mccabe thiele fug algorithm
TRANSCRIPT
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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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Gilliland Correlation
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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Gilliland Correlation
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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Gilliland Correlation
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