McCabe Thiele FUG Algorithm

8/21/2019 McCabe Thiele FUG Algorithm

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McCabe Thiele

FUG Algorithm

Rex Gaumer Ph.D.


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Joke of the Day

Base jumping is not a trial and error activity


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McCabe Thiele Review from last time

Review

Requires VLE data

Applies to Binary distillation

Today

Rectification Operating Line

Stripping Section Operating Line


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Steps for McCabe Thiele

Acquire T XY data for binary mixture.

Plot X, Y values for the more volatile componentof the mixture.

Do a mass balance on the system to specify theseparation of the stream into the bottoms streamand the distillate stream.

Can you specify the recovery and purity of the

lighter component in the distillate? Can you specify the recovery and purity of the

heavier component in the bottoms?


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Steps for McCabe Thiele

Find the minimum Reflux ratio for the column.

Determine the operating line for the rectificationsection.

Determine the stripping section operating lineeither analytically or graphically.

Step off tray stages from top of column.

Switch over from the Rectifier line to the Stripper

line when the X value of the vertical line to thenext stage is less than the intersection of the twolines.


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T XY, XY Diagram Construction

LIQUID

PHASE VAPOR PHASE

T, K X, n C4 X, n C5P, n C4,mm Hg P, n C5, mm Hg

308.39 0 1 2344.96 760.00

302.98 0.1 0.9 2021.39 619.85

298.03 0.2 0.8 1753.55 511.61


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T XY, XY Diagram Construction

VAPOR PHASE

T, K

P, n C4,

mm Hg

P, n C5, mm

Hg

TOT. P.,

mm Hg Y, n C4 Y, n C5

308.39 2344.96 760.00 760.00 0.0000 1.0000

302.98 2021.39 619.85 760.00 0.2660 0.7340

298.03 1753.55 511.61 760.00 0.4615 0.5385

LIQUID

PHASE VAPOR PHASE

T, K X, n C4 X, n C5

P, n C4,

mm Hg P, n C5, mm Hg

308.39 0 1 2344.96 760.00

302.98 0.1 0.9 2021.39 619.85298.03 0.2 0.8 1753.55 511.61


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Starting a Plot for Butane Propane

CPE 523, Lect. 16


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Rectifying Section Operating Line

CPE 523, Lect. 16

The mole balance from the top of the column to the

top of stage m+1 for a binary distillation is:

Dmm DxLxVy 1

By writing just one Vand one L, weve made theassumption of Constant Molal Overflow. If we wanted

to plot this on ourxvs. y plot, what would we need to

know?

V, L, D, andxD. Where do we get these?

The distillate concentration is something we can

choose, and those other flows are all related to the

reflux ratio L/D, that we set.


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Stripping Section Operating Line

CPE 523, Lect. 16

Well need the same analysis for the stripping section of

the column. What does a mole balance from any stagebelow the feed to the bottom look like?

Bmm BxyVxL 1

Remember two differences here: the vapor and liquidflowrates (and their ratio) are not identical to those in the

rectifying section, and if we have a partial reboiler, then

that also counts as a stage (since we approach equil.

there). Do we need to know the same parameters here?

Yes, at least equivalent ones: the bottoms compositionxB,

and the boilup ratio

B

VVB


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Operating Conditions

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

MoleFrac.MeOH

Mole Frac. MeOH

McCabe Thiele, MeOH IPA; Min Reflux Graph

X Y Curve

Total Reflux Op line

Dist. Comp.

Feed Comp

q line bubble pt.

q line, satd vapor

Min R Bubbl q line

Min R Satd Vap q line


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Relation to Design Parameters

CPE 523, Lect. 16

In the discussion section, we also showed the

following relation:

The same rearrangement can be used to find D/V:

1

R

R

DD

DL

DL

DL

L

V

L

1

1

RDL

D

V

D

So what does the equation for the line look like in

terms of the parameters we can set?

