design a distillation column with a total condenser and partial re boiler for the following...
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Design a Distillation Column With a Total Condenser and Partial Re Boiler for the Following SeparationTRANSCRIPT
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Inda kola weri
Design a distillation column with a total condenser and partial re boiler for the following separation .
DATAsystem ethanol-water
Feed rate -150 K mole /hr
Feed composition 28mole % ethanol
98% of ethanol recovery is required??????????????????
Operating pressure: 1 bar
Feed composition: 50% sat liquid and 50% sat vapor
Distillate composition: 82% mole ethanol
Column type: packed column
Packing type: raschig rings
Select a suitable packing material ,packing size ,pressure drop across packing or percentage of flooding and a reflux ratio .obtain an appropriate HETPvalue for HTU from the literature and determine the number of ideal stages required ,the column height and the diameter of the column ,feed tray location and the condenser and reboiler heat loads .
Detail calculation
Graphical constructions data used for the calculation ,
Assumptions made
Reference
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1. Selection of packing material and packing size
Material Heart of the distillation column is begin with the selection of packing material ..In this distillation
column design Raschig types rings are used as packing material .they are usually made up by ceramic or
metal or carbon.
Ceramic packing are resistant to corrosion and comparatively cheap but which are heavy and may require
a stronger packing support and foundations.so ceramic packaging is rejected from the design.Metal,
carbon steel packings are usually the first choice for noncorrosive services. Here in this problem water-
ethanol mixture is separated using packing distillation column which mixture is comparatively low
corrosive .so in this case carbon steel packing is selected which offer higher efficiency , a wider range
geometries , higher turndown are unbreakable , and have a higher compression resistance .
SIZE The size of packing used influences the height and diameter of a column, the pressuredrop and cost of
packing. When packing size is increased, the cost per unitvolume of packing and the pressure drop per
unit height of packing are reduced, but in other side which will reduce the mass transfer efficiency.
Reduced mass transfer efficiency results in a tallercolumn .So for this design 38 mm Size metal Raschig
type ring is selected as a packing material and column diameter is expected to maintain around 0.3 to 0.9
m.
Here the column
Column diameter Use packing size
<0.3 m (1 ft) <25 mm (1 in.)
0.3 to 0.9 m (1 to 3 ft) 25 to 38 mm (1 to 1.5 in.)
>0.9 m 50 to 75 mm (2 to 3 in.)
Figure 1-1: Raschig ring
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Table 1: Raschig Ring data table
Packing method = random type packing
Pressure Drop Pressure drop can be assumed from the [1][3] . it can be assumed as a 0.75 inch water /ft packing . that means which is equal to the 62.5 mm water /m packing .
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HETP value
HETP value for a packing size of 38 mm for full scale plant can be assumed as a 0.66 m .
Calculation
F,XF
D,XD
W,Xw
Figure 0-2 : Volume 6 page no 640
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F - Feed (Kmol/hr)
D – Distillate (kmol/hr)
W – Bottom product (kmol/hr)
X - mole fraction of heptane
G – Upward gas flow rate in rectifying section
G’ – Upward gas flow rate in stripping section
L – Downward liquid flow rate in rectifying section
L’ – Downward liquid flow rate in stripping section
F=Feed rate
X=mole composition of ethanol
D= Top product rate
B=Bottom product rate
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F=150 kmol/hr XF=0.28 XD = 0.82
E
th
a
n
ol
entering rate as feed = 0.28 X 150 Kmol/hr
=42 Kmol/hr
If 98% of ethanol is recovered from the top product
Ethanol mole leaving rate from the distillate = 42 X 0.98 = 41.16 Kmol/hr
Mole composition in the feed= D*XD =41.16
o D=41.16/0.82 = 50.195 Kmol /hr
Mass balance for the system
Figure 0-4 : Distillation Column Diagram
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F=D+B
150=50.195+ B
B=99.805 Kmol/hr
Mass balance for the ethanol
F.XF =D.XD+ B.XB
XB=(42-41.16)/99.805 =0.0084
Water-ethanol equilibrium data can be founded as follow .
Source: :physical property table, mcgraw-hill [1]
By using the ethanol water liquid equilibrium data VLE diagram is drawn .
Table 2: Ethanol-water liquid equilibrium at 1 Bar
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Figure 0-5:VLE of water ethanol
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Assumptions
The lines are made straight by the assumption of constant molar overflow Liquid rate is constant and the vapor rate constant. from tray to tray in each section of the column
between addition (feed) and withdrawal (product) points.
