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Transcript of McCabe Thiele Graphical Equilibrium-Stage - 12.pdf · McCabe Thiele Graphical Equilibrium-Stage ...

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    Limiting condition

    McCabe Thiele Graphical

    Equilibrium-Stage

    When analyzing or designing a process, it is useful to look at limiting

    cases to assess the possible values of process parameters. In

    distillation analysis, separation of a pair of components can be improved

    by increasing the number of stages while holding reflux constant, or by

    increasing the reflux flow for a given number of stages. This tradeoff

    sets up two limiting cases:

    1. Total Reflux (minimum ideal stages)

    2. Minimum Reflux (infinite ideal stages)

    The design tradeoff between reflux and stages is the standard economic

    optimization problem chemical engineers always face -- balancing capital costs

    (the number of trays to be built) vs. the operating cost (the amount of reflux to be

    recirculated). A good design will operate near a cost optimum reflux ratio.

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    D

    LRD

    McCabe Thiele Graphical

    Equilibrium-Stage

    If the reflux ratio ( ) is increased to very large value, the

    operating lines become the 45o line. The infinite reflux ratio occurs

    in real life when the column is operated under what are called (total

    reflux) condition

    a) Minimum number of plates:

    Under these conditions, no feed is added to the column (F=0) and

    no products are withdrawn (D=0, B=0), but the vapor is raised up

    and condensed to the column. So the column is just circulating

    vapor and liquid up and down. Most columns are started up under

    total reflux conditions.

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    Distillation of Binary Mixture

    Since the liquid flow rate in the column is same as the vapor flow

    rate, and

    0.1V

    L

    V

    L

    The operating line

    nD

    nn xDL

    Dxx

    DL

    Ly

    1 m

    Bmm x

    BL

    Bxx

    BL

    Ly

    1,

    The composition in the base of the column under total reflux = xB, and

    the composition of the liquid in the reflux drum = xD

    In this case the number of ideal plates is minimum.

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    Binary Multistage Distillation

    The minimum number of ideal plates can be done by:

    a) Graphically as shown in the figure

    y

    XD XF

    XB

    XB

    x

    y1

    y2

    y3

    y4

    X1

    X2

    X3

    Operating lines

    as total reflux

    Composition of liquid

    in reflux drum

    Composition of liquid

    in re-boiler

    y1 = xD

    y2 = x1

    y3 = x2

    y4 = x3

    xB = xB

    Minimum number of

    plates = 3+reboiler

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    Binary Multistage Distillation

    b) Analytically (using Fenske Equation)

    This equation gives the number of plates required under total reflux at

    constant .

    It is applicable to multi-component system as well as binary system

    (= constant, total reflux, ideal system).

    It is very useful for getting quick estimates of the size of a column.

    Derivation of Fenske Equation

    Consider two component (A,B) forming ideal solution

    product bottomin ration mole

    product in top ratio mole

    /

    /

    /

    /

    BA

    BA

    BB

    AA

    B

    AAB

    xx

    yy

    xy

    xy

    K

    K

    (1)

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    An ideal mixture follows Raoults law and = vapor product ratio

    Binary Multistage Distillation

    P

    xP

    P

    PxPP A

    sat

    AAA

    sat

    AA Ay

    P

    xP

    P

    PxPP B

    sat

    BBB

    sat

    BB By

    sat

    B

    sat

    A

    BB

    sat

    B

    AA

    sat

    A

    BB

    AA

    B

    AAB

    P

    P

    PxxP

    PxxP

    xy

    xy

    K

    K

    /

    /

    /

    /

    sat

    B

    sat

    A PP /

    does not change much over the range of temperature

    encountered,AB constant

    1

    , 1 A

    A

    B

    A

    A

    A

    B

    A

    x

    x

    x

    x

    y

    y

    y

    y

    (2)

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    Binary Multistage Distillation

    Substitute (2) in (1)

    1

    1

    1

    1

    1

    1

    n

    n

    AB

    n

    n

    x

    x

    y

    y

    AB

    A

    A

    A

    A

    x

    x

    y

    y

    11

    DL

    Dxx

    DL

    Ly Dnn

    1

    For plate n+1

    Since D = 0 (total reflux), L / V= 1.0 ,

    Then yn+1 = xn and 1

    1

    1

    1

    n

    n

    AB

    n

    n

    x

    x

    x

    x

    zero

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    Binary Multistage Distillation

    At the top of the column, if a total

    condenser is used y1 = xD , n = 0

    Substitute in (2)

    1

    1

    1

    1 x

    x

    x

    xAB

    D

    D

    For plate (1)

    xD

    y1

    water

    Re-boiler

    Vb yb

    Lb, xb

    steam

    x1

    x2

    x3

    xn

    xn-1

    x0

    y2

    y3

    y4

    yn-1

    yn

    yr

    B

    BAB

    n

    n

    x

    x

    x

    x

    1

    1

    For plate (n)

    . . . .

