of theoretical stages for both total reflux and finite reflux. The column efficiency was then found.

The results showed that the number of theoretical stages for total reflux was 2 and for finite reflux was 4. The column efficiency for total reflux was 25% and for finite reflux was 50%. Fenske's equation was also used to find the number of theoretical stage for total reflux; this value also came to 2.

The quantifiable errors in this experiment were quite low, with the highest value at 3% and the lowest at 0.0089%.

## Introduction & objectives

Distillation is one of the most widely used processes for separating liquid mixtures into several different components. Distillation can be carried out using two methods. The first method is boiling the liquid mixture to be separated and to condense the vapour, without letting any liquid return to the still. There is then no reflux. The second method returns a part of the condensate to the still under such conditions that the liquid comes in contact with the vapour on the way to the condenser. Both methods can be run as a batch or continuous process. [i]

Distillation is usually the cheapest and best method for separating liquid mixtures to its components except when:

- The volatility difference between the components is too small
- The mixture is highly fouling or extremely corrosive
- A compound is thermally unstable [ii]

The main part of a distillation system is the distillation column. The feed can be input at different locations in the column but must be introduced where the liquid composition is similar to the feed composition. The section above the feed point location is known as the rectification section, the section below the feed point location is known as the stripping section. The liquid product is collected at the bottom of the column, whereas the distillate is collected at the top. To increase the purity of the products there is often a reflux. This means the liquid product goes into a reboiler and back into the column. For the distillate, the stream goes into a condenser and is then split into a product stream and a stream going back into the column. This system is known as finite reflux, as the output stream is split into a product and a reflux. A total reflux system would mean that everything from the top of the column returns as a reflux, therefore there is no product.

Inside the column can either fill filled with packing or contain trays. Packing is usually classed in three ways.

Random or dumped packing - as the name suggests, the packing is randomly packed such as Raschig rings

Structured or strategically arranged packing - crimped layers of wire mesh or corrugated sheets such as Sulzer® Wire Gauge Packing

Grids - similar to structured packing but these are open-lattice structured such as Koch High-Capacity Flexigrid®

There are also three types of trays which are used. Bubble cap tray, sieve trays and valve trays. Bubble cap trays were used primarily in the 1960's but are now only used for special applications. The most common trays used today are sieve or valve trays. A bubble cap tray is a flat perforated plate with chimney-like pipes, known as risers, around the holes. Liquid and froth are trapped on the tray to a depth at least equal to the riser height. This gives rise to the unique property of the bubble cap tray to operate at low vapour and liquid rates. The sieve tray is a flat perforated plate which allows vapour to rise through the holes. The velocity of the vapour prevents the liquid from flowing down the holes (known as weeping). If weeping occurs, the liquid will flow through the holes resulting in reduced efficiency.

The column we are using in our experiment uses sieve trays

The main objective of this experiment is to:

- Determine the number of theoretical plates.
- Determine the column efficiency for finite reflux for a mixture of Methanol and Water.
- Determine the column efficiency for total reflux for a mixture of Methanol and Water.

## Theory

F, ZF

B, XB

D, XD

L

V

L, xN

V, yN+1Mass balances using diagram below

Where F is the feed

B is the bottom product

D is the distillate

V is the vapour flow

L is the liquid flow

ZF, XB and XD are the corresponding mole fractions for the more volatile component

x (liquid) and y (vapour) are the mole fractions for the more volatile component

Overall mass balance

(1)

Overall material balance

(2)

Top of the column overall balance

(3)

Top of the column material balance

(4)

Rearranging equation 4 in terms of yn+1 and using equation 3 gives:

(5)

Reflux ratio is given as:

(6)

Substituting equation 6 into 4 gives:

(7)

Equation 7 is the equation for the operating line for the rectification section. The rectification section can also be found graphically by drawing a line through the points; (XD, XD) and (0, XD/R+1)

The bottom operating line is given by:

iii(8)

Where L' and V' are the liquid and vapour flow in the stripping section

The bottom operating line can also be found graphically by connecting (XB, XB) to the intersection of the top operating line and the feed line.

The feed line is given by:

Rectification:

(9)

Stripping:

(10)

Combining equations 9 and 10 and substituting the overall material balance from equation 2 gives:

(11)

If we define the fraction of vapour in the feed as f, then V-V'=fF and L-L'=-(1-f)F, therefore:

(12)

(13)

Equation 13 is the equation for the q-line. q is defined as the ratio of heat to vaporise 1 mol of feed to the molal latent heat of the feed

(14)

Where Q is the flowrate and Î» is the latent heat

The full equation for the q-line is:

(15)

Where xq and yq are the points of intersection of the rectifying and the stripping operating lines. XF is the mole fraction of the more volatile component in the feed.

For the calculation of q-line:

(16)

Where Î» is the latent heat

H is the enthalpy

Cp is the specific heat capacity

Tb is the temperature at the boiling point

T is the initial temperature

To obtain the specific heat of a mixture, the following equation is used

(17)

Where x is the mass fraction of components A or B

M is the molecular mass of A or B

To find the theoretical stages for this column, a McCabe-Thiele method must be used, where the feed line and operating lines must be drawn on a VLE diagram.

For the column efficiency, the following equation is used

(18)

The theoretical number of stages can also be calculated using Fenske's Method [iv] :

(19)

Where n is the number of theoretical stages (not including the reboiler)

Î± is the relative volatility, which is given by:

(20)

## Experimental Details & Procedure

Experimental apparatus

A distillation column with:

- 8 sieve plates
- A 12 litre partial reboiler
- two 5 litre feed tanks
- a peristaltic feed pump
- a reflux valve
- a condenser
- a top product tank
- a bottom product tank

An electrical console and a PC which takes readings at each thermocouple, which are placed on each sieve tray

A rotameter to adjust the cooling water flow

4 flasks

A density meter

A stopwatch

A measuring cylinder

A beaker

A calibration curve to find the pump dial setting

A graph to find the composition of methanol at 20°C

Safety

Methanol is a poison if ingested and is moderately toxic by intravenous routes into the body. It is mildly toxic by inhalation.

