Effect of Particle Diameter and Apparent Particle Density on Internal Solid Circulation Rate in Air-Spouted Beds Asok Chatterjee Indian Institute of Technology, Bombay, India
Quantitative evaluation of the internal circulation rate of solids in a spouted bed system would be helpful to a study of fundamentals of the technique. In this study, unsteady-state mixing data obtained by batch air spouting of two differently colored region beds were utilized in a mathematical flow model to obtain the rate of solid circulation. A 150-mm.-diameter column fitted with a cone of 30" angle (half angle) and an inlet orifice of 9.52-mm. diameter was used for spouting sand, coal, mustard, and sago. The effect of fluid mass flow rate on the rate of solid circulation i s more dominating than other factors investigated. Solid circulation rates were correlated with reduced fluid mass flow rate, particle diameter, and particle density.
W = 870 Gr ( p p )
MATHUR
and Gishler (1955a,b) first developed the spouted bed technique and used it for drying wheat. Cowan et al. (1957), Johnston et al. (1961), Becker and Sallans (1961), Buchanan and Manurung (1961), and Peterson (1962) used the technique for drying, mixing, and carbonization. I t should also be possible to use this technique for roasting ores, cracking petroleum, gasification of coal, hydrocarbon synthesis, and chemical reaction engineering. The solid movement in such a solidfluid contact system is the determining factor for its applicability, regulates energy and mass transfer modes, and influences chemical reactions occurring in spouted beds. I n spite of its importance, very little information is available in the literature. Mathur and Gishler (1955a) estimated solid flow in the annulus from the particle velocity observed a t the column wall. Thorley et al. (1959) followed the same principle of' estimation, taking into account the radial movement of the particles in a semicircular sectioned column. Particle velocity data a t the wall do not reflect the solid flow pattern in the top section of the bed or the cone region. However, about two thirds of the solid enters the spout a t the cone region and the rest along the spout. Becker (1961) gave restricted relationships of local flow of particles into the spout from particle velocity a t the wall. He also measured the maximum cycle time from the lapse of time required for the reappearance of specified particles in certain regions of the bed. The shortcircuiting a t the top and inward movement of solid in the cone region restrict the validity of the assumptions involved. I n the present study, a method is utilized, which is not affected by the complicated spouted solid circulation pattern, to evaluate the solid circulation rate quantitatively.
(19~)"~;
Solid Circulation Model
The entire circulation of solid particles is through the turbulent, axial, upward jet, where particles enter in varied numbers a t all levels of the bed height. Mixing occurs subsequently, when the particles which have been carried upward drop down in a random fashion. The behavior is likely to be similar, whether the spouting is brought about by air or a liquid such as water. An attempt was made to find an equation for the solid circulation rate from a momentuq balance and an energy balance for the flow process across the bed height. However, no suitable correlation was found. I t was therefore necessary to estimate W quantitatively. Let us consider the air-spouted bed as illustrated in Figure 1, where the solid particles in both bed sections have the same density and mean particle size. The variation in x and y with time is established by a vertical up and down movement of particles due to gross upward flow of air. Movement of particles in any other direction is negligible. SIand S2 will not vary with time, so long as there is continuity of flow. A material balance on the tracer in both regions can be utilized to find the solid exchange across the boundary of the two regions (Zesz and Othmer, 1960). SI dxldt is the rate of change in the quantity of tracer in the upper section. This is equal to the rate of inflow of tracer into the upper section minus the rate of outflow of tracer from the upper section. The former is equal to toy and the latter is equal to wx, where u: is the solid mass circulation rate, in kilograms per second. The tracer balance equation for the upper section is
Si dx
dt = U ( y -
X)
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No.4, 1970
(1) 531
II
-
_----
Sla + SPb= S ,
- ---II
Equation 7 becomes (a -
5, K g . 0 F TOTAL SOLIDS
a Kg
T R A C E U / K 9 OF m r A L S O L I D S AT
s 1
t.0
Ln
lRAC€'R/JCg OF
K
TOTAL SOLIDS AT TIME
f,
x-
b)Sn
+
=W(%1 +%)
s 2
1
t
S, ~
SI + SP
or
Ln
~
1 z, ="is. +,-I s,1 1 - In (a - b )
x - x,
(8)
where
z,=s,S+P s, ~
and
x,=
SI
~
s,+ s,
When the initial condition is such that a = 1 and b = O-that is,
~
I
SIX A,,
2, Ln -= x - x,
and, for the lower section,
Sp d y l d t =
W(X -
y)
The initial conditions where t = 0 are
x=a
(3)
y=b
(4)
and Summation of Equations 1 and 2 leads to
SI d x j d t + Sp d y j d t = 0 which shows that there is no change in the total quantity of the tracer. When this equation is integrated from 0 to t and substituted in Equations 3 and 4, it gives
S,x - Sla + S2y - S,b = 0
(5)
or
y = S 1 / S 2 ( a- x)
+b
(6)
Substituting Equation 6 into Equation 1,
dx
u: . - - dt
SI
This equation is integrated between the limits t = 0 and concentration of tracer = a
t and concentration of tracer = x
On rearranging, the equation is
When the total tracer in the whole bed equals the total solids initially a t the upper section, 532
SI
Equation 8 takes the form
Figure 1. Model of spouted bed, solid circulation
t =
+ s2y =
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 1970
u:
1
(k
+
