Gas Scrubbing Lecture

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    Rate-Base Method for Packed Columns

    Absorption and stripping are frequently conducted in packed columns, particularly when

    (1) the required column diameter is less than 2 ft;

    (2) the pressure drop must be low, as for a vacuum service;

    (3) corrosion considerations favor the use of ceramic or polymeric materials; and/or

    (4) low liquid holdup is desirable.Note: Structured packing is often favored over random packing for revamps to overcome

    capacity limitations of trayed towers.

    Packed columns are continuous differential contacting device that do not have the

    physically distinguishable stages found in trayed towers. Thus, packed columns are bestanalyzed by mass transfer considerations rather than by the equilibrium-stage concept for

    trayed tray. Nevertheless, in practice, packed-tower performance is often analyzed on the

    basis of equivalent equilibrium stages using a packed height equivalent to a theoretical

    (equilibrium) plate (stage), called the HETP or HETS and defined by the equation

    t

    T

    N

    l

    um stagesequilibriequivalent number of

    ghtpacked heiHETP

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    outoutinin GyxLyGLx ll

    assuming dilute solutions

    such that Gl=Gin=Gout=GandLl=Lin=Lout=L

    ininoutout GyxLyGLx ll

    for the absorber

    G

    L

    xyG

    L

    xy inout

    for the stripper

    G

    Lxy

    G

    Lxy outin

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    ~For the case of absorption, with mass

    transfer of the solute from the gas stream to

    the liquid stream, the two-film theory can

    be applied as illustrated in Figure 6.30.

    ~A concentration gradient exists in each film.

    ~At the interface between the two phase,

    physical equilibrium is assumed to exist.

    ~As with trayed tower, an operating line and

    an equilibrium line are of great importance

    in a packed column.

    ~For a given problem specification, the

    location of the two lines is independent of

    whether the tower is trayed or packed.

    ~The method for determining the minimum

    absorbent liquid or stripping vapor flow

    rates in a packed column is identical to the

    method for trayed tower.

    )()( II xxakyyakr xy

    The rate of mass transfer per unitvolume of packed bed is

    a represents the area for mass transfer

    per unit volume of packed bed.

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    ak

    ak

    xx

    yy

    xxakyyakr

    y

    x

    xy

    I

    I

    II )()(

    The composition of the interface

    depends on the ratio, kxa/kya, of

    the volumetric mass transfer

    coefficients

    The slope -kxa/kya, determines

    the relative resistances of thetwo phase to mass transfer.

    AE is the gas-phase

    driving force (y-yI)

    AF is the liquid-phase

    driving force (x-xI)

    mass transfer resistance

    entirely in liquid phaseyy I

    slight solubility;highK-value

    mass transfer resistance

    entirely in gas phasexx I

    strong solubility;

    lowK-value

    turbulence

    dispersion

    )*(*)( xxaKyyaKr xy

    y* x x* y

    akK

    akxxyy

    akakaK xyxyy

    1*111

    I

    I

    aKkakyy

    xx

    akakaK yxyxx

    11*111

    I

    I

    K K-value

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    For a dilute system, a differential material

    balance for the solute over a differentialheight of packingdl, gives:

    SdlyyaKGdy y *)(

    S is the cross-sectional area of the tower.

    in

    out

    *0

    y

    y

    Tyly

    yy

    dy

    G

    aSlKdl

    G

    aSKT

    OGOG

    y

    yy

    T NHyy

    dy

    aSK

    Gl

    in

    out *

    aSKGHy

    OG in

    out *y

    yOG

    yydyN

    ~HOG is the overall height of a transfer unit (HTU) based on the gas

    phase. Experimental data show that the HTU varies less with G

    thanKya. The smaller the HTU, the more efficient is the contacting.~NOG is the overall number of transfer units (NTU) based on the gas

    phase. It represents the overall change in solute mole fraction

    divided by the average mole fraction driving force. The larger the

    NTU, the greater is the extent of contacting required.

    in

    out

    in

    out inout )/()/1(*

    y

    y

    y

    y KxLKGyyLKG

    dy

    yy

    dy

    AA

    AKxyKxyAANOG

    /)1(

    )}/1()]/()][(/)1ln{[( inoutinin

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    AA

    AHOG

    /)1(

    )/1ln(HETP

    AAANN tOG/)1()/1ln(

    A>1, NTU>Nt

    A=1, NTU=Nt

    A

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    Example 6.9

    Repeat Example 6.1 for absorption in a tower packed with 1.5-in. metal Pall rings. If

    HOG=2.0 ft, compute the required height.

