BasicModesofOperation
2.1Amixturecontaining48.6percentb enzeneand51.4percentethylenechlorideistobedistilledinabatchdistillationcolumnwith20theoretical plates.Thecolumnisoperatingundertheconstantrefluxmodeatareflux ratioequalto9.8.Assumetherelativevolatilityofbenzenewithrespect toethylenechlorideis1.109.
a)Findtheconcentrationoftheproductwhen95.4percentofthetotalmixtureisdistilled.Assumethattheinitialdistillatecompositionis approximately0.722.
b)Iftheoriginalfeedis100molesandthevaporboil-uprateis100 moles/hr,whatisthetimerequiredtocompletetheoperation?
c)Simulatethevariablerefluxoperationassumingtherefluxratiovaries from5.0to20.0.Findtheendcompositionsandthetotaltime.
2.2Abatchdistillationcolumnoperatingatatmosphericpressureistobe designedtoseparateamixturecontaining15.67molepercentCS2 and 84.33molepercentCCl4 intoanoverheadproductcontaining91percent CS2 .Assumethecolumntobeoperatinginthevariablerefluxmodewith aninitialrefluxratioof3.0.
a)Howmanytheoreticalplatesarerequiredfortheprocess?
b)Ifthedistillateisstoppedwhentherefluxratioisequalto15.0,what istheamountofdistillateobtained?
c)Whatistheheatrequiredperkmoleofproduct?
LatentheatfortheCS2 andCCl4 mixtureis25,900kJ/kmolandthedata fortheequilibriumcurveisgivenbelow.
xCS2 .0296.0615.1106.1435.2585.3900.5318.6630.7575.8604 yCS2 .0823.1555.2660.3320.4950.6340.7470.8290.8780.9320
2.3Ifthesamesystemisoperatingwiththeconstantrefluxmodeofoperation, withtheinitialproductcompositionof95percentandwitharefluxratio of5.0,
a)Howmanytheoreticalplatesarerequired?
b)Simulatetheconditionandstoptheoperationwhentheaveragedistillatecompositionis0.90.Whatistheamountofdistillatecollectedatthis stage?WhatisthebatchtimeifV=100moles?
c)Findtheheatrequiredperkmoleofproduct.
2.4Amulticomponentmixturecontainingmeta,orthoandparamono-nitrotolueneistobedistilledusingadistillationcolumncontainingeighttheoreticalplates.Thefeedcompositionatthestartofoperationis0.6,0.36, 0.04ofmeta,orthoandpara-mono-nitro-toluenerespectively.Thecolumn isoperatingatarefluxratioequalto3.0andwithconstantrefluxmodeof operation.Assumethattheproductcompositionvariesfrom0.94to0.85. Therelativevolatilitiesofmeta,ortho,andpara-mono-nitro-toluenecan beassumedas1.7,1.16and1.0respectively.Usetheplate-to-platecalculationmethodtocalculatetherelationbetweenthedistillatecomposition andthestillcompositionatanyinstant.
a)Plotthedistillatecompositionsofmeta,orthoandpara-mono-nitrotolueneversusthestillcompositionofmeta-mono-nitro-toluene.
b)Plotthestillcompositionsoforthoandpara-moono-nitro-tolueneversus thestillcompositionofmeta-mono-nitro-toluene.
c)Findthefractiondistilledattheendoftheoperation.
2.5ThesamecolumninExample2.4isoperatedwiththevariablerefluxmode ofoperation.Thedistillatepurityofthemeta-mono-nitro-tolueneistobe maintainedat0.98.Assumethattherefluxratiovariesfrom10to80.
a)Plotthedistillatecompositionsoforthoandpara-mono-nitro-toluene versusthestillcompositionofmeta-mono-nitro-toluene.
b)Plotthestillcompositionsoforthoandpara-mono-nitro-tolueneversus thestillcompositionofmeta-mono-nitro-toluene.
c)Plotrefluxratioversusthestillcompositionofmeta-mono-nitrotoluene.s
c)Findthefractiondistilledattheendoftheoperation.
2.6ConverseandGross,in1963,solvedthemaximumdistillateoptimalreflux problemgivenbelow(ConverseandGross,1963).
