Distillation
DESIGN CONSIDERATIONS * System: Ethanol – water * Feed rate: 225kmol/h * Feed composition: 28 mol% ethanol * Feed condition: 50% saturated liquid & 50% saturated vapor * 97% of ethanol recovery is required * Operating pressure: 1bar * Distillate composition: 81 mol% ethanol * Column type: Sieve tray column * Operating condition: 70% of flooding
Applying material balance to the rectifying section (Eqn 01);
V=L+D
Applying material balance for the more volatile component - C2H5OH (Eqn 02);
V×yn+1=L×xn+D×xD
From equation 01 & 02;
L+D×yn+1=L×xn+D×xD
yn+1=LL+D×xn+DL+D×xD
D, xD
W, xW
F, xF
D, xD
W, xW
F, xF
yn+1=LDLD+1×xn+1LD+1×xD
Therefore, equation for Top Operating Line (TOL); yn+1=RR+1×xn+1R+1×xD Applying overall material balance for the column;
F=D+W
225=D+W
Applying material balance for ethanol (MVC);
225×0.28=D×0.81+W×xw
Since 97% of ethanol recovery is desired;
D×0.81=225×0.28×0.97
D=75.4444 kmol/h
Therefore,
W=225-75.4444
W=149.5556 kmol/h
225×0.28=75.4444×0.81+149.5556 ×xw xw=0.0126 Equation for the q-line is given by; yq=qq-1xq-xFq-1 Since the feed is 50% saturated liquid & 50% saturated vapor, q=0.5
Therefore;
yq=0.50.5-1xq-0.280.5-1 yq=-xq+0.56 Under the minimum reflux ration condition, TOL and q-line intersect on the equilibrium curve. Therefore, q- line is plotted on the Ethanol – water equilibrium curve, through the point xF,xF≡0.28, 0.28 with an intercept of +0.56.
Top Operating Line for the minimum reflux ratio is plotted through the point xD,xD≡0.81, 0.81 and the point of intersects of q-line with equilibrium curve. Under this condition, intercept of top Operating Line (+0.4) gives the value of1Rmin+1×0.81.
Therefore, by solving 1Rmin+1×0.81=0.4
Rmin=1.025
In general practice, reflux ratio (R) is maintained such that, 1.2Rmin<R<1.5Rmin
Therefore, let’s estimate operating reflux ratio R=1.5Rmin=1.5×1.025=1.5375
So the intercept of Top operating Line under R=1.5375 is given by, 11.5375+1×0.81=0.3192
Top Operating Line is created by plotting a straight line through xD,xD≡0.81, 0.81 with an intercept of +0.32.
Then the operating line for the stripping section can be plotted as a straight line passing through the point of intersect of q-line and the TOL and the point xw,xw≡0.01, 0.01
By preparing the equilibrium stages on the graph, number of equilibrium stages was found to be 19. Since a partial re-boiler is used, it also acts as a theoretical plate; therefore the number of ideal stages required in the column is 19-1=18.
Feed tray location is 17th tray from the top.
OVERALL COLUMN EFFICIENCY
O’Connell’s Correlation
A quick estimate of the overall column efficiency can be obtained from the correlation given by O’Connell (1946). The overall column efficiency is correlated with the product of the relative volatility of the light key component (relative to the heavy key) and the molar average viscosity of the feed, estimated at the average column temperature. The correlation was based mainly on data obtained with hydrocarbon systems, but includes some values for chlorinated solvents and water-alcohol mixtures. It has been found to give reliable estimates of the overall column efficiency for hydrocarbon systems; and can be used to make an approximate estimate of the efficiency for other systems. The method takes no account of the plate design parameters; and includes only two physical property variables.
Eduljee (1958) has expressed the O’Connell correlation in the form of an equation:
Eo=51-32.5logμaαa
µa: the molar average liquid viscosity of the feed, mNs/m2 αa: average relative volatility of the light key
Average column temperature was assumed based on the following data.
Conditions of the top plate = 81% ethanol & 19% water Mole fraction of Ethanol | Temperature (oC) | 0.0000 | 99.65 | 0.0526 | 97.91 | 0.1053 | 96.28 | 0.1579 | 94.74 | 0.2105 | 93.29 | 0.2632 | 91.91 | 0.3158 | 90.61 | 0.3684 | 89.37 | 0.4211 | 88.18 | 0.4737 | 87.05 | 0.5263 | 85.97 | 0.5789 | 84.94 | 0.6316 | 83.95 | 0.6842 | 83.00 | 0.7368 | 82.08 | 0.7895 | 81.20 | 0.8421 | 80.35 | 0.8947 | 79.53 | 0.9474 | 78.74 | 1.0000 | 77.98 |
Mole fraction of Ethanol | Temperature (oC) | 0.0000 | 99.65 | 0.0526 | 97.91 | 0.1053 | 96.28 | 0.1579 | 94.74 | 0.2105 | 93.29 | 0.2632 | 91.91 | 0.3158 | 90.61 | 0.3684 | 89.37 | 0.4211 | 88.18 | 0.4737 | 87.05 | 0.5263 | 85.97 | 0.5789 | 84.94 | 0.6316 | 83.95 | 0.6842 | 83.00 | 0.7368 | 82.08 | 0.7895 | 81.20 | 0.8421 | 80.35 | 0.8947 | 79.53 | 0.9474 | 78.74 | 1.0000 | 77.98 |
Conditions of bottom plate = 1.26% ethanol & 98.74% water
By interpolating;
Temperature of the top plate = 80.76oC where the mole fraction of ethanol is 81%
Temperature of the bottom plate = 97.69oC where the mole fraction of ethanol is 1.26%
Therefore;
Average column temperature can be approximated as 97.69+80.762=89.21oC.
