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• janelle ramdahin

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Q.

A 60 mole % methanol, 20 mole % ethanol, 20 mole % i-propanol mix 99 mole % methanol. Assume ideal behavoir of the mixture. The data Reflux ratio (R) = 3, Feed = 100 moles / hr. Calculate number of stage All streams are saturated liquids. Input Data: R= % of lighter fraction in distillate Component MeOH LK EtOH HK I-ProH Total ----------

3 =

Feed

α 60 20 20 100

1.68 1 0.45

L, liquid rate =

180 moles/hr

V, vapour rate =

240 moles/hr

fLK / fHK

=

3

=

F * xLK / F * xHK

=

3

=

( xLK / xHK)Feed

=

3

Design equations used : Rectifying section : Material balance : Equilibrium : Striiping Section: Material balance : Equilibrium :

Calculations for rectifying stages : Stages iteration Component di αi MeoH 59.4 EtoH 0.6

1.68 1

I- Propanol Desired to locate the Feed plate Iteration ChIteration Check for lLK / l Hk = (D

0

0.45

3

Desired to locate the Feed plate Iteration ChIteration Check for lLK / l Hk = (D

3

As the desired l LK / l HK for Stage = So, the Feed stage from the top is =

12

Calculation for the Stripping Section: L' =

280 moles/ hr

V' = V =

240 moles/ hr

Equlibrium equation : Stages iteration Component bi MeoH EtoH I- Propanol Desired to locate the Feed plate Iteration ChIteration Check for lLK / l Hk = (D

Desired to locate the Feed plate Iteration ChIteration Check for lLK / l Hk = (D

αi 0.6 19.4 20 3

3

1.68 1 0.45

Desired to locate the Feed plate Iteration ChIteration Check for lLK / l Hk = (D

3

As the desired l LK / l HK for Stage = So, the Feed stage from the bottom is =

Result : Number of Number of Feed plate Reboiler

plates in enriching section = plates in stripping section = = = Total -----------------------

Lewis Matheson Method

ol, 20 mole % i-propanol mixture is to be fractionated to produce a distillate containing 99% of the methanol in t voir of the mixture. The data required is given below. r. Calculate number of stages.

99% Distillate di xid 59.4 0.6 0 60

Bottoms, bi xib 0.99 0.6 0.01 19.4 0 20 40

0.015 0.485 0.5

L=R*D V = L+D

Vn,i= ln-1,i + di

Material balance :

ln,i= (L(vn,i/α)/ (∑(vn,i/α)))

quilibrium :

Material balance :

l'm+1,i= v'm,i+ bi

quilibrium :

v'mi= V' * ( αi * bi/ ∑αi * bi)

1

vi,1

2 3 vi,1 / α li,1 vi,2 vi,2 / α li,2 vi,3 237.6 141.4286 176.9964243 236.3964 140.7122 175.5054 234.9054 2.4 2.4 3.003575685 3.603576 3.603576 4.494615 5.094615

0 0 240 143.8286

0 180 58.92857143

7

0 0 240 144.3157

0 180 39.04793

0 240

8

9

vi,7 vi,7 / α li,7 vi,8 vi,8 / α li,8 vi,9 224.9529365 133.9006 161.8159471 221.2159 131.6762 157.5281 216.9281 15.04706347 15.04706 18.18405294 18.78405 18.78405 22.47192 23.07192 0 0 0 0 0 0 0 240 148.9476 180 240 150.4602 180 240 8.898783324 7.009997

3.086847 is the

12 Iteration stage

Stage

L' = L + F

vi,n' =

V' * (αi * li,n-1'/∑αi * li,n-1') 1 2 bi * αi vi,1 l,i1' αi * li,1' vi,1' li,2' αi * li,2' 1.008 8.226333 8.826332971 14.82824 15.16925 15.76925 26.49234 19.4 158.3243 177.7242655 177.7243 181.8114 201.2114 201.2114 9 73.4494 93.44940152 42.05223 43.01932 63.01932 28.35869 29.408 240 280 234.6047 240 280 256.0625 0.049663072 0.078372

6

7

li,6' αi * li,6' vi,6' li,7' αi * li,7' 74.76497345 125.6052 96.32621 96.92621 162.836 172.7064892 172.7065 132.4481 151.8481 151.8481 32.52853734 14.63784 11.22572 31.22572 14.05157 280 312.9495 240 280 328.7357 0.432901935 0.63831

11 li,11'

12 αi * li,11' vi,11'

li,12'

αi * li,12'