Dx

R

x

R

Ry

1

1

1


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Stripping Section Op. line: parameters

CPE 523, Lect. 16

Just like for the rectifying section, we can write the

stripping section operating line in terms of the vaporboilup and the desired bottoms composition:

Make sure you can derive this equation if you are

given material balances around the bottom of the

column. To plot this one, we can choose to set thebottoms composition. Can we set the boilup ratio?

Not independently, since its linked to the other flows

in the column by an overall component mole balance

BBB

B xV

xV

Vy

11


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Finding the Boilup Ratio

CPE 523, Lect. 16

If the feed is a saturated liquid, then we know by a feed

stage material balance that

Given those balances, and the definitions of R=L/V and

VB=V/B, one can derive that

VVFLL and

DBRVB 1

We know that we can set R independently. Can we set B/D?

Not independently, since BxDxFz BDF

The stripping section line can also be plotted by connecting the bottoms

composition to the intersection of the feed line and the rectification operating

line.


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Conclusions

CPE 523, Lect. 16

The McCabe-Thiele method allows us to visualize

the difficulty of a separation using distillation,. We

can graphically step off equilibrium stages to see

how many are required for the rectifying and

stripping sections of a column Thexvs yplot can be constructed by using only

information about the chemical system itself, and by

setting degrees of freedom for the column (purities

and reflux ratio)


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References

CPE 523 Lecture notes by Dr. Kyle Camarda.

Wikipedia.


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The FUG Algorithm

Specify the desired splits of the key

components.

Estimate the split of the non-key componets.


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FUG Algorithm, (contd.)

Start loop section Estimate column pressure drop. This

requirement will force iterations on the

process.

Estimate Column Ts using dew and bubble

points

Calculate minimum theoretical stages, Fenske

Calculate splits of non-key components, Fenske

Return to start of loop section if splits need to

be changed significantly.

End Loop Section


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FUG Algorithm, (contd.)

Calculate the minimum reflux ratio, Underwood

Calculate actual theoretical stages for the specifiedreflux ratio.

Use the Gilliliand correlation to determine the numberof theoretical stages required for the separation.

Calculate feed stage location using the Kirkbrideequation.

Estimate new pressures for the column and redo FUGcalculation.

Calculate condenser and reboiler duties


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The FUG Algorithm

CPE 523, Lect. 21

This handy

flowchart showsyou the steps

required to

design a column

using the FUGmethod

Remember

this is only used

to get a good

initial guess for

a rigorous

simulation!


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Mass Balance

Decide the type of stream split that is required.

Is the priority product purity or product recovery?

This decision is usually made at a higher pay gradedue to the downstream use of the product.

If you need purity you will want to take theproduct off as a distillate not bottoms to avoidsludge which will accumulate in the bottoms.

Is the priority product recovery?

This is driven by the value of the product.

Down stream purification may be required toremove contaminants while minimizing loss of thevaluable product.


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Column T and P

Based on past experience or an educated guess

estimate a Pressure drop across the column.

Calculate a reboiler T based on the P at the bottom

of the column using a bubble point calculation. Calculate a feed tray T based on an intermediate P at

the middle of the column.

Calculate a distillate T based on the minimum P usinga dew point calculation.


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Key Components

CPE 523, Lect. 21

Rank the components by volatility.

In this example we want to recover 98% of the Hexanein the distillate and 99 % of the Heptane in the bottoms.

I assumed a small distribution of the non-keys and we

will check this assumption on the first pass of this

example.

COMPONENT FRACT MOLES B.P., C

n C5 0.04 4 35.9

LK n C6 0.4 40 68.5

HK n C7 0.5 50 98.1

n C8 0.06 6 125.1

1 100


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The FUG Algorithm

CPE 523, Lect. 21

This handy

flowchart showsyou the steps

required to

design a column

using the FUGmethod

Remember

this is only used

to get a good

initial guess for

rigorous

simulation!