Equation 9 is a straight-line equation with a slope of linearity equal to w and passing through the origin. Whether the line will pass through the origin depends on how quickly the stable spouting starts, the inflow of air, and how instantaneously time is recorded with a stop watch. T o avoid error, a number of values of t and x a t a constant rate of air flow should be used to evaluate w in accordance with Equation 9. Working with either too low or too high values of (SI/ S p ) would make w very sensitive to the exactness of observations o f t and x. The present investigation is confined t o solid systems consisting of essentially uniform spheroidal particles of average diameter in the range of 1 to 3 mm. and apparent density in the range of 1 to 3 grams per cc. Experimental Setup and Procedure
A spouted bed column consisting of a cylindrical portion, a conical section, and a calming section was connected to the fluid supply line. The cylindrical portion of the 150-mm.-diameter column was constructed to !4 6-inch (1.58-mm.) mild steel sheet. I t s length was 325 mm., in certain cases extended to 650 mm. by joining two cylindrical portions by Araldite adhesive and supported by 50-mm.-wide semicircular clamp joints. The 30" half angle cone was made of %-inch (3.17mm.) mild steel plate. The cylindrical portion and the cone were smooth-welded, so that flow was not restricted. The cylindrical portion was fitted with a 30 x 200 mm. Perspex window to observe the bed visually. The cone was permanently brazed with a brass coupling piece a t the bottom, to which the adjustable calming section could be bolted. The calming section was made of brass with pressure tapping located a t the bottom of its flange. I n the column, a detachable air inlet orifice plate with neoprene rubber packing to maintain the joints air-tight and
a copper screen of 0.083-mm. size opening to hold the bed materials were placed between the brass coupling and the calming section (Figure 2 ) . The orifice plate of "-inch (9.52-mm.) diameter was made of brass, 8 mm. thick and with a sharp edge with a 2-mm. emergent portion at the top, to maintain the air jet along the axis of the column all the time. The bottom of the calming section was connected to the air supply from the compressor, using pressure tubing. The cylindrical portion and the cone were fixed in position with portland cement plaster and the column, cone, and calming section assembly were mounted on a steel stand with a top bar to hold them.
A schematic representation of the experimental unit with essential parts of the setup is shown in Figure 3. The compressed air was supplied through the %-inch (12.7mm.) i.d. pressure rubber tubing which was connected with a 160 x 80 mm. calcium chloride bed to dry the air, two %-inch globe valves, one for flow control and the other for air supply, one quick shutoff attachment, an orifice meter with calibrated mercury manometer, and finally the bottom of the calming section attached to the cone of the column. Pressure tapping a t the bottom of the calming section was connected with a mercury manometer for pressure drop reading. I t was possible to read the scale of the manometers to &1 mm. However, this would lead to only a 0.1% error in the total air flow rate and a 1% error in pressure drop across the bed. The fluid used in this work was atmospheric air dried over a calcium chloride bed having a density of 0.0012 gram per cc. and a viscosity of 0.0192 cp. Solids used were crushed quartz stone, a bituminous type of coal, mustard seeds, and sago. Each solid was sized to 2.84-, 1.98-, 1.41-, and 1.08-mm. average diameter, assuming the particles were spheroidal. An arithmetic mean was taken between two screen sizes for calculating the average diameter of the particles. The densities of the solids were determined using a 10-cc. pycnometer. Densities of 2.64, 1.36, 1.20, and 1.12 grams per cc. for sand, coal, mustard, and sago, respectively, were found. Tracer and Analysis
CLAN
Figure 2. Cylindrical portion, cone, and calming section Details of metal column Dimensions in millimeters
The essential requirement for the tracer was that it should have the same physical properties as the nontracer material, so that the characteristics of spouting were not affected by its presence and the tracer could be easily detected in mixtures with nontracer. Considering the size range and the physical properties of the solids used, the most convenient tracer was prepared by coloring the solid particles. This made no difference in physical propertiese.g., average particle size and density between tracer and nontracer. Analysis was carried out by visual separation and weighing of colored and noncolored particles in each sample. Sand and coal particles were colored with water-washable red, green, and yellow dyes. Sago and mustard particles were colored with red, white, gray, and
1 1
Figure 3. Schematic diagram of experimental setup Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 1970
533
