3520 MEB
Salt Lake City, Utah 84112
March 31, 2006
Dr. B. Tyler
Beehive State Laboratories
Salt Lake City, UT 84112
Dear Dr. Tyler:
On March 2, 2006, we proposed to make the following improvements to the fluidized
beds in MEB 3520: install ball valves on the exit plumbing of each bed; install
thermocouples on the inlet and outlet of the two beds that lacked thermocouples; install a
temperature controller for the heater and thermocouples on the inlet and outlet of the
heater; find new and unique particles that can be used in future experiments. Our project
is described in detail in the attached report entitled “Improving the Fluidized Beds in
Senior Lab.”
After the improvements were made to the system, we performed a number of tests at
different temperatures and flow rates. The column closest to the heater experienced the
least amount of heat loss and pressure drop of the incoming air because the air went
through the least amount of piping. However, all three columns heated up much faster
with the PID controller than without (30 minutes to reach steady state compared to two
hours in previous experiments). No problems with bleed-back were encountered, which is
a result of the newly installed ball valves on the exit streams. Tests were performed more
efficiently because all three columns could be utilized. We were able to perform eight
tests on two different materials in the course of two days, a task that would have taken
four days before the upgrades were made. The particles we collected were crushed walnut
shells and an unknown ceramic material. We found that the experimental results
correlated quite well with theory for the walnut shells. However, we experienced a wide
variety of experimental difficulties with the unknown ceramic materials and we don’t
recommend using the unknown material in future experiments. It was unknown to some
degree how much the use of column 1 affected the experimental results. It was found
that the pressure drop of column 1 had a much flatter response with increasing flow rate.
Therefore, it is recommended to perform experiments on this column with various
materials to determine how much the column affected the results.
The improvements we made on the fluidized beds made the apparatus more efficient and
precise. In order to be able to investigate the establishment of thermal equilibrium, it
would be beneficial to install a thermocouple rod that extends into the particle bed in one
of the columns.
Sincerely,
Brandon Grimm
Matthew Walker
Katie Peterson
IMPROVING THE FLUIDIZED BEDS IN SENIOR LAB
by
Katie Peterson, Matthew Walker and Brandon Grimm
Assigned: March 2, 2006
Due: March 31, 2006
Submitted: March 31, 2006
ii
Table of Contents
Summary……………………………………………………………………. v
I.
Introduction…………………………………………………………... 1
II.
Theory……………………………………………………………....... 2
III. Apparatus and Procedure…………………………………………….. 7
IV. Results and Discussion of Results …………………………………..10
V.
Conclusions and Recommendations ………………………………...15
Nomenclature ……………………………………………………………... 16
References ………………………………………………………………… 17
Appendices
A. Raw Data …………………………………………………………… 18
B. Sample Calculations ………………………………………………... 25
C. Major Items of Equipment …………………………………………. 27
D. Uncertainty Analysis………………………………………………... 28
E. MSDS Information………………………………………………….. 30
iii
List of Figures
No. Title
An example of an experimental fluidization curve
1
Side-view schematic of a small cross-sectional area of the column
2
Schematic of the fluidized beds with the air flow pattern for the first
3
4
5
6
column.
The logarithm of the walnut shell pressure drop of column 3 versus the
logarithm of the volumetric fluid flow with respective error bars at 25˚C.
The logarithm of the unknown material’s pressure drop of column 1
versus the logarithm of the volumetric fluid flow with respective error
bars at 25˚C.
The pressure drops of columns 1 and 3 versus the flow rate when the
columns were empty.
Page
2
3
9
11
13
13
List of Tables
No.
1
2
3
Title
Densities and average particle diameters of unknown material and
walnut shell material.
Minimum fluidization flow rates for the walnut shell material at 25˚C,
30˚C, 50˚C, and 70˚C.
Minimum fluidization flow rates for the unknown material at 25˚C,
30˚C, 50˚C, and 70˚C.
iv
Page
8
12
14
SUMMARY
Improving the Fluidized Beds in Senior Lab
Group E:
K. Peterson, B. Grimm, M. Walker
Report Date: March 31, 2006
In this project, the members of Group E made improvements to the fluidized beds located
in Room 3250 of the Senior Lab. These improvements were based on previous
experiments, which showed that the performance of the columns could be made more
efficient.
The improvements made to the columns were:
1) Install ball valves to prevent bleed-back from one column to another and to
isolate the columns so that maintenance may be performed on one while another
is being used for experimentation.
2) Install thermocouples on the remaining two columns in order to make all three
columns usable for temperature experiments.
3) Install a controller and thermocouples on heater to provide temperature control.
4) Find and test the minimum fluidization properties of two new particles (walnut
shells and unknown ceramic material) that can be used in future experiments.
Two minor improvements were made in addition to those set forth in the original
proposal:
1) Insulate the lower section of piping to decrease temperature loss from the air.
2) Remove an extraneous piece of piping.
The improvements made on the fluidized beds made the apparatus more efficient and
precise. It is estimated that experimentation time was reduced by a factor of four. It was
found that the walnut shells behaved according to theory. The ceramic material, on the
other hand, showed no clear minimum fluidization velocity. It is suspected that this is a
result of a poor distributor cap on column. Therefore, it is recommended to perform
more experiments on column 1 using other materials to validate this suspicion. Overall,
it would be beneficial to replace the distributor caps as none of the three behave the same.
Also, in order to better investigate the establishment of thermal equilibrium, a
thermocouple rod would have to be installed that extends into the particle bed.
v
I. INTRODUCTION
Fluidized beds were developed simultaneously yet independently in America and Europe
in the 1920’s. However, they were not widespread until Standard Oil used them in a
novel approach to crack petroleum in the 1930’s. After this technological discovery, the
use of fluidized beds continued to increase during and after the period of World War II
[1]. Ever since the 1940’s, fluidized beds have become a vital part of chemical and
combustion processes and are still researched heavily today.
Fluidized beds have applications in a wide variety of chemical reactions, such as
combustion and catalytic cracking. They are also used in physical and mechanical
processes, such as coating and drying [2]. Each application requires that different
materials be fluidized. To do so, a fluid must be blown through the material in a column.
Each material requires a minimum velocity of the fluid to fluidize. The minimum
fluidization velocity is dependent on properties of the material and the fluid. For some
materials, it is easy to predict the minimum fluidization velocity. For others, however,
the minimum fluidization velocity does not compare well with theory and must be
determined experimentally. The minimum fluidization velocity of a material can be
determined by recording the pressure drop across the column at different velocities of the
fluid. If a log-log plot of the flow rate of the fluid versus the pressure drop across the
column is made, the point at which the bed fluidizes can be read from the plot by
observing a depression in the curve [3].
The purpose of this project was to make the following improvements to the fluidized beds
in Senior Lab: install thermocouples on the first two columns to be able to perform
temperature experiments in them; put ball valves on the outlets of first two columns to
prevent fluid bleed-back from one column to another; install a PID controller and
thermocouples on the heater to get more robust and desirable temperature control; and
find more unique particles that can be used in the beds.
II. THEORY
To find the minimum fluidization velocity by experimental methods, the logarithm of the
pressure drop is plotted versus the logarithm of the gas velocity. Figure 1 is an example
of such a plot, where the lower end of the curve represents a fixed bed, the middle
represents the fluidized bed, and the end of the curve represents solid transport [4]. As
the gas velocity increases at the lower end of the curve, the pressure drop across the
column increases due to the increasing particle resistance to flow. The fixed bed is
present until Point 1 is reached. According to Boterrill [5], the pressure at Point 1 is
greater than that of Point 2 because additional pressure is required to break the packing
and interlocking of the particles before fluidization can occur. Once fluidization occurs
at Point 2, the logarithm of the pressure drop does not change as a function of gas
velocity. At Point 3, the particles become entrained in the fluid and are carried from the
bed.
log pressure drop
There exist several other approaches in determining the minimum fluidization velocity of
a fluidized bed column. The following approach is similar to that given by Davidson [6]
and Kozeny [7] and is a theoretical approach from first principles to find the minimum
velocity.
5
1
4
3
3
2
2
1
0
0
5
10
log (gas velocity U)
Figure 1: An example of an experimental fluidization curve with a fixed bed region, fluidized bed
region, and solid transport region.
In order to determine the minimum fluidization velocity, it is first necessary to obtain a
model that closely approximates the behavior of fluid flow through a small crosssectional area of the column. Figure 2 shows a schematic of such a model with an
inclined fluid flow through a passage that approximates the same flow characteristics as a
packed bed.
When a fluid flows around a particle as modeled in Figure 2, the friction coefficient cf
and the Reynolds number are as follows:
cf 
2 o
um2
2
(1)
Re 
and
UD
.