172.1843297 79.42883487 28.38683545 280 2.167781133

3.052975366 13

stage

11 12 1 1 25 Stages

289.2697 181.9914 182.5914 306.7535 79.42883 49.97193 69.37193 69.37193 12.77408 8.036693 28.03669 12.61651 381.4726 240 280 388.742 2.632064

ning 99% of the methanol in the feed and having a purity of

4 5 vi,3 / α li,3 vi,4 vi,4 / α li,4 vi,5 vi,5 / α li,5 139.8246 173.6721 233.0721 138.7334 171.4389 230.8389 137.4041 168.7491 5.094615 6.327873 6.927873 6.927873 8.561075 9.161075 9.161075 11.25092

0 144.9192

0 180 27.44558

0 0 240 145.6613

0 180 20.0254

10

0 0 240 146.5652

0 180 14.99869

11

vi,9 / α li,9 vi,10 vi,10 / α li,10 vi,11 vi,11 / α li,11 129.1239 152.7131 212.1131 126.2578 147.4356 206.8356 123.1164 141.8021 23.07192 27.28686 27.88686 27.88686 32.56444 33.16444 33.16444 38.19789 0 0 0 0 0 0 0 0 152.1958 180 240 154.1447 180 240 156.2808 180 5.596581 4.527502 3.712302

3 4 5 vi,2' li,3' αi * li,3' vi,3' li,4' αi * li,4' vi,4' li,5' 24.83051 25.43051 42.72325 37.74224 38.34224 64.41497 54.26545 54.86545 188.5897 207.9897 207.9897 183.7406 203.1406 203.1406 171.1329 190.5329 26.57979 46.57979 20.9609 18.51712 38.51712 17.3327 14.60168 34.60168 240 280 271.6739 240 280 284.8883 240 280 0.122268 0.188747 0.287958

8

9

10

vi,7' li,8' αi * li,8' vi,8' li,9' αi * li,9' vi,9' li,10' 118.8817 119.4817 200.7292 139.7977 140.3977 235.8681 157.5716 158.1716 110.8597 130.2597 130.2597 90.71923 110.1192 110.1192 73.56512 92.96512 10.25863 30.25863 13.61638 9.483116 29.48312 13.2674 8.863285 28.86328 240 280 344.6053 240 280 359.2547 240 280 0.917257 1.27496 1.701408

13 vi,12'

li,13'

14 αi * li,13' vi,13'

li,14'

αi * li,14' vi,14'

189.3823 189.9823 319.1703 194.4658 42.82857 62.22857 62.22857 37.91497 7.789133 27.78913 12.50511 7.619184 240 280 393.9039 240 3.05298

195.0658 57.31497 27.61918 280 3.403401

327.7106 197.8858 57.31497 34.60925 12.42863 7.504944 397.4542 240

6 vi,6 vi,6 / α li,6 228.1491 135.803 165.5529 11.85092 11.85092 14.44706

0 0 240 147.6539

12

0 180 11.45928 13

vi,12 vi,12 / α li,12 vi, 13 vi, 13 / α li, 13 201.2021 119.7632 135.9563 195.3563 116.2835 130.0652 38.79789 38.79789 44.04373 44.64373 44.64373 49.93482 0 0 0 0 0 0 240 158.5611 180 240 160.9272 180 3.08685 2.604699

αi * li,5' vi,5' 92.17395 74.16497 190.5329 153.3065 15.57076 12.52854 298.2776 240

αi * li,10' vi,10' 265.7283 171.5843 92.96512 60.02883 12.98848 8.386835 371.6819 240

Q.

Calculate the number of stages using the lewis- Matheson method for separation of a multicomponent mixture, the data of which are given Distillate = 38.5 moles/hr, Bottom 61.5 moles/hr, Feed = 100 moles All streams are saturated liquids. Input Data: R= 1.722 % of lighter fraction in distill = Component Methane Ethane (LK) Propylene (HK) Propane i-Butane n-Butane Total ----------

Feed 5 35 15 20 10 15 100

α 7.356 2.091 1 0.901 0.507 0.408

L, liquid rate =

66.297

moles/hr

V, vapour rate = 104.797 fLK / fHK = F * xLK / F * xHK =

( xLK / xHK)Feed

99% Distillate di 5.005 31.955 0.9625 0.5775 0 0 38.5

moles/hr

=

2.333333

=

2.333333

=

2.333333

Design equations used : Rectifying section : Material balance : Equilibrium : Striiping Section: Material balance : Equilibrium :

Calculations for rectifying stages : Stages iteration

1

Component di Methane 5.005 Ethane (LK) 31.955 Propylene (HK) 0.9625 Propane 0.5775 i-Butane 0 n-Butane 0 Desired to locate the Feed plate Iteration ChIteration Check for lLK / l Hk 2.333333

αi 7.356 2.091 1 0.901 0.507 0.408

vi,1 13.62361 86.98151 2.619925 1.571955 0 0 104.797

7 vi,7 5.8466576691 68.471945802 15.462564224 15.015832305 0 0 104.797

Desired to locate the Feed plate Iteration ChIteration Check for lLK / l Hk 2.333333

