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7/26/2019 Fluid Flow Through Randomly Packed Columns and Fluidized Beds
1/6
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
2/6
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 capillary, occur with a frequency t,httt is s tatisti
cally related t o t'lie number of particles per unit length. For thes
reasons, a correction factor must be applied t o each term . Thes
factors may be designated as 01 and p.
Th e values for
a
and
3
can be determined ex;pe~imentally nd
generally app roximates (a/2 )2a,h ich has been proposed on t,heore
cal
grounds ( 12 ) . Experiments with randomly
packed
m:tter
al s
of
known specific surface have led
to
adopt,ioii
of
a value of
for 2a, which is close to the theoretical value of 4.035.
Integration of Equation 6, assuming isothermal espansiori o
an ideal gas, leads
to
the equation:
where
urn
s the superficial velocity
at'
the mean pressure, and
W /
is the mass
f l o ~
ate per unit area
of
the empty tube. Leva
et a
( 1 5 ) reported t'liat' in packed tube s, xlicn the viscous forces a
predominant, the pressure drop is proport,ional to
1
t ) * / e
\-hereas, at higher flow rates , the corresponding dependence upo
the void fraction is
1
- ) / e 3 viliich is just a-ha,t
would
be ex
pected from Equation
7 .
From Equation 7, a plot, of AP: L2im
08.
TV/A would give
straight line, t.he intercept and slope leading to values
of
01 and
Typical
plots
of
data obtained l o test this dependence of pressur
drop on gas flow rate are shown in Figure 1.
Pressure drop measurements ivere made
in a
glass tube,
1
inc
in inside diameter and 30 inches long, fitted with a fritted-gla
disk t o obtain uniform gas flow at the bot tom an d with pressur
7/26/2019 Fluid Flow Through Randomly Packed Columns and Fluidized Beds
3/6
June
1949
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 1181
size
(19).
These plots demonstrate the validity
of
Equation
7
within the range of experimental accuracy. Values for a and p
for
all
the da ta are given in Table I, together with references to
sources of those data taken from the literature. The lines shown
in Figure 3 for the da ta of Oman and Watson
(19)
are not those
used in determining the constants. These data fell int o high and
low density groups each of nearly, bu t no t quite, t he same frac-
tional void volume. For these dat a, Equation 7 was first divided
by
(1
-
~/e3,
eading to plots with common intercepts conven-
ient for determining a. Similarly, a division by 1 - )/e3 led to
plots with common slopes
for
determining p.
Using the relation for
a
sphere, D
=
6/&, Reynolds number,
N R ~D P U n P j m / ~ ,
an be used totra nsfor mEqu ation7 to th e form
8 )
a l - - e P 1 E
A P / L
=
[ + 96 --l v R a ] s T s Pj,u:
Thus the friction factor would become:
f = a [ 1 + 9 6 " l - ' ]
NR
9)
An examination of the values of
cy
and
P
given in Table I and
of
Equation 8 indicates t he relative importance of the viscosity and
kinetic terms. For Reynolds numbers around
60,
with
E
= 0.35,
the two have nearly equal effects upon pressure drop.' For
N z c
=
0.1, viscosity accounts for
99.8 ,
while for N R ~ 3000, kinetic
effects account for 97 of the pressure drop. Because packed
columns are generally operated in the range from
N R ~
1
to
10,000, both term s are essential in calculations of pressure drop
Mater i al Spheres, Inc h (Approx imate) Although the theoretical development has been based on ran-
-tCeli te spheres 0.25
domly packed beds, th e same treatment can be applied to d at a ob-
-I- Cel i te cy l lndera 0.25.25 0.36.46 tained
(9,
I? ) for geometrically arranged packings. In these
0 Raschig
r i ngs
0.375 0.55 cases the coefficients may differ markedly for different arrange-
0 Berl saddles
0.5 0.71
ments even a t the same frac tional void volume.
e
Figure 3.
