hand calculations for distillation towers

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50. Hand Calculations for Distillation Towers

Vapor-Liquid Equilibrium, Absorption, and Stripping Calculations

50.1. Introduction

The top of a distillation tower works like an absorber whereas the bottom of

a distillation tower works like a stripper. The upper and lower parts of a

tower are the rectification section, which is the upper portion above the feed

inlet, and the stripping section, which is the lower portion between the feed

inlet and reboiler vapor return nozzle.

In this chapter we will discuss single theoretical stage Bubble-Point and Dew

Point calculations and give examples as to how these can be used in our

work. Then we'll discuss the use of the Absorption Factor and Stripping

Factor chart, which can be used to design distillation towers. In order to use

this chart in that way it is necessary to consider a distillation tower as two

separate towers. The top of the tower is considered an absorber. The chart is

then used in a different way to design the lower part of the distillation tower

as a stripper.

Distillation towers were designed using this same chart for nearly half a

century before the first computer simulations were ever written. Indeed, the

use of computer simulations in design did not really begin until the early

1960s.

As long as we pay attention to the assumptions needed when using this

chart, it is still a valuable tool that provides an understanding of how the

process works and what to expect when conditions change.

Hand Calculations for Distillation Towers

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50.2. Bubble Point and Dew Point Calculations

I will demonstrate how to do these calculations, although we have used them

elsewhere in this book. But first allow me to point out one of the ways in

which you might use them, which is to check on the composition of lab

samples. Suppose we take a bomb sample of the vapor and another bomb

sample of the liquid from a reflux drum. Working through the Bubble Point

and Dew Point calculations will provide a cross-check on the distillation

results. If the lab distillation results don't add up to 100%, then something is

missing from the analysis. In which case, ask yourself if its light ends that are

missing. Perhaps you were sloppy in your sample taking and lost vapors in

handling or maybe sampled a liquid that was hot into a bottle instead of

taking a bomb sample. Maybe there was residue when the lab performed the

distillation so there was thermal cracking during the distillation test. Either

way, an analysis that does not add up to 100% indicates something amiss, it

could be a problem with your calculation, or with the lab sample, or the lab

distillation result.

Norm used to include Bubble Point and Dew Point calculations in his refinery

troubleshooting seminars, as a test question for any process engineers who

attended (Fig. 50.1). As only about 10% of the engineers could ever answer

the question, he has mostly discontinued the use of this in the seminar. But

because I like the way the seminar was when I first attended in the 1980s, I

think we all deserve to understand this.

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50.2.1. Bubble Point

We are going to use a reboiler as an example (see Fig. 50.2).

Figure 50.1. The bubble point and dew point calculation example,

extracted from our seminar manual.




When vapor is first formed in the reboiler it is in contact with the liquid from

which it was formed. We say that the vapor formed while in contact with the

liquid from which it was formed is "in equilibrium with" that liquid.

Dalton's law says that the total pressure (P ) (i.e., in the vapor space in this

reboiler) is the sum of the partial pressures of all the components of the

vapor.

Where P and P are the partial pressures. We could express all of

these in psia, or all in mm Hg, or all in atmospheres just as long as we keepthe total pressure and partial pressures all in the same units.

Meanwhile Raoult's law allows us to find the partial pressure of a component

via its vapor pressure (P ) and its mol% (X) in the liquid with which the vapor

is in equilibrium.

or

Figure 50.2. Using bubble point to calculate vapor composition in a

reboiler.

T

Butane Propane

V



By combining these ideas we can find the mole percentage of each

component in the vapor (Y):

or

Let's put some numbers to this. We'll take the vapor pressures from a Cox

vapor pressure chart (Fig. 50.3).

Figure 50.3. A Cox vapor pressure chart.




Hence the total pressure P = 180 + 60 = 240 psia. And now we can find the

mole percent of each component in the vapor as follows:

50.2.2. Dew Point

Looking at Raoult's law again: The partial pressure of a component is given

by its vapor pressure multiplied by its mole percentage in the liquid phase,

just as we said in the Bubble Point calculation:

or

Alternatively we could write this as:

or

Whereas for the Bubble Point calculation we calculated the vapor composition

in equilibrium with a liquid, for the Dew Point calculation we are given the

vapor composition and will calculate the composition of the liquid that is inequilibrium with the vapor.