(2)
All symbols are defined in the Nomenclature section at the end of this document. Based
on fluid flow through the column, the volume of the passage is equal to the void volume
L*ε within the packed volume and the void fraction is:

Am
.
cos( )
(3)
The hydraulic mean diameter of the fluid flow passage is:
HD 
4 Am
.
l
(4)
Pressure gradient and mean
fluid flow
λ
Passage Area Am
Length L/cos λ
Figure 2: Side-view schematic of a small cross-sectional area of the column used to derive the
minimum fluidization velocity. All symbols are defined in the Nomenclature section at the end of this
document.
Assuming that the surface area of the passage wall is equal to the surface of the particles,
Equation (4) can be substituted into Equation (3) to obtain the hydraulic mean diameter
of the passage as follows:
3
HD 
4
.
a
(5)
The fluid flow interstitial velocity within the passage shown in Figure 2 is:
um Am  U .
(6)
The volume flow rate through a unit cross-section of packing, using Equations (3) and (6)
then becomes:
um 
U
.
 cos( )
(7)
To obtain the minimum fluidization velocity, it is necessary to define the area of the
passages’ walls as:
Am 
Ll
.
cos( )
(8)
The actual flow of the fluid is caused by the pressure gradient acting in the direction
shown in Figure 2. The pressure gradient causes a mean shear stress to act on the passage
walls, which is described from Equation (8) and is as follows:
o 
p cos( )
.
La
(9)
Substituting from Equations (7) and (9) into Equation (1) then gives the friction
coefficient for the fluid traveling through the passage:
cf 
2p   3 cos3  

 .
U 2 L 
a

(10)
Similarly, substituting from Equations (4) and (7) into Equation (2) gives the Reynolds
number for the packing
Re 
U  4 

.
  a cos( ) 
(11)
At low Reynolds numbers, the Poiseuille equation for laminar flow is given as:
cf 
4
16
.
Re
(12)
Substituting Equations (12) and (11) into Equation (10) yields the following equation for
the pressure drop per unit length of the column which can be used to find the minimum
fluidization velocity:
p
2Ua2
.
 3
L  cos 2 
(13)
However, the actual value of ε can be very difficult to find experimentally and the actual
value of λ varies depending on the column and particles used. In order to simplify
Equation (13) into a more usable form, it is necessary to define that for a bed of spheres
containing N spheres of diameter d, per unit volume, the surface area is:
a  d p2 N ,
(14)
and the void fraction is:
 