Construction of Q line
q factor=Energy convert 1mol of feed ¿ saturated vapor ¿Molar heat of vaporization
q=0.5/1 q=0.5
equation of Q line
Y= qq−1
− 1q−1
Xf
Y = - X – 2Xf = - X+ 2* 0.28 = -X+0.56
After constructing Q line Minimum reflux ratio is calculated
by connecting the point (Xd ,Xd) and point of intersection between the q-line and the equilibrium
curve. R of this curve is known as the minimum reflux ratio .
R/ (R+1)=0.82−0.410.82−0
Rmin = 1
Ractual = 1.5 * R min [2] = 1.5
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Figure 0-6 : VLE with Minimum Reflux ratio
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Using the value R min Top operating line and Bottom operating line of the Distillation curve is derived .
TOL
Yn+1=( RR+1 )Xn+ 1
R+1Xd
Yn+1= 0.6 .Xn + 0.4* 0.82 = 0.6 Xn + 0.328
By combing the points (Xb,Xb) and intersection point of the q line and TOL BOL is drawn . ( fig3 )
Equation of the BOL
BOL is passed through the points (0.145,0415) and (0.0084,0.0084)
So equation of the line
Y=2.97657x - 0.0166
Equation of bottom line (general formula)
Y=( L'
L'−B )X− BL'−B
X b
L'
L'−B=2.97657, here B = 99.805 Kmol/hr L’=150.29 Kmol/hr
BOL
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BOL
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Number of ideal stage = 33-1 =32stages [from the stair case construction of the graph(in
annex 1) ]
Location of the feed tray = 30 th tray ( ?????? Wite the figure
no )
From the calculated value R =1.5 following can be found
Molar flow rate (Kmol/hr)
F Feed (Kmol/hr) 150
D – Distillate (kmol/hr) 50.195
B– Bottom product (kmol/hr) 99.805
G – Upward gas flow rate in rectifying section 126.3875
G’ – Upward gas flow rate in stripping section 50.485
L – Downward liquid flow rate in rectifying section 76.1925
L’ – Downward liquid flow rate in stripping section 150.29
Here G’=L’-B and G = L+B
F,XF
G
W,Xw
L
D,XD
G’ L’
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Column height
=number of stages * HETP = 32* 0.66 m =21.12 m
Height of the stripping section =
Height of the Rectifying section =29*0.66 = 19.14 m
Calculation of Column Diameter
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In Rectifying section and Stripping section, from stage to stage composition of G and L are varied, so it is
not possible to get Constant Mass flow rate of vapor and Constant Mass flow rate of liquid. So in this
calculation, It is better to Take an average value of the Mass flow rate across the Rectifying Section and
stripping section .
For rectifying section
Molar flow rate (Kmol/hr)
F Feed (Kmol/hr) 150
D – Distillate (kmol/hr) 50.195
G – Upward gas flow rate in rectifying section
126.3875
L – Downward liquid flow rate in rectifying section
76.1925
One stage above the feed tray :
Composition of the ethanol in liquid = 0.24 { Temperature at the 82.5 oC }
Composition of the ethanol in the vapor = 0.47
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At the top stage
Composition of the Ethanol in liquid = 0.82
Composition of the ethanol in vapor = 0.82
Temperature at the top = 78.5oC
Average temperature of the stripping section = (78.5+82.5)/2 =80.5oC
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Molar flow rate (Kmol/hr)
F Feed (Kmol/hr) 150
D – Distillate (kmol/hr) 50.195
G – Upward gas flow rate in rectifying section
126.3875
L – Downward liquid flow rate in rectifying section
76.1925
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Average Molar fraction in the liquid = 0.45
Average Molar fraction in the vapor = 0.64
Density of the liquid at 80.5 o C .
Density of ethanol at temp @ 80.5 = 725.238 Kg/m3
Density of water at temp 80.5 = 961.778 Kg/m3
Mass fraction of ethanol in liquid (w/w) =0.45* 46/(0.55*18+0.45*46)=0.676
Mass of water in liquid (w/w) =1-0.676 =0.324
Volume of the ethanol = 676 /725.238 m3 =0.932
Volume of water = 324/961.778 m3 = 0.3368
Molar mass of mixture = 0.55*18 +0.45*46.05 = 30.625 g/mol
Density of the mixture = (1000)/(0.932+0.3368)*103=788.1Kgm-3
Liquid Flow rate (L*) =76.1925*30.625 = 2333.39 Kg/hr
Density of the vapor @ 80.5 o C
Saturated vapor pressure of ethanol Peo = 829.434 mmHg =110.5 KPa
Saturated vapor pressure of water Pwo = 361.785 mmHg =48.2 KPa
Average Molar fraction of ethanol in the vapor = 0.64
Average molar fraction of the Water in the vapor = 0.36
Average molecular weight of the Water and ethanol in the vapor mixture =
(0.64* molecular mass of ethanol* 0.36 molecular mass of water )
=0.64* 46.04+ 18.01*0.36 =35.9492 Kg/Kmol
Vapor flow rate = G’*35.9492 Kg/hr = 4543 Kg/hr
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By applying Raoult’s Law
PT= XePeo+XwPw
o = 0.64* 110.5 + 48.2* 0.36 = 88.07 KPa
Density of the vapor
By applying Gas Law
Assumption :Compressibility factor of the Water-ethanol vapor is approximately equal to 1 .