Suppose we did not know the liquid composition for the bottom product as

was given in the Bubble Point calculation in the previous section, but instead

we did have the composition of the vapor at the operating temperature so

that the partial pressure of each component was also easy to calculate. We

could then find the composition of the liquid by calculating the mol

percentage of each component in the liquid that was in equilibrium with the

vapor.

For example:

T



or

But although using the exact same set of numbers as for the Bubble Point

calculation may help demonstrate this Dew Point calculation, let's try a

different example to demonstrate the Dew Point calculation.

Let's look at the reflux drum of that same distillation tower that we used for

the Bubble Point calculation (see Fig. 50.4). Again the vapor coming off the

reflux drum is in equilibrium with the liquid in the reflux drum. Using our Cox

vapor pressure chart (Fig. 50.3), we find the following.

In this case we do not have the total pressure (P ) in the vapor space above

the liquid in the reflux drum, but we still want to find the composition of the

liquid in the reflux drum that is in equilibrium with that vapor.

Traditional calculation methods allow us two choices. At this point we have

two options.

Figure 50.4. Overhead of a C – C splitter.3 4

T





50.2.2.1. OPTION A

Make a guess at the total pressure (P ), then use the relationship from

Dalton's law to find the partial pressures of each component, as in:

Then having found the partial pressure for each component, we could use the

relationship from Raoult's law to find the mol% of each component in theliquid which is in equilibrium with the vapor, as in:

Where i in this case would be either butane or propane.

Having then calculated mol% in the liquid for each component, if these do not

add up to 100% when added together, one must start all over again at thebeginning of Option A by making a revised guess of the total pressure.

This kind of calculation is known as iterative . One would keep going through

this procedure making new guesses at the total pressure until such time as

the mol% for each component, when all added together, did reach 100%, no

more and no less than 100%. Each time we go through a series of

calculations like this we call it an iteration . This method could also be

referred to as an iterative method, iterating on Total Pressure.

50.2.2.2. OPTION B

The traditional alternate would be to use the relationship with the

Equilibrium constant, also known as the equilibrium ratio, K .

Where i in this case would be either butane or propane.

T

i



With

In order to use this method we need an extra chart to provide K for different

values of temperature. Such a K versus T chart is given in Chap. 11 of

Chemical Engineering: Vol. II , 3rd ed. by Coulson and Richardson. Actually

this chart in the third edition is in SI units, so we would need to convert the

temperature from degrees Fahrenheit to absolute temperature (i.e., Kelvin orK) in the SI system to use it. This is done as follows:

But here at last is a nontraditional and third option for this Dew Point

calculation. It is a direct calculation using the vapor pressure chart.

50.2.2.3. OPTION C

Refer again to Fig. 50.4, the reflux drum of the C C splitter with 10 mol%

Butane and 90 mol% Propane in the vapor, and the reflux drum temperature

at 100°F.

In this case i is either butane or propane. The next step is to add together all

the values of y ÷ P for each component:

i

i

4

3 4

i V.i


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The last step is to calculate for the mol% for each component in the liquid (X )

from:

We call this Option C direct calculation method, "Norm's method." It's not

found in any of our textbooks or notes, but it works. If you don't believe us,

check the validity as follows, using the values for X that we just found. From

Raoult's law:

Thus total pressure (P ) in reflux drum via "Norm's method" is:

Now we can check Option C, "Norm's method," using our Bubble Point

calculation method together with the total pressure that we have just found

(P = 142.8 psia) and the liquid composition that "Norm's method" gave us for

the reflux drum, which was 28.6% Butane and 71.4% Propane, to see if we

can arrive at the vapor composition as shown in Fig. 50.4.

Thus via Bubble Point calculation:

i

T

T

Pressure (P )Mol% in Liquid

(x)

Partial

Pressure (psia) V




Thus the mol% (Y) of each component in the reflux drum vapor is:

We were satisfied with this and hope you will find Option C a useful tool.

50.3. The Absorption Factor or Stripping Factor Chart

The Absorption factor or Stripping factor chart, as it is sometimes known, is

shown in Fig. 50.5. It provides simple calculation methods for hydrocarbons

when considering either an Absorber tower or a Stripper tower in

hydrocarbon service, but for combination Absorber-Stripper towers the

calculation procedures become iterative and a lot more complex. So for acombination Absorber-Stripper tower it is best not to attempt to use this

chart. It is actually better to resort to a computer simulation. In fact, as a

point of historical interest, Norman tells me that it was when the idea of

combined Absorber-Stripper towers was first invented that brought about

the use of computer simulations so as to handle all the intricate and

cumbersome calculations needed to design them.