Temperature (oC) | Viscosity of ethanol (Pa.s) | 60.00 | 5.8357E-04 | 62.63 | 5.5938E-04 | 65.26 | 5.3645E-04 | 67.89 | 5.1470E-04 | 70.53 | 4.9405E-04 | 73.16 | 4.7445E-04 | 75.79 | 4.5582E-04 | 78.42 | 4.3811E-04 | 81.05 | 4.2126E-04 | 83.68 | 4.0523E-04 | 86.32 | 3.8997E-04 | 88.95 | 3.7543E-04 | 91.58 | 3.6157E-04 | 94.21 | 3.4836E-04 | 96.84 | 3.3575E-04 | 99.47 | 3.2372E-04 | 102.11 | 3.1224E-04 | 104.74 | 3.0127E-04 | 107.37 | 2.9078E-04 | 110.00 | 2.8076E-04 |
Temperature (oC) | Viscosity of ethanol (Pa.s) | 60.00 | 5.8357E-04 | 62.63 | 5.5938E-04 | 65.26 | 5.3645E-04 | 67.89 | 5.1470E-04 | 70.53 | 4.9405E-04 | 73.16 | 4.7445E-04 | 75.79 | 4.5582E-04 | 78.42 | 4.3811E-04 | 81.05 | 4.2126E-04 | 83.68 | 4.0523E-04 | 86.32 | 3.8997E-04 | 88.95 | 3.7543E-04 | 91.58 | 3.6157E-04 | 94.21 | 3.4836E-04 | 96.84 | 3.3575E-04 | 99.47 | 3.2372E-04 | 102.11 | 3.1224E-04 | 104.74 | 3.0127E-04 | 107.37 | 2.9078E-04 | 110.00 | 2.8076E-04 |
Temperature (oC) | Viscosity of water (Pa.s) | 60.00 | 4.7420E-04 | 62.63 | 4.5513E-04 | 65.26 | 4.3725E-04 | 67.89 | 4.2049E-04 | 70.53 | 4.0474E-04 | 73.16 | 3.8994E-04 | 75.79 | 3.7602E-04 | 78.42 | 3.6290E-04 | 81.05 | 3.5054E-04 | 83.68 | 3.3888E-04 | 86.32 | 3.2787E-04 | 88.95 | 3.1747E-04 | 91.58 | 3.0762E-04 | 94.21 | 2.9831E-04 | 96.84 | 2.8948E-04 | 99.47 | 2.8112E-04 | 102.11 | 2.7318E-04 | 104.74 | 2.6564E-04 | 107.37 | 2.5848E-04 | 110.00 | 2.5168E-04 |
Temperature (oC) | Viscosity of water (Pa.s) | 60.00 | 4.7420E-04 | 62.63 | 4.5513E-04 | 65.26 | 4.3725E-04 | 67.89 | 4.2049E-04 | 70.53 | 4.0474E-04 | 73.16 | 3.8994E-04 | 75.79 | 3.7602E-04 | 78.42 | 3.6290E-04 | 81.05 | 3.5054E-04 | 83.68 | 3.3888E-04 | 86.32 | 3.2787E-04 | 88.95 | 3.1747E-04 | 91.58 | 3.0762E-04 | 94.21 | 2.9831E-04 | 96.84 | 2.8948E-04 | 99.47 | 2.8112E-04 | 102.11 | 2.7318E-04 | 104.74 | 2.6564E-04 | 107.37 | 2.5848E-04 | 110.00 | 2.5168E-04 |
By interpolating to the temperature of 89.21oC; viscosity of water is 3.4316E-04 Pa.s and viscosity of ethanol is 3.6474E-04 Pa.s
Molar average liquid viscosity of the feed is given by;
0.28×3.6474×10-4+0.72×3.4316×10-4=3.4920×10-4Pa.s
Relative volatility αE,W=KEthanolKWater=pEthanolopsyspWateropsys=1.70380.7692=2.2150
Eo=51-32.5log3.4920×10-4×103×2.2150=54.6254%
But, Column efficiency Eo=Number of ideal stagesNumber of actual stages×100%
Therefore; Number of actual stages=19-10.546254=33
TRAY SPACING
A reasonable value must be selected considering construction, maintenance and cost.
Typical range is 0.15m to 0.9m.
In this design, tray spacing is considered as 0.6m.