    Solution

    From Example 6.1, G=180 kmol/h,L=151.5 kmol/h,yin=0.020,xin=0.0, andK=0.57.

    For 97% recovery of ethyl alcohol, by material balance,

    68.32000612.0

    02.0

    477.1)180)(57.0(

    5.151

    000612.0)180)(02.0)(97.0(180

    )180)(02.0)(03.0(

    out

    in

    out

    y

    y

    KG

    L

    A

    y

    unitstransfer5.7477.1/)1477.1(

    )}477.1/1()68.32](477.1/)1477.1ln{[(

    /)1(

    )}/1()]/()][(/)1ln{[( inoutinin

    AA

    AKxyKxyAA

    NOG

    The packing height is ft15)5.7(0.2 NHl OGOGT

    NTU>Nt (=6.1)

    due toA>1

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    Example 6.10

    Experimental data have been obtained for air containing 1.6% by volume SO2 being scrubbed

    with pure water in a packed column of 1.5 m

    2

    in cross-sectional area and 3.5 m in packedheight. Entering gas and liquid flow rates are 0.062 and 2.2 kmol/s, respectively. If the outlet

    mole fraction of SO2 in the gas is 0.004 and column temperature is near ambient with KSO2=40,

    calculate from the data:

    (a) TheNOG for absorption of SO2

    (b) TheHOG in meters(c) The volumetric overall mass transfer coefficient,Kya for SO2 in kmol/m

    3-s-( y).

    Solution

    (a) Assume a straight equilibrium line because the system is dilute in SO2

    004.0016.089.0)062.0)(40(

    2.2outin yy

    KGLA

    unitstransfer75.389.0/)189.0(

    )}89.0/1()004.0/016.0](89.0/)189.0ln{[(

    /A)1(A

    )}/1()]/()][(/)1ln{[( inoutinin

    AKxyKxyAANOG

    (b) lT=3.5m,HOG= lT/NOG=3.5/3.75=0.93 m

    (c) G=0.062 kmol/s, S=1.5 m2

    ,Kya=G/HOGS=0.062/[(0.93)(1.5)]=0.044 kmol/m3

    -s-( y)

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    Example 6.11

    A gaseous reactor effluent consisting of 2 mol% ethylene oxide in an inert gas is scrubbed

    with water at 30 C and 20 atm . The total gas feed rate is 2,500 lbmol/h, and the water rateentering the scrubber is 3,500 lbmol/h. The column, with a diameter of 4 ft, is packed in two

    12-ft-high sections with 1.5-in. metal Pall rings. A liquid redistributor is located between the

    two packed sections. Under the operating conditions for the scrubber, the K-value for

    ethylene oxide is 0.85 and estimated values ofkya and kxa are 200 lbmol/h-ft3- y and 165

    lbmol/h-ft3- x, respectively. Calculate: (a)Kya and (b)HOG

    ytflbmol/h5.98)165/85.0()200/1(

    1

    1

    111 3

    ak

    K

    ak

    aKak

    K

    akaK

    xy

    y

    xyy

    Solution

    ft02.2)6.12)(5.98(

    500,2

    aSK

    GH

    y

    OG

    ft0.1)6.12)(200(

    500,2

    aSk

    GH

    y

    G ft68.1)6.12)(165(

    500,3

    aSk

    LH

    x

    L

    22 ft6.124/)4(14.3 S

    A

    H

    HHL

    GOG 65.1)500,2)(85.0(

    500,3 KG

    LA

    ft02.265.1

    68.10.1

    A

    HHH L

    GOG

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    Packed Columns Efficiency, Capacity, and Pressure Drop

    Liquid holdup

    Flooding

    Pressure drop

    Column diameterGas/liquid flow rates per

    unit inside cross-sectional

    area of the column

    KGa orKLa

    HTUPacking height

    Liquid Holdup ~The lowest curve corresponds to zero liquid flow,

    that is, the dry pressure drop.