yellow enamel paints and regenerated by washing with kerosine. Regenerated particles were dried and screened before re-use. A tracer-nontracer ratio-Le., S1/S2equal to 0.5 or 50'c--was convenient in the spouted bed system, and was used throughout the present work. T o obtain minimum spouting velocity, the columns were first filled with the required weight of solids and by operating the compressor and regulating the globe valves sufficient air was made t o pass through the particle-filled bed so that an air jet could pierce through the core of the bed. After the spout burst, the flow of air was brought down to the minimum spouting condition. On lowering the flow of air still more, an unstable spouting occurred and the spout frequently failed. Comparatively stable spouting was observed in the case of particles of smaller diameter in the minimum spouting region. The value of the minimum spouting air mass flow-i.e., G,-was kept slightly above the experimental minimum condition below which the spout failed. G,, were measured for different solids and their various sizes. Mixing data were obtained when columns were filled with batches of nontracer particles and the spouting was carried on a t the desired rate of air flow. Sufficient time was given to attain steady-state conditions. Then previously weighed tracer particles were poured from the top to the spouted bed and simultaneously time was measured by a stop watch until the end of the run. Manometer readings indicating the flow rate and the time elapsed were noted. The run was stopped by operating the quickshutoff attachment. Elapsed time was within 4 to 60 seconds, while the air mass flow rate varied between 10 and 40 kg. per hour. Piercing of the spout through the stationary bed of the two distinctly colored regions a t the onset of the run delivered a higher air flow rate than required and a lot of intermixing occurred before the spouting started. Therefore tracer was dropped from the top of the bed. Four samples were then collected from the top of the mixed-color bed from different circumferential positions by a specially designed spoon with push button and gear system as shown in Figure 2, which smoothly picked particles from the surface. The average of those four tracer concentrations was taken. The solid was then discharged from the bed by removing the calming section. A weight equal to tracer weight was removed from the discharged material. The discharged material was again recharged in the column for the next run and a differently colored tracer was used, keeping elapsed time and mass flow rate of air the same as in the earlier run. The time required to regenerate the particles was thus curtailed by changing the tracer color. An average value of tracer concentration was calculated from two such runs. The above procedure was repeated for sand, coal, mustard, and sago and for four average particle sizes (2.84, 1.98, 1.41, and 1.08 mm.).
on semilog paper, straight lines were obtained, passing through the origin (Figure 4 ) . The slopes of the straight lines in the figure give the kilograms of solids circulated per second in the respective runs. With increasing air mass flow rate, the solid mass circulation was also increased, because higher kinetic energy in the inlet air was available for being transferred t o the particulate system, which could therefore attain a higher momentum. Reduced air mass flow rate ( G r ) , the ratio of air mass flow rate (G) to that of minimum air mass flow rate required for spouting ( G m s )was , calculated against solid mass circulation per hour, W , and is shown in Figure 5 for the coal-air system. The W us. Gr figure shows that W increases linearly with Gr. The rate of increase is greater for larger than for smaller diameter particles a t the same Gr value. This is as expected, as most of the energy associated with the air is utilized for larger diameter particles, a t the same value of reduced air mass flow rate. The regular gradient of this rate of increase is shown in Figure 6, where W I G r is plotted against D,, keeping p p constant for each solid. This shows that the reduced solid mass flow ratio is linear with D,. The slope of linearity is the same for the four average particle diameters with varying intercepts. The main two forces influencing particle movement in a spouted bed are accelerating force by the frictional drag on the particles by the particle-fluid mixture upstream and decelerating force due to gravity. This decelerating force is less in the case of low density particles and it
Results and Discussion
The mixing runs were conducted a t a higher value of the air mass flow rate than the minimum, because the spout had to stand the disturbance due to top pouring of the tracer material. The tracer concentration, x , was used in Equation 9 derived from the spouted bed solid circulation model; when Z , , / ( x - X ~ J was plotted against (lisl+ l / S 2 ) t 534
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4,1970
(iifd)t Figure 4. Linear fitting of mixing data of coal-air system to evaluate W G = 12.01 to 14.39;D, = 150 mm.; Do = % inch (9.52 mm.); B = 30";D, = 1.08 m m .
is evident from W us. Gr that W increases with decrease in apparent particle density a t the same value of D, and Gr. The degree of increase of solid mass circulation rate can be observed when W / G r is plotted against p , keeping D, constant for each solid. Figure 7 shows that the reduced solid mass flow ratio is linear, p , having the same value of negative slope of linearity for the four different average particle diameters with respective intercepts. The experimental data were then empirically correlated among solid circulation rate, reduced fluid mass velocity, apparent particle density, and average particle diameter by plotting the data on log-log graph paper in the usual method. The exponents and the constant were evaluated from the slopes and the intercept.
The following equation was obtained.
The experimentally determined W were then compared with the W calculated from Equation 10. This is shown in Figure 8, where the experimentally determined solid circulation rate was plotted for the four solids and their four average diameters against the calculated rate by using Equation 10. The standard deviations of most of the calculated values from the observed values were within 17%. Data of Thorley et al. (1959) showed no variation of solid circulation with a systematic change in the reduced fluid mass flow rate. Only wheat was used as the solid.
1100
3000
t-
2000
-
1000-
31;
W 1000
-
-
900-
B
800-