Butane 50 28.6

Propane 180 71.4




But let's go back to the use of this chart for the separate Absorber tower or

separate Stripper tower. First, the Absorption Factor, A, is defined as:

Figure 50.5. Absorption factor or stripping factor chart.



where A = absorption factor

L = moles of liquid

V = moles of vapor

K = equilibrium constant or equilibrium ratio, as previously defined in

bubble point and dew point calculations as:

where

And

or as:

where P = partial pressure of component i

P = total pressure

P = vapor pressure of component i

Hence the absorption factor is also defined as:

As the action of stripping is taken to be effectively the reverse of absorption,

the stripping factor for which we write S is defined as the reciprocal of the

absorption factor.

Thus:

i

i

T

V.I



or

or

The chart assumes that the absorption factor, A, will remain fairly constant

over the range of theoretical stages. The horizontal axis describes the

number of theoretical stages we have assumed 50 percent efficiency for the

trays in the tower, which means that whatever the number of trays in the

tower, we then have half that number as the number of theoretical stages.

The vertical axis refers to the amount rejected or the amount lost. For an

absorber tower this is the amount of the light key component not absorbed

in the lean oil, but when the chart is used for a stripper tower, this is the

amount not stripped out. In reference to this chart the term "amount" that I

am using refers to the fraction and not the percent; this just means that the

sum of all the fractions of the light key component present in the system add

up to 1. Whereas if we refer to the percent, then the sum of each of the

percentages of the light key component present would add up to 100. The

vertical axis also assumes zero light key component in the lean oil, which is

often not the case.

A more classical definition of the vertical axis of this chart can be found in

either Mass Transfer Operations by R. E. Treybal or Separation Processes

by C. J. King, but be warned, neither of these books is for the faint of heart,

especially in the sections where absorption or stripping are concerned. So if you choose to look up these references, please don't get despondent as some

of the verbiage (or in places, lack of verbiage) would break the heart of the

most aspiring and ardent student.

Let us now clarify the use of this handy chart with some examples.

50.3.1. Absorption or Stripping Factor Chart for Absorption

A wet gas stream containing propane as the light key component from a cat

cracker (FCC) is being fed to an absorber (see Fig. 50.6).

5,6




The absorber tower has 20 trays, which for this calculation we will assume to

Figure 50.6. An FCC wet gas absorber tower.



be 50 percent efficient so we can say that this tower has 10 theoretical

stages.

The lean oil rate is 2000 barrels per day, and with existing current operation

there is 90 percent recovery of the propane to the rich oil (i.e., 10 percent

loss of propane to the dry gas). We will assume zero light key component in

the lean oil (i.e., we are assuming there is no propane in the lean oil).

90% Recovery Propane to Rich Oil = 10% Loss Propane to Dry Gas

We now plot this existing operation on the chart to find A (the absorption

factor). See Fig. 50.7. From the chart we find:




Management wants to improve recovery of the Propane, so operations

decides to increase the lean oil rate. If the lean oil rate is now doubled, and

we assume that the vapor rate (V) and equilibrium constant (K) remain the

Figure 50.7. Absorption plot for an FCC absorber with 10 theoretical

stages and 10% loss of propane from feed to dry gas.



same at the increased lean oil rate as they were at the original lean oil rate,

then we can simply multiply the absorption factor by 2 so as to obtain the

new absorption factor at the new lean oil rate of 4000 barrels per day, as

follows:

Old lean oil rate 2000 B/D

New lean oil rate 4000 B/D

Thus

Therefore

Hence the absorption factor A at 4000 B/D is also doubled, but the number of

theoretical stages is still 10. Again we refer to the chart and this time plot

the condition at the new lean oil rate of 4000 barrels per day. (See Fig. 50.8.)




Assume no propane in the lean oil. From the chart (Fig. 50.8):

Figure 50.8. Absorption plot for an FCC absorber with 10 theoretical

stages and A = 1.96.




Therefore,

This represents an approximate 10 percent increase in recovery of propane

to rich oil by doubling the lean oil rate.

You may note that in order to use this chart we have had to sketch in a line to

represent the appropriate line for the value of the absorption factor between

existing lines for A on the chart. Also, we should be cautious about assuming

that there is none of the light key component (in this case Propane) in the

lean oil, as this is not always true.