    ~Over an almost 10-fold range of air velocity, the

    pressure drop for air flowing up through thepacking is proportional to air velocity to the 1.86

    power.

    ~As liquid flows down through the packing at an

    increasing rate, gas-phase pressure drop for agiven gas velocity increases.

    ~Below a certain limiting gas velocity, the curve

    for each liquid velocity is a straight line parallel

    to the dry pressure drop curve. In this region, the

    liquid holdup for each liquid velocity is constant.

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    ~For a liquid velocity of 40 m/h, specific liquid

    holdup is 0.08 m3

    /m3

    of packed bed until asuperficial gas velocity of 0.8 m/h is reached.

    ~Instead of a void fraction, , of 0.94 for the gas

    to flow through, the effective void fraction is

    reduced by the liquid holdup to 0.94-0.08=0.86,

    causing an increased pressure drop.

    ~For a given liquid velocity, the upper limit to

    the gas velocity for a constant liquid holdup is

    termed the loading point. Below this point, the

    gas phase is the continuous phase.

    ~Above this point, liquid begins to accumulate

    or load the bed, replacing gas holdup and

    causing a sharp increase in pressure drop.

    ~Finally, a gas velocity is reached at which theliquid surface is continuous across the top of

    the packing and the column is flooded.

    ~At the flooding point, the pressure drop

    increases infinitely with increasing gas velocity.

    ~The region between the loading point and

    the flooding point is the loading region;

    significant liquid entrainment is observed,

    liquid holdup increase sharply, masstransfer efficiency decrease, and column

    operation is unstable.

    ~Typically, the superficial gas velocity at

    the loading point is approximately 70% ofthat at the flooding point.

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    3/23/1

    Re

    Fr12

    a

    a

    N

    Nh hL

    L

    L

    Although a packed column can operate in the loading region, most packed columns are

    designed to operate below the loading point, in the preloading region. The specific liquid

    holdup in the preloading region depends on packing characteristics, and the viscosity,

    density, and superficial velocity of the liquid according to the dimensionless expression

    L

    L

    L

    LL

    a

    u

    a

    uN

    L

    rceviscous fo

    orceinertial fnumbernoldsliquid ReyRe L is the kinematic viscosity

    g

    auN L

    L

    2

    Fr nal forcegravitatio

    orceinertial fnumberFroudeliquid

    The ratio of specific hydraulic area of packing, ah, to specific surface area of packing,

    a, is given by

    5for85.0/

    5for/

    Re1.0

    Fr25.0

    Re

    Re1.0

    Fr15.0

    Re

    LLL

    LLL

    NNNCaa

    NNNCaa

    hh

    hh

    ~Value ofa and Ch are characteristic of the particular type and size of packing, as

    listed, together with packing void fraction, , and other packing constants in Table 6.8.

    ~Because the specific liquid holdup is constant in the preloading region, the aboveequation does not involve gas-phase properties or gas velocity.

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    ~At low liquid velocities, liquid

    holdup can becomes so small

    that the packing is no longer

    completely wetted.

    ~When th i s occurs , pack ing

    efficiency decreases dramatically,

    particularly for aqueous systems

    of high surface tension.

    0.0012Plastic

    0.0009Bright metal

    0.0003Oxidized or etched metal

    0.00015Ceramic

    uL,min

    , m/sType of Packing Material

    To ensure complete wetting of packing, proven

    liquid distributors and redistributors should be

    used and superficial liquid velocities should

    exceed the following values:

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    Example 6.12

    An absorption column is to be designed using oil absorbent with a kinematic viscosity of

    three time of water at 20 C. The superficial velocity will be 0.01m/s, which is safely abovethe minimum value for good wetting. The superficial gas velocity will be such that operation

    will be in the preloading region. Two packing materials are being considered: (1) randomly

    packed 50-mm metal Hiflow rings and (2) metal Montz B1-200 structured packing. Estimate

    the specific liquid holdup for each of these two packings.

