MULTICOMPONENT DISTILLATION*

Multi-Component Distillation (MCD) The Problem

For multi-component systems, C > 2, no. of equations obtained from mass and energy balances with the equilibrium relationship will always be one less than the number of unknowns.

A complete analytical solution for multi-component distillation is difficult to attain. trial and error with the additional unknown assumed to be known

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EQUILIBRIUM DATA IN MCDRaoults Law can be used to determine equilibrium compositions.In hydrocarbon systems, because of non idealities, equilibrium data are represented as yi = Kixi where: Ki is the vapor-liquid equilibrium constant or distribution coefficient of i

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EQUILIBRIUM DATA IN MCDRelative volatility for each individual component can be defined as:i = Ki /KjWhere j denotes the base componentValues of Ki will be a stronger function of temperature than the i *

BOILING PT., DEW PT. AND FLASH DISTILLATIONBOILING POINT -For multicomponent mixture, BP must satisfy yi = 1.0For a mixture of A,B,C,D with C as base component yi = Kixi = Kc ixi =1.0 Calculation is a trial and error process.-When final temperature is known, vapor composition is calculated fromyi = ixi / (ixi )

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BOILING PT., DEW PT. AND FLASH DISTILLATIONDEW POINT - trial and error

xi = (yi/Ki)= (1/Kc) (yi/i)=1.0 Kc = (yi/i)xi = (yi/i)/(yi/i) *

FLASH DISTILLATION OF MCD*

FLASH DISTILLATION OF MCDf = V/F fraction of feed vaporized1 f = L/F fraction of the feed remaining as liquidComposition of i in the vapor yi = Kixi = [(f 1) xi/f] + xiF/fxi = xiF /[f(Kci 1) + 1] = 1.0 - solved by trial and error by assuming T - when xi = 1.0, proper T has been chosen

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MCD Some Additional Terminology

Fractional recoveriesKey componentsNon-key componentsSplits distributing and Non-distributing systems

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MCD Fractional Recoveries*What are fractional recoveries?

MCD Fractional RecoveriesFractional recoveries are often specified in MCD.

A fractional recovery, FRi, is the amount or flow rate of component i in the distillate or bottoms stream with respect to the amount or flow rate of component i in the feed stream:

It is the simple relationships expressed by the right-hand-side equations that make the use of fractional recoveries useful.

These are also often specified simply as % recovery.

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Lecture 16

MCD Key Components

The components that have their distillate and bottoms composition specified are known as the key components.

The most volatile of the key components is termed the light key (LK).

The least volatile of the key components is termed the heavy key (HK).

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MCD Non-Key Components

All other components not specified in the distillate or botoms are termed non-key components (NKs).

If a non-key component is more volatile than the light key, then it is termed a light non-key (LNK).

If a non-key component is less volatile than the heavy key, it is a heavy non-key (HNK).

If a non-key component is neither a heavy non-key nor a light non-key, then it is an intermediate non-key (INK) or simply NK.*

MCD Non-Key Component Splits

The split of the nonkey components is generally defined as to where the nonkey components are obtained with respect to the distillate or bottoms stream.

One can have two types of situations concerning the split of the nonkey components:Sharp split Non-distribution of non-keysSplit Distribution of non-keys

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MCD Non-distribution of NKs

Nondistribution of nonkeys means that essentially all of the nonkeys are obtained in either the distillate stream or the bottoms stream. We obtain a sharp split of the NKs.

Nondistribution of nonkeys can be assumed when:All of the non-keys are either HNKs or LNKsThe fractional recoveries of the LK in the distillate and HK in the bottoms are relatively large.*

MCD Distribution of NKs

Distribution of nonkeys means that the non-keys are not sharply split between the distillate stream or the bottoms stream. We obtain a split of the NKs.

Distribution of nonkeys occurs when:Not all of the non-keys are either HNKs or LNKs we have NKs.The fractional recoveries of the LK in the distillate and HK in the bottoms are not relatively large.

