Feed Compositions
Mass flow rate | Molar flow rate | Mole fractions | |
H2CH4 C2H2 C2H4C2H6 C3H4 C3H6 C3H8 | 101.04 1894.5 101.04 3953.19 429.42 151.56 1528.28 50.52 | 50.52 118.40 3.88 141.18 14.3 3.78 36.38 1.148 | 0.136 0.32 0.01 0.381 0.038 0.01 0.098 0.003 |
Top Compositions
Mass flow rate | Molar flow rate | Mole fractions | |
H2CH4C2H4 | 101.041875.07 37.84 | 50.50117.19 1.35 | 0.290.69 0.0079 |
Bottom Compositions
Mass flow rate | Molar flow rate | Mole fractions | |
CH4 C2H2 C2H4C2H6 C3H4 C3H6 C3H8 | 9.43 101.04 3915.35 429.42 151.56 1528.23 50.52 | 1.21 3.60 139.38 14.314 3.789 36.38 1.148 | 0.006 0.017 0.698 0.071 0.0189 0.181 0.005 |
Let top temperature is 172k
Mole fractions | K | X/k | |
H2CH4C2H4 | 0.290.69 0.0079 | 0.00 0.75 0.1 | 0.00 0.92 0.079 |
1.00 |
So top temperature is 172 k
Let bottom temperature is T=280k
Mole fractions | k | kx | |
CH4 C2H2 C2H4C2H6 C3H4 C3H6 C3H8 | 0.006 0.017 0.698 0.071 0.0189 0.181 0.005 | 4.01 1.53 1.21 0.84 0.34 0.30 0.26 | 0.02 0.026 0.851 0.063 0.006 0.05 0.0013 |
1.00 |
So bottom temperature is 280k
To find feed condition
Let T=218k
Mole fractions | k | kx | |
H2CH4 C2H2 C2H4C2H6 C3H4 C3H6 C3H8 | 0.136 0.32 0.01 0.381 0.038 0.01 0.098 0.003 | 2.40 0.612 0.55 0.356 0.136 0.12 0.104 | 0.768 0.006 0.209 0.013 0.001 0.011 0.0003 |
1.00 |
This temperature is very close to feed temperature which is 215k
So feed is at its boiling point
Pinch temperatures
Upper pinch =Top temperature+1/3(bottom temperature -top temperature)
Upper pinch=208k
Bottom pinch=Top temperature+2/3(bottom temperature-top temperature)
Bottom pinch=244k
Rm using gilliand method
Rm=1/(µab-1)[xda/xna -µabxdb/xnb]
µab=7.1
xda=0.69
xdb=0.0079
xna=rf/(1+ rf)(1+åµxfh)
µ | µxfh | |
H2CH4 C2H2 C2H4C2H6 C3H4 C3H6 C3H8 | 7.1 1.29 1.00 0.71 0.45 0.429 0.105 | 0.026 0.0045 0.042 0.0003 |
0.0728 |
Rf=0.32/0.381
Rf=0.839
Xna=0.468
Xnb=0.558
Rm=1/7.1-[0.69/0.468-7.1(.0079/0.558)]
Rm=0.163
No of stages at total reflux using fenske’s equation
N+1=log[(xa/xb)d(xb/xa)]/logµab
N+1=5
N=4
Theoratical no of stages using Gilliand relation
R | R-Rm/R+1 | N-Nm/n+2 | N |
0.2 0.4 0.6 0.8 1.0 2.0 5.0 | 0.0308 0.169 0.273 0.358 0.418 0.612 0.806 | 0.7 0.48 0.46 0.385 0.30 0.19 0.1 | 18 9.46 8.0 7.75 6.57 5.40 4.60 |
As we observe that there is slight change in no. of plates after R=0.4
So 9 theoratical plates is optimum answer
Reflux ratio=0.4
No. of theoratical plates(N)=9
R=Ln/D
Ln=805.58Kg/hr
Vn=Ln+D
Vn=2819.53 Kg/hr
Lm=Ln+F
Lm=9015.13 Kg/hr
Vm=Lm-W
Vm=2829.58 Kg/hr
Finding Densities
For top
For liquid phase
For CH4 and C2H4
Density=PM/Tc(0.0653/zc0.773 –0.09T)]
For H2
Density=PM/RT
Mole fractions | Density | Mole fractions*Density | |
H2CH4C2H4 | 0.290.69 0.0079 | 0.005 0.34 0.624 | 0.0014 0.2346 0.0049 |
