1) VLE curve generation (Assuming ideal behaviour given by raoult' law)Pt 101300 PaFor H2, saturation vapour pressure, Ps exp(9.64596-83.5177/T+1.9804ln(T)) Boiling point of hydrogenFor T2, saturation vapour pressure, Ps exp(15.8148-164.486/T+0.707997ln(T)) Boiling point of tritium

T K Ps,H2(A) Ps,T2(B) Pt x y separation factor

13 4028.491 145.1848 101300 26.04863 #VALUE!15 12596.02 868.1444 101300 8.563518 1.06482 0.12434417 31071.61 3446.31 101300 3.542177 1.086487 0.30672920 89574.25 16505.84 101300 1.160476 1.026148 0.884247

20.3 98127.33 18836.5 101300 1.040013 1.00744 0.9686821 120366.8 25276.9 101300 0.799487 0.949967 1.188221

21.5 138328.7 30836.69 101300 0.655522 0.895137 1.36553522 158134.5 37294.92 101300 0.52967 0.826842 1.561052

22.5 179884.1 44742.12 101300 0.418507 0.743167 1.77575623 203676.5 53271.42 101300 0.319328 0.64205 2.010627

23.5 229610.3 62978.12 101300 0.229979 0.521279 2.26663724 257783.1 73959.23 101300 0.148734 0.37849 2.544749

24.5 288291.2 86313.1 101300 0.074201 0.211169 2.84591625 321230.3 100139 101300 0.005251 0.016652 3.17107926 394776.5 132606 101300 -0.119411 -0.465357 3.89710328 575090.6 219584.1 101300 -0.33272 -1.888887 5.67710330 804332.5 341113.6 101300 -0.517711 -4.110681 7.940103

Average value of separation factor 1.969825

Separation factor (y/(1-y)/(x/(1-x))

Equation for generating VLE data for hydrogen tritium cryogenic distillation 1.9698x/(1+x0.969)

2) To determine the enthalpy concentration diagram (Ponchon Sovariet method)

The enthalpy concentration diagram is needed to determine the no of trays from the tie line.

Q 360 gmoles/day

xF 0.75 m.f of h2 in the feedxD 0.982759 mf of h2 in the distillatexW 0.029412 mf of h2 in the residue

3) Mc cab thiele method to determine the no of trays

Assume reflux ratio values no. stagesR xD Intercept D L=R*D q=1 q=0

0.605 0.982759 0.612311 0.0115 0.006957 kmoles/hr --0.7 0.982759 0.578093 0.0115 0.00805 kmoles/hr 9 --

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

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0.8

1

1.2

Column F

50 wt% H2(A)50 wt% T2(B)F

0.8 0.982759 0.545977 0.0115 0.0092 kmoles/hr 8 --0.908 0.982759 0.515073 0.0115 0.010442 kmoles/hr 8 161.029 0.982759 0.484356 0.0115 0.011833 kmoles/hr 8 11

2 0.982759 0.327586 0.0115 0.023 kmoles/hr 7 74 0.982759 0.196552 0.0115 0.046 kmoles/hr 6 6

q line determination

q=(Hg-Hf)/(Hg-Hl) The quantity q is the heat required to convert 1 mol of feed from its condition Hf to a saturated vapor, divided by the molal latent heat

T x,y diagram

20.321

21.522

22.523

23.524

24.525

Boiling point of hydrogen 20.3 KBoiling point of tritium 25 K

0 0.2 0.4 0.6 0.8 1 1.20

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0.8

1

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Column F

The quantity q is the heat required to convert 1 mol of feed from its condition Hf to a saturated vapor, divided by the molal latent heat

Problem Definition: A system consisting a mixture containning hydrogen (50%) and tritium(50%) at 10 K is to be contimuously rectified at 1 std atmosphere pressure at a rate of 360 gmoles/day to provide a distillate containning 95% hydrogen and a residue containning 1% hydrogen(by weight). The feed gas is to be cooled to cryogenic temperature to bring the gases to its boiling temperature. Liquid helium is emploed to condensehydrogen and tritium to liquid state. The distillate is to be totally condensed into a liquid and the reflux returned at the bubble point.Determine1) VLE data2) quantity of products3) enthalpy of feed and products 4) minimum reflux ratiominimum number of theoretical trayscondensor and reboiler heat loads

360 gmoles/day

xF 0.75 m.f of h2 in the feedxD 0.982759 mf of h2 in the distillatexW 0.029412 mf of h2 in the residue

Material balance

F=D+W Overall balanceFxF=DxD+WxW Component materail balance

D+w 0.0150.01125 DxD+WxW

D 0.0115 kmoles/hrW 0.0035 kmoles/hr

50 wt% H2(A)50 wt% T2(B)F

95% H2 D

1% H2 W

Problem Definition: A system consisting a mixture containning hydrogen (50%) and tritium(50%) at 10 K is to be contimuously rectified at 1 std atmosphere pressure at a rate of 360 gmoles/day to provide a distillate containning 95% hydrogen and a residue containning 1% hydrogen(by weight). The feed gas is to be cooled to cryogenic temperature to bring the gases to its boiling temperature. Liquid helium is emploed to condensehydrogen and tritium to liquid state. The distillate is to be totally condensed into a liquid and the reflux returned at the bubble point.