As the desired l LK / l HK for Stage = So, the Feed stage from the top is =

6

Stages

Calculation for the Stripping Section: L' =

166.297 moles/ hr

V' = V =

104.797 moles/ hr

Equlibrium equation : Stages iteration Component bi Methane 0 Ethane (LK) 3.075 Propylene (HK) 14.022 Propane 19.434 i-Butane 9.963 n-Butane 15.006 Desired to locate the Feed plate Iteration ChIteration Check for lLK / l Hk 2.333333

vi,n' = αi 7.356 2.091 1 0.901 0.507 0.408

bi * αi 0 6.429825 14.022 17.510034 5.051241 6.122448 49.135548

Desired to locate the Feed plate Iteration ChIteration Check for lLK / l Hk 2.333333

Desired to locate the Feed plate Iteration ChIteration Check for lLK / l Hk 2.333333

As the desired l LK / l HK for Stage =

2.3426206325

So, the Feed stage from the bottom is

7

Result : Number of Number of Feed plate Reboiler

plates in enriching section = plates in stripping section = = = Total -----------------------

5 6 1 1 13

Lewis Matheson Method

wis- Matheson method for the data of which are given below : es/hr, Feed = 100 moles / hr, R = 1.722

xid 0.13 0.83 0.025 0.015 0 0 1

Bottoms, bi 0 3.075 14.022 19.434 9.963 15.006 61.5

xib 0 0.05 0.228 0.316 0.162 0.244 1

L=R*D V = L+D

Vn,i= ln-1,i + di ln,i= (L(vn,i/α)/ (∑(vn,i/α))) l'm+1,i= v'm,i+ bi v'ri= V' * ( αi * bi/ ∑αi * bi)

for reboiler stage

2

3

vi,1 / α 1.852041 41.59804 2.619925 1.744678 0 0 47.81469

li,1 2.567929141 57.67737193 3.632632069 2.419066861 0 0 66.297 15.87757054

vi,2 7.572929 89.63237 4.595132 2.996567 0 0 104.797

vi,2 / α 1.02949 42.86579 4.595132 3.325823 0 0 51.81624

li,2 1.317195 54.84523 5.879305 4.255271 0 0 66.297 9.328522

8 vi,7 / α 0.794815 32.74603 15.46256 16.66574 0 0 65.66915

vi,3 6.322195 86.80023 6.841805 4.832771 0 0 104.797

vi,3 / α li,3 0.859461 1.044035 41.51135 50.42615 6.841805 8.311123 5.363785 6.51569 0 0 0 0 54.5764 66.297 6.067309

9

li,7 vi,8 vi,8 / α li,8 vi,9 vi,9 / α li,9 0.802413891 5.807414 0.78948 0.772326 5.777326 0.78539 0.750256 33.05910791 65.01411 31.09235 30.41679 62.37179 29.82869 28.49435 15.61039922 16.5729 16.5729 16.21281 17.17531 17.17531 16.407 16.82507899 17.40258 19.31474 18.89507 19.47257 21.61218 20.64539 0 0 0 0 0 0 0 0 0 0 0 0 0 0 66.297 104.797 67.76947 66.297 104.797 69.40157 66.297 2.117761849 1.876096 1.736719

2.518399 is the

6 Iteration stages

L' = L + F

V' * (αi * li,n-1'/∑αi * li,n-1') 1 vi,1 l,i1' αi * li,1' 0 0 0 13.71362 16.78862278 35.10501 29.90632 43.92832228 43.92832 37.34565 56.77965112 51.15847 10.77336 20.7363591 10.51333 13.05804 28.06404472 11.45013 104.797 166.297 152.1553 0.382182198

for remaining stages 2 vi,1' li,2' 0 0 24.17859 27.25359 30.25565 44.27765 35.23541 54.66941 7.241063 17.20406 7.886282 22.89228 104.797 166.297 0.615516

3 αi * li,2' 0 56.98726 44.27765 49.25714 8.72246 9.340051 168.5846

vi,2' 0 35.42491 27.52426 30.61965 5.422131 5.806044 104.797

li,3' 0 38.49991 41.54626 50.05365 15.38513 20.81204 166.297 0.926676

stage

Stages

6 li,6' 0 64.2560805 31.31573622 38.20603732 13.52105012 18.99809584 166.297 2.051878329

αi * li,6' 0 134.3595 31.31574 34.42364 6.855172 7.751223 214.7052

vi,6' 0 65.58046 15.28512 16.80208 3.34599 3.783349 104.797

7 li,7' 0 68.65546 29.30712 36.23608 13.30899 18.78935 166.297 2.34262

αi * li,7' 0 143.5586 29.30712 32.64871 6.747658 7.666055 219.9281

vi,7' 0 68.40648 13.96501 15.55729 3.215297 3.652919 104.797

8 li,8' 0 71.48148 27.98701 34.99129 13.1783 18.65892 166.297 2.554095

11 li,11' 0 74.91346692 26.34823262 33.50918453 13.02334717 18.50276875 166.297 2.843206525

