McCabe-Thiele Method 1

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McCabe-Thiele Method 1

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    Jawaharlal Nehru TechnologicalUniversity Kakinada

    III Year B. Tech. Petrochemical EngineeringII em.

    !ass Trans"er #$eration % I

    &ITI''(TI#NE)UI'IB*IU! T(+E ,(',U'(TI#N

    !c,(BE-TIE'E !ET#&

    Presentation /y

    Pro". K. 0. *ao(cademic (dvisor 1 0isiting Pro"essor

    chool o" Petroleum ,ourses

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    !c,a/e-Thiele !ethod

    It is a gra$hical method andinvolves calculation o" total num/ero" e2uili/rium stages re2uired "or a

    given se$aration using material/alance and e2uili/rium relations.

    The following notations shall be used :

    y : mole fraction of more volatile component in vapour

    phase

    x : mole fraction of more volatile component in liquid

    phase

    V : molar flowrate of vapour, mole/time

    L : molar flowrate of liquid, mole/time

    F : molar flowrate of feed vapor or liquid or mixed!,

    mole/time

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    *e"er to the 3igure that shows several $latesinside a distillation column. (ssume that the$lates are num/ered serially "rom the to$ downand that the $late under consideration is the n-th $late "rom the to$. Then the $late

    immediately a/ove this $late is $late 4n-56 andthe $late immediately /elow this $late is $late4n756.

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    "treamTotal #olar

    Flowrate

    $omposition

    #ole Fraction

    #V$!

    Vapor leaving

    plateVn yn

    Liquid leaving

    plate

    Ln xn

    Vapor entering

    plateVn%& yn%&

    Liquid entering

    plateLn'& xn'&

    There are four streams ( vapor and (

    liquid! associated with this plate, eachwith its own flow rate and concentration:

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    Ideal Plate1Tray1tage(n ideal $late is one where the va$orleaving the $late is in e2uili/rium withthe li2uid leaving the same $late 4seethe e2uili/rium diagram 8 9

    nand y

    nare

    in e2uili/rium6.

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    )n each plate, the vapor rising to it and the liquid

    flowing down to it are not in equilibrium* Thus there is

    a concentration difference driving force! for masstransfer between the two phases

    The system tends to reach equilibrium on each tray

    because some of the less volatile component

    condenses from the rising vapor into the liquid, thusincreasing the concentration of the more volatile

    component in the vapor as it moves upwards, e*g* yn+

    yn%&

    *

    some of the more volatile component is vaporiedfrom the liquid on the tray, thus decreasing the

    concentration of the more volatile component in the

    liquid as it moves downwards, e*g* xn'&

    + xn*

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    The changes in va$or and li2uid $hase mole"ractions are shown in the 3igure. The com/inede:ect is a gradual increase in concentration o"

    the more volatile com$onent in the va$or as itmoves u$ the column; and a gradual increase inconcentration o" the less volatile com$onent inthe li2uid as it moves down the column. ee the3igure

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    -ubble .oint Temperature

    The temperature at which the first bubble of vapor is

    formed*

    ew .oint Temperature

    The temperature at which the first dew of liquid is formed*

    The vapor and liquid streams inside the column areassumed to be saturated at their respective dew points

    and bubble points corresponding to the position in the

    column*

    The heat released by one mole of vapor uponcondensation is approximately equal to the heat required

    to vaporie one mole of the liquid: the number of

    molecules passing from the vapor phase to the liquid

    phase and vice versa will be approximately the same*

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    0f the molar heats of vaporiation are approximately

    constant, we can assume that the flows of liquid and

    vapour are nearly constant in each section of the

    column,i.e.

    L&1 L

    (1 L

    21 ********* 1 L

    n1 constant

    V& 1 V

    ( 1 V

    2 1 ********* 1 V

    n 1 constant

    This is the important concept of constant molaloverflow*

    "eparation is achieved with the vapor rich in the

    more volatile component leaving the top of the

    column, and the liquid rich in the less volatilecomponent leaving the bottom of the column*

    The temperature decreases as one moves up the

    column, i*e* Tn%&

    + Tn+ T

    n'&*

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    $alculation of Total 3umber of 4quilibrium "tages

    Procedure:

    The VLE data must be available at the operating pressure of the

    column.

