Air Out
Solid Flow
Air In Pressure Drop Curve for Spouted Bed
-
I
I I
Packing
1.
Air flows through bed in air jet form-no cavity or internal spout (iet) formation 2. Small cavity opens up near orifice-start of internal solids-air jet. Solid circulation begins in lower column 3. Internal solids-air jet progresses up column 4. Internal solids-air jet at maximum pressure drop 5. Internal solid-air jet breaks through top of bed. Spouting begins
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LOUIS A. MADONNA and RICARDO
F. LAMA1
Chemical Engineering Department, University of Ottawa, Ottawa, Ontario, Canada
How to Calculate
Pressure Drop in Spouted Beds Equations presented here should help the design engineer develop specialized equipment needed to move fluids through spouted beds
SPOUTING
occurs when a bed of solid particles is continuously agitated by an upward jet stream of fluid. The particles, carried upward in a central core, fall back into the annular space around the spout and move uniformly downward. Thus, continuous circulation of the solids and a good fluid-solid contact are achieved. This investigation correlates pressure drops in the beds with experimental variables, but with column diameter and air inlet orifice held constant. A general equation for pressure drop in packed beds (Equation 7) can be applied to pressure drop in spouted beds. Variations of pressure drop up to and including maximum value represent the flow of fluid through packed beds. In this work the laminar flow condition is Present address, National
Research
Council, Ottawa, Ontario, Canada.
covered. For the 6-inch column with a GO-degree cone angle : AP,vr _ _ _- 1120 GpX2 (1 - 6 ) 2 L Dp2 Pf gc 6 ' The average value of K equal to 1120 does not hold for rape seed, white millet, and small pellets of polyethylene. Transitional flow prevails at spouting, and data have been correlated :
For pipe flow:
Let the velocity of the fluid through the pores be given by : (4)
Theoretical Principles
Leva ( 3 )derived an equation in which the shape factor is directly related to the dimensions of the packed particles. X = 0.205
S
v&3
He ( 3 ) also derived a general theoretical equation for fluid flow in packed beds, by establishing its analogy to fluid flow in empty pipes.
where v is the average velocity of the fluid approaching the bed, k , is the proportion of effective voids in the bed, and 6 is the porosity ratio, expressed as volume of voids per unit volume of packed tube. Assuming that the dimensions of the voids are of the same order of magnitude as the particle diameter, then D, = 4r, where r is a modified hydraulic radius of the interstices. By definition, let VOL. 52,
NO.
2
FEBRUARY 1960
169
This is the setup for measuring pressure drop in spouted beds A. B. C. D.
E.
F.
:-d
G.
H. 1.
m L! (5)
where kp,6 represents the effective volume of the packing interstices, (1 - 6) k,s the effective surface of particles, and A the particle shape factor. k , is the proportion of the effective area of the packing. Substituting Equations 4 and 5 into 2 gives AP - = K1/r2-"
On rearranging and replacing S / v p by 6/D, (the expression for spheres) and p t v by G, Equation 6 becomes :
1.
Compressed air supply Globe valve Pressure regulator Pressure g a g e Rotameter Air control valve W a t e r manometer 4-inch I.D. column, 60' cone 6-inch I.D. column, 60' cone 6-inch I.D. split column
Experimental Equipment. Four columns were used, the first three of borosilicate glass, and the last of aluminum: 6-inch diameter, 60-degree cone angle 6-inch diameter, flat bottom 4-inch diameter, 60-degree cone angle 6-inch diameter, split column, flat bottom The spouting medium, air, was supplied from a compressor and either of two rotameters metered the flow rate. T h e pipes leading to the columns were provided with a 2-foot calming section of brass pipe. The equipment also consisted of a filter, pipes, fittings, and valves to control the air flow rate. Static pressures relative to atmospheric pressure were read off three vertical manometers, connected to pressure taps located above the orifice plates. Mercury Fahrenheit thermometers were used to measure the air temperature at different points. Standard flow conditions were 14.7 p.s.i.a. and 70' F.
170
volume of one particle, v,
-
'4 n
,
6
T( 1.4224)(28.3)
Pressure Drop. T o determine pressure drop caused by solids alone, data were collected for the empty columns at different flow rates. The bed was allowed to spout for ll/z minutes before each run. Example of calculation : L = 4 inches; 6-inch diameter column, 60degree cone angle Manometer reading = 1.14 inches of water; 10 S.C.F.M. Correction factor for empty column = -0.1 ..~ 1.14 - (-0.1) = 1.24 inches of water 5.2 lb./sq. ft. 1.24 inches of water X inches of water = 6.45 lb./sq. ft. lb./ft. Pressure drop per foot = 6.45 4,12ft.