1
3
Nd p .
6
(15)
Substituting Equations (11), (12), (13), and (14) into Equation (13) gives an intermediate
equation for the pressure drop per unit length:
2
p  72  U 1   
.
 2 
L  cos   d p 2 2
(16)
If it is assumed that the particles are spherical and that at incipient fluidization they
arrange themselves in the loosest possible mode of packing while remaining in contact
with each other, a void fraction of 0.476 can be used. Also, it was determined
experimentally by Carman [8] that the mean angle at which fluid flows is approximately
50.7˚. If it is recognized that at incipient fluidization the pressure drop across the column
is enough to support the weight of the particles, the following equation can be written:
P
  s   g 1    .
L
(17)
By combining Equations (14) and (15) and using a void fraction of 0.476 and an average
value of 50.7˚ for λ, the minimum fluidization velocity equation can be found. This is the
final theoretical equation in which all parameters and variables are easily obtained:
0.00114 gd p  s   
2
U mf 

5
.
(18)
It may be necessary to determine some of the variables in Equation (18) experimentally.
For example, if the average diameter of the particle in the column is unknown, it is
possible to find it experimentally through the use of sieve trays. Sieve trays are used to
separate the particles into size ranges by shaking the sample through a series of sieves.
The weight of the sample on each tray is then measured and the mass fraction of each
particle size in relation to the total sample weight is calculated. The average particle
diameter for the sample can be found using the weighted average diameter equation as
follows:
d p   xi Di .
(19)
In addition, if the bulk density of the particles in the column is unknown, it is relatively
simple to find their. A measured weight of sample can be placed in a graduated cylinder
with water in it. The amount of water displaced by the sample can be measured and the
density can then be found by the following:

weightofsample
.
waterdisplaced
(20)
As stated in the Introduction section, the turbulent nature of fluidized beds leads to
excellent heat transfer properties. According to theory, “thermal equilibrium is quickly
established between the gas and the particles because of the very large surface area
exposed by the small particles”.
6
III. APPARATUS AND PROCEDURE
The experimental apparatus is assembled in the Chemical Engineering Senior Laboratory
located in Room 3520 of the Merrill Engineering Building. The fluidized beds consist of
three glass columns, 3.9±0.1 inches in diameter and approximately 8 feet tall, with
distributor caps at the bottom of each column to distribute the air flow evenly throughout
the bed. A schematic picture of the three columns is shown in Figure 3. Air flows into
the bottom of each column and out the top. Valves at the inlet and outlet of the beds
allow the user to direct air flow through one specific column. The volumetric flow rate of
the incoming air can be varied from 0 to 600 SCFH. Different bed materials are poured
into the columns by taking off the top sections and are removed by way of an industrial
vacuum. According to Smith [3], if the bed depth is less than 300 mm (~1 ft), the
minimum fluidization velocity is a function of bed depth. Therefore, a bed depth
between 1 and 2 ft should be used. Air flow into the columns is controlled by valves on
the control bench. The flow rate is measured by a flow meter and the pressure drop
across the column is measured by a pressure gauge attached to each column. The
temperature of the air entering the columns may be manipulated by a heater. The heater
is controlled by a Honeywell PID, inventory #201953 with a type-K thermocouple at the
outlet of the heater. Type-T thermocouples located at the inlet and outlet of the columns
and the heater measure the temperature of the entering and exiting air. The temperature
can then be recorded by the Opto-22 data acquisition system.
The tasks performed to improve the fluidized bed were as follows:
1.
The exit piping was disassembled in order to install ball valves that would
prevent bleed-back. The pipes were then cut and threaded using a Ridgid 535
pipe threader to accommodate the new valves and fit into the existing system,
seen in Figure 3. The piping was reassembled using pipe sealant and enough
force to prevent pressure loss through leaks. Each column was isolated using
the new ball valves and leaks were found by spraying soapy water on the
column to find where the air was escaping. Leaks were then fixed by
resealing the piping and retesting the system.
2. A 1/8th inch hole was drilled into the inlet and outlet of each column for typeT thermocouples to be inserted. An epoxy, Thermalbond 4952, was used to
cement each thermocouple into place. However, before installation, each
thermocouple was checked to ensure working operation. The thermocouples
were not calibrated at this time as this was done by the manufacturer.
Thermocouples were also installed on the inlet and outlet of the heater to
monitor the air temperature coming into the system and leaving the heater. A
third thermocouple was inserted into the heater outlet for use by the PID
controller. Once the epoxy was dry, all thermocouples were wired into Opto22 to allow for data acquisition.
3. Insulation was applied to the piping to reduce the heat loss from the system.
Also, an unused stagnant section of piping was removed to reduce heat losses.
7
The experimental procedure to test the ceramic material and walnut shells was as follows:
1. The fluidized beds were set up as per Smith’s [3] instructions and as outlined
above. The tests were performed on one column at a time, where each column
was isolated from the others by closing the exit stream ball valves of the two
unused columns.
2. The pressure drop across each empty column had to be subtracted from the
experimental pressure drops to account for the pressure drop caused by the
distributor cap. Therefore, the pressure drop of each empty column had to be
measured at various flow rates before any material could be added to the
column. Figure 6 shows the resulting plot of the pressure drop of the empty
columns versus flow rate for the first and third columns.
3. The densities and diameters of the bed particles had to be determined to make
theoretical calculations. The density was determined by weighing a certain
amount of material. Then, that amount of material was added to a known
volume of water and the amount of water displaced was noted. The density
was found by dividing the weight of the sample by the water displaced. The
particle diameter was determined by shaking a sample through a series of
sieve trays. The particle size distribution was determined by weighing the
amount of sample deposited on each sieve tray. The average particle diameter
was then determined from the resulting particle size distribution. The densities
and particle diameters of the two materials are summarized in Table 1.
4. The flow rate of air was varied from 150 to 400 SCFH in increments of 10
SCFH at room temperature. At each flow rate, the pressure drop across the
column was recorded. Each material was tested at least two times to obtain
statistics for the experiment. A log-log plot like Figure 1 was then prepared
from the data (see Figures 4 and 5).
5. The air was then heated. The Opto-22 data acquisition system was used to
record the temperature continuously. Step 4 was repeated at 30, 50 and 70ºC
to find the dependence of the minimum fluidization flow rate on temperature
(see Appendix A for additional plots).
The density and viscosity of air were required to calculate the theoretical
minimum fluidization volumetric flow rate of each material at different temperatures.
Incropera [9] lists several thermophysical properties of air, including density and
viscosity, at a range of temperatures. These values were used in the theoretical
calculations.
Table 1: Densities and average particle diameters of glass beads and course gravel.
Material
Ceramic
Density (ρp, kg/m3)
400
Average Particle Diameter (dp, m)
1.24x10-3
8
Walnut Shells
9.00x10-4
753.2
Figure 3: Schematic of the fluidized beds with the air flow pattern for the first column.
9
IV. RESULTS AND DISCUSSION OF RESULTS