PV=nRT
where P = absolute pressure N/m2 (Pa),V = volume m3,n = mols of gasT = absolute temperature, K,R = universal gas constant, 8,314 J K"1 mol"1 (or kJ K"1 kmol"1).
Density =PM/RT = ( 88070*35.94) /(8.314 * 353.5) = 1.074 Kg/m3
Viscosity of the mixture
μmix=¿3
μmix =X1 μ11/3+X2 μ2
1/3
=={(0.45*0.43001/3 +0.55*0.356351/3 }1/3
=0.3888 mPa
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Lw* = average molar mass * molar flow rate = 2333.39 Kg/hr
V*w=average molar mass * molar flow rate = 4543 Kg/hr
76.1925126.38
√1.074 /¿ ¿788.14 =0.02
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For pressure drop 42 , K4 value is equal to 1.9
For pressure Drop 83 , K4 value is equal to the 3.3
For pressure drop 62.5 K4 can be found to be a = 2.6
At flooding K4 is equal to the = 6
So percentage of flooding = √ 2.66
=65.82 % satisfactory
Fp= 270 m3/m2
=
V* =[ 2.6∗1.074∗(788.14−1.074 )13.1∗270∗¿¿
]1/2
V*=1.61Kg/m2s
Column Area required = (mass flow rate of vapor / V*)
=(4543/3600)/1.61) =0.7838m2
= π*d2/4 =0.7838
d=0.99 m
Diameter of the rectifying section =0.99m ~1 m
Packing size to column size ratio = (1/0.038 ) =26.31
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Diameter of the Stripping section .
For Stripping section
Molar flow rate (Kmol/hr)
F Feed (Kmol/hr) 150
B– Bottom product (kmol/hr) 99.805
G’ – Upward gas flow rate in stripping section
50.485
L’ – Downward liquid flow rate in stripping section
150.29
At the feed tray :
Composition of the ethanol in liquid = 0.12 { Temperature at the 358. K =85.5 oC }
Composition of the ethanol in the vapor = 0.47
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At the bottom stage
Composition of the Ethanol in liquid = 0.02
Composition of the ethanol in vapor = 0.15
Temperature at the top = 96.5 oC
Average temperature of the stripping section = (96.5+85.5 )/2 =91oC
Average Molar fraction of ethanol in the liquid = 0.05
Average Molar fraction of ethanol in the vapor = 0.32
Average mass fraction of ethanol liquid =0.05*46/(0.05*46+0.95*18) =0.118
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Density of the liquid at 91 o C .
Density of ethanol at temp @ 91 = 713 Kg/m3
Density of water at temp @91 = 954 Kg/m3
Volume of the ethanol = 118 /713 m3 =0.165
Volume of water = 881/954 Kg/m3 = 0.963
Density of the liquid mixture = 1000/(0.165+0.963) =886.52 Kg/m3
Average molecular weight of the liquid = 19.5 Kg/Kmol
Average mass flow rate of liquid = 19.5 * 150.29 =2930 Kg/hr
Density of the vapor @ 91 o C
Saturated vapor pressure of ethanol Peo = 164 Kpa
Saturated vapor pressure of water Pwo = 361.785 mmHg =72.74 KPa
Average Molar fraction of ethanol in the vapor = 0.32
Average molar fraction of the Water in the vapor = 0.68
Average molecular weight of the Water and ethanol in the vapor mixture =
(0.32* molecular mass of ethanol* 0.68 molecular mass of water )
=0.32* 46.04+ 18.01*0.68 =26.9796 Kg/Kmol
Vapor flow rate = G’*26.9796 Kg/hr = 1362 Kg/hr
By applying Raoult’s Law
PT= XePeo+XwPw
o = 0.32* 164+ 72.74 * 0.68 = 101.94 KPa
Density of the vapor
By applying Gas Law
Assumption :Compressibility factor of the Water-ethanol vapor is approximately equal to 1 .