Absolute density of the packing was determined by liquid displacement of a known weight of the particles ( 2 ) . The tests were carried out in pycnometers and liquids such as water, benzene, or ethyl alcohol were used.
(8)
Example of calculation, using 60 particles of old wheat which weighed 2.1155 grams: CzHs OH displaced = 1.1665 cc. 2.1155 1 1665 Absolute density = L-.- = 1.4224 g./cc 0.7843
D, =
19.35 lb./sq. ft.-ft. Exponent n in Equation 7 can have any value, ranging from 1 for completely laminar flow to 2 for turbulent flow.
Using the number of particles for each test and amount of liquid displaced, volume of one particle and diameter of a sphere, D,, having an equivalent volume were determined : Volumeofdisplaced number particles -
= 0.3625 cm.
D, = 0.1431 inch T o determine Kozeny corrections for voidage, pressure drops were arbitrarily taken to a common basis of 40% voidage. This correction was made possible by (1
- 6y-n 63
Example of calculation, using old wheat packing : For laminar flow AP (1 - 0.4)' (0.3935)s = (0.4)* (0.6065)z
~-
( Y ) ~ o(r)
0.9318
(y)
For transitional flow AP (1 - 0.4)'.'6 (0.3935) 40 L (0.40)3 (0.6055)'.'5 0.933
-
(g)
Bulk density of the packing was determined by pouring a slow and steady stream of known quantities of packing into a 6-inch full column and 6-inch split column. The height of the column was recorded before and after 2 minutes of spouting.
8.0
1
6 " i.D.
FULL
COLUMN
(6O0CONE)
7.0 c
-i
6.0
-
5
5.0
P
40
0
Figure 1. Pressure drop increases with increase in rate of gas flow until the point of maximum pressure drop is reached
INDUSTRIAL AND ENGINEERING CHEMISTRY
=
0
a
n w
3.0
a
3 v) v)
w
2.0
a
P 1.0
0 0
5
10
S.C F M
I5
20
25
(14 7psi.3; 70'F)
30
35
P R E S S U R E DROP I N S P O U T E D B E D S Porosities were calculated from absolute density and the after-spouting bulk density :
Shape factors for normal packings, evaluated from the Brownell’s sphericity us. porosity chart (7), are similar to those calculated from Equation 1.
Discussion of Results Visual Observations. SLUGGING. This condition describes the effect of large bubbles of air passing through the bed. These bubbles are able to separate the bed into two sections. While part of the bed is raised like a solid piston and acts as a packed bed, the bottom section may be spouting. The 6-inch column showed neither the tendency to move the central core toward the sides of the container nor the slugging effect in the range of particle diameters and air flow rates studied. At high bed depths, considerable fluctuation of the bed top occurred in the split column. Presentation of Results. As the gas flow rate increases, the pressure drop
increases because of friction through the bed until the point of maximum pressure drop is reached (Figure 1). This section of the curve represents the flow of the fluid stream through a packed bed. Deviations from linearity prior to the point of maximum pressure drop are small and have not been taken into account. At the point of maximum pressure drop, the internal spout has experienced a considerable development, whereas the bed is just beginning to expand (top, left). Further increase in the gas flow rate beyond this point will bring about a decrease in pressure drop and increase in the height of the bed, until a sudden and sharp decrease in pressure drop will indicate that the spout has broken through the top of the bed (lower left). The shape of the pressure drop curves at various bed depths is similar. The points of maximum pressure drop, AP,,,, and pressure drop a t spouting, AP., are easily distinguished from other points along the curve. Unreliable values for pressure drop in the bed were obtained with a pressure tap located below the orifice plate.