Therefore; Column height=33×0.6=19.8m
FLOODING VAPOR VELOCITY Uf
The liquid-vapor flow factor FLV is given by;
FLV=LwVwρvρL
Lw - liquid mass flow-rate, kg/s
Vw - vapor mass flow-rate, kg/s
Assumptions I. Liquid and vapor mass flow rates throughout the rectifying section and stripping section remains constant (L, V & L’, V’). II. Liquid and vapor densities throughout the rectifying section remain constant and equals to that of the top plate. III. Liquid and vapor densities throughout the stripping section remain constant and equals to that of the bottom plate. IV. Assume that the molecular weight of the vapor & liquid is same as ethanol (46g/mol) for rectifying section and similar to water (18g/mol) for stripping section
Reflux ratio R=LD
Therefore; L=R×D=1.5375 ×75.4444=115.9958kmol/h
By applying material balance for the feed tray and since the feed is 50% saturated liquid and 50% saturated vapor,
L'=L+0.5F
L'=115.9958+0.5×225=228.4958 kmol/h
Applying material balance for the total condenser;
V=D+L
V=75.4444+115.9958=191.4402 kmol/h
Applying material balance for the partial re-boiler;
L'=V'+W
V'=228.4958-149.5556=78.9402 kmol/h Density of Water at 1bar | Temperature(oC) | Liquid(kg/m3) | Vapor(kg/m3) | 60.00 | 979.6811 | 0.6504 | 62.63 | 978.3650 | 0.6453 | 65.26 | 977.0220 | 0.6403 | 67.89 | 975.6517 | 0.6353 | 70.53 | 974.2542 | 0.6305 | 73.16 | 972.8291 | 0.6257 | 75.79 | 971.3763 | 0.6210 | 78.42 | 969.8956 | 0.6163 | 81.05 | 968.3869 | 0.6117 | 83.68 | 966.8500 | 0.6072 | 86.32 | 965.2846 | 0.6028 | 88.95 | 963.6905 | 0.5984 | 91.58 | 962.0676 | 0.5941 | 94.21 | 960.4157 | 0.5898 | 96.84 | 958.7346 | 0.5856 | 99.47 | 957.0240 | 0.5815 | 102.11 | 955.2837 | 0.5774 | 104.74 | 953.5135 | 0.5734 | 107.37 | 951.7132 | 0.5694 | 110.00 | 949.8826 | 0.5655 |
Density of Water at 1bar | Temperature(oC) | Liquid(kg/m3) | Vapor(kg/m3) | 60.00 | 979.6811 | 0.6504 | 62.63 | 978.3650 | 0.6453 | 65.26 | 977.0220 | 0.6403 | 67.89 | 975.6517 | 0.6353 | 70.53 | 974.2542 | 0.6305 | 73.16 | 972.8291 | 0.6257 | 75.79 | 971.3763 | 0.6210 | 78.42 | 969.8956 | 0.6163 | 81.05 | 968.3869 | 0.6117 | 83.68 | 966.8500 | 0.6072 | 86.32 | 965.2846 | 0.6028 | 88.95 | 963.6905 | 0.5984 | 91.58 | 962.0676 | 0.5941 | 94.21 | 960.4157 | 0.5898 | 96.84 | 958.7346 | 0.5856 | 99.47 | 957.0240 | 0.5815 | 102.11 | 955.2837 | 0.5774 | 104.74 | 953.5135 | 0.5734 | 107.37 | 951.7132 | 0.5694 | 110.00 | 949.8826 | 0.5655 |
Density of Ethanol at 1bar | Temperature(oC) | Liquid(kg/m3) | Vapor(kg/m3) | 60.00 | 753.2286 | 1.6632 | 62.63 | 750.6419 | 1.6502 | 65.26 | 748.0347 | 1.6373 | 67.89 | 745.4065 | 1.6247 | 70.53 | 742.7568 | 1.6123 | 73.16 | 740.0851 | 1.6000 | 75.79 | 737.3908 | 1.5879 | 78.42 | 734.6732 | 1.5760 | 81.05 | 731.9318 | 1.5643 | 83.68 | 729.1659 | 1.5528 | 86.32 | 726.3749 | 1.5414 | 88.95 | 723.5580 | 1.5302 | 91.58 | 720.7145 | 1.5192 | 94.21 | 717.8436 | 1.5083 | 96.84 | 714.9446 | 1.4976 | 99.47 | 712.0165 | 1.4870 | 102.11 | 709.0585 | 1.4766 | 104.74 | 706.0696 | 1.4663 | 107.37 | 703.0489 | 1.4562 | 110.00 | 699.9954 | 1.4461 |
Density of Ethanol at 1bar | Temperature(oC) | Liquid(kg/m3) | Vapor(kg/m3) | 60.00 | 753.2286 | 1.6632 | 62.63 | 750.6419 | 1.6502 | 65.26 | 748.0347 | 1.6373 | 67.89 | 745.4065 | 1.6247 | 70.53 | 742.7568 | 1.6123 | 73.16 | 740.0851 | 1.6000 | 75.79 | 737.3908 | 1.5879 | 78.42 | 734.6732 | 1.5760 | 81.05 | 731.9318 | 1.5643 | 83.68 | 729.1659 | 1.5528 | 86.32 | 726.3749 | 1.5414 | 88.95 | 723.5580 | 1.5302 | 91.58 | 720.7145 | 1.5192 | 94.21 | 717.8436 | 1.5083 | 96.84 | 714.9446 | 1.4976 | 99.47 | 712.0165 | 1.4870 | 102.11 | 709.0585 | 1.4766 | 104.74 | 706.0696 | 1.4663 | 107.37 | 703.0489 | 1.4562 | 110.00 | 699.9954 | 1.4461 |
By interpolation,
Density of ethanol (liquid) at 80.76oC = 731.8898 kg/m3
Density of water (liquid) at 80.76oC = 968.1172 kg/m3
Density of ethanol (vapor) at 80.76oC = 1.5711 kg/m3
Density of water (vapor) at 80.76oC = 0.6129 kg/m3
Ethanol mole fraction at top plate = 0.81
Water mole fraction at top plate = 0.19
Ethanol mass fraction at top plate = 0.92
Water mass fraction at top plate = 0.08
Therefore,
Liquid density at rectifying section =0.92×731.8898+0.08×968.1172=750.7880 kg/m3
Vapor density at rectifying section =0.92×1.5711+0.08×0.6129=1.4944 kg/m3
Density of ethanol (liquid) at 97.69oC = 713.8562 kg/m3
Density of water (liquid) at 97.69oC = 958.0158 kg/m3
Density of ethanol (vapor) at 97.69oC = 1.4981 kg/m3
Density of water (vapor) at 97.69oC = 0.5840 kg/m3
Ethanol mole fraction at bottom plate = 0.01
Water mole fraction at bottom plate = 0.99
Ethanol mass fraction at bottom plate = 0.03
Water mass fraction at bottom plate = 0.97
Therefore,
Liquid density at stripping section =0.03×731.8562+0.97×958.0158=951.2310 kg/m3
Vapor density at stripping section =0.03×1.4981+0.97×0.5840=0.6114 kg/m3
For rectifying section,
FLV=115.9958×463600191.4402×4636001.4944750.7880=0.0270
Using the graph K1 value with a plate spacing of 0.6m; K1 = 0.11
Then; UfRect=K1ρL-ρvρv=0.11750.7880-1.49441.4944=2.4631m/s
Since the operating condition is given as 70% flooding, (Ua) actual vapor velocity required through the column is given by;
UaRect=0.7Uf=0.7×2.4631=1.7242m/s
Volumetric vapor flow rate through rectifying section Vg=Vwρv=191.4402×4636001.4944 =1.6369m3/s
Net area An is given by;
An=VgUa=1.63691.7242=0.9494m2
As the first trial, assume down comer area Ad≈0.12Ac
Therefore; An=Ac-Ad=Ac-0.12Ac
Ac=An1-0.12=0.94940.88=1.0789m2
Ac=π4×Dc2
Therefore column diameter Dc=4Acπ=4×1.0789π=1.1723m
For stripping section,
FLV=228.4958×18360078.9402 ×1836000.6114951.2310=0.0734
Using the graph K1 value with a plate spacing of 0.6m; K1 = 0.1
Then; UfStrip=K1ρL-ρvρv=0.1951.2310-0.61140.6114=3.9431m/s
Since the operating condition is given as 70% flooding, (Ua) actual vapor velocity required through the column is given by;
UaStrip=0.7Uf=0.7×3.9431=2.7602m/s
Volumetric vapor flow rate through stripping section V'g=V'wρv=78.9402 ×1836000.6114=0.6456m3/s
COLUMN DIAMETER Dc
Net area An is given by;
An=V'gUa=0.64562.7602=0.2339m2
As the first trial, assume down comer area Ad≈0.12Ac
Therefore; An=Ac-Ad=Ac-0.12Ac
Ac=An1-0.12=0.23390.88=0.2658m2
Ac=π4×Dc2
Therefore column diameter Dc=4Acπ=4×0.2658π=0.5819m
Since two column diameters as 1.1723m & 0.5819m were resulted for rectifying & stripping sections respectively, considering the design feasibility, 1.1723m was considered as the overall column diameter.