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PV=nRT
where P = absolute pressure N/m2 (Pa),V = volume m3,n = mols of gasT = absolute temperature, K,R = universal gas constant, 8,314 J K"1 mol"1 (or kJ K"1 kmol"1).
Density =PM/RT = ( 101.94*26.97) /(8.314 * 364) = 0.908 Kg/m3
Viscosity of the liquid mixture at 91 o C
μwater =0.31222 mPa
μethanol = 0.34693
μmix=¿3
μmix =X1 μ11/3+X2 μ2
1/3
=={(0.05 *0.346931/3 +0.95*0.31221/3 }1/3
=0.3138 mPa
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29301362
√0.908/¿886.52¿=0.068
For pressure drop 62.5 K4 can be found to be a = 0.6
At flooding K4 is equal to the = 0.9
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So percentage of flooding = √ 0.60.9
*100 =80 % satisfactory
Fp= 270 m3/m2
=
V* =[ 0.6∗0.908∗(886.52−0.908 )13.1∗270∗¿¿
]1/2
V*=0.77 Kg/m2s
Column Area required = (mass flow rate of vapor / V*)
=(1362/3600)/0.8) =0.4913 m2
= π*d2/4 =0.4913m2
D=0.79 m
Diameter of the rectifying section ~0.8 m
Packing size to column size ratio = (0.8/0.038 ) =20.81
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Feed tray location
It can be assumed as feed is fed into column at 2.5th stage .
So the height of the column = 2.5*HETP = 1.65 m
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Condensor heat loadFlow rate of the vapor stream of the stripping section (G) 126.38 kmol/hr
As we have 82%( mol/mol)ethanol in this stream,
Latent heat of this mixture
Temperature of the distillate product =351 K (vapor molar fraction of 0.82 )
Latent heat of ethanol (@ 1 bar , 351 K )
Normal boiling point of ethanol= 351 K
Latent heat of ethanol at normal boiling point = 39300kJ/Kmol.
Latent heat of water (@ 1 bar , 351 K )
Latent heat of water at boiling point =40860 KJ/Kmol
Critical temperature =647 K
Tb = 373
T=351
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Lv=40860[ 647−351647−373
]0.38
Latent heat of water at 351 K = 42076.925 KJ/Kmol
Lv mixture = 42076KJ/Kmol *.18 + = 39300kJ/Kmol * 82=
Therefore condensor heat load (Qc) = G x λ = 126.3875 Kmol/hr x 39799.68 KJ/Kmol
= 5.03 x 106 kJ/hr
= 5.03 x 106 /3600kJ/s (kW) = 1397 KW
Reboiler heat loadA partial reboiler will be used in the distillation colum here. Therefore, only a part of the liquid leaving
from the bottom of the column will be evaporated again. Actually the part vaporized in the reboiler is
equal to the upwards vapor flow in the stripping section.
Vaporized Mixture flow rate can be found as the 50.485 Kmol/hr
As this liquid stream consists of 97% octane (3% heptane), it is reasonable to assume latent heat of octane
as the overall latent heat of this liquid stream and the molecular weight of octane as the molecular weight
of whole stream.
G’=50.485 Kmol/hr
L’ =150.29 Kmol/hr
B = 99.805 Kmol/hr => Xb=0.02
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Therefore latent heat of the liquid stream leaving the column (λL’) = 298 kJ/kg
Therefore reboiler heat load (QR) = (G’x molecular weight) x λ = 395.15 x 114.2 x 298
= 13.45 x 106 kJ/hr
= 3735 kJ/s (kW)
Reference
[1] http://highered.mcgraw-hill.com/sites/dl/free/0072849606/315014/physical_properties_table.pdf
[2]volume 6
[3]
[4]
[5]
Information
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Annex
Top operating Line calculation (0.81-0.7) 12 stages
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Total=22 stages
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26
Total No of stages 29
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![Page 42: Design a Distillation Column With a Total Condenser and Partial Re Boiler for the Following Separation](https://reader031.vdocuments.mx/reader031/viewer/2022012319/55cf9cc8550346d033ab095d/html5/thumbnails/42.jpg)
30
Stripping section = 3 stages
![Page 43: Design a Distillation Column With a Total Condenser and Partial Re Boiler for the Following Separation](https://reader031.vdocuments.mx/reader031/viewer/2022012319/55cf9cc8550346d033ab095d/html5/thumbnails/43.jpg)