Air Permeabi l i ty of Various Materials
(Data
o f
Oman and Watson,
19
Fract ional
A v . Diam. of Void Volume
9 Celi t e spheres 0.25 0.38
0 Cel i te cy l inders
+ Raschig r ings 0.375 0.62
+
Berl saddles 0.5 0.76
0.46
taps at the top and at a point
just above the fritted-glass
disk. Gas flow was measured
with a series
of
capillary flotv-
meters, each calibrated against
wet-test meters. Reproducible
results in this small glass tube
were most easily obtained if
the size range of material in
the bed was not
too
great and
if the bed was thoroughly
mixed by full fluidization be-
fore packing to th e desired
density. Excessive pa c ki ng
generally disturbed the inci-
dence and uniformity of ex an-
sion. A brief summary ofthe
conditions for which experi-
mental d at a were obtained is
as follows: parti cle size, 0.2 to
1.0
mm.; particle density,
1.5,
2.5,
7.8, 8.6, and 10.8 grams
p e r c c . ; p a r t i c l e s h a p e ,
spherical and pulverized; gases
employed, hydrogen, methane ,
nitrogen, and carbon dioxide;
gas
velocities, up to 100 em.
per second.
Figures
2
and 3 show data
taken from the literature for
experiments with air flowing
through beds of lead shot 1.5
to
6.5
mm. in diameter ( 5 ) and
Celite spheres, Celite cylin-
ders, Raschig rings, and Berl
saddles, each ranging from
0.25 to 0.75 inch in nominal
Material
Table I. Coefficients for Pressure Drop Equation
Specific
Sample
Surface, Weight, Void
Fluid Cm.-1 Grams Fraction I
Pulverized coke Different gases 60-370
.
.
0.52-0.64 2.5
Glass beads
Iron shot
Lead shot
Lead shot
Copper shot
Lead shot
Lead shot
Lead shot
Hydrogen 264.0
200 0,343 1. 9
Carbon dioxide
105.2 200
0 . 3 3 0 1 . 8
Nitrogen 105.2
200
0.330 1.9
Nitrogen 127.2 300 0.375 2. 0
Nitrogen 127.2 200 0.375 2. 0
Carbon dioxide 127.2 300 0.375 1 .8
Nitrogen
78.0 200 0.371 2.0
Nitrogen 120.7 500
0.350 1 .9
Carbon dioxide
120.7 500 0.350 1 8
Nitrogen 106.8 300 0.352 1.8
Methane 106.8 300 0.352 1 .8
Air
Air
Air
Air
Air
Air
Air
Air
Nitrogen 75.2 1000 0.364 1.9
Nitrogen 75.2 300 0.364 1.9
Nitrogen 59.75 500 0.366 1.8
Carbon dioxide 90.0 500 0.372 , 1 . 8
Water Different . . 0.380 2.5
w e s
40.6
. .
0,375 2 .0
1 9 . 5 . . 0.383 2.3
19.5 . . 0.390 2 .2
9.57 , . 0.421 2.8
9.57
, .
0.397 2.8
2 7 . 5 . . 0 , 3 0 3
1 . 9
22.2
. .
0.325 2 .5
19.8 . . 0,320 3 .0
. . 0 . 3 7 8 5 . 8
pheres, Celite Air 11 .5
Air 11.5 . . 0.466 5 .8
Cylinders, Celite Air 8. 78 . . 0.365 5 .7
Air
8 . 7 8 , . 0.457. 4.9
Berl saddles, clay Air 11 .55 .,. 0.713 6.6
Air 11.84 . . 0.764 6 .6
Raschig rings, clay Air 12.2 3
. .
0.555 8 .3
Air 12.23 . . 0.622 9.9
Rhombohedral 3a Water 7.56 . . 0.260 2.2
Orthorhombic 4a Water
7 .56 . . 0.395 3 .4
Orthorhombic 2 clear
Water 7.56 . . 0.395 3.3
Orthorhombic 2' blocked
Water 7.56
. .
0.395 8 .7
. . ,
1.7-3.00
a Configurations an d orientations of geometrical packings are described in detail in
B).
Various inateriais Different gases , , , , . .
P
Source
2 . 3
. .
3 . 0
. .
3 . 1 . .
2 . 8 . .
2 . 5 . .
2.6 . .
2 . 5
. .
2 . 7 . .
2 . 7 . .
3 . 1 . .
2.7
. .
3 . 1 . .
3 . 3
, .
3 . 3
. .
2 . 9
. .