AREA CALCULATION
Down comer area,
Ad=0.12Ac=0.12×1.0789=0.1295m2
Active area,
Aa=Ac-2Ad
Aa=1.0789-2×0.1295=0.8199m2
Hole area,
Ah=0.1Aa=0.1×0.8199=0.0820m2
AdAc×100%=0.12951.0789×100%=12
Using figure 11.31, lwDc=0.75
Where, lw = weir length
Therefore, lw=0.75×1.1723=0.8792m Weir liquid crest (how) how=750LρLlw23 Where, L = liquid flow rate (kg/s) ρL = Liquid density (kg/m3) For 1atm distillation columns hw =40-90mm. Therefore, assume hw =50mm Stripping Section L=1.1425 kg/s ρL=951.2310 kg/m3 lw=0.8792m how=7501.1425951.2310×0.879223 =9.2339mm how+hw=9.2339+50=59.2339mm Stripping Section L=1.1425 kg/s ρL=951.2310 kg/m3 lw=0.8792m how=7501.1425951.2310×0.879223 =9.2339mm how+hw=9.2339+50=59.2339mm Rectifying Section L= 1.4822 kg/s ρL= 750.7880 kg/m3 lw=0.8792m how=7501.4822750.7880×0.879223 =12.8606mm how+hw=12.8606+50=62.8606mm
Rectifying Section L= 1.4822 kg/s ρL= 750.7880 kg/m3 lw=0.8792m how=7501.4822750.7880×0.879223 =12.8606mm how+hw=12.8606+50=62.8606mm
Using figure 11.30, K2 for both rectifying & stripping sections ≈30.4
Hole diameter (dh) varies from 2.5 – 12mm. Therefore, hole diameter is assumed to be 5mm.
Then the minimum design velocity through the holes id given by,
Uh=K2-0.925.4-dhρv
Uh For rectifying section =30.4-0.925.4-51.4944=9.8490m/s
Uh For stripping section =30.4-0.925.4-50.6114=15.3980m/s
Actual vapor velocity through the holes is given by;
=Volumetric flow rate of gasAh
For rectifying section =1.63690.0820=19.9622m/s
For stripping section =0.64560.0820=7.8732m/s
Although the condition;
Actual vapor velocity through the holes ≥Uh
Is satisfied for rectifying section, it does not satisfied by the stripping section.
Therefore, let’s consider the following changes in plate designing for stripping section. * Down comer area (Ad) is 18% of total area (Ac) * Hole area (Ah) to active area (Aa) ratio is changed to 0.06 from 0.1 * Hole diameter is 4mm
Under these new considerations plate calculation for the stripping section was repeated.
Down comer area,
Ad=0.18Ac=0.18×1.0789=0.1942m2
Active area,
Aa=Ac-2Ad
Aa=1.0789-2×0.1942=0.6905m2
Hole area,
Ah=0.06Aa=0.06×0.6905=0.0414m2
AdAc×100%=0.19421.0789×100%=18
Using figure 11.31, lwDc=0.85
Where, lw = weir length
Therefore, lw=0.85×1.1723=0.9965m Weir liquid crest (how) how=750LρLlw23 Where, L = liquid flow rate (kg/s) ρL = Liquid density (kg/m3) For 1atm distillation columns hw =40-90mm. Therefore, assume hw =50mm For stripping section L=1.1425 kg/s ρL=951.2310 kg/m3 lw=0.9965m how=7501.1425951.2310×0.996523 =8.4944mm how+hw=8.4944+50=58.4944mm Using figure 11.30, K2 for stripping sections ≈30.4
Hole diameter (dh) varies from 2.5 – 12mm. Therefore, hole diameter is assumed to be 4mm.
Then the minimum design velocity through the holes id given by,
Uh=K2-0.925.4-dhρv
Uh For stripping section =30.4-0.925.4-40.6114=14.2470m/s
Actual vapor velocity through the holes is given by;
=Volumetric flow rate of gasAh
For stripping section =0.64560.0414=15.5829m/s
Actual vapor velocity through the holes ≥Uh
Therefore, now the condition is satisfied for both rectifying section as well as stripping section.
Therefore, the design is safe for weeping.