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Distribution of the Components

CPE 523, Lect. 21

How do we estimate the distribution of each

component in the distillate and bottoms? First of all, use the specifications needed (i.e. if

80% A should be recovered in the distillate, then

20% of it is in the bottoms). The specifications are

usually made on the keys, but not always

If

1or1 ,, LKiHKi

then put 100% of that component in the

appropriate outlet flow


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More Distribution

CPE 523, Lect. 21

What options do we have if a non-key has a BP close

to the BP of a key component (and thus might

distribute)?

Try to find literature data to suggest a reasonable split

fraction Simulate a three-component system in a flash at

different pressures & temperatures, to see the

probable vapor and liquid distributions.

If all else fails, do some experiments Remember, these are just estimates for the FUG

method, which gives estimates for rigorous simulation


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Mass Balance

Perform an overall Mass Balance for the

distillation column. Set stream compositions

using required purity and recovery priorities.

Fenske and Underwood equations assume

optimum feed tray location. You want to

estimate the column temperature and

pressure profile.


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The Fenske Equation

Given our assumptions about key components, we can

use the Fenske equation to find the number of stagesrequired at total reflux (Nmin) At total reflux with equal heat duties, one can show that

CPE 523, Lect. 21

kikikk xyLV ,1,1 and

Note stages are numbered from the bottomhere. For the bottom stage

2,1,1,1,1, and iiiii xyxKy

2,2,2,1,1,2, stage,2ndFor the.So iiiiii xKyxKx

headed?rewe'whereSee.meansThis 1,1,2,2, iiii xKKy


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The Fenske Equation, cont.

CPE 523, Lect. 21

Now, make the big assumption that is similar on all trays,

and use an average value:

Solve for Nminto give

minmean1,

1,

1,

1, N

NHK

HK

LK

NLK

x

x

x

x

log

log1,

1,

1,

1,

min

NHK

HK

LK

NLK

xx

xx

N


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Fenske Calculation

Ln [(xdi/xbi) / (xdj/xbj)] / Ln (ALPHA lk hk) =

Nmin + 1


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FENSKE TOP BTM

CALCULATION ALPHA lk

hk

ALPHA lk

hk

AVG

2.61 2.22 2.41

LN (AVG) 0.8788

Xdi 0.8970 Xdj 0.0114

Xbi 0.0142 Xbj 0.8792xdi/xbi= 63.1281 xdj/xbj= 0.0130

Ln [(xdi/xbi) /

(xdj/xbj)]=8.49

Nmin

plates

reqd8.66


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Underwood Equation for Rd min

theta = 1.48

CMPD ALPHAlk hk

Xfi (ALPHA i *

Xfi) /

(ALPHA i -THETA)

ALPHA

lk hk

Xdi (ALPHA lk

hk * Xdi) /

(ALPHA lkhk - theta)

n C5 7.74 0.04 0.05 8.16 0.09 0.11

LK n C6 2.46 0.40 1.01 2.61 0.90 2.07

HK n C7 1.00 0.50 -1.04 1.00 0.01 -0.02n C8 0.41 0.06 -0.02

1.00 0.00 0.00 2.16 Rdm 1.16


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Estimate Trays from Minimum Reflux

and Minimum trays

We will use the Gilliland Correlation


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Gilliland Correlation


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Determine the X value to read the graph for

the correlation.

We have Rd min. How do we determine Rd for

an operating column?

I have mentioned a multiplier in the range of

1.2 to 1.3 to adjust Rd min to estimate Rd.

This comes from a Peters and Timmerhaus

text on Plant Design.


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f07 22


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Rd min is 1.16. We will use an Rd of 1.39 in

the Gilliland Correlation.

When we read the Gilliland Correlation this

gives a Y value of 0.53 which corresponds to

20 theoretical trays required for this column.