Results of Improvements on the Fluidized Beds
Ball valves were installed on each column to be able to isolate them and prevent bleedback through adjoining columns. The ball valves will help stop clogging of the pipes.
They will do this by preventing entrained particles from traveling into stagnant sections
of piping and building up in the pipes, thus creating blockage.
The installed PID controller will supply future experimenters with exact temperatures,
which quantitative results will aid in experimental minimum fluidization velocity
calculations and improve accuracy. The PID controller will also be used to prevent large
overshoots of the heater and provide more robust process control.
The other major improvement was the installation of thermocouples on the first and
second columns along with the heater. With these upgrades on the system, the first and
second columns can now be used because the air temperatures are recorded by OPTO 22
for data processing. With the installation of thermocouples on the heater, real time
effects of the varying air stream temperature and the heating element duty can be seen.
Now that the first column is available, it will be the best choice for the reduction of heat
losses during experimentation since it is the closest to the heater and has much less piping
that contributes to heat loss and pressure drop.
With the combination of the three upgrades, this system can be used to its full capacity.
All three columns can be run independently and even in parallel (theoretically). Also, the
process of changing a particle bed can be done while another column is being run, thus
reducing dead time for experimentation. All three columns can be loaded and
experiments performed in one day, whereas it would have taken at least three full days to
perform the same volume of work.
The minor improvement of removing a section of stagnant piping and applying insulation
to the lower sections of piping will reduce the heat loss from the system and allow for
more robust process control.
Minimum Fluidization Flow Rates
The experimental raw data are listed in Table A-1 through Table A-5 of Appendix A.
Two materials (crushed walnut shells and an unknown grey-white ceramic material) were
used in the column in an attempt to find their minimum fluidization velocity and the
effect of temperature on this velocity. The temperatures that were used during the
experiment were 25˚C, 30˚C, 50˚C, and 70˚C. It was not advised to run experiments at
temperatures higher than 80˚C because the epoxy which holds the thermocouples in place
degrades at 90˚C.
10
Before the experiments could be run, the effect of the distributor cap on the pressure drop
of columns 1 and 3 was determined by finding the pressure drop across each column
when it was empty. This data is shown in Tables A-1 and A-2. The data was then used
to normalize the experimental data as proscribed above.
The walnut shells were placed in column 3 and the unknown material was placed in
column 1. Figure 4 shows the resulting data for the walnut shells at 25˚C. This plot
shows the logarithm of the pressure drop versus the logarithm of the fluid volumetric
flow rate with the associated error bars. From the graph, the minimum fluidization flow
rate was found to be 340 ± 40 SCFH. This value was then compared with theory by
employing Equation (18). Using this equation with a density of 753.2kg/m3 and a
particle diameter of 0.90 mm, it was found that the theoretical minimum fluidization
velocity of the walnut shells at 25˚C was 365 ± 29 SCFH, which is surprisingly close to
the experimental minimum flow rate value.
ln(dP) vs ln(SCFH) @ 25C
0
5.6
5.65
5.7
5.75
5.8
5.85
5.9
5.95
6
6.05
6.1
-0.2
-0.4
-0.6
ln(dP)
-0.8
-1
-1.2
-1.4
-1.6
-1.8
ln(SCFH)
Figure 4: The logarithm of the walnut shell pressure drop of column 3 versus the logarithm of the
volumetric fluid flow with respective error bars at 25˚C.
The minimum fluidization flow rate of the walnut shells was also found experimentally at
temperatures of 30˚C, 50˚C, and 70˚C. Figures A-3 through A-5 show the logarithm of
the pressure drops of column 3 versus the logarithm of the volumetric flow at elevated
temperatures with the associated error bars. From these figures, the minimum fluidization
velocities of the walnut shells at the elevated temperatures were found and are shown in
Table 2. As seen, these values correlate quite well with theory. Overall, the
experimental and theoretical velocities decrease with increasing fluid temperature. This
is due to the increase of viscosity of the air with increasing temperature, which effect is
supported by the viscosity in the denominator as shown in Equation (18).
Table 2: Minimum fluidization flow rates for the walnut shell material at 25˚C, 30˚C, 50˚C, and 70˚C.
11
Minimum Fluidization Flow Rate, SCFH @25˚C
Minimum Fluidization Flow Rate, SCFH @30˚C
Minimum Fluidization Flow Rate, SCFH @50˚C
Minimum Fluidization Flow Rate, SCFH @75˚C
Experimental
Values
340 ± 40
320 ± 40
310 ± 40
300 ± 40
Theoretical
Values
366 ± 29
355 ± 39
342 ± 38
320 ± 36
The next material analyzed was an unknown grey-white ceramic material. Figure 5
shows the resulting data for the unknown material at 25˚C using column 1. The data for
30˚C, 50˚C, and 70˚C are found in Figures A-4, A-5 and A-6. It was difficult to obtain
the minimum fluidization flow rate From Figure 5. As seen, there is not a definite trend
on the graph where the pressure drop lowers to indicate the release of the material from
the packing. One of the possible reasons for this effect is that the material was rather
porous. While attempting to measure the density of this particle, it was found that the
material absorbed a large amount of water. It is possible that the many pores of the
particle affected the minimum flow rate by altering the flow through the particle and
causing a limited pressure drop.
Another possibility is that the distributor cap data for column 1 was much different than
the data for column 3. Figure 6 shows a graph of the distributor cap data for columns 1
and 3. As seen, the slope of column 1 is much flatter than column 3, which would affect
the result because changes in data would be smoothed more for column 1 than for column
3. This would make a determination of minimum fluidization flow rate more difficult