T x, y daigram at constant pressure and varying temperature References: Treybal & Randell Barron)

x T y T1.040013 20.3 1.00744 20.30.799487 21 0.949967 21 T,x,y diagram for low boiling component0.655522 21.5 0.895137 21.5

0.52967 22 0.826842 220.418507 22.5 0.743167 22.50.319328 23 0.64205 230.229979 23.5 0.521279 23.50.148734 24 0.37849 24 440.074201 24.5 0.211169 24.5 40.005251 25 0.016652 25

References: Treybal & Randell Barron)

T,x,y diagram for low boiling component

4444

Asuppose we have P. we need to calculate t hydrogen

tritiumHYDROGEN

INSERT P= 101325LNP-A=X 1.88012845149651

T 2CLNT 1.37270867638092X-CLNT 0.507419775115593T(X-CLNT) 1.01483955023119VALUE=T(X-CLN 84.5325395502312

Hydrogentritium

system pressure (Pa) 101325T estimate

mole fraction hydrogen T1sat T2sat Tb0.1 20.407 25.04043 24.577111368098 24.32322139180150.2 20.407 25.04043 24.1137971485 23.68012619805350.3 20.407 25.04043 23.650482928902 23.10487754363190.4 20.407 25.04043 23.187168709303 22.59010278605710.5 20.407 25.04043 22.723854489705 22.12858174382970.6 20.407 25.04043 22.260540270107 22.2605402701070.7 20.407 25.04043 21.797226050509 21.79722605050880.8 20.407 25.04043 21.333911830911 21.33391183091060.9 20.407 25.04043 20.870597611312 20.8705976113124

1 20.407 25.04043 20.407283391714 20.4072833917142

Antoines equation form is given as lnP=A-B/(T+clnT)

saturation temperatures at give pressure.

B C HYDROGENTRITIUMlnP=A-(B/T)+ClnT P:Pa T:KA 9.64596 15.8148

B 83.5177 164.486C 1.9804 0.707997

#DIV/0!

PRESSURE 101325 101325 calculating pressureHYDROGEN TRITIUM T P1sat P2sat

LNP-A=X 1.8801284515 -4.288712 277232 81779.78

T saturation at 101325 Pa 20.407283844 25.04045CLNT 5.9726722956 2.280099

goal seek function used here.

X-CLNT -4.092543844 -6.568811T(X-CLNT) -83.51770387 -164.486VALUE=T(X-CLNT)-B -3.86931E-06 2.745E-05

p1sat p2sat LNP-A=X CLNT X-CLNT T(X-CLNT) VALUE=T(X-CLNT)-B277231.955716294 81779.782698 -4.503015 2.259524 -6.762539 -164.4867 -0.000723239496.554053732 66782.111487 -4.705609 2.240553 -6.946162 -164.486 -1.3E-06208935.532803104 55206.200227 -4.895969 2.223142 -7.119111 -164.4862 -0.000188184017.843940782 46196.437373 -5.074142 2.207189 -7.281331 -164.486 -1.79E-05163538.083576775 39111.916423 -5.240618 2.192575 -7.433192 -164.486 -2.27E-06169218.975467487 -515.9632012 Err:502 2.196784 Err:502 Err:502 Err:502149873.635075052 -11955.14851 Err:502 2.181893 Err:502 Err:502 Err:502132162.559305782 -22025.23722 Err:502 2.166682 Err:502 Err:502 Err:502116006.254670358 -30806.29203 Err:502 2.151137 Err:502 Err:502 Err:502101325.005579187 #DIV/0! #DIV/0! 2.135242 #DIV/0! #DIV/0! #DIV/0!

tritium because T optimised using p2sat (same goal seek function

lnP=A-(B/T)+ClnT P:Pa T:K

calculating pressure

saturation temperature of hydrogen at 101325 Pa 20.4072 Ksaturation temperature of tritium at 101325 Pa 25.04045 K pressure temperature equation is

hydrogenhence Tx-y diagram is as follows tritium

T P1sat P2sat P x1 y120.4072 101322.49109 19729.002875 101325 1.0000307489 1.0000059871 pure hydrogen