2 . 6
2 . 6 cih
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1182
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. 6
perimentally with glass beads, lead shot, and iron s h o t
with various gases. The curves are drawn according
to Equation
12,
the break points corresponding to eo,
the void fraction
of
the fixed bed.
For relatively shoit columns of fine,
low
density
material, t he
u:
term of Equation 7 can be neglectrd
and Equation 12 can be approximated as:
3 2&fi
(urn
?in,
13)
_ _
1
-
p s g
nhere
the
zero subscript designates value> at the
in-
cidence of expansion. TVithin the range of fractional
void voluines usually cncountered, the left-hand mem-
ber
of
Equation 13 is nearly pioportional t o the Erac-
tional increase in column height. A constant, c, for the
approximate relation
(141
can be chosen such tha t t he calculated values of colunin
_ _ -
J j r - = c -
1 L
I - t
1
O o
Ov3*4 a 12 16 2 2 4 28
32
36
S U P E R F I C I A L V E L O C I T Y ,
U M ,
C M / S E C
Figure
4.
Expans ion of Beds of Glass Beads
height deviate froin the true ralues by
no t
more iliar.
370 in the range from zero to 30% expansion for F ,
greater than
0.35.
Curves drawn according to Equat ion
12
wi t h break poin ts a t
e o )
A v . Diam. of
Gas Spheres, Mm .
This approximation leads
t o
the equation
:
H2
coz
Nz
0.227
0.570
0.570
(16;
THE EXPANDED BED
or for a given bed m d fluid
AL/Lo = constarit urn- um0
(16)
hen the pressure gradient becomes equal to the buoyant
weight of
tmhe
acking pelunit volume of the bed,
Equation 1.3can be written more directly as
(10)
Equation 6 remains valid, the pres-
Thr fractiorial void
dP
dL
= (1
) P a V Y
17 )
the bed begins t o expand.
sure gradient being given in Equation 10.
These equations off er convenient ineaus for determining t he
volume increases with
f low
rate. Eliminating
t,hc
pi urc gradi- expansion of fluidized beds. With a knodedge of the properties
ent betiwen Equat>ions and 10:
of the fluid arid the dcnsit>y nd specific surface of the material,
e
..__
==
~ _ _
3
a s i2fl u,,2;
111, >
?I,, o
1 - E
P d
gives the fract>ionalvoid volunie in terms of t he corre-
sponding velocity, u . This equation is not rigorous as
applied to t he entire column in terms
of
urn, ecause it
neglects the variation in fractional void volume over the
length
of the
bed due
t o
the effect of gas expansion
upon velocity. However, this change in 6 i s nearly
proportional
t o
the one third
power
of velocity, and the
use of urn ives a fitirly accurate average
E
over the en-
tire column. A rigorous solut,ion would involve the
substit,utionof appropria te values of t various lengths
L n Equation 11, plotting t os. L, rid graphically ob-
taining the average e over the entire column. This
procedure
is
hardly warranted , for the use of urn nd the
over-all fractional void volume yields results ivell with-
in t,he liniit,s of experimental accuracy. Therefore,
Equat,ion
11
can be written as:
Independen t knowledge
of S ,
s not essential. Esperi-
mental da ta for the fixed bed give values of (as:) nd
PS,). 8 1 1
dependence upon particle size
and
shape is
involved in these quantities. As illustrated
in
Figures
4
to 6, this relation has been verified ex-
S U P E R F I C I A L V E L O C I T Y , U CM./SEC.
Figure 5.
Expansion of Beds of M e t a l S h o t
(Curves draw n according to Equation 1 2 wi th break po in ts a t
ea
Mater i a l G a s Spheres, M m .
Av. Diam.
of
Iron
Lead
Iron
Na
cox
M ?
0.472
0.497
0.770
7/26/2019 Fluid Flow Through Randomly Packed Columns and Fluidized Beds
5/6
June 1949
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
11
can be obtained from Equati on 17 for fluidized systems of fine ma-
terial of
low
density. More generally,
a
single observation of
AL/Lo
will determine th e constant
of
Equation
16.
In t he event
umocannot be obtained from Equation 12 because of lack of in-
formation, ano ther set of values of aL/Lo s.
urn
will determine
urn, s well.