Internal spout at point of maximum pressure drop
60
In
8-
-
9 v
6-
0 h 8 C,
Old Wheat Newwheat Barley Rape Seed Vet c h e 5 Split Pear S m a l l Po Ilets
*- + 6 Big Pellets Soy Beans - 0 White Millet I
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l
l
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,
0
Internal spout breaking through top of bed
Figure 2. Plotting maximum pressure drop against modified Reynolds number gives a series of straight lines VOL. 52, NO. 2
FEBRUARY 1960
171
Small pressure drops in the bed are completely masked by the pressure drops through the orifice. Pressure drop data obtained with the pressure tap located above the orifice plate were easily reproduced. MAXIMUM PRESSURE DROP. Figure 2 is produced in a series of straight lines with slopes of unity, and thus
Straight lines with slopes of unity were also obtained when pressure drops in the packed bed region were plotted against Reynolds number. Pressure drop data from Figure 2 at Reynolds number 90 and modified by introducing the shape factor were corrected to 40y0 voids and plotted against the corresponding particle diameters. The slope of the straight line is equal to -3.0, indicating that
4o
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20
-
-
-
+ 4-
-
$10
a
Figure 3. Transitional flow exists at the spouting point within the range studied
-
N,
$
8
4
-
-
I
.am
QI-’
-
2
1 6” FULL 20
30
50
A straight line with slopes of -3.0 shows the effect of particle diameter on pressure drop. The 6-inch-diameter column and the 6-inch-diameter split column behave similarly. Pressure drop us. Reynolds number relationship, characterized for n = 1.25, indicates that transitional flow exists at the spouting point, within the range of conditions studied. By substitution of n = 1.25 in the general equation (Equation 7), the following correlation is obtained:
The restrictions on the above equations are : The physical characteristics of the packings, the fluid properties, and the data on maximum pressure drop for the 6-inch-diameter column with 60’ cone and the 6-inch-diameter split column made possible the evaluation of K. The values of K are considerably lower for rape seed and white millet than for the rest of the packings. The 6-inch-diameter column with flat bottom produced low values for pressure drop, whenever small bed depths were tested. This effect could indicate a distortion of the pattern of flow in the bed due to the “dead section” of packing formed at the bottom of the column. With increasing bed depths, this dead section of packing gradually becomes insignificant in relation to the total amount of packing material. SPOUTING POINT. Graphical presentation of the pressure drop data at spouting in the form of log AP8/L us. log Re may be observed in Figure 3. Straight lines of slope of 1.25 for different packings indicate the variation of pressure drop with the gas flow rate; hence
1 72
70
100
Re V
In so far as the evidence of pressure drop is concerned, the behavior of the spouted bed up to the point of maximum pressure drop is similar to that of a packed bed with viscous flow. A general correlation covering all the variables was not developed experimentally because derivation of relationships such as pressure drop us. fluid density and pressure drop us. fluid viscosity was beyond the scope of the present work. The value of n = 1 was substituted in the general equation (Equation 7) and the following correlation was obtained:
COLUMN
The kinematic viscosities of the fluids used should be close to that of air at 70’ F. and 14.7 p.s.i.a. The equivalent particle diameters should be from 0.079 to 0.25 inch. The data were collected for 6-inchdiameter columns and an orifice of 0.5 inch. The void fractions of the beds studied varied from 0.358 to 0.525. Nomenclature
D,
=
G
=
K1 =
k,
=
L = M = Re = S =
INDUSTRIAL AND ENGINEERING CHEMISTRY
diameter of the equivalent volume sphere of a packing particle, inches or feet mass velocity of fluid flowing, based on cross-sectional area of column, lb./sq. ft. X hr. constant of permeability dependent uDon nature of bed, cu. ft./ (sec.)isec.) proportion of effectivr voids in bed length of bed, feet nu&ber of packing particles per gram modified Reynolds number surface area of particle of arbitrary shape, sq. ft.
=
d,
=
f
=
g,
=
n
=
200
300 400
P
volume of fluid flowing through bed, cu. ft. column diameter, inches function of conversion factor, 4.17 X loR ft./hr.2 slope of lines when plotting AP/L us. Re
Subscripts: m = metered r = modified hydraulic radius of in-
terstices velocity of fluid based on total cross-sectional area, ft. isec. u p = volume of packing particle AP = pressure drop across entire bed, lb./sq. ft. u
=
Subscripts: A4 = maximum S = at spouting 6 = bed voidage h = particle shape factor p = fluid viscosity, lb./sec. X ft. or lb./hr. X ft. p = density, lb./cu. ft. Subscripts: b = bulk = fluid s = solids
f
Acknowledgment
The authors acknowledge indebtedness to the Canadian National Research Council for assistance in providing a grant for the research work. literature Cited (1) Brownell, L. E., Dombrowski, H. S., Dickey, C. A., Chem. Eng. Progr. 46, 415 (1950). (2) Cowan, C. B., Peterson, W. S., Osberg, G. L., Can. Eng. J . 41, GO ( 1 9 5 8 ) . ( 3 ) Leva, Max, Chem. Eng. Progr. 43, ‘ 549-54 (1947).
RECEIVED for review March 3 , 1958 ACCEPTEDOctober 23, 1959