20.5 104148.73474 20527.986743 101325 0.9662316493 0.993158684920.8 113675.91824 23284.81803 101325 0.8633613463 0.9685999883

21 120366.78508 25276.896752 101325 0.7997496326 0.950044827421.2 127336.66828 27398.679279 101325 0.7397219162 0.929619780521.4 134591.98132 29655.708054 101325 0.6829791998 0.90721464321.6 142139.13136 32053.608834 101325 0.6292506914 0.882715486721.8 149984.51707 34598.086467 101325 0.5782908197 0.8560046318

22 158134.52657 37294.92063 101325 0.5298765986 0.826960622322.2 166595.53545 40149.96152 101325 0.4838052972 0.795458204322.4 175373.90488 43169.12552 101325 0.4398923758 0.761368306622.6 184475.97978 46358.390845 101325 0.3979696546 0.724558025622.8 193908.08709 49723.793181 101325 0.3578836878 0.6848906123

23 203676.53413 53271.421321 101325 0.3194943163 0.642225462723.2 213787.60702 57007.412815 101325 0.2826733785 0.596418111723.4 224247.56917 60937.949633 101325 0.2473035604 0.547320229723.6 235062.65986 65069.253858 101325 0.2132773676 0.494779623223.8 246239.09287 69407.583404 101325 0.1804962062 0.4386402377

24 257783.05523 73959.22778 101325 0.1488695595 0.378742165124.2 269700.70594 78730.503896 101325 0.1183142494 0.314921653824.4 281998.17488 83727.751923 101325 0.0887537728 0.247011122124.6 294681.56166 88957.331209 101325 0.0601177059 0.174839175624.8 307756.93465 94425.616251 101325 0.0323411668 0.0982306277

25 321230.32994 100138.99275 101325 0.0053643316 0.017006523825.04045 324004.25106 101324.89123 101325 4.88445E-07 1.561888E-06 pure tritium

pressure temperature equation is A B CP=exp(A-B/t+Cln t) 9.64596 83.5177 1.980400

15.8148 164.486 0.707997

y1.0000310.9662320.863361

0.799750.7397220.6829790.6292510.5782910.5298770.4838050.439892

0.397970.3578840.3194940.2826730.2473040.2132770.180496

0.148870.1183140.0887540.0601180.0323410.005364

4.884E-07 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

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y-x plot45 line

x

y

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y-x plot45 line

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y-x plot45 lineq liner 0.6R0.8R 1R 1.1r 1.2R 1.3R 1.4R 1.5R 1.6R 1.8R 2R 3R 4

x

y

preparing q line for q=1 0.75 0.8 0.85 0.9 0.950.75 0.75 0.75 0.75 0.75

x 0 0.982R xD intercept y

0.6 0.982 0.61375 0.61375 0.9820.7 0.982 0.577647 0.577647 0.9820.8 0.982 0.545556 0.545556 0.9820.9 0.982 0.516842 0.516842 0.982

1 0.982 0.491 0.491 0.9821.1 0.982 0.467619 0.467619 0.982

1.15 0.982 0.456744 0.456744 0.9821.2 0.982 0.446364 0.446364 0.982

1.25 0.982 0.436444 0.436444 0.9821.3 0.982 0.426957 0.426957 0.982

1.35 0.982 0.417872 0.417872 0.9821.4 0.982 0.409167 0.409167 0.982

1.45 0.982 0.400816 0.400816 0.9821.5 0.982 0.3928 0.3928 0.982

1.55 0.982 0.385098 0.385098 0.9821.6 0.982 0.377692 0.377692 0.9821.8 0.982 0.350714 0.350714 0.982

2 0.982 0.327333 0.327333 0.9823 0.982 0.2455 0.2455 0.9824 0.982 0.1964 0.1964 0.982

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

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y-x plot45 lineq liner 0.6R0.8R 1R 1.1r 1.2R 1.3R 1.4R 1.5R 1.6R 1.8R 2R 3R 4

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10.75

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y-x plot45 lineq liner 0.6R0.8R 1R 1.1r 1.2R 1.3R 1.4R 1.5R 1.6R 1.8R 2R 3R 4

x

y

preparing q line for q=0 0.750.75

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10

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y-x plot45 lineq liner 0.6R0.8R 1R 1.1r 1.2R 1.3R 1.4R 1.5R 1.6R 1.8R 2R 3R 4

x

y

00.75 0.75 0.75 0.75 0.75