Equation
15
has been verified experimentally for pulverized
coke and for fine glass beads with various gases. Equ ation 16 has
been found to apply more generally, even when the second term
of
Equation
7
cannot be neglected, except tha t th e slope mus t then
be determined experimentally and can no longer be predicted
from a knowledge of
01
and p
T H E FLUIDIZED
BED
As
the gas flow rate is increased, bed expansion continues ac-
cording t o Equatio n
12.
There is a limit, however, to t he homo-
geneous expansion of the bed. At higher flow ra tes pa rt of th e gas
flows throu gh a denser but expanded bed which constitut es a con-
tinuous phase, while the balance of the gas passes through the bed
in bubbles which probably contain solids in suspension. The bub-
bles constitute
a
discontinuous phase. The solids are violently
agitated and th e condition may be termed tu rbul ent or two-phase
fluidization. Increasing flow rate causes
a
larger portion of the
gas to flow in the discontinuous phase, approaching a final limit
with all th e solids in suspension.
With spherical particles, two-phase fluidization was found to
begin when the void fraction exceeded a value
of
about 0.46.
This value is nearly t ha t for th e void fraction for spheres packed
in cubical arrangement, the loosest stable form. This observation
suggests th at two-phase fluidization does not sta rt before the bed
at tai ns th e equivalent of th e loosest stable configuration. The
loosest stable volume was obta ined by fluidizing the bed, cutting
down the gas flow slowly, and observing the volume when the
gas was completely cut off. After the materi al was packed tightly,
gas was let in and th e rat e of
flow
increased slovvly until two-phase
fluidization began. Th e volume at the sta rt of bubble formation
was
the same as t hat obtained by the reverse procedure.
Experiments with closely screened samples of pulverized coke
from
16
to
100
mesh gave loosest stable volumes corresponding
to void fractions from
0.60
to
0.70
and fractional increase in be
height ranging from 15 to
20 .
These estima tes for void fractio
of coke are arbitrari ly based upo n a density of 1.4 for the co
which allows for pore volumes not available for fluid flow. Th
loosest stable packing volumes-Le.
,
loobest bulk density-
for
materials having irregular shapes and surface cannot b
estimated theoretically, but are easily determined as has bee
described.
I n two-phase fluidization, t he denser but expanded phase su
rounding the rising bubbles moves towards th e bottom of th e be
The rising bubbles carry
a
portion of the solids to complete th
pat h of circulation. While the solids circulate, there is no su
stanti al circulation
of
gas.
Because the gas does not flow homogeneously through t
bed, contact time and surface effectively contacted are indete
minate. However, for relatively fine solids of low density, th
final term of Equ ation 7 can be neglected a nd th e expansion equ
tion can be used in th e form of Equat ion
17.
These equations, f
a given bed, depend upon specific gas properties and flow rat
only through the product of viscosity times superficial velocit
For
thi s reason, a constant product of viscosity times superfici
velocity was chosen as a criterion for a stan dard s ta te of fluidiz
tion for a series
of
kinetic stud ies involving gaseous reactions wi
60-
to 100-mesh coke. With a suitabl e correction for the parti
pressure of the reac ting gas component, the resulting r ate co
stants gave a good Arrhenius plot and were direc tly proportion
to the amount
of
coke in the bed.
S U P E R F I C I A L V E L O C I T Y , U C M / S E C
Figure 6. Expansion of Beds of Lead Shot
(Curves
drawn according to Equat ion 12 w i th
break
p o i nt s a t eo)
A v.
Diam. o f
Gas
Spheres, Mm
Nn
HI
NS
0.798
0.562
1.004
SUMMARY
A
general equation has been developed which relates pressu
drop t o gas flowfor fixed beds. The equation shows tha t the rat
of pressure drop to superficial velocity is a linear function of ma
flow rate.
Its
coefficients depend upon fractional void volum
specific surface of packing material, and fluid viscosity. A tran
formation of the equation shows th at the fi iction factor impli
itly involves the fractional void volume and is not a function o
th e Reynolds number alone, as has often been assumed.
A
fixed bed expands with increasing fluid flow after th e pressu
drop equals the buoya nt weight of th e solids per unit area of t h
bed. The general equation for the fixed b
applies also
t o
the expanding bed; the valu
of the coefficients remain unchanged. Her e th
total pressure drop stays constant while th
fractional void volume increases.