    Solution

    0.5470.979200.0Montz metal B1-200

    0.8760.97792.350-mm metal Hiflow rings

    Cha, m2/m3Packing

    At 20 C for water, kinematic viscosity, = / =1 10-6 m2/s. Therefore, for the oil,

    = / =3 10-6 m2/s.

    aa

    uN

    L

    L

    L 6Re 103

    01.0

    8.9

    )01.0( 22

    Fr

    a

    g

    auN L

    L

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    0.0020416.67Montz metal B1-200

    0.00094236.150-mm metal Hiflow ringsPacking LNRe LNFr

    ingMontz Packfor506.0)00204.0()67.16)(547.0)(85.0(85.0/

    Packingfor Hiflow909.0)000942.0()1.36)(876.0)(85.0(85.0/

    1.025.01.0Fr

    25.0Re

    1.025.01.0Fr

    25.0Re

    NNCaa

    NNCaa

    LL

    LL

    hh

    hh

    3/23/1

    Re

    Fr12

    a

    a

    N

    Nh hL

    L

    L

    50-mm metal Hiflow rings

    333/23/1

    /mm0637.0909.01.36

    )000942.0(12hL

    333/23/1

    /mm0722.0506.067.16

    )0204.0(12hL

    Montz metal B1-200

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    Capacity and Pressure drop

    ~The column diameter is determined so as to safely avoid flooding and operate in thepreloading region with a pressure drop of no greater than 1.5 in. of water head per foot of

    packed height (equivalent to 0.054 psi/ft of packing).

    ~For random packings, a nominal packing diameter not greater than one-eighth of the

    diameter of the column is selected; otherwise, poor distribution of liquid and vapor flow over

    the cross-sectional area of the column can occur, with liquid tending to migrate to the wall of

    the column.

    8/14/12.0

    3

    2

    '

    '4ln

    L

    G

    w

    L

    L

    GpG

    G

    L

    g

    au

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    Leva presented the generalized pressure drop

    correlation (GPDC)

    }{}{

    )(2OH

    2

    LL

    gPo uffg

    FuY

    L

    5.0

    4

    Go

    GT

    fu

    GMD

    uo

    is the superficial gas velocity at flooding

    fis the fraction of floodingFp=packing factor(=a/

    3

    )

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    Example 6.13

    Air containing 5 mol% NH3 at a total flow rate of 40 lbmol/h, enters a packed column

    operating at 20 C and 1 atm, where 90% of the ammonia is scrubbed by a countercurrentflow of 3,000 lb/h of water. Use the GPDC chart of Figure 6.36 to estimate the superficial

    gas flooding velocity, the column inside diameter for operation at 70% of flooding, and the

    pressure drop per foot of packing for two packing materials:

    (a) One-inch ceramic Rasching rings (FP=179 ft2/ft3)

    (b) One-inch metal IMTP packing (FP=41 ft2

    /ft3

    )

    Solution

    Because the superficial gas velocity is highest at the bottom of the column, calculations

    are made for there.Inlet gas:

    MG=0.95(29)+0.05(17)=28.4 G=40 lbmol/h

    G=PMG/RT=(1)(28.4)/[(0.730)(293)(1.8)]=0.0738 lb/ft3

    Existing liquid:

    Ammonia absorbed =0.90(0.05)(40)=1.8 lbmol/h

    Water rate=166.7 lbmol/h

    Mole fraction of ammonia=1.8/(166.7+1.8)=0.0107

    ML=0.0107(17)+0.9893(18)=17.9 L=1.8+166.7=168.5 lbmol/hTake: L=62.4 lb/ft3 and L=1.0 cP

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    092.04.62

    0738.0

    )4.28)(40(

    )9.17)(5.168(

    5.05.0

    L

    G

    G

    LLG

    GM

    LMFX

    0.1}{

    14.1}{

    125.0

    L

    L

    uf

    f

    YFrom Figure 6.36

    PPLLgP

    oFg

    Fg

    uffFgYu

    L 7.92)0.1)(14.1)(0738.0(

    4.62125.0}{}{

    1

    )(2OH2

    8.541IMTP packing

    4.1179Raschig rings

    uo, ft/sFP, ft2/ft3Packing

    g=32.2 ft/s

    11.55.95IMTP packing

    16.52.87Raschig ringsDT, inuG = fuo, ft/sPacking

    5.0

    4

    Go

    GT

    fu

    GMD

    f=0.70

    FLG=0.092 and

    Y=0.702(0.125)=0.088

    The pressure drop is 0.88

    in. of water head per footof packed height for both

    packing

    The IMTP packing has a much greater capacity than the Raschig rings,

    since the required column cross-sectional area is reduced by about 50%.