If you find that the light key component is present in the lean oil, then the

method described above may not be valid, and you should refer to one of the

classical reference texts such as Mass Transfer Operations by Treybal or

Separation Processes by King for guidance as to how to proceed with the

calculation. Note that the higher the recovery of the light key component, the

more critical it becomes that there should be no light key component in the

lean oil, otherwise the method we show here may not produce correct

results.

50.3.2. Stripping Factor or Absorption Factor Chart for Stripping

50.3.2.1. C ASE I: INCREASING THE NUMBER OF TRAYS

A de-ethanizer tower has 10 trays, we will assume the trays have 50 percent

efficiency in this case, hence, there will be five theoretical stages. Ninety

percent of the Ethane is being stripped out of the Naphtha stream, thus 10percent of the Ethane fed to the tower in the Naphtha stream is left in the

bottoms product (Fig. 50.9).

5,6




Summarizing:

Therefore

Figure 50.9. Stripping in a de-ethanizer.



Refer to Fig. 50.10. We will now use the lines that we used in the previous

example for absorption as A for the reciprocal of A, that is, we will now take

the alternate use of these lines as




From the chart,

Figure 50.10. Stripper with S = 1/A = 1.2 has 5 theoretical stages,

then doubled theoretical stages.



If we now double the number of trays so that there are now 20 trays with 50

percent efficiency, then the number of theoretical stages will now be 10, but

the stripping factor S will remain the same: 1.2.

Summarizing:

New Situation:

To find the new amount of Ethane remaining in the bottoms now that we

have doubled the number of theoretical stages, we need to refer to the chart

again. See Fig. 50.10. Follow the curved line for "1/A = 1.2" to the point where

it intersects the vertical line for 10 theoretical stages.

Next read off the fraction of Ethane that now remains in the bottoms from the

vertical axis on the left to find, that is, percent of ethane from the feed now

remaining in the bottoms. That is equivalent to 97 percent of ethane in the

naphtha feed now stripped out.

Summarizing, we now have:

Therefore,




50.3.2.2. C ASE II: INCREASING THE R ATE OF STRIPPING V APOR

In this case the de-ethanizer shown in Fig. 50.9 is stripping out 80 percent of

the ethane from the naphtha feed stream. Thus there is 20 percent of the

ethane from the feed left in the bottoms. There are 10 trays with 50 percent

efficiency, therefore we have five theoretical stages.

Summarizing:

Therefore,

We now refer to the chart shown in Fig. 50.11. Plot 0.2 (feed ethane

remaining in bottoms) on the vertical axis and 5 (theoretical stages) on the

horizontal axis. The intersection on the chart gives a stripping factor of 0.92.

Thus:





Theoretical Stages = 5

Then from the chart:

Figure 50.11. Stripper with 5 theoretical stages with doubled

stripping vapor rate.



Suppose we now double the vapor rate by doubling the reboiler duty. There

will still be five theoretical stages. But the stripping factor is now doubled

because we are assuming that the naphtha feed rate and bottoms product

rate remain constant. Thus:

If

and

K = Equilibrium constant and remains unchanged because the pressure and

temperature are constant. Therefore

Again summarizing:

Ethane as light key from feed now in bottoms at old vapor rate

New situation:

Therefore

Therefore



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1. E. V. Thompson and W. H. Ceckler, Introduction to Chemical Engineering

(McGraw-Hill, 1977), ISBN 0-07-064396-2.

2. American Petroleum Institute (API) Data Books, www.api.org. American

Petroleum Institute, New York. Vapor Pressure of Normal Paraffin

Technical Data Book, Ch. 5, P. 5A1.1, 1970.

3. Wikipedia, http://en.wikipedia.org/wiki/vapor_pressure.

4. J. M. Coulson and J. F. Richardson, Chemical Engineering: Vol. II , 3rd

Edition (Pergamon Press), ISBN 0-08-022919-0, 1980.

5. R. E. Treybal, Mass Transfer Operations (McGraw-Hill, 1955).

6. C. J. King, Separation Processes , 2nd Edition (McGraw-Hill, 1980), ISBN 0-

07-034612-7.

Citation

Norman P. Lieberman; Elizabeth T. Lieberman: Working Guide to Process Equipment,

Fourth Edition. Hand Calculations for Distillation Towers, Chapter (McGraw-Hill

Professional, 2014), AccessEngineering

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hand calculations for distillation towers

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