0.240 |
Avg Density=0.240g/cm3
Avg Density=240kg/ m3
For gaseous phase
P=35atm
T=172k
M=15.46
R=82.05atm. cm3/g-mol.k
Vap.density=PM/RT
Vap.density=0.0323g/ cm3
=32.3kg/ m3
For Bottom
Density of liquid phase
Density=PM/Tc(0.0653/zc0.773 –0.09T)]
Mole fractions | Density | Mole fractions*density | |
CH4 C2H2 C2H4C2H6 C3H4 C3H6 C3H8 | 0.006 0.017 0.698 0.071 0.0189 0.181 0.005 | 0.006 0.017 0.698 0.071 0.0189 0.181 0.005 | 0.000867 0.0084 0.332 0.028 0.011 0.097 0.0025 |
0.479g/ cm3 |
Avg.density=0.479g/ cm3
Avg.density=479kg/ cm3
For vapor phase
Vap.density=0.047g/ cm3
Vap.density=47kg/ m3
Column area and diameter
At Top
Flooding vapor velocity uf=K1[(rl-rg)/ rg]1/2
FLV=Lw/Vw[rg/rl]
FLV=0.114
Plate spacing=0.45m
K1=0.02
Vapor velocity=0.045m/s
Assume 80% flooding
Vapor velocity=0.80*0.045=0.036
Volumetric vapor flow rate=2819.53/38.3*3600
Volumetric vapor flow rate=0.0204
Net area required=0.566m2
At bottom
FLV=1.002
Plate spacing=0.45m
K1=0.0125
Flooding vapor velocity uf=0.037
Assume 80% flooding
Vapor velocity=0.80*0.037=0.0296
Volumetric vapor flow rate=2829.53/47*3600
Volumetric vapor flow rate=0.0167
Net area required=0.0167/0.0296
Net area required=0.60m2
As there is no appreciable difference in column areas of top and bottom
So
Net column area=0.60m2
Take downcomer area 15%of net area
Column cross sectional area=0.69m2
Column Diameter=[A*4/P]
Column Diameter=0.827m
Liquid flow patterns
Maximum volumetric liquid rate=9015.13/479*3600
Maximum volumetric liquid rate=5.22*10-3
A single pass plate can be used
Plate design data
Column Diameter Dc=0.878m
Column AreaAc=0.69m2
Down comer Area=0.09m2
Net Area An=0.60m2
Active Area Aa=Ac-2Ad
Active Area Aa=0.51m2
Hole Area Ah=0.051m2(take hole area 10% of active area)
(Ad/Ac)*100=13.04
From graph
Lw/Dc=0.76
Weir length lw=0.76*0.878
lw=0.667
Weir height=50mm
Hole diameter=5mm
Plate thickness=5mm
Check weeping
For Top
Maximum liquid rate=805.58/3600=0.318
Minimum liquid rate,at 70% turn down=0.7*0.318=0.223Kg/sec
Minimum how=750[Lw/rl*lw]
Minimum how=1.044mm
how+hw=50+1.044
how+hw=51mm
From graph
K2=30
Uh min=[K2-0.90(25.4-dh)]/ (rv)1/2
Uh min=1.880m/sec
Actual min. vapor velocity=0.783*0.7/0.051=10.74m/sec
Actual min vapor velocity is quite large than min velocity for flooding
For bottom
Maximum liquid rate=9015.13/3600=3.57
Minimum liquid rate,at 70% turn down=0.7*3.57=2.50Kg/sec
Minimum how=750[Lw/rl*lw]
Minimum how=30mm
how+hw=50+30
how+hw=80mm
From graph
K2=30.8
Uh min=[K2-0.90(25.4-dh)]/ (rv)1/2
Uh min=4.33m/sec
Actual min. vapor velocity=0.793*0.7/0.051=10.77m/sec
Actual min vapor velocity is quite large than min velocity for flooding
Plate pressure drop
For Top
Max vapor velocity through holes=0.783/0.051=15.68m/s