using column 1. Therefore, further experimentation should be done on column 1 using
other materials to see if the distributor cap does in fact smooth the data.
However, based on the subtle pressure drop changes, experimental minimum fluidization
velocities were assumed. These assumptions are subject to significant error and may not
be minimum fluidization flow rates at all. Table 3 shows the experimental minimum
fluidization flow rates as well as the theoretical minimum fluidization flow rates at 25˚C,
30˚C, 50˚C, and 70˚C. The density was assumed to be 400kg/m3 because it was
significantly lighter than the walnut shells. The density was not measured experimentally
because the unknown material would absorb much water, thus affecting the results.
Table 3: Minimum fluidization flow rates for the unknown material at 25˚C, 30˚C, 50˚C, and 70˚C.
Minimum Fluidization Flow rate, SCFH @25˚C
Minimum Fluidization Flow rate, SCFH @30˚C
Minimum Fluidization Flow Rate, SCFH @50˚C
Minimum Fluidization Flow rate, SCFH @75˚C
12
Experimental
Values
320 ± 200
340 ± 200
320 ± 200
NA
Theoretical
Values
366 ± 29
358 ± 28
345 ± 28
323 ± 26
ln(dP) vs ln(SCFH) @ 25C
0.6
0.4
0.2
0
ln(dP)
4.8
5
5.2
5.4
5.6
5.8
6
-0.2
-0.4
-0.6
-0.8
ln(SCFH)
Figure 5: The logarithm of the unknown material’s pressure drop of column 1 versus the logarithm of the
volumetric fluid flow with respective error bars at 25˚C.
Distributor Cap Pressure Drop
3.50
3.00
y = 0.0049x + 0.0505
R2 = 0.9962
Pressure Drop (psi)
2.50
2.00
Column 3
Column 1
Linear (Column 3)
Linear (Column 1)
1.50
1.00
y = 0.0032x - 0.0007
R2 = 0.9955
0.50
0.00
0
100
200
300
400
500
600
700
-0.50
SCFH
Figure 6: The pressure drops of columns 1 and 3 versus the flow rate when the columns were empty.
13
If the subtle changes do indicate minimum flow rates, then the data matches surprisingly
well. However, due to the many uncertainties in this analysis, it is recommended to
perform more experiments using column 1 with other materials to see if the distributor
cap does affect the results significantly.
14
IV. CONCLUSIONS AND RECOMMENDATIONS
The improvements made on the fluidized beds made the apparatus more efficient. The
addition of thermocouples to the two columns allows users to perform experiments with
all three columns. Thus, users can set up all three columns simultaneously, resulting in
less time setting up and cleaning out the columns. The addition of the heat control
system results in quicker responses of the heater to user-input temperatures. Adding ball
valves to the plumbing prevents bleed-back from one column to the next, thus saving
users’ time spent on column maintenance. Users may also clean out and/or set up one
column while experiments are being run on another. In experiments performed after the
improvements were made, experimentation time was reduced by a factor of about four
compared to before the improvements were made.
In addition to making the apparatus more efficient, the improvements made give users
more control over the experiments they run. Users can specify the heat they desire to run
experiments at. It was found that the experimental minimum fluidization flow rates for
the walnut shells correlate quite well with theory. However, it was found that the
experimental results for the unknown material did not give respectable results at all. An
attempt was made to infer minimum fluidization flow rates, but these assumptions are
suspect to great error. Therefore, users may perform experiments on walnut shells if they
so desire, although it is not recommended that the unknown ceramic be used for future
experimentations. If a reason was found to do so, users could run the three columns in
parallel. In short, the capabilities of the apparatus have been increased.
It is recommended that distributor caps be investigated for replacement as none of the
three behave the same. However, this is a very expensive venture and should not be done
without careful consideration. In addition, it is recommended to test additional materials
in column 1 due to the flat response of this column’s distributor cap with increasing air
flow. This effect could potentially alter and smooth the pressure drop results. Also, in
order to investigate the establishment of thermal equilibrium in a bed of particles, a
thermocouple rod should be installed that extends into the bed. Again, this would be an
expensive venture, but it is one that could further increase a users understanding of the
fluidized beds.
15
Nomenclature
Symbol
a
Am
cf
Di
dH
dp
g
HD
l
L
N
Re
U
Um
um
xi
Definition
Units
Surface area per unit packed volume of packing
m2/m3
Cross-sectional area of the fluid passage around the particle m2
Friction coefficient for the column packing
Sieve tray diameter for sieve tray I
m
Hydraulic mean diameter of the spaces between the packing m
Average particle diameter
m
Gravitational constant (9.81)
m/s2
Hydraulic mean diameter of the passage
m
Perimeter of the passage cross-section
m
The length of the fluid flow passage
m
Number of spheres in a particular bed
Reynolds’s number
Interstitial velocity through the column
m/s
Minimum fluidization velocity of the particles
m/s
Gas velocity through the particles
m/s
Weight mass fraction of the corresponding sieve tray
kg
Greek
Δp
ε
λ
μ
ρ
ρs
Pressure drop across the column
Void fraction of the particles in the bed
The inclined angle of the fluid flow passage
Viscosity of the fluid used in the column
Density of the fluid traveling through the column
Density of the particles in the fluidized bed
16
Pa
˚
kg/m*s
kg/m3
kg/m3
References
[1] University of WA webpage: faculty.washington.edu/finlayso/Fluidized_Bed/FBRIntro/history_fbr.htm
[2] Azbel, D. S., and N. P. Cheremisinoff, 1983, Fluid Mechanics and Unit Operations, Ann Arbor
Science Publishers, Ann Arbor, MI, pp. 914.
[3] Smith, G. D., “Fluidization Experiment,” University of Utah, Salt Lake City, UT, February 1986.
[4] Zenz, F.A., and Othmer, D.F. Fluidization and Fluid-Particles Systems, Reinhold Publishing (1960)
[5] Botterill, J.S.M., Fluid-Bed Heat Transfer, Academic Press (1975)
[6] Davidson, J.F., and Harrison, D., Fluidized Particles, Cambridge University Press (1963)
[7] Kozeny, J. Uber kapillare Leitung des Wassers im Boden, S.B. Akad. Wiss. Wien, Abt. IIa (1927)