αi * li,11' 0 156.6441 26.34823 30.19178 6.602837 7.54913 227.336

vi,11' 0 72.20953 12.14597 13.91776 3.043765 3.479986 104.797

12 li,12' 0 75.28453 26.16797 33.35176 13.00677 18.48599 166.297 2.876973

αi * li,12' 0 157.4199 26.16797 30.04993 6.59443 7.542282 227.7746

vi,12' 0 72.42748 12.03964 13.8257 3.034037 3.470135 104.797

13 li,13' 0 75.50248 26.06164 33.2597 12.99704 18.47614 166.297 2.897073

4

5

6

vi,4 6.049035 82.38115 9.273623 7.09319 0 0 104.797

vi,4 / α 0.822327 39.39797 9.273623 7.872574 0 0 57.36649

li,4 0.950342 45.53123 10.71729 9.098134 0 0 66.297 4.24839

10

vi,5 5.955342 77.48623 11.67979 9.675634 0 0 104.797

vi,5 / α 0.80959 37.05702 11.67979 10.73877 0 0 60.28518

11

4 vi,3' 0 45.99068 23.73493 25.76419 4.456205 4.850996 104.797

li,4' 0 49.06568 37.75693 45.19819 14.41921 19.857 166.297 1.299515

vi,6 5.895325 72.70746 13.80704 12.38718 0 0 104.797

vi,6 / α 0.801431 34.77162 13.80704 13.74825 0 0 63.12834

12

vi,10 vi,10 / α li,10 vi,11 vi,11 / α 5.755256 0.782389 0.734537 5.739537 0.780252 60.44935 28.9093 27.14115 59.09615 28.26215 17.3695 17.3695 16.30715 17.26965 17.26965 21.22289 23.55482 22.11416 22.69166 25.18498 0 0 0 0 0 0 0 0 0 0 104.797 70.61601 66.297 104.797 71.49702 1.664372

αi * li,3' 0 80.50332 41.54626 45.09834 7.800262 8.491314 183.4395

li,5 0.890325 40.75246 12.84454 11.80968 0 0 66.297 3.172747

li,11 0.723504 26.20662 16.01361 23.35326 0 0 66.297 1.636521

vi,12 5.728504 58.16162 16.97611 23.93076 0 0 104.797

vi,12 / α 0.778753 27.81522 16.97611 26.56022 0 0 72.13031

αi * li,5' 0 120.8484 34.15958 37.0796 7.028064 7.885416 207.001

vi,5' 0 61.18108 17.29374 18.77204 3.55805 3.992096 104.797

5 αi * li,4' 0 102.5963 37.75693 40.72357 7.310537 8.101654 196.489

vi,4' 0 54.71953 20.13758 21.71983 3.899059 4.321 104.797

li,5' 0 57.79453 34.15958 41.15383 13.86206 19.327 166.297 1.691898

αi * li,8' 0 149.4678 27.98701 31.52716 6.681397 7.612839 223.2762

vi,8' 0 70.15426 13.13599 14.7976 3.135983 3.573165 104.797

9 li,9' 0 73.22926 27.15799 34.2316 13.09898 18.57917 166.297 2.696416

αi * li,9' 0 153.1224 27.15799 30.84267 6.641184 7.580299 225.3445

vi,9' 0 71.20992 12.62989 14.34346 3.088498 3.525236 104.797

αi * li,13' 0 157.8757 26.06164 29.96699 6.589498 7.538263 228.0321

vi,13' 0 72.55514 11.97718 13.77197 3.028344 3.464369 104.797

14 li,14' 0 75.63014 25.99918 33.20597 12.99134 18.47037 166.297 2.908943

αi * li,14' 0 158.1426 25.99918 29.91858 6.586611 7.535911 228.1829

vi,14' 0 72.62977 11.94058 13.74063 3.025017 3.460999 104.797

10 li,10' 0 74.28492 26.65189 33.77746 13.0515 18.53124 166.297 2.787229

αi * li,10' 0 155.3298 26.65189 30.43349 6.61711 7.560744 226.593

vi,10' 0 71.83847 12.32623 14.07518 3.060347 3.496769 104.797

li,6 0.841658 36.51695 14.50006 14.43833 0 0 66.297 2.5184

li,12 0.715774 25.56575 15.60323 24.41225 0 0 66.297 1.638492

13 vi, 13 5.720774 57.52075 16.56573 24.98975 0 0 104.797

vi, 13 / α li, 13 0.777702 0.710303 27.50873 25.12472 16.56573 15.13008 27.73557 25.3319 0 0 0 0 72.58773 66.297 1.660581