fluid flow through randomly packed columns and fluidized beds

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  • 7/26/2019 Fluid Flow Through Randomly Packed Columns and Fluidized Beds

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    Fluid

    Flow

    through

    Randomly

    Packed Columns and Fluidized Beds

    T h e ra t io o f pressure grad ient t o super f ic ial f lu id ve loc i ty

    in

    packed colu mns is shown

    t o be a l in ear funct i on of f lu id mass f low rate. Th e constants of th e l inear relat ion

    involve part i cle specific surface, fract ion al void volum e, and f luid viscosity. These

    cons tants can be used t o p redict t h e degree of bed expansion w it h increasing gas f low

    af ter th e pressure gradient reaches th e buo yant weight of sol ids per u n i t vo lume of th e

    bed. Form al equat ions are developed t h at perm it est i mat io n of gas flow rates corre-

    sponding to Inc idence of tur bu lent or two-phase f lu idization-a state of f low i n which

    gas bubbles, wit h entrained sol ids, r ise thro ugh t he bed and cause intense c ir culat ion

    of solids. A con stant p rod uct of gas viscosity t im es superf icial velocity ma y serve as a

    cr i ter ion of a standard state in f lui dized systems used for reactio n k in eti c studies.

    SABRI ERGUN

    A N D A.

    A. ORNING

    COAL RESEARCH LAEORATO RY AN D DEPARTMENT O F CHE M I CAL E NOI NE E RI NG,

    CA NE 51E I NSTI T UTE

    O F

    T E CHNOL OOY, PI T T SE URG

    H

    PA.

    HE

    use of fluidized beds for kinetic studies of heterogeneous

    T eactions offers advantag es in ease of tem pera ture control

    even for highly exothermic reactions. However, it is essential to

    know the gas velocities needed to produce fluidization, and inter-

    pretatio n of da ta requires either a standard st at e of fluidization

    or

    some basis

    of

    correction for changes in bed volume and for

    nonuniformity of contact between gases and solids. This has re-

    quired

    a

    st ud y of the laws of fluid flow and new experimental d at a

    to describe the conditions of gas flow

    for

    rates ranging continu-

    ously from zero through those needed for fluidization.

    If the behavior of a packed bed is followed when a gas stream is

    introduced from the bot tom, the pressure drop a t first increases

    with flow ra te without bed expansion-i.e., th e fractional void

    volume remains unchanged. When the flow rat e is sufficient to

    cause a pressure gradient equal to t he buoyant weight of th e sol-

    ids per unit volume, further increase in flow rat e causes th e bed to

    expand-i.e., increases th e fractional void volume-the pressure

    drop remaining substantially constant. Up to

    a

    certain gas flow

    rate the expansion does not involve channeling

    or

    bubble flow,

    provided the column

    is

    subjected to some vibration. In this re-

    gion the bed increasingly acquires fluid properties, ceases to

    maintain it s normal angle of repose, and can be said to be par-

    tially fluidized. Until t he gas flow ra te is sufficient to cause bub-

    ble flow, there

    is

    no

    gross

    circulation or mixing of solids.

    With increasing gas flow rates bubbles appear and t he bed be-

    comes fully fluidized-i.e., i t can no longer main tain a n angle of

    repose greater than zero-there is no resistance to penetration by

    a

    solid except buoyancy, and the solids are circulating

    or

    mixing.

    Continued increase in flow ra te causes passage of larger bubbles

    with increasing frequency. This fluidized bed is not homogeneous

    with regard t o concentration of solids. For this reason, i t can ap-

    propriately be described as two-phase fluidization. With in th e

    fluidized bed

    a

    denser but expanded bed constitutes the continu-

    ous

    phase, while bubbles, which probably contain solids in sus-

    pension, constitute the discontinuous phase. Th e relative pro-

    portion of these phases varies with flow rat e.

    The three distinctly different states-the fixed bed, the ex-

    panded bed, and th e fluidized bed-are considered sepa rate ly in

    th at order.

    THE FIXED BED

    Th e fured bed is identical with randomly packed beds involved

    in th e determina tion of th e specific surface of fine powders by the

    air permeability method

    (1,

    6-8,

    10-18)

    and with randomly

    packed colunins

    ( 3 , 5 ,9,16,18-20) as

    used in absorption, extrac-

    tion, distillation, or catalyti c reactions.