Plate thickness/Hole dia=1
Ah/Aa=0.1
From graph
Co=0.84
hd=51(uh/Co)2rv/rl
hd=140.32mm
hr=12.5*103/rl
hr=52mm
ht=hd+(hw+how)+hr
ht=243mm
For bottom
Max vapor velocity through holes=0.793/0.051=15.78m/s
Plate thickness/Hole dia=1
Ah/Aa=0.1
From graph
Co=0.84
hd=51(uh/Co)2rv/rl
hd=110.32mm
hr=12.5*103/rl
hr=26mm
ht=hd+(hw+how)+hr
ht=216mm of liquid
Downcomer liquid back up
For Top
Hap=hw-10=40mm
Area under apron Aap= Haplw
Area under apron Aap=0.026m2
As it is less than Ad=0.09m2
Use Aap in equation
hdc=166[Lwd/rlAap]2
hdc=6mm
Backup in down comer
hb= hdc+(hw+how)+ht
hb=0.30m
0.30<1/2(plate spacing+weir height)
0.30<0.32
Residance time
tr=Adhbcrl/lwd
For bottom
Hap=hw-10=40mm
Area under apron Aap= Haplw
Area under apron Aap=0.026m2
As it is less than Ad=0.09m2
Use Aap in equation
hdc=166[Lwd/rlAap]2
hdc=7mm
Backup in down comer
hb= hdc+(hw+how)+ht
hb=79+216+7=302mm
hb=0.31m
0.31<1/2(plate spacing+weir height)
0.301 <0.32
so tray spacing is acceptable
Residance time
tr=Adhbcrl/lwd
Check Entrainment
Uv=0.783/0.60=1.305
%age flooding=1.305/0.045
%age flooding=30
Flv=0.114
Y=0.02
So thats satisfactory
No. of holes per tray
Area of one hole=1.964*10-5m2
No. of holes=0.051/1.964*10-5
No. of holes=2596
Overall Efficiancy Calculations
Mole fractions | m | Mole fractions*m | |
H2CH4 C2H2 C2H4C2H6 C3H4 C3H6 C3H8 | 0.136 0.32 0.01 0.381 0.038 0.01 0.098 0.003 | 0.0075 0.008 0.0082 0.0085 0.0095 0.012 0.15 0.22 | 0.0012 0.00256 0.000082 0.00323 0.000361 0.000012 0.0147 0.000066 |
0.022 |
Eo=0.492[m(aLK/Hk)av]-0.245
Eo=0.492[0.02(7.1)]-0.245
Log Eo=-0.09
Eo=75
Actual no of plates=9/0.75
Actual no of plates=12
Location of feed
Log NA/NB=0.206 log {(B/D) (x HK /x LK) [(x LK) B/(x HK)] 2}
Log NA/NB=0.206 log {200.27/169.06 (0.381/0.32) (0.006/0.0079)2}
NA/NB=0.995
NA+NB=11
NA=6, NB=5
Feed enters the column 6 theoretical stages above the bottom stage
As far as I know Gilliland's correlation is valid for the relative volatility values of 1.1 to 4.05. Although the average volatility of the methane is 10 while ethylene is heavy key, you applied Gilliland's correlation. Is there a reference stating the applicability of Gilliland's correlation in this case?
ReplyDeleteHow did you arrive at 7.1 for the relative volatility ?
ReplyDeletehow did you find the k values at such low temps?
ReplyDeleteif i have to design a demethanizer by an external reflux and the pressure of entering feed streams are so different i.e of one is 30 bar and other is of 60 bar...so I have to use valve to enter the feed streams at same pressure or not?
ReplyDeleteif there are two side reboilers with two feed streams and one external reflux then which method should be use
ReplyDeleteNo references or workings? Very hard to understand
ReplyDelete