Sorting Plastic Waste

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  • Topic: Pressure, Partial pressure, Vapor pressure
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  • Published : May 7, 2013
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Multicomponent distillation
1) Mass balances
The feed flowrate is 350 kmols hr-1 and the feed composition is known: 48 mol% propene, 50 mol% propane and 2 mol% butane. The distillate stream composition: 99.9 mol% propene and 0.1 mol% propane. The bottom product stream contains 0.5 mol% propene but the mole fractions of propane and butane are unknown. Therefore, mass balances are carried out around the distillate column. Overall mass balance: F=D+B

Component mass balance for propene: xFF=yDD+xBB
0.48×350=0.999×F-B+0.005B, B=182.75 kmols hr-1
D=F-B=350-182.75=167.25 kmols hr-1
Component mass balance for propane: xFF=yDD+xBB,
0.5×350=0.001×167.25+xB×182.75
xB=0.5×350-0.001×167.25182.75=0.9567
Component mass balance for butane: xFF=yDD+xBB,
0.02×350=xB×182.75, xB=0.0383
Thus, the mole fractions of propane and butane in the bottom stream are xB=0.9567, xB=0.0383. The light key will be propene and the heavy key will be propane.

2) Calculation of the bubble point of the feed, distillate and bottom product Assumptions:
* the system pressure is taken as the atmospheric pressure 101325 Pa * the system is treated as an ideal system
The bubble point temperatures of the feed, distillate and bottom product have been calculated by solving the following equation. The equation is solved by trial and error until the sum of partial pressures exerted by each component equals the system pressure. xpropenePpropenesat+xpropanePpropanesat+xbutanePbutanesat=101325 The vapour pressure of each component is calculated using the relationships below: Propene: lnPsat=57.263-3382.4T-5.7707lnT+1.0431×10-5T2

Propane: lnPsat=59.078-3492.6T-6.0669lnT+1.0919×10-5T2
Butane: lnPsat=66.343-4363.2T-7.046lnT+9.4509×10-6T2
The feed bubble point was calculated TF=228.6 K
The corresponding vapour pressures of the feed components:
Ppropenesat=116275 Pa, Ppropanesat=90505 Pa, Pbutanesat=13018 Pa The same calculations were repeated for the distillate and bottom streams. Distillate: TD=225.5 K, Ppropenesat=101348 Pa, Ppropanesat=78632 Pa, Bottom: TB=231.8 K,

Ppropenesat=133923 Pa, Ppropanesat=104586 Pa, Pbutanesat=15615 Pa

3) Calculation of Minimum Number of Stages at Total Reflux The minimum number of stages is calculated using Fenske equation Nmin=log10xLK, DxLK, BxHK, BxHK, Dlog10αLK,HK
where xLK, D=0.999 – mole fraction of propene in the distillate xLK, B=0.005 – mole fraction of propene in the bottom
xHK, B=0.9567 – mole fraction of propane in the bottom
xHK, D=0.001 – mole fraction of propane in the distillate
αLK,HK=3 (αLK,HK)D × (αLK,HK)F × (αLK,HK)B - combination of relative volatilities at the temperature of the distillate, feed and bottom product. Realtive volatiltiy=α=KLKKHK, Ki=yixi-equilibrium constant For vapour liquid equilibrium between an ideal solution and an ideal gas mixture xiPisat=yiP rearranging the equilibrium relationship gives Ki=yixi=PisatP Therefore, αLK,HK=KLKKHK=PLKsatPHKsat

Using the vapour pressures of components calculated for the feed, distillate and bottom product at the bubble point allows finding the volatilities at the temperature of the feed, distillate and bottom product. (αLK,HK)D =PLKsatPHKsat=10134878632=1.289 , (αLK,HK)F =PLKsatPHKsat=11627590505=1.285 , (αLK,HK)B =PLKsatPHKsat=133923104586=1.281

αLK,HK=31.289×1.285×1.281B=1.285
Having substituted all values into Fenske equation gives
Nmin=log100.9990.0050.95670.001log101.285=48.5

4) Calculation of Minimum Reflux Ratio
Propene and propane are present in both distillate and bottom products, therefore they are distributed components. However, butane is an undistributed component since it is present in the bottom product. As a result of this, not all components are distributed so the system is Class 2. The minimum reflux ratio is estimated using:

i=1Nαi,HKxF,iαi,HK-ϕ=1 ϕ is adjusted to find a solution and its values is limited to 1<ϕ< αLK,HKF
The...
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