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Results

from

graph

=(Rd-Rdmin)

/ (Rd+1)

(N-Nmin)

/ (N+1)

(N-Nmin) /

(N+1)

N N1.1 x 1.10 0.05 0.60 0.60 23.1 24

1.2 x 1.20 0.10 0.53 0.53 19.5 20

1.3 x 1.30 0.14 0.50 0.50 18.3 19

1.5 x 1.50 0.21 0.45 0.45 16.6 17

2.0 x 2.00 0.35 0.36 0.36 14.1 15


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12.0

14.0

16.0

18.0

20.0

22.0

24.0

1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

TotalTr

aysinColumn

Rd/Rd min

Trays Required for Separation from

Gilliland correlation

Trays

Effect of Reflux Ratio on Trays in the

Column


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f07_33a


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f07_33a


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f07_33c


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Next Step in FUG

Estimate feed location. Kirkbride developed anequation that estimates the feed tray location.It has dissappeared from a lot of text books. I

found a version of this equation in the lecturenotes of Dr. Randel Price from ChristianBrothers University.

The goal is to match the composition of the

liquid portion of the feed with the liquidcomposition of the feed tray in the column.


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Kirkbride Equation

Nr/Ns = [(XFhk/XFlk)*(XBlk/XDhk)]^2*(B/D)^0.206

Nr = number rectification stages

Ns = number of stripper stages XFhk = fraction heavy key in the feed

XFlk = fraction light key in the feed

XBlk = fraction light key in the bottoms

XBhk = fraction heavy key in the bottoms


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Kirkbride Results

(XFhk/XFlk) 1.25 [(XFhk/XFlk) *

(XBlk/XDhk)^2

*B/D)]^0.206

= 0.2000

(XBlk/XDhk) 0.02 Nr + Ns = 20

B/D 1.29 Nr/Ns 0.20(XBlk/XDhk)^2 = 0.000251 Nr = 3.34

[(XFhk/XFlk) *

(XBlk/XDhk)^2*B/D] = 0.000404

Ns = 16.66


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Pressure Drop in Column

There has to be a pressure drop for the vaporto rise up through the column. A typicalpressure drop is 0.1 psig/tray

This means we will need to adjust our traypressures and make another pass throughFUG.

Top pressure will remain 760 mm Hg. Feedpressure will increases to 790 mm Hg. Bottompressure will increase to 936 mm Hg.

N K S lit


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Non-Key Splits

CPE 523, Lect. 22

Writing a simple mole balance on a non-key gives

Now, if we rearrange the previous equation and include

this, we get

iii bdf

1

and

1

min

min

min

mean,

mean,

mean,

N

HKi

HK

HK

N

HKiHK

HKi

i

N

HKiHK

HK

ii

bd

bd

f

d

bd

fb

What if we use both of these

equations to compute thedistribution of a non-key?

The errors will cause the mole

balance not to close. Instead,

use the smaller one, and

compute the other via the mole

balance above

n C5 btm = 6.4 e-08

n C8 dist = 4.0 e-09

Th O ll Pl


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The Overall Plan

CPE 523, Lect. 22

Just a reminder of the overallcalculation procedure

Currently, we have estimates ofeach of the critical values required to

perform a rigorous simulation. Except

for the pressure drops in the column.

On this first pass we assumed Btm P

of 780 mmHg. With 33 trays the Btm

P will be increasesd to 936 mm Hg.

The number of trays in the rectifyer

increases the feed pressure to 790

mm Hg.

Then we repeat our FUG calculations

and check our results.

FUG R l i h P


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FUG Results with new Pressure

estimate

Pass 1 Pass 2

Plates min 8.66 8.82

Reflux min 1.16 1.22

Plates theo 20 20

Plates real 33 33

Rectifier 5.5 6

Stripper 27.5 28


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Heat Duty

Now the T, Pressure and plate estimates are

stable. We have the information to calculate the

cooling duty on the condenser and the heating

duty on the reboiler. However, we will not do these duty calculations

in this example.

The column parameter we have calculated can beused to perform a rigorous calculation.


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References

McCabe, Smith, Harriott, Unit Operations of Chemical Enginering, 7th

Ed. McGraw-Hill Book Company, New York, 2005.

Dr. Kyle Camarda

McCabe Thiele FUG Algorithm

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