    Attempts to determine the specific surface

    of

    powders by the

    air permeability method have led to

    a

    considerable amount

    of

    work in connection with the pressure drop through fine powders

    and filter beds a t low flow rates. The following equation, based

    upon viscosity, was first developed by Kozeny

    (IS),

    roposed by

    Carman

    8) or

    use with liquids, and later extended b y Lea and

    Nurse

    (14)

    o include measurements with gases:

    J t has been found satisfactory for small particles having specific

    surfaces less than

    1000

    to

    2000 sq.

    cm. per gram. Arne11

    (1 )

    and

    others have modified it to include terms which account for the

    changing flow character istics in extrcmely fine spaces,

    a

    modifics,

    tion that

    is

    not

    of

    particul ar interest for the present purpose.

    On the other hand,

    a

    considerable amount of work has been

    done in correlating data for packed columns

    at

    higher fluid veloc-

    ities where the pressure d rop appears to va ry with some power

    of

    the velocity, the exponent ranging between 1 and 2. Blake (8

    suggested th at this change of relationship between pressure drop

    and velocity is entirely analogous to tha t which occurs in ordinary

    pipes and proposed a friction factor plot similar to t ha t of Stan

    ton a nd Pannell (20). The equat ion used was th at for kinetic ef

    fect modified by

    a

    friction factor which in turn is

    a

    function o

    Reynolds number

    (9).

    A P = 2jpiu2/Dp 2

    where

    f = d N R s )

    Recent workers

    7 , 1 5 )

    have included t he effect

    of

    void fractio

    by the addition of another factor in Equation

    2.

    It is usually

    given in t he form

    (1 - )m / s 3

    where

    rn

    is either 1

    or

    2.

    A study

    of

    these different procedures showed tha t

    for

    fluid

    flow

    at

    low velocities through fine powders, viscous forces account fo

    the pressure drop within the accuracy of measurement, wherea

    for higher velocities, kinetic effects become more important bu

    do not alone account for t he pressure drop without t he aid of fac

    tors which in turn are functions

    of

    flow rate .

    This trans ition from t he dominance of viscous to kinetic effect

    for most packed systems, is smooth, indicating th at there shou

    be a continuous function relating pressure drop t o flow rate.

    1179

  • 7/26/2019 Fluid Flow Through Randomly Packed Columns and Fluidized Beds

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    1180 I N D U S T R I A L

    A N D

    E N G I N E E R I N G C H E M I S T R Y Vol.

    41, No.

    I

    W / A , G .

    /

    ( S E C X C M ~ )

    0.02 a04 a06 0

    F igure 1.

    Permeabi l i ty of Beds of Glass and Lead

    Spheres

    Mat eri al Gas Spheres,

    Rlm.

    Void

    V o l u m e

    + Glass N 0.570 0 330

    coz

    0.570 0.330

    Lead Nz 0.562 0.352

    CHI

    0.562 0.352

    N 0.497 0.350

    A v . D i a m .

    o f

    Frac t i ona l

    I

    W / A . G / SECJ CM~)

    Figure

    2.

    A i r

    Permeabi l i ty

    o f

    Lead

    Shot

    (Data

    of

    Burk e and P lumrn er ,

    5 )

    A v . Diam. of Fract ional

    Spheres , M m . Vo id Vo lume

    6.34

    3.08

    1.48

    0.397

    0.383

    0.374

    general relationship ma y be developed, using the Kozeriy assunip-

    tion tha t the granular bed is equivalent to

    8.

    group of parallel and

    equal-sized channels, such that the total internal surface and the

    free internal volume are equal to the t otal packing surface and th e

    void volume, respectively, of the randomly packed bed. The

    pressure drop through

    a

    channel is given by the Poiseuille equa-

    tion :

    dP/dL = 32 fiux/DZ (3)

    t o which

    a

    term representing kinetic energy

    loss,

    analogous

    to

    that

    introduced by Brillouin

    4 )

    or capillary flow, may be added.

    dP/dL = 32

    pu*/DZ

    f

    /B

    pju*'/Do

    4)

    Using relationships for cylindrical channels, the number

    of

    channels per un it are a an d their size can be eliminated in favor of

    specific surface and the frac tional void volume by means of t he

    following equations:

    S , = A - L T D ~ / L T D ~ / ~ ) ~

    NirDZ/4

    =

    aD2

    14

    2L* = U E

    and

    This leads to:

    (5)

    This equation, like many others that relate pressure drop

    to

    polynomials of t he fluid flow rat e, differs from them in that the

    coefficients hav e definite theoretical significancc.

    1 1 - e2

    dP/dL =

    2

    (

    pu

    S + -__

    8 3

    P/U2S,

    For a

    packed

    b e d , the flow pat h is sinuous and the strea m line

    frequently converge and diverge. The kinetic losses, which occu

    only orice for the cap

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