    Separation must be specified.

    feed condition (temperature, composition), distillate and bottom

    compositions and the reflu! ratio, "hich is defined as the ratio of

    reflu! li#uid over the distillate product. This is sho"n in the $igure

    belo".

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    e num er o eore ca s ages requ re or a g ven

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    e num er o eore ca s ages requ re or a g venseparation is then the number of triangles that can bedrawn between these operating lines and theequilibrium curve. The last triangle on the diagramrepresents the reboiler.

    To obtain the number of theoretical trays using theMcCabe-Thiele Method, we shall use the section analysisthat is rst carried out by partitioning the column into 3sections rectifying, feed and stripping sections asshown the gure below

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    The McCabe-Thiele Method involves the steps givenbelow to determine the number of theoretical stages

    % !nalysis of the "ectifying section, and determine the"#$ using %

    &and "

    % !nalysis of the 'eed section, and determine the feedcondition (q)

    % &etermination of the feed line (q-line) using %'and q

    % $ocate the intersection point between "#$ and q-line% !nalysis of the *tripping *ection, and determine the

    *#$using (+) and %

    % 5.*ecti"ying ection #$erating 'ine 4*#'6% Consider the rectifying section as shown in the 'igure

    below. (*ystem shows a total condenser and thereu% is at bubble point)

    http://www.separationprocesses.com/Distillation/DT_Chp04l.htmhttp://www.separationprocesses.com/Distillation/Fig044.htmhttp://www.separationprocesses.com/Distillation/Fig044.htmhttp://www.separationprocesses.com/Distillation/DT_Chp04l.htm
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    Material balance around the envelope / 0 #1T

    Thus, we have($

    n2 &) y

    n20 $

    n%

    n2 & %

    &

    1nder constant molal overow assumption$0 $

    40 .......... $

    n-0 $

    n0 $

    n20 $ 0 constant

    OMB: Vn+1 = Ln+ D

    CMB: Vn+1 yn+1 = Lnxn+ D xD

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    50 5

    40 .......... 5

    n-0 5

    n0 5

    n20 5 0 constant

    The subscripts can be dropped. Thus, the equationsimplies to($ 2 &) y

    n

    2 0 $ %n

    2 & %&

    "e-arranging in the form y 0 f(%), we have

    ntroducing "eu% "atio " 0 $ 6 &,

    This is the )perating Line 4quation for the rectifying

    section, or 5)L in short*

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    ,haracteristics8 traight 'ine E2uation

    slo$e *14*756; constant "or given value o" *

    Interce$t 4514*756 9&; constant "or given * and$urity o" distillate 9

    &

    The o$erating line $asses through the $oint49

    &; 9

    &6 on the

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    &, diagonal (note y

    0 %&), draw a

    hori8ontal line tothe left until it

    touches theequilibrium curvethis gives the point(%

    , y

    ).

    'rom this point (%,

    y) draw a vertical

    line down to the"#$ this gives thepoint (%

    , y

    4). n

    this manner we

    had obtained onetriangle (no.)where thehori8ontal distanceis (%

    & - %

    ) and the

    vertical distance is

    (y - y4). #netrian le is

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    The di7erence (%&

    - %) represents

    the decrease in

    the concentrationof the morevolatilecomponent in theliquid phase as itsmoves down one

    tray, i.e. from tray to tray 4. Thedi7erence (y- y4)

    represents theincrease in the

    concentration ofthe more volatilecomponent in thevapor phase as itsmoves up one

    tray, i.e. from tray4 to tra . *ee

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    4 t d ti f ' d th li

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    4. ntroduction of 'eed the q-line

    Consider the section of the distillation column ( see the'igure below) at the tray where the feed is introduced(9nown as the feed tray location), say tray f

    3ig. ,ase a. ,old

    3eed

    !s an e%ample, considerthe 'igure above wherebythe feed is a cold liquid. nthis case, all the liquidfeed will go to thestripping section. naddition, because thefeed is cold, it will also

    condense some of therising vapor. !s a result,the amount of liquid owin the stripping section $:is much larger than the

    liquid ow in the rectifyingsection $. The vapour owin the rectifying section 5,is lower than the vapourow in the stripping

    section 5: because of thecondensation into the

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