A
gener
form of the equation suitable for caIculatio
of
iractional void volume has been given. Wi
suitable approximations equations have bee
developed which permit direct calculation o
such readily observable quantities as fraction
expansion
or
height of th e bed. A knowled
of specific surface of th e solids is n ot necessar
Measurement
of
pressure drop versus flow ra
in the fixed bed, employing any gas at a su
able pressure and temperature,
is
sufficient
determine and
pS,.
The void fraction f
the fixed bed, however, mus t be known.
Expansion is homogeneous until the be
att ain s th e loosest stable configuration of th
solids. With gases, addit ional increase in flo
ra te causes appearance of bubbles. Und
these conditions, th e bed is fluidized (two-pha
fluidization). Th e loosest bulk density of an
packing material can be determined by fluidizi
a
sample with a gas in
a
column and reducin
the
gas
flow slowly. A knowledge of the loo
est bulk density i s sufficient to estimate flo
rates corresponding
to
the incidence of tw
phase fluidination for any gas under any cond
tions of pressure and temper ature.
7/26/2019 Fluid Flow Through Randomly Packed Columns and Fluidized Beds
6/6
1184
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.
6
Fo r kinetic s tudies of heterogerieous ieact.ons in fluidized beds,
a constant product
of
gas viscosity times superficial velocity may
serve as a criter ion of a standard st at e of fluidization-Le., it will
ensure a constant st ate of fluidization a t different temperatures ,
pressures, and gas compositions. Use
of
this criterion for a kinetic
study of ste am and oxygen reactions with coke in fluidized beds, to
be reported elsewhere, led to reaction ra tes th at were proportional
t o
the weight of t he coke in the bed an d gave good Arrhenius plot^.
d
=
u =
D , =
D ,
=
L =
V =
LYP.
=
AP
=
s, =
*
=
11
=
I / =
c =
=
3 =
P, =
pr n
=
a =
c =
N O M EN C L AT U R E
cross-sectional area of column,
sq.
cm.
dimensionless constant
diameter of bed, cm.
diameter of a channel, em.
diameter of a spherical particle, em.
length
of
bed, em.
number of channels per unit area of colurnri
Reynolds number
pressure drop, dynes pcr
sq.
cm.
specific surface,
sq.
em. per cc. of solid particle
average velocity through channel, em. per second
superficial velocity,based on emp ty tube , cin. per second
superficial gas velocity a t mean of entrance and exit
weight rat,e of fluid fiom, grams pcr second
dimensionless coefficient
dimensionless coefficient
fractional void volume
density of fluid, grains per cc.
gas density at mean
of
entrance an d exit pressures,
giiiiiis
pressures, cm. per second
-
per cc.
p a = density
of
solid particles, grams per cc
fi =
viscosity of fluid, poise
LITERATURE
CITED
Arnell,
J.
C.,
Can.
J . Research, 24, A-B, 103 (1946).
Becker,
J.
C.,
M.S.
thesis, Carnegie Institute
of
Technology
Blake,
F.E., Trans.Am. nst . Chem.
Engrs.,
14,415
1922).
Brillouin,
M . ,
LeGons sur
la
viscosit6 des liquides et
des gaz,
Burke,
S .
P., and Plummer, w. B.,
IXD. NG.
Hmf.,
20, 119
1947.
Paris, Gauthier-Villars, 1907.
119281.
Carman,
P.
C., J .
SOC.
Chem. Ind. , 57 , 2251 (1938).
I b i d . ,
58,
1-7T
(1939).
Carman, P. C., Trans.
Inst.
C h e m .
Engrs.,
15, 150-66 (1937).
Chilton, T.
H.,
and Colburn,
A.
P., IND.
ENG.
CHEX.,
3,
913
(1931).
Teubner, 1930.
Forchheimer, Ph., Hydraulik, 3 aufl., p. 54, Leipzig,
B.
G
Forchheimer, Ph., Z. B er . deu t . ITLQ.,
5 ,
1782 (1901).
Hitchcock, D. I., J . Gen . P h p i o l . , 9, 755 (1926).
Kozeny, J . ,
S i t zber .
A k a d . Wiss Wien, M a t h . - n a t u ~ w ,
Klame
Lea,
F. M.,
and Nurse,
R.
W.,
J . SOC.C h e m .