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Key and Non-Key ExampleConsider a distillation column with the following feed components:propanenbutanenpentanenhexane

The recoveries for nbutane and npentane are specified for the distillation.

What are the key and nonkey designations for this separation?

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Key and Non-Key ExampleComponent volatilities can be determined from the K values.

From the DePriester charts, the order of volatility is: propane > nbutane > npentane > nhexane

Since the recoveries of nbutane and npentane are specifieddesignate LK, HK and NK

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Key and Non-Key ExampleIf the recoveries of n-butane and n-hexane are specified:

Volatilitiespropane > n-butane > n-pentane > n-hexane

Component Designation PropaneLight Non-Keyn-butaneLight Keyn-pentaneNon-Keyn-hexaneHeavy Key*

Key and Non-Key ExampleIf only the recovery of nbutane is specified:Volatilitiespropane > nbutane > npentane > nhexane

Component Designation PropaneLight NonKeynbutaneKeynpentaneNonKeynhexaneNonKey*

Key and Non-Key ExampleConsider a distillation column with the following feed components:MethaneEthaneEthylenePropylenePropaneIt is specified that a distillate concentration, xD, for ethylene is required.What are the key and non-key designations for this separation?

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Key and Non-Key ExampleOne source for determining the order of the component volatilities can be determined from the K values, which can be found from the DePriester charts, for example.The order of volatility is: methane > ethylene > ethane > propylene > propaneSince xD for ethylene is specified it is a key component.*

Key and Non-Key Example Component Designation MethaneLight Non-KeyEthyleneLight KeyEthane Non-KeyPropyleneNon-KeyPropaneNon-Key

There is no heavy key specified for this problem.

What if an xD for ethylene and an xB for propylene are specified?

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Key and Non-Key Example Component Designation MethaneLight Non-KeyEthyleneLight KeyEthane Non-KeyPropyleneHeavy KeyPropaneHeavy Non-Key

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TOTAL REFLUX FOR MCD(FENSKE EQ.)Calculates Nmin for total reflux Nm = *Where: xLD is mole fraction of LK in Distillate xHD is mole fraction of HK in Distillate xLW is mole fraction of LK in Bottoms xHW is mole fraction of HK in Bottoms L,av = (LD LW)^0.5

TOTAL REFLUX FOR MCDDistribution/concentration of other components in the distillate and bottoms at total reflux can be determined by: xiDD xiWW

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Minimum Reflux Ratio for MCDUNDERWOOD EQUATIONS*ai is based on average T of top and bottom tower-Trial and error process:Solve check if bet. of LK and HK =1.0 Rm

NUMBER OF STAGES AT OPERATING REFLUX RATIO FOR MCDEMPIRICAL CORRELATION BY ERBAR AND MADDOX (Fig. 11.7-3, p.749,Geankoplis)Graph of R/R+1 vs Nm/N (Rm based on Underwood method)Estimate of feed plate location(Kirkbride)

*Ne is the number of theoretical stages above the feed plateNs is the number of theoretical stages below the feed plate

The following feed of 100 mol/h at the boiling point and 405.3 kPa pressure is fed to a fractionating tower: n-butane(xA=0.40), n-pentane(xB= 0.25), n-hexane(xc=0.20), n-heptane(xD = 0.15). This feed is distilled so that 95% of n-pentane is recovered in the distillate and 95%of n-hexane in the bottoms. Calculate the ff:Moles/hr and composition of distillate and bottomsTop and bottom temperature of towerMinimum stages for total reflux and distribution of trace componentsMinimum reflux using Underwood methodNo of theoretical stages if R=1.3Rm using Erbar-MaddoxLocation of feed tray using Kirkbride

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Component Designation PropaneLight NonKeynbutaneLight KeynpentaneHeavy KeynhexaneHeavy NonKey*