    . . . .

    . . . .

    n

    n

    AB

    n

    n

    x

    x

    x

    x

    1

    1 1

    1

    For re-boiler plate

    For plate (2) 2

    2

    1

    1

    1

    1 x

    x

    x

    xAB

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    Binary Multistage Distillation

    If all equations are multiplied together and all the intermediate terms

    canceled,

    B

    Bn

    AB

    D

    D

    x

    x

    x

    x

    1) (

    1

    B

    BN

    AB

    D

    D

    x

    x

    x

    x

    1) (

    1

    1min

    AB

    BBDD xxxxNln

    )]1//()1/ln[(1min

    AB

    BBADBA

    AB

    BD xxxxN ln

    )//()/ln(

    ln

    ])ration mole/()ration moleln[(1or min

    Where n= Nmin + reboiler

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    McCabe Thiele Graphical

    Equilibrium-Stage

    Example:

    Calculate the minimum number of trays required to achieve a

    separate from 5 mole % bottoms to 90 moles % distillate in a binary

    column with =2.5

    solution xB = 0.05 , xD = 0.9

    61.419163.0

    14.5 ,

    5.2ln

    )]05.01/05.0/()9.01/9.0ln[(1 minmin

    NN

    AB

    BBDD xxxxNln

    )]1//()1/ln[(1min

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    McCabe Thiele Graphical

    Equilibrium-Stage

    Example: in a mixture to be fed to a continuous distillation column, the mole

    fraction of phenol is 0.35, of o-cresol 0.15, of m-cresol 0.3 and of xylenes

    0.2. it is hoped to obtain a product with a mole fraction of phenol 0.952, of

    o-cresol 0.0474, of m-cresol 0.0.0006. if p-o= 1.26, m-o=0.7, estimate how

    many theoretical plates would be required at total reflux. Assume no phenol in the bottoms.

    Solution:

    A light component (o-cresol) B heavy component (m-cresol)

    Total balance 100=D + B

    For phenol 100*0.35=D*0.952+B*xB,p

    = zero

    D= 36.8 Kmol, B = 63.2 Kmol

    For o cresol

    100*0.15=0.0474*36.8+xB,o*63.2 xB,o=0.21

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    McCabe Thiele Graphical

    Equilibrium-Stage

    o-m= 1/0.7=1.43 43.1ln

    )]474.0/21.0/()0006.0/0474.0ln[(1min N

    5.13min N

    component Feed top Bottms

    phenol 0.35 0.952 0 p-o= 1.26

    o-cresol 0.15 0.0474 0.21 o-o= 1.0

    m-cresol 0.3 0.0006 0.474 m-o=0.7

    xylenes 0.2 0 0.316

    For m cresol

    100*0.3=0.0006*36.8+xB,m*63.2 xB,m=0.474

    xB,X=0.316

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    McCabe Thiele Graphical

    Equilibrium-Stage

    b) Minimum Reflux Ratio

    The next figure shows how changing the reflux ratio affects the

    operating lines: the lower the reflux ratio, the closer the operating

    line moves toward the equilibrium curve, and the larger the number

    of plates.

    If the reflux ratio finally reduced to the point where either operating

    line intersects or becomes tangent to the VLE curve, an infinite

    number of plates will be required and the reflux ratio is minimum.

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    To obtain the RDmin

    McCabe Thiele Graphical

    Equilibrium-Stage

    111

    D

    Dn

    D

    Dn

    R

    xx

    R

    Ry

    1intercept ab

    min

    D

    D

    R

    x

    1min D

    D

    R

    x

    x

    a

    b x`

    (xD,xD)

    y

    xD

    xD

  • Dr Saad Al-Shahrani ChE 334: Separation Processes

    McCabe Thiele Graphical

    Equilibrium-Stage

    If the equilibrium curve

    has a cavity upward, e.g.,

    the curve for water-

    ethanol shown in the

    figure in this case the

    minimum reflux ratio

    must be computed from

    the slope of the operating

    line (ac