MaximumDistillateProblem–Maximizetheamountofdistillateof aspecifiedconcentrationforaspecifiedtime. Usetheirsystemtocomparethethreemodesofoperation.
2.7Findtheheatdutyofthereboilerfortheminimumtimeproblemsolved inthesectiononoptimalreflux(Section2.4).
2.8BowmanandCichelli,in1949,presentedaveryinterestingconceptofpole heightforabinarybatchdistillationcolumn.Apoleheightisdefinedas theproductofthemid-pointoftheslopeofthedistillatecomposition versusmaterialremaininginthestillcurveandtheamountofthematerialremaininginthestillatthattime.Figure2.1illustratestheconcept
FIGURE2.1
ThePoleHeightConcept(repro ducedfromBowmanandCichelli,1948)
ofpoleheight.Theystatedthatthepoleheightisinvarianttotheinitialconcentrationandprovidesagoodmeasurefordefiningsharpnessof separation.
Take100molesofabinarymixturecontainingcomponentA&Bwitha relativevolatility1.5.Useafivetheoreticalstagebatchdistillationcolumn andaconstantrefluxoperationwitharefluxequalto5.0.Varytheinitial compositionfrom xA equalto0.5to0.4andplotthedistillatecomposition versustheamountremaininginthestill.Calculatethepoleheightforeach case.Verifytheconcept.
BatchDistillation:Simulation,OptimalDesignandControl:SolutionManual 2.9Problem2.8describedthepoleheightconceptproposedbyBowmanand Cichelli.Usetheabovedefinitiontoprovethat:
a)Atatotalrefluxcondition(minimumnumberofplates),thepole height S isrelatedtothenumberofplates N bythefollowingrelation.
b)Ataninfinitenumberofplates(minimumrefluxcondition)andmoderatelygoodseparation,therefluxcanbeexpressedas:
Assumethatatmoderateseparationthequantityof xB isextremely small.
Solution:APoleheightforbinarymixtureisdefinedas
aRayleighequationgives
xD =0 5 α
;Hence,
FromEquations2.2and2.5
FromEquation2.3
FromEquations2.4,2.6,and2.9
Forsharpseparations αN islarge,resultingin α2N 1= α2N .Further,forsharpseparations,onecanassumethatamountofmaterial remaininginthepotisequaltoamountofheavycomponentinthe originalcharge.Therefore,
CombiningEquations2.12andpole-8resultsin
bAtminimumreflux(infinitenumberofplates),Underwood’sequationsforbinaryseparationwithrelativevolatility α aregivenby
Forbinarycomponent,fromEquation2.14
SimplifyingEquation2.15resultsin
BatchDistillation:Simulation,OptimalDesignandControl:SolutionManual
Substitutingvalueof xB
Replacing φ intermsof xB xD =
Rayleighequationintermsofpoleheightasshownin(a).
FromEquation2.22
At xD =0.5., xB <<xD ,Hence xD xB = xD .Also,since xB is small(1+(α 1)xB )=1.Therefore,
Simplifying,
FIGURE 2.1
Schematic of a Batch Distillation Column
dD/dt R= = L j L 0 dD/dt L 0
condenser
reboiler x D 1 N x B -th Plate
L j L j-1 yj V j+1 x j-1 V j y j+1 x j
Slope = R
2.2
McCabe–Thiele Method for Plate-to-Plate Calculations
1 y
McCabe–Thiele Method for the Constant Reflux Mode
0.4 0.60.8 1 x
FIGURE 2.4
Graphical Integration for Example 2.1
Slope = R R + 1 1 1
Slope = R R + 1 2 2
2.5
McCabe–Thiele Method for the Variable Reflux Mode
2.6
Graphical Integration for Calculation of Batch Time for Example 2.2
Graphical Integration for Calculation of Reboiler Heat Duty for Example 2.2
2.8
McCabe–Thiele Procedure for the Third Mode of Operation
Slope = R R1+1
Slope = R R +1 1 2 2 B2 x
FIGURE 2.9
Graphical Integration for the Rayleigh Equation for the Third Mode of Operation
Graphical Integration for Calculation of Batch Time for the Third Mode of Operation
The Pole Height Concept (Reproduced from Bowman and Cichelli, 1948)