Side effects include optic nerve neuropathy, visual field changes, headache, cough and other respiratory effects

It is also highly flammable

No naked flame must be brought near methanol

Latex gloves should be worn when handling anything containing methanol

Lab coats and goggles should be warn at all times

Experimental Procedure

Set the cooling water flow to 3 l/min

Turn on the reboiler heater and set the heat input to 1.5kW

Once the column has filled up with liquid set the heat input of the reboiler down to 0.65kW

Once the column has reached steady state under total reflux (the temperatures of the trays should be constant i.e. straight horizontal lines on the computer. The temperatures of each tray will be different, but should all be constant) take sampled from the top and bottom product streams. Label these flasks top (total reflux) and bottom (total reflux) respectively. Leave these samples to cool to approximately 20°C

Allow the column to return to steady state and then determine the condensate flowrate by sampling the condensate in a measuring cylinder over the length of 1 minute.

Make sure to clear the liquid held up in the pipes before taking this measurement

Determine the feed flow F which gives a distillate flow equal to three times the bottom flow i.e. D=3B

This can be determined by using the following equations:

and and

L is known, R is given as 2. Therefore D can be calculated. From D, B can be calculated. Using D and B, F can be calculated

Using the value of F, find the pump dial setting using the calibration curve given

Set the reflux ratio R to 2. And turn on the reflux valve and the feed pump

Open the valve to the bottom product receiver (this now becomes a finite reflux)

Once steady state is reached, take sampled from the top and bottom products using the flasks given and label these flasks top (finite reflux) and bottom (finite reflux) respectively. Leave them to cool to approximately 20°C

Record the feed temperature

Once all the 4 samples in the flasks have reached approximately 20°C, use the density meter to measure their densities and temperatures. Use the density/composition graph to find the mol% composition of methanol and record the results.

The reflux ratio is equal to 0 therfore the operating line is the y=x line on the McCabe Thiele diagram. Plotting points (xD, xD) as (90.0, 90.0) and (xB, xB) as (21.0, 21.0) and (xF, xF) as (25.0,25.0)

Looking at the McCabe Thiele diagram (Graph 1) it can be seen that there are 3 theoretical stages. The number of theoretical stages without the reboiler is 2.

## Finite Reflux (Graph 2)

Plotting points (xD, xD) as (92.1, 92.1) and (xB, xB) as (20.5, 20.5) and (xF, xF) as (25.0,25.0)

The specific heat capacity can be found using equation 17:

For latent heat:

q can now be found:

The gradient for the feed line is:

This feed line starts at point (25.0, 25.0)

To find the top operating line, the y intercept in equation 7 is needed

So the top operating line runs from (92.1, 92.1) to (0, 30.7)

Looking at the McCabe Thiele diagram (Graph 2) it can be seen that there are 5 theoretical stages. The number of theoretical stages without the reboiler is 4.

Column efficiency

## Total reflux

## Finite reflux

calculating number of theoretical stages using Fenske's equation for total reflux

Firstly, we need to calculated the relative volatility using equation 20:

xmeth is the average between 0.579 and 0.665 at liquid mol% of 20.0 and 30.0. The average is 0.622

Using equation 21:

(rounded up to integer)

According to Fenske's equation the number of theoretical stages not including reboiler for the total reflux is 2.

## Discussion

From the results above it can be seen that the column at total reflux has 2 number of theoretical stages (without a reboiler) while the column with finite reflux has 4. Therefore the column efficiency of the finite reflux is higher, at 50%, while the total reflux efficiency is 25%.

These results correlate with predictions and Fenske's equation always shows that the number of theoretical stages for total reflux is 2. At total reflux, there is no product and the fluids keep cycling around and separating. However, in a finite reflux, a distillate is collected while a fresh feed is added. The reason for the number of stages being very low is that water and methanol have very different boiling points; therefore it is fairly easy to separate a mixture of water and methanol. The reason for the higher efficiency at finite reflux is because the product is collected and a level or purity is maintained. It must be noted that the reflux ratio used at finite reflux was 2. At other reflux ratios, the results would be different.

## Errors and Limitations

Looking at table 3 it can be seen that the errors calculated were very small, with the highest error at approximately 3%. The combination of error for the feed parameter (q) is very small with a value of 0.0089%. This shows that quantifiable errors are not the reason for the majority of the error in this experiment.

Errors may have occurred due to the following:

The column may not have reached steady state before samples were taken

Using the graphs to determine the pump dial setting for the flowrate was not easy to read

The dial for the reflux valve and the cooling water flowrate may not have been set correctly

When measuring the flowrate of the liquid flow L, one person was timing while another was using the cylinder to collect the liquid. There may have been an error in the coordination of both people. One person may not have closed the valve when it needed to be closed, therefore causing more liquid to go into the cylinder. Giving a slightly inaccurate flowrate.

Using the graph to determine the composition of methanol from the density was difficult to read, especially as the density was given to 3 decimal places.

The samples were not exactly 20°C before their compositions were read off the graph (which was based on the sample being 20°C)

The McCabe-Thiele diagram also allows for human error as the stages may not be entirely accurately drawn

## Improvements

Wait longer for the column to reach steady state

All dials and settings should be digital so they can be set more accurately

The samples should be cooled to exactly 20°C before measuring the density

More repeats of the experiment should be done to ensure reliability of results

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