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    Dp is an effective packing material diameter

    ~At low superficial gas velocities (modified

    NRe1,000). Thus, dry pressure data shownin Figure 6.34 for Bialecki rings show an

    exponential dependency on gas velocity of

    about 1.86.

    Theoretically based models for predicting pressure drop in packed beds with countercurrent

    gas/liquid flows have been by Stichlmair et al., who use a particle model, and Billet and

    Schultes, who use a channel model. Both models extend well-accepted equations for dry-bedpressure drop to account for the effect of liquid holdup.

    Similar to that flow throughan empty, straight pipe.

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    Billet and Schultes developed a correlation for dry-gas pressure drop, Po, similar in

    form to that of Figure 6.37. Their dimensionally consistent correlating equation is

    wc

    Goo

    T

    o

    Kg

    ua

    l

    P 1

    2

    2

    3 lT=height of packing

    Kw=a wall factor

    T

    P

    w D

    D

    K

    1

    1

    3

    21

    1

    aDP

    16

    wall factor effective packing diameter

    08.0ReRe

    8.164

    GGNN

    CPow

    G

    GpoK

    DuN

    G )1(

    Re

    dry-packing resistance coefficient

    Cp is a packing constant, determined

    from experimental data, and tabulated

    for a number of packings in Table 6.8

    When the packed tower is irrigated, the liquid holdup causes the pressure drop toincrease. The experimental data are reasonably well correlated by

    200exp

    Re5.1

    L

    Nh

    P

    P L

    o

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    Mass Transfer Efficiency

    ~The mass transfer efficiency of a packed column is incorporated in the HETP or the more

    theoretically based HTUs and volumetric mass transfer coefficients.

    ~The HETP concept lacks a sound theoretical basis, its simplicity, coupled with the relative

    ease with which equilibrium-stage calculations can be made with computed-aided

    simulation programs, has made it a widely used method for estimating packed height.

    ~In the preloading region and where good distribution of vapor and liquid is initiated and

    maintained, values of the HETP depend mainly on packing type and size, liquid viscosity,and surface tension.

    Kister took the following relations for rough estimates:

    1.Pall rings and similar high-efficiency random packings with low-viscosity liquids:

    HETP, ft=1.5DP, in.2.Structured packing at low-to-moderate pressure with low-viscosity liquids:

    HETP, ft=100/a, ft2/ft3+4/12

    3.Absorption with viscous liquid:

    HETP=5 to 6 ft

    4.Vacuum service:HETP, ft=1.5DP, in.+0.5

    5.High-pressure service (>200 psia):

    HETP for structured packings may be greater than predicted by HETP, ft=100/a, ft2/ft3+4/12

    6.Small-diameter columns,DT

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    In general, lower values of HETP are achieved with smaller-size random packings,

    particularly in small-diameter columns, and with structured packings, particularly

    those with large values ofa, the packing surface area per packed volume.

    The experimental data of Figure 6.38 for

    no.2 (2-in.-diameter) Nutter rings from

    Kunesh show that in the preloading region,

    the HETP is relatively independent of the

    vapor-flowF-factor:

    5.0)(GouF

    provided that the ratio L/G is maintained

    constant as the superficial gas velocity, uo,

    increased. Beyond the loading point, and asthe flooding point is approached, the HETP

    can increase dramatically like the pressure

    drop and liquid holdup.

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    ~Experimental mass transfer data for packed columns are usually correlated in terms of

    volumetric mass transfer coefficients and/or HTUs, rather than in terms of HETPs.

    ~The data are obtained from experiments in which either the liquid-phase or the gas-phase

    mass transfer resistance is negligible, so that the other resistance can be studied and

    correlated independently.