Number of holes in a tray (rectifying section)
=Ahπ4dh2=0.0820π45×10-32=4178
Number of holes in a tray (stripping section)
=Ahπ4dh2=0.0414π44×10-32=3298
Applying material balance to the rectifying section (Eqn 01);
V=L+D
Applying material balance for the more volatile component - C2H5OH (Eqn 02);
V×yn+1=L×xn+D×xD
From equation 01 & 02;
L+D×yn+1=L×xn+D×xD
yn+1=LL+D×xn+DL+D×xD
D, xD
W, xW
F, xF
D, xD
W, xW
F, xF
yn+1=LDLD+1×xn+1LD+1×xD
Therefore, equation for Top Operating Line (TOL); yn+1=RR+1×xn+1R+1×xD Applying overall material balance for the column;
F=D+W
225=D+W
Applying material balance for ethanol (MVC);
225×0.28=D×0.81+W×xw
Since 97% of ethanol recovery is desired;
D×0.81=225×0.28×0.97
D=75.4444 kmol/h
Therefore,
W=225-75.4444
W=149.5556 kmol/h
225×0.28=75.4444×0.81+149.5556 ×xw xw=0.0126 Equation for the q-line is given by; yq=qq-1xq-xFq-1 Since the feed is 50% saturated liquid & 50% saturated vapor, q=0.5
Therefore;
yq=0.50.5-1xq-0.280.5-1 yq=-xq+0.56 Under the minimum reflux ration condition, TOL and q-line intersect on the equilibrium curve. Therefore, q- line is plotted on the Ethanol – water equilibrium curve, through the point xF,xF≡0.28, 0.28 with an intercept of +0.56.
Top Operating Line for the minimum reflux ratio is plotted through the point xD,xD≡0.81, 0.81 and the point of intersects of q-line with equilibrium curve. Under this condition, intercept of top Operating Line (+0.4) gives the value of1Rmin+1×0.81.
Therefore, by solving 1Rmin+1×0.81=0.4
Rmin=1.025
In general practice, reflux ratio (R) is maintained such that, 1.2Rmin<R<1.5Rmin
Therefore, let’s estimate operating reflux ratio R=1.5Rmin=1.5×1.025=1.5375
So the intercept of Top operating Line under R=1.5375 is given by, 11.5375+1×0.81=0.3192
Top Operating Line is created by plotting a straight line through xD,xD≡0.81, 0.81 with an intercept of +0.32.
Then the operating line for the stripping section can be plotted as a straight line passing through the point of intersect of q-line and the TOL and the point xw,xw≡0.01, 0.01
By preparing the equilibrium stages on the graph, number of equilibrium stages was found to be 19. Since a partial re-boiler is used, it also acts as a theoretical plate; therefore the number of ideal stages required in the column is 19-1=18.
Feed tray location is 17th tray from the top.
OVERALL COLUMN EFFICIENCY
O’Connell’s Correlation
A quick estimate of the overall column efficiency can be obtained from the correlation given by O’Connell (1946). The overall column efficiency is correlated with the product of the relative volatility of the light key component (relative to the heavy key) and the molar average viscosity of the feed, estimated at the average column temperature. The correlation was based mainly on data obtained with hydrocarbon systems, but includes some values for chlorinated solvents and water-alcohol mixtures. It has been found to give reliable estimates of the overall column efficiency for hydrocarbon systems; and can be used to make an approximate estimate of the efficiency for other systems. The method takes no account of the plate design parameters; and includes only two physical property variables.
Eduljee (1958) has expressed the O’Connell correlation in the form of an equation:
Eo=51-32.5logμaαa
µa: the molar average liquid viscosity of the feed, mNs/m2 αa: average relative volatility of the light key
Average column temperature was assumed based on the following data.
Conditions of the top plate = 81% ethanol & 19% water Mole fraction of Ethanol | Temperature (oC) | 0.0000 | 99.65 | 0.0526 | 97.91 | 0.1053 | 96.28 | 0.1579 | 94.74 | 0.2105 | 93.29 | 0.2632 | 91.91 | 0.3158 | 90.61 | 0.3684 | 89.37 | 0.4211 | 88.18 | 0.4737 | 87.05 | 0.5263 | 85.97 | 0.5789 | 84.94 | 0.6316 | 83.95 | 0.6842 | 83.00 | 0.7368 | 82.08 | 0.7895 | 81.20 | 0.8421 | 80.35 | 0.8947 | 79.53 | 0.9474 | 78.74 | 1.0000 | 77.98 |
Mole fraction of Ethanol | Temperature (oC) | 0.0000 | 99.65 | 0.0526 | 97.91 | 0.1053 | 96.28 | 0.1579 | 94.74 | 0.2105 | 93.29 | 0.2632 | 91.91 | 0.3158 | 90.61 | 0.3684 | 89.37 | 0.4211 | 88.18 | 0.4737 | 87.05 | 0.5263 | 85.97 | 0.5789 | 84.94 | 0.6316 | 83.95 | 0.6842 | 83.00 | 0.7368 | 82.08 | 0.7895 | 81.20 | 0.8421 | 80.35 | 0.8947 | 79.53 | 0.9474 | 78.74 | 1.0000 | 77.98 |
Conditions of bottom plate = 1.26% ethanol & 98.74% water
By interpolating;
Temperature of the top plate = 80.76oC where the mole fraction of ethanol is 81%
Temperature of the bottom plate = 97.69oC where the mole fraction of ethanol is 1.26%
Therefore;
Average column temperature can be approximated as 97.69+80.762=89.21oC.