Ind.,
5 8 ,
277-831
Leva, Max, and Grummer,
M., Chem. Eng. Progress,
43,
549-54,
Lindquist, E. , Premier Congrbs des Grandes Barrages. Vol. V.
Martin, J.,
Sc.D.
thesis, Carnegie Institute
of
Technology, 1948
Muskat,
M.,
Flow
of
Homogeneous Fluids through Porous Me
Oman, A . O . ,
and
Watson,
K . M., AVatl.Petroleum Sews, 36
Stanton, T.
E., and
Pannell,
J. R., T r a n s . R o y Soc.
(London
136
Aht.
IIa). 271-306 (1927).
(1939).
633-8, 713-18
(1947).
pp. 81-99.
Stockholm, 1933.
dia,
New
York, McGraw-IIill
Book Co.,
1937.
R795-802 (1944).
(A)
214, 199-224 (1914).
RECEIVED anuary 15, Y4 4,
Flow Characteristics
of
Solids-
as
Mixtures
In
a Horizontal and Vertical Circular Con
Th e isot hermal f low characteris t ics of a solids-gas mix-
tu re (alu mi na, s i l ica, catalyst , and air ) are invest igated in
a ho r izon tal and vert ical glass con dui t
17 mm
in ins ide
diamet er for var ious rates of ai r f low and sol ids f low.
Pressure drops across test sections
2.0
fee t in length) are
accurately measured for a ser ies of air f low rates in w hic h
th e ra t io o f so l ids to a i r
is
varied f rom 0 o
16.0
pounds of
solids per pound of air . Th e sol ids (catalyst ) are int ro-
duced i n to t he f low system t hrou gh a mix ing nozzle fed
by a slide valve-controlled weighin g t an k, an d have a size
d is t r i but io n vary ing f ro m par t ic les less than
10
m ic rons t o
URISG World War
11,
one of t he most remarkable develop-
D
ment s in engineering was th e application
of
the continuous
flow process to catalytic synthesis. , The advantages resulting
from a
cont inuous cata lyti c process-continuous regeneration
of
catalyst, control of catalyst activity, reaction rate control result-
ing from the constancy
of
temperature and thorough mixing in
reactors, and finally the economy of long on-stream periods-
need not be discussed here. The fluid catalytic units or today
offer a most at tracti ve means
of
carrying out t he ma ny Fischer-
Tropsch reactions heretofore considered too complex and costly
from a commercial point
of
vieF.
Although a large number
of
fluid catalytic crackers have been
designed a nd successfully operated, there appears t o be a scarcity
of
design information
in
the literature on the hydrodynamic
behavior of multicomponent, multiphase systems.
This particu-
part ic les greater than 220 micro ns. Ai r velocit ies i n t h e
solids-free approach section vary from
50
t o
150
feet per
second. Several typ es of nozzles fo r feeding solids are
invest igated for stabi l i t y of f low in t h e system (absence of
pressure surges) and some qual i tat i ve in for mat io n is pre-
sented on th e type o f nozz le y ie ld ing th e most u n i for m
typ e of mix i ng. Qual i t at ive observat ions on th e f low
in t h e sol ids feed l ine, mix ing nozzle, hor izontal and
vert ical test sect ions, and sh ort and long radi us bends,
and th e behavior of a mult i effect cyclone separator are
discussed.
LEONARD FARBAR
UNIVERSITY
O F
CALIFORNIA. B E R K E L E Y
4,
CALIF.
Iar field of unit operations has been given some consideration in
the past; however, the investigations th at have been reported
are limited in their application to t he fluid units by the fact tha t
studies were limited to particles
of
fixed and relatively large sizes
Considerable
work
has been carried out on the investigation
of
the flow charac teris tics of gas-liquid mixtures 1, 5,
6 )
and
a
certain amount
of
attention
( 3 , 9)
has been given to the pneu-
matic conveyance of relatively large solid particles in which the
size spect rum was rather limited. Gasterstadts ( 5 ) investiga-
tion of th e transportation of wheat app ear s to be the first detailed
stu dy indicating the possibility th at
a
simple relationship may
exist in closed conduits between the pressure drop
of
a single
phase (gaseous) flowing and that encountered when more than
one phase
is
present.
Recommended