    ~For applications where both resistance may be important, the two resistances are added

    together according to the two-film theory of Whitman to obtain the overall resistance.

    ~Two film theory assumes the absence of any mass transfer resistance at the interface

    between the gas and liquid phases, thus, the two phases are in equilibrium at the interface.

    ak

    K

    akaK xyy

    11*)()()( II yyaKxxakyyakr yxy

    akH

    akaK LgG

    '11 *)()()( II PpaKccakppakr GLg cHpcHp

    '*

    ' II

    lbmol/ft3-h-atmmol/m3-s-kPakga, KGa

    h-1s-1kLa, kGa, KLa

    ft/hm/skL,kG

    lbmol/ft3-hmol/m3-skya,kxa,Kxa, Kyalbmol/ft

    3

    -hmol/m3

    -sr

    American EngineeringSI

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    ~Instead of using mass transfer coefficient directly for column design, the transfer unit concept

    of Chilton and Colburn is often employed because HTUs:

    (1)have only one dimension (length),

    (2)generally vary with column conditions less than mass transfer coefficients,

    (3)are related to an easily understood geometrical quantity, namely, height per theoretical stage.

    ak

    K

    akaK xyy

    11LGOG H

    L

    KGHH

    aKkakaK yxx

    111 GLOL H

    KG

    LHH

    aSk

    LM

    H LL

    L

    L

    ~Figure 6.39 show the data for three different

    size Berl-saddle packings for the stripping of

    oxygen from water by air, in a 20-in.-I.D.

    c o l u m n o p e r a t e d a t n e a r - a m b i e n t

    temperature and pressure in the preloading

    region.

    ~The effect of liquid velocity onkL

    a is seen to be

    quite pronounced, withkLa increasing at about

    the 0.75 power of the liquid mass velocity.

    ~Gas velocity was to have no effect onkLa in the

    preloading region.

    ~HL does not depend as strongly askLa on liquidvelocity.

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    Figure 6.40 shows the data on the effect of

    liquid velocity on kLa in the preloading

    region for two different size ceramic

    Hiflow ring packings using the system of

    CO2-air-H2O.

    Figure 6.41 shows the data on the effect of

    the F-factor on kLa at a constant liquid

    flow rate with 50-mm plastic Pall rings

    and Hiflow rings using the system of CO2-

    air-H2O.

    ~Up to an F-factor value of about of 1.8 m-1/2-s-1-kg1/2,

    which is in the preloading region, no effect gas velocity

    is observed.

    ~Above the loading limit, kLa increases with increasing

    gas velocity because of increased liquid holdup, which

    increase interfacial surface area for mass transfer.

    nLLL uDCak

    2/11

    n=0.6~0.95, 0.75 typical value

    The exponent on the diffusivity isconsistent with the penetration theory.

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    ~Figures 6.42 and 6.43 show the data for twodifferent plastic packings using the system

    of NH3-air-H2O.

    ~The kGa vlaues are proportional to about

    the 0.75 power ofF.

    ~The liquid velocity also affects the kGa

    values, probably because as the liquid rate

    is increased, the holdup increases and more

    interfacial surface is created.

    ''67.02

    nL

    mGG uFDCak

    DG=gas diffusivitym=0.65~0.85, 0.8 typical value

    n=0.25~0.5

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    ~The development of correlations for mass transfer from experimental data is difficult

    because, as shown by Billet in a comprehensive study with metal Pall rings, values ofthe mass transfer coefficients are significantly affected by the technique used to pack

    the column and the number of liquid feed distribution points per unit of column cross

    section, when this number is less than 10 points/ft2.

    ~When 25 points/ft2

    are used andDT/Dp>10, column diameter has little, if any, effect onmass transfer coefficients for packed height up to 20 ft.

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    Billet and Schultes assume

    (1)uniform distribution of gas and liquid over the cross-sectional area of the column and

    apply the two-film theory of mass transfer.(2)for the liquid-phase resistance, the liquid flows in a thin film through the irregular

    channels of the packing, with continual remixing of the liquid at points of contact with

    the packing such that penetration theory can applied.