Temperature (oC) | Viscosity of ethanol (Pa.s) | 60.00 | 5.8357E-04 | 62.63 | 5.5938E-04 | 65.26 | 5.3645E-04 | 67.89 | 5.1470E-04 | 70.53 | 4.9405E-04 | 73.16 | 4.7445E-04 | 75.79 | 4.5582E-04 | 78.42 | 4.3811E-04 | 81.05 | 4.2126E-04 | 83.68 | 4.0523E-04 | 86.32 | 3.8997E-04 | 88.95 | 3.7543E-04 | 91.58 | 3.6157E-04 | 94.21 | 3.4836E-04 | 96.84 | 3.3575E-04 | 99.47 | 3.2372E-04 | 102.11 | 3.1224E-04 | 104.74 | 3.0127E-04 | 107.37 | 2.9078E-04 | 110.00 | 2.8076E-04 |
Temperature (oC) | Viscosity of ethanol (Pa.s) | 60.00 | 5.8357E-04 | 62.63 | 5.5938E-04 | 65.26 | 5.3645E-04 | 67.89 | 5.1470E-04 | 70.53 | 4.9405E-04 | 73.16 | 4.7445E-04 | 75.79 | 4.5582E-04 | 78.42 | 4.3811E-04 | 81.05 | 4.2126E-04 | 83.68 | 4.0523E-04 | 86.32 | 3.8997E-04 | 88.95 | 3.7543E-04 | 91.58 | 3.6157E-04 | 94.21 | 3.4836E-04 | 96.84 | 3.3575E-04 | 99.47 | 3.2372E-04 | 102.11 | 3.1224E-04 | 104.74 | 3.0127E-04 | 107.37 | 2.9078E-04 | 110.00 | 2.8076E-04 |
Temperature (oC) | Viscosity of water (Pa.s) | 60.00 | 4.7420E-04 | 62.63 | 4.5513E-04 | 65.26 | 4.3725E-04 | 67.89 | 4.2049E-04 | 70.53 | 4.0474E-04 | 73.16 | 3.8994E-04 | 75.79 | 3.7602E-04 | 78.42 | 3.6290E-04 | 81.05 | 3.5054E-04 | 83.68 | 3.3888E-04 | 86.32 | 3.2787E-04 | 88.95 | 3.1747E-04 | 91.58 | 3.0762E-04 | 94.21 | 2.9831E-04 | 96.84 | 2.8948E-04 | 99.47 | 2.8112E-04 | 102.11 | 2.7318E-04 | 104.74 | 2.6564E-04 | 107.37 | 2.5848E-04 | 110.00 | 2.5168E-04 |
Temperature (oC) | Viscosity of water (Pa.s) | 60.00 | 4.7420E-04 | 62.63 | 4.5513E-04 | 65.26 | 4.3725E-04 | 67.89 | 4.2049E-04 | 70.53 | 4.0474E-04 | 73.16 | 3.8994E-04 | 75.79 | 3.7602E-04 | 78.42 | 3.6290E-04 | 81.05 | 3.5054E-04 | 83.68 | 3.3888E-04 | 86.32 | 3.2787E-04 | 88.95 | 3.1747E-04 | 91.58 | 3.0762E-04 | 94.21 | 2.9831E-04 | 96.84 | 2.8948E-04 | 99.47 | 2.8112E-04 | 102.11 | 2.7318E-04 | 104.74 | 2.6564E-04 | 107.37 | 2.5848E-04 | 110.00 | 2.5168E-04 |
By interpolating to the temperature of 89.21oC; viscosity of water is 3.4316E-04 Pa.s and viscosity of ethanol is 3.6474E-04 Pa.s
Molar average liquid viscosity of the feed is given by;
0.28×3.6474×10-4+0.72×3.4316×10-4=3.4920×10-4Pa.s
Relative volatility αE,W=KEthanolKWater=pEthanolopsyspWateropsys=1.70380.7692=2.2150
Eo=51-32.5log3.4920×10-4×103×2.2150=54.6254%
But, Column efficiency Eo=Number of ideal stagesNumber of actual stages×100%
Therefore; Number of actual stages=19-10.546254=33
TRAY SPACING
A reasonable value must be selected considering construction, maintenance and cost.
Typical range is 0.15m to 0.9m.
In this design, tray spacing is considered as 0.6m.
Therefore; Column height=33×0.6=19.8m
FLOODING VAPOR VELOCITY Uf
The liquid-vapor flow factor FLV is given by;
FLV=LwVwρvρL
Lw - liquid mass flow-rate, kg/s
Vw - vapor mass flow-rate, kg/s
Assumptions I. Liquid and vapor mass flow rates throughout the rectifying section and stripping section remains constant (L, V & L’, V’). II. Liquid and vapor densities throughout the rectifying section remain constant and equals to that of the top plate. III. Liquid and vapor densities throughout the stripping section remain constant and equals to that of the bottom plate. IV. Assume that the molecular weight of the vapor & liquid is same as ethanol (46g/mol) for rectifying section and similar to water (18g/mol) for stripping section
Reflux ratio R=LD
Therefore; L=R×D=1.5375 ×75.4444=115.9958kmol/h
By applying material balance for the feed tray and since the feed is 50% saturated liquid and 50% saturated vapor,
L'=L+0.5F
L'=115.9958+0.5×225=228.4958 kmol/h
Applying material balance for the total condenser;
V=D+L
V=75.4444+115.9958=191.4402 kmol/h
Applying material balance for the partial re-boiler;
L'=V'+W
V'=228.4958-149.5556=78.9402 kmol/h Density of Water at 1bar | Temperature(oC) | Liquid(kg/m3) | Vapor(kg/m3) | 60.00 | 979.6811 | 0.6504 | 62.63 | 978.3650 | 0.6453 | 65.26 | 977.0220 | 0.6403 | 67.89 | 975.6517 | 0.6353 | 70.53 | 974.2542 | 0.6305 | 73.16 | 972.8291 | 0.6257 | 75.79 | 971.3763 | 0.6210 | 78.42 | 969.8956 | 0.6163 | 81.05 | 968.3869 | 0.6117 | 83.68 | 966.8500 | 0.6072 | 86.32 | 965.2846 | 0.6028 | 88.95 | 963.6905 | 0.5984 | 91.58 | 962.0676 | 0.5941 | 94.21 | 960.4157 | 0.5898 | 96.84 | 958.7346 | 0.5856 | 99.47 | 957.0240 | 0.5815 | 102.11 | 955.2837 | 0.5774 | 104.74 | 953.5135 | 0.5734 | 107.37 | 951.7132 | 0.5694 | 110.00 | 949.8826 | 0.5655 |