[8] Carman, P.C. Flow of Gases Through Porous Media, Trans. Instn Chem. Engrs, Lond., 15, 150 (1956)
[9] Incropera, F. P., and D. P. DeWitt, 2002, Fundamentals of Heat and Mass Transfer, John Wiley &
Sons, Inc., New York, NY, pp. 917.
17
Appendix A – Raw Data
Table A-1: Distributor-cap pressure drop data for column 3 as a function of flow rate.
Flow rate
Run #1
Run #2
Run #3
SCFH@25˚C
Δp @25˚C , psi
Δp @25˚C , psi
Δp @25˚C , psi
50
0.43
0.39
0.40
100
0.54
0.51
0.55
150
0.75
0.74
0.76
200
0.99
0.99
0.99
250
1.20
1.2
1.21
300
1.47
1.48
1.49
350
1.70
1.7
1.69
400
2.00
2.00
1.99
450
2.22
2.22
2.25
500
2.50
2.52
2.51
550
2.65
2.76
2.76
600
3.05
3.04
3.01
Table A-2: Distributor-cap pressure drop data for column 1 as a function of flow rate.
Flow rate
Run #1
Run #2
SCFH@25˚C
Δp @25˚C , psi
Δp @25˚C , psi
50
0.43
0.39
100
0.54
0.51
150
0.75
0.74
200
0.99
0.99
250
1.20
1.2
300
1.47
1.48
350
1.70
1.7
400
2.00
2.00
450
2.22
2.22
500
2.50
2.52
550
2.65
2.76
600
3.05
3.04
18
Table A-3: The pressure drop of column 3 as a function of flow rate and temperature for
the walnut shell material.
Flow
Run #1 Run #2 Run #1 Run #2 Run #1 Run #2 Run #1 Run #2
Rate,
@25˚C @25˚C @30˚C @30˚C @50˚C @50˚C @75˚C @75˚C
SCFH
250
1.70
1.68
260
1.66
1.67
1.72
1.72
270
1.67
1.68
1.77
1.79
280
1.66
1.65
1.68
1.67
1.73
1.73
1.84
1.86
290
1.67
1.67
1.7
1.7
1.78
1.80
1.93
1.95
300
1.73
1.73
1.75
1.75
1.85
1.89
1.99
1.99
310
1.78
1.79
1.81
1.80
1.90
1.92
2.05
2.05
320
1.84
1.84
1.86
1.84
1.97
1.98
2.10
2.11
330
1.88
1.88
1.90
1.90
2.02
2.03
2.17
2.17
340
1.93
1.93
1.97
1.96
2.08
2.08
2.24
2.25
350
2.01
2.0
2.02
2.02
2.14
2.16
2.29
2.30
360
2.07
2.08
2.07
2.10
2.21
2.23
2.36
2.37
370
2.14
2.14
2.16
2.17
2.27
2.29
2.40
2.42
380
2.19
2.21
2.23
2.22
2.36
2.35
2.47
2.48
390
2.26
2.27
2.29
2.28
2.42
2.40
400
2.32
2.31
2.34
2.34
410
2.37
2.36
2.39
2.40
420
2.41
2.41
2.43
2.44
430
2.49
2.46
2.50
2.50
-
19
Table A-4: The pressure drop of column 1 as a function of flow rate and temperature for
the unknown material.
Flow
Run #1 Run #2 Run #1 Run #2 Run #1 Run #2 Run #1 Run #2
Rate,
@25˚C @25˚C @30˚C @30˚C @50˚C @50˚C @75˚C @75˚C
SCFH
150
0.29
0.33
0.28
0.27
0.31
0.33
0.33
0.33
160
0.31
0.34
0.28
0.29
0.33
0.34
0.35
0.33
170
0.34
0.36
0.31
0.32
0.34
0.35
0.37
0.35
180
0.35
0.37
0.33
0.35
0.36
0.36
0.39
0.38
190
0.37
0.40
0.35
0.36
0.37
0.38
0.42
0.40
200
0.39
0.42
0.36
0.37
0.39
0.40
0.44
0.43
210
0.41
0.44
0.37
0.39
0.42
0.42
0.46
0.46
220
0.43
0.48
0.40
0.41
0.44
0.45
0.48
0.47
230
0.44
0.50
0.44
0.43
0.46
0.47
0.49
0.50
240
0.47
0.52
0.46
0.46
0.48
0.49
0.51
0.52
250
0.48
0.54
0.48
0.48
0.50
0.50
0.53
0.55
260
0.50
0.57
0.51
0.49
0.51
0.53
0.57
0.56
270
0.52
0.59
0.53
0.51
0.53
0.55
0.59
0.59
280
0.55
0.60
0.55
0.53
0.56
0.57
0.62
0.62
290
0.58
0.63
0.56
0.56
0.60
0.60
0.64
0.65
300
0.60
0.65
0.58
0.58
0.64
0.62
0.66
0.68
310
0.63
0.67
0.61
0.60
0.66
0.65
0.69
0.70
320
0.64
0.68
0.63
0.63
0.67
0.66
0.72
0.71
330
0.66
0.70
0.65
0.65
0.69
0.69
0.73
0.73
340
0.68
0.72
0.67
0.66
0.72
0.71
0.75
0.75
350
0.70
0.74
0.69
0.69
0.74
0.74
0.76
0.76
360
0.73
0.76
0.72
0.70
0.76
0.77
370
0.76
0.78
0.74
0.72
0.79
0.79
380
0.78
0.80
0.76
0.75
0.81
0.82
Table A-5: Sieve-tray data for the walnut shells.
Particle
Sample
Mass
Size, μm
Weight, kg
Fraction
1397
0.02
3.7
991
0.38
70.04
850
0.12
22.20
701
0.01
1.85
600
0
0
425
0
0
Bottom
0.01
1.85
0.54
1
Sum
20
Table A-6: Sieve-tray data for unknown material.
Particle
Sample
Mass
Size, μm
Weight, kg
Fraction
2362
0
0
1981
0
0
1317
0.34
65.38
991
0.15
28.8
850
0.02
3.85
600
0.01
1.92
Bottom
0
0
0.52
1
Sum
-1
5.6
5.65
5.7
5.75
5.8
5.85
5.9
5.95
6
6.05
6.1
-1.1
ln(dP)
-1.2
-1.3
-1.4
-1.5
-1.6
ln(SCFH)
Figure A-1: The logarithm of the walnut shell’s pressure drop of column 3 versus the
logarithm of the volumetric fluid flow with respective error bars at 30˚C.
21
-0.75
5.5
5.55
5.6
5.65
5.7
5.75
5.8
5.85
5.9
5.95
6
-0.8
-0.85
-0.9
ln(dP)
-0.95
-1
-1.05
-1.1
-1.15
-1.2
-1.25
ln(SCFH)
Figure A-2: The logarithm of the walnut shell’s pressure drop of column 3 versus the
logarithm of the volumetric fluid flow with respective error bars at 50˚C.
-0.5
5.45
5.5
5.55
5.6
5.65
5.7
5.75
5.8
5.85
5.9
5.95
6
-0.55
-0.6
-0.65
ln(dP)
-0.7
-0.75
-0.8
-0.85
-0.9
-0.95
ln(SCFH)
Figure A-3: The logarithm of the walnut shell’s pressure drop of column 3 versus the
logarithm of the volumetric fluid flow with respective error bars at 70˚C.
22
0.6
0.4
0.2
0
ln(dP)
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
-0.2
-0.4
-0.6
-0.8
ln(SCFH)
Figure A-4: The logarithm of the unknown material’s pressure drop of column 1 versus
the logarithm of the volumetric fluid flow with respective error bars at 30˚C.
0.6
0.4
ln(dP)
0.2
0
4.8
5
5.2
5.4
5.6
5.8
6
-0.2
-0.4
-0.6
ln(SCFH)
Figure A-5: The logarithm of the unknown material’s pressure drop of column 1 versus
the logarithm of the volumetric fluid flow with respective error bars at 50˚C.
23
0.5
0.4
0.3
0.2
ln(dP)
0.1
0
4.9
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
-0.1
-0.2
-0.3
-0.4
-0.5
ln(SCFH)
Figure A-6: The logarithm of the unknown material’s pressure drop of column 1 versus
the logarithm of the volumetric fluid flow with respective error bars at 70˚C.
24
Appendix B – Sample Calculations
The following sample calculations use the walnut shell data from Tables A-1, A-3, and
A-5 from Appendix A.
Constants- All constants were found at the respective temperature at which the
experimental run occurred. The following constants were found for the 25˚C operating
temperature. All symbols are defined in the Nomenclature section above.
ρ = 753.2 kg/m3
ρs = 2300 kg/m3
μ = 1.836e-5 kg/m-s
g = 9.81 m/s2
Calculation of Particle Diameter – The average particle diameter needs to be found in
order to use Equation (18). The data from Table A-5 was used in Equation (18) to find
the average particle diameter of the walnut shells.
The mass fraction of sample in each sieve tray is found first. The following is an
example of finding the mass fraction for the 991μm tray for the walnut shells.
0.38
 0.7004
0.54
Once the mass fractions are found, Equation (19) is used to find the average particle
diameter.
0.991* 0.704  0.85 * 0.222  0.701* 0.0185  0.6 * 0  0.425 * 0  0.899 μm
Calculation of Minimum Fluidization Velocity – Equation (18) is then employed to find
the minimum fluidization velocity of the walnut shells at 25˚C.