    )(I

    LLhL ccakr 5.0

    2

    L

    LL

    t

    Dk

    penetration theory time of exposure of the

    liquid film before remixing

    au

    h

    u

    rh

    u

    dht

    L

    L

    L

    HL

    L

    HL

    L

    44

    h

    L

    LL

    L

    hL

    LL

    a

    u

    auD

    h

    ak

    uH

    2/14

    2

    h

    L

    LL

    L

    L

    La

    u

    auD

    h

    CH

    2/16/14

    12

    11

    hG

    oL

    V

    GaD

    auNN

    ah

    CH

    GG

    3/1

    Sc

    4/3

    Re

    2/1

    4

    2/1 )()(4

    )(1

    G

    Go

    a

    uN

    G

    Re

    GG

    G

    DN

    G

    Sc

    LGOG HL

    KGHH

    OGOGT

    NHl

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    Example 6.14

    For the absorption of ethyl alcohol form CO2 with water, as considered in Example6.1, a 2.5-ft-I.D. tower, packed with 1.5-in. metal Pall-like Rings, is to be used. It is

    estimated that the tower will operate in the preloading region with a pressure drop of

    approximately 1.5 in. of water head per foot of packed height. From example 6.9, the

    required number of overall transfer units based on the gas phase is 7.5. EstimateHG,

    HL,HOG, HETP, and the required packed height in feet using the following estimatesof flow conditions and physical properties at the bottom of the packing:

    S i

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    Solution

    Cross-sectional area of tower = (3.14)(2.5)2/4 = 4.91 ft2.

    Volumetric liquid flow rate = 6,140/61.5 = 99.8 ft

    3

    /h.uL = superficial liquid velocity = 99.8/[(4.91)(3,600)] = 0.0056 ft/s = 0.0017 m/s

    uo = superficial gas velocity = 17,480/[(0.121)(4.91)(3,600)] = 8.17 ft/s = 2.49 m/s

    Packing characteristic for the 1.5-inch metal Pall-like rings

    a=149.6 m2/m3 =0.952

    Ch=approximately 0.7 CL=1.227 CV=0.341

    Estimation of specific liquid holdup,hL:

    8.17)1064.0)(6.149(

    0017.0 6

    Re

    L

    L

    auN

    L

    522

    Fr 104.48.9

    )6.149()0017.0( gauN L

    L

    321.0525.01.0Fr

    25.0Re /mm3.67)6.149(45.045.0)104.4()8.17)(7.0(85.085.0/ aNNCaa hhh

    LL

    323/2

    3/153/2

    3/1

    Re

    Fr/mm023.0)64.0(

    8.17

    )104.4(1212

    a

    a

    N

    Nh hL

    L

    L

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    Estimation ofHL:

    ft62.0m19.03.67

    0017.0

    )0017.0)(6.149)(1082.1(

    )952.0)(023.0(4

    12

    1

    227.1

    1

    41211

    2/1

    9

    6/1

    2/16/1

    au

    auDh

    CH

    h

    L

    LL

    L

    L

    L

    Estimation ofHG:

    2220)1075.0)(6.149(

    49.2

    5Re G

    Go

    a

    u

    N G 968.0100775.0

    1075.0

    4

    5

    Sc

    GG

    G

    DN G

    ft80.1m55.0

    )3.67)(100775.0(

    )6.149)(49.2()968.0()2220(

    )6.149(

    )952.0(4)023.0952.0(

    341.0

    1

    )()(4

    )(1

    4

    3/14/3

    2/1

    4

    2/1

    3/1Sc

    4/3Re

    2/1

    4

    2/1

    aD

    auNN

    ah

    CH

    hG

    oL

    V

    GGG

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    ft23.2)62.0(69.080.1)62.0(

    7.18

    6140

    05.44

    1748057.0

    80.1 HL

    KGHH LGOG

    Estimation ofHOG:

    Estimation of Packed Height:

    ft7.16)5.7)(23.2( NHl OGOGT

    Estimation of HETP:

    ft67.2)69.0/1/()69.0/11(

    )69.0ln(23.2

    /)1(

    )/1ln(HETP

    AA

    AHOG

    69.0

    7.18

    6140

    05.44

    1748057.0

    A