Density of Water at 1bar | Temperature(oC) | Liquid(kg/m3) | Vapor(kg/m3) | 60.00 | 979.6811 | 0.6504 | 62.63 | 978.3650 | 0.6453 | 65.26 | 977.0220 | 0.6403 | 67.89 | 975.6517 | 0.6353 | 70.53 | 974.2542 | 0.6305 | 73.16 | 972.8291 | 0.6257 | 75.79 | 971.3763 | 0.6210 | 78.42 | 969.8956 | 0.6163 | 81.05 | 968.3869 | 0.6117 | 83.68 | 966.8500 | 0.6072 | 86.32 | 965.2846 | 0.6028 | 88.95 | 963.6905 | 0.5984 | 91.58 | 962.0676 | 0.5941 | 94.21 | 960.4157 | 0.5898 | 96.84 | 958.7346 | 0.5856 | 99.47 | 957.0240 | 0.5815 | 102.11 | 955.2837 | 0.5774 | 104.74 | 953.5135 | 0.5734 | 107.37 | 951.7132 | 0.5694 | 110.00 | 949.8826 | 0.5655 |
Density of Ethanol at 1bar | Temperature(oC) | Liquid(kg/m3) | Vapor(kg/m3) | 60.00 | 753.2286 | 1.6632 | 62.63 | 750.6419 | 1.6502 | 65.26 | 748.0347 | 1.6373 | 67.89 | 745.4065 | 1.6247 | 70.53 | 742.7568 | 1.6123 | 73.16 | 740.0851 | 1.6000 | 75.79 | 737.3908 | 1.5879 | 78.42 | 734.6732 | 1.5760 | 81.05 | 731.9318 | 1.5643 | 83.68 | 729.1659 | 1.5528 | 86.32 | 726.3749 | 1.5414 | 88.95 | 723.5580 | 1.5302 | 91.58 | 720.7145 | 1.5192 | 94.21 | 717.8436 | 1.5083 | 96.84 | 714.9446 | 1.4976 | 99.47 | 712.0165 | 1.4870 | 102.11 | 709.0585 | 1.4766 | 104.74 | 706.0696 | 1.4663 | 107.37 | 703.0489 | 1.4562 | 110.00 | 699.9954 | 1.4461 |
Density of Ethanol at 1bar | Temperature(oC) | Liquid(kg/m3) | Vapor(kg/m3) | 60.00 | 753.2286 | 1.6632 | 62.63 | 750.6419 | 1.6502 | 65.26 | 748.0347 | 1.6373 | 67.89 | 745.4065 | 1.6247 | 70.53 | 742.7568 | 1.6123 | 73.16 | 740.0851 | 1.6000 | 75.79 | 737.3908 | 1.5879 | 78.42 | 734.6732 | 1.5760 | 81.05 | 731.9318 | 1.5643 | 83.68 | 729.1659 | 1.5528 | 86.32 | 726.3749 | 1.5414 | 88.95 | 723.5580 | 1.5302 | 91.58 | 720.7145 | 1.5192 | 94.21 | 717.8436 | 1.5083 | 96.84 | 714.9446 | 1.4976 | 99.47 | 712.0165 | 1.4870 | 102.11 | 709.0585 | 1.4766 | 104.74 | 706.0696 | 1.4663 | 107.37 | 703.0489 | 1.4562 | 110.00 | 699.9954 | 1.4461 |
By interpolation,
Density of ethanol (liquid) at 80.76oC = 731.8898 kg/m3
Density of water (liquid) at 80.76oC = 968.1172 kg/m3
Density of ethanol (vapor) at 80.76oC = 1.5711 kg/m3
Density of water (vapor) at 80.76oC = 0.6129 kg/m3
Ethanol mole fraction at top plate = 0.81
Water mole fraction at top plate = 0.19
Ethanol mass fraction at top plate = 0.92
Water mass fraction at top plate = 0.08
Therefore,
Liquid density at rectifying section =0.92×731.8898+0.08×968.1172=750.7880 kg/m3
Vapor density at rectifying section =0.92×1.5711+0.08×0.6129=1.4944 kg/m3
Density of ethanol (liquid) at 97.69oC = 713.8562 kg/m3
Density of water (liquid) at 97.69oC = 958.0158 kg/m3
Density of ethanol (vapor) at 97.69oC = 1.4981 kg/m3
Density of water (vapor) at 97.69oC = 0.5840 kg/m3
Ethanol mole fraction at bottom plate = 0.01
Water mole fraction at bottom plate = 0.99
Ethanol mass fraction at bottom plate = 0.03
Water mass fraction at bottom plate = 0.97
Therefore,
Liquid density at stripping section =0.03×731.8562+0.97×958.0158=951.2310 kg/m3
Vapor density at stripping section =0.03×1.4981+0.97×0.5840=0.6114 kg/m3
For rectifying section,
FLV=115.9958×463600191.4402×4636001.4944750.7880=0.0270
Using the graph K1 value with a plate spacing of 0.6m; K1 = 0.11
Then; UfRect=K1ρL-ρvρv=0.11750.7880-1.49441.4944=2.4631m/s
Since the operating condition is given as 70% flooding, (Ua) actual vapor velocity required through the column is given by;
UaRect=0.7Uf=0.7×2.4631=1.7242m/s
Volumetric vapor flow rate through rectifying section Vg=Vwρv=191.4402×4636001.4944 =1.6369m3/s
Net area An is given by;
An=VgUa=1.63691.7242=0.9494m2
As the first trial, assume down comer area Ad≈0.12Ac
Therefore; An=Ac-Ad=Ac-0.12Ac
Ac=An1-0.12=0.94940.88=1.0789m2
Ac=π4×Dc2
Therefore column diameter Dc=4Acπ=4×1.0789π=1.1723m
For stripping section,
FLV=228.4958×18360078.9402 ×1836000.6114951.2310=0.0734
Using the graph K1 value with a plate spacing of 0.6m; K1 = 0.1
Then; UfStrip=K1ρL-ρvρv=0.1951.2310-0.61140.6114=3.9431m/s
Since the operating condition is given as 70% flooding, (Ua) actual vapor velocity required through the column is given by;
UaStrip=0.7Uf=0.7×3.9431=2.7602m/s
Volumetric vapor flow rate through stripping section V'g=V'wρv=78.9402 ×1836000.6114=0.6456m3/s
COLUMN DIAMETER Dc
Net area An is given by;
An=V'gUa=0.64562.7602=0.2339m2
As the first trial, assume down comer area Ad≈0.12Ac
Therefore; An=Ac-Ad=Ac-0.12Ac
Ac=An1-0.12=0.23390.88=0.2658m2
Ac=π4×Dc2
Therefore column diameter Dc=4Acπ=4×0.2658π=0.5819m
Since two column diameters as 1.1723m & 0.5819m were resulted for rectifying & stripping sections respectively, considering the design feasibility, 1.1723m was considered as the overall column diameter.
AREA CALCULATION
Down comer area,
Ad=0.12Ac=0.12×1.0789=0.1295m2
Active area,
Aa=Ac-2Ad
Aa=1.0789-2×0.1295=0.8199m2
Hole area,
Ah=0.1Aa=0.1×0.8199=0.0820m2
AdAc×100%=0.12951.0789×100%=12
Using figure 11.31, lwDc=0.75
Where, lw = weir length
Therefore, lw=0.75×1.1723=0.8792m Weir liquid crest (how) how=750LρLlw23 Where, L = liquid flow rate (kg/s) ρL = Liquid density (kg/m3) For 1atm distillation columns hw =40-90mm. Therefore, assume hw =50mm Stripping Section L=1.1425 kg/s ρL=951.2310 kg/m3 lw=0.8792m how=7501.1425951.2310×0.879223 =9.2339mm how+hw=9.2339+50=59.2339mm Stripping Section L=1.1425 kg/s ρL=951.2310 kg/m3 lw=0.8792m how=7501.1425951.2310×0.879223 =9.2339mm how+hw=9.2339+50=59.2339mm Rectifying Section L= 1.4822 kg/s ρL= 750.7880 kg/m3 lw=0.8792m how=7501.4822750.7880×0.879223 =12.8606mm how+hw=12.8606+50=62.8606mm
Rectifying Section L= 1.4822 kg/s ρL= 750.7880 kg/m3 lw=0.8792m how=7501.4822750.7880×0.879223 =12.8606mm how+hw=12.8606+50=62.8606mm
Using figure 11.30, K2 for both rectifying & stripping sections ≈30.4
Hole diameter (dh) varies from 2.5 – 12mm. Therefore, hole diameter is assumed to be 5mm.
Then the minimum design velocity through the holes id given by,
Uh=K2-0.925.4-dhρv
Uh For rectifying section =30.4-0.925.4-51.4944=9.8490m/s
Uh For stripping section =30.4-0.925.4-50.6114=15.3980m/s
Actual vapor velocity through the holes is given by;
=Volumetric flow rate of gasAh
For rectifying section =1.63690.0820=19.9622m/s
For stripping section =0.64560.0820=7.8732m/s
Although the condition;
Actual vapor velocity through the holes ≥Uh
Is satisfied for rectifying section, it does not satisfied by the stripping section.
Therefore, let’s consider the following changes in plate designing for stripping section. * Down comer area (Ad) is 18% of total area (Ac) * Hole area (Ah) to active area (Aa) ratio is changed to 0.06 from 0.1 * Hole diameter is 4mm
Under these new considerations plate calculation for the stripping section was repeated.
Down comer area,
Ad=0.18Ac=0.18×1.0789=0.1942m2
Active area,
Aa=Ac-2Ad
Aa=1.0789-2×0.1942=0.6905m2
Hole area,
Ah=0.06Aa=0.06×0.6905=0.0414m2
AdAc×100%=0.19421.0789×100%=18
Using figure 11.31, lwDc=0.85
Where, lw = weir length
Therefore, lw=0.85×1.1723=0.9965m Weir liquid crest (how) how=750LρLlw23 Where, L = liquid flow rate (kg/s) ρL = Liquid density (kg/m3) For 1atm distillation columns hw =40-90mm. Therefore, assume hw =50mm For stripping section L=1.1425 kg/s ρL=951.2310 kg/m3 lw=0.9965m how=7501.1425951.2310×0.996523 =8.4944mm how+hw=8.4944+50=58.4944mm Using figure 11.30, K2 for stripping sections ≈30.4
Hole diameter (dh) varies from 2.5 – 12mm. Therefore, hole diameter is assumed to be 4mm.
Then the minimum design velocity through the holes id given by,
Uh=K2-0.925.4-dhρv
Uh For stripping section =30.4-0.925.4-40.6114=14.2470m/s
Actual vapor velocity through the holes is given by;
=Volumetric flow rate of gasAh
For stripping section =0.64560.0414=15.5829m/s
Actual vapor velocity through the holes ≥Uh
Therefore, now the condition is satisfied for both rectifying section as well as stripping section.
Therefore, the design is safe for weeping.
Number of holes in a tray (rectifying section)
=Ahπ4dh2=0.0820π45×10-32=4178
Number of holes in a tray (stripping section)
=Ahπ4dh2=0.0414π44×10-32=3298