2
kg
kg 
m

0.00114   753.2 3  1.170732 3   9.81 2  9.0 4 m
m
m
m 
s

 0.371
kg
s
1.836  10 5
ms
(From Equation 18).
The minimum fluidization volumetric flow rate can then be found from the minimum
fluidization velocity.
25
m 

 0.371 
s   3600 s    0.1625 ft 2  363.55SCFH

hr
 0.3048 ft 


m

26
Appendix C – Major Items of Equipment
Fluidized Beds
3.9’’ Diameter
Approximately 8’ tall
Kimax Beaded Process Pipe
Pipe Valve and Fitting Company
2737 S 300 W Suite E
SLC, UT 84115
Heater
Control System: Opto 22
PID Controller
Honeywell UDS 3000 PID
Inventory Number: #201953
27
Appendix D – Uncertainty Analysis
All reported uncertainties are reported to be the maximum of the standard deviations for
the measurements.
σΔP = ± 0.08 psi
σwalnut shell diameter = ± 10μm
σunknown material diameter = ± 10μm
σTemp = ± 2.0˚C
σwalnut shell experimental fluidization flow = ± 70 SCFH
σunknown material experimental fluidization flow = ± 80 SCFH
σwalnut shell theoretical fluidization flow = ± 30 SCFH
σunknown material theoretical fluidization flow = ± 30 SCFH
Theoretical Error:
The following is an example of how the error is propagated through the theoretical results
when finding the minimum fluidization velocity:
 0.00114  2     s   9.81 d p   d p



U  
f

   0.00114 * 2  753.2  1.17   9.81 9.0e  4 1.0e  6 

1.836 10 5



= 0.0357 m/s
The error continues to propagate when finding the minimum fluidization flow rate:
m
s * 3600 s    0.1625 2 ft 2  35SCFH
ft
hr
0.3048
m
0.0357
Experimental Error:
Due to the graphical nature of the error bars, the experimental error was found
graphically using a spreadsheet.
Particle Size Error
Because there was an insufficient number of sieve trays close enough in diameter,
the error was analyzed using a spreadsheet. The error was found to be ± 100μm for the
walnut shells and ±100μm for the unknown material.
28
Temperature Errors
It was assumed that the error incurred in these thermocouples was approximately
±2.0˚C because the Omega website stated that for K-type thermocouples the error was
±0.7ºC. This was verified by looking on the control screen and noticing that the different
in temperatures from the top and the bottom of the columns.
29
Appendix E – MSDS Information
The following is the Material Safety Data Sheet for walnut shells:
Material Safety Data Sheet
May be used to comply with OSHA’S Hazard Communication Standard,
29CRF1910.1200. Standard must be consulted for specific requirements.
U.S. Department of Labor
Occupational Safety and Health Admin. (Non-Mandatory Form)
Section I
IDENTITY: (As used on label and list) WALNUT SHELL
Manufacturer’s Name:
Emergency Telephone Number:
Address:
Telephone for Information:
Eco-Shell, Inc.
(530) 824-8794 or (530) 529-1585
5230 Grange Road, Corning, CA 96021
(530) 824-8794
Section II – Hazardous Ingredients/Identity Information
The chemicals listed under section II of the MSDS for this product is not reportable
under SARA 313. If the product is reportable under this regulation, it will be noted in
section II.
Section III
Boiling Point
Vapor Pressure (MM Hg)
Vapor Density (Air – 1)
Solubility in water:
Odor and appearance:
Flash Point:
Flammable limits:
Media used in extinguishing:
Special fire fighting procedure:
N/A
N/A
N/A
Specific Gravity (H20-1)
Melting Point
Evaporation
Not water soluble
No odor – Light brown in color
380°F
470°F
Water
None
1.2
N/A
N/A
Fire and Explosion Hazards:
If improperly handled, stored and/or exposed to and ignition source, this material
may burn. High concentrations of dust in air can explode if sufficient temperature
and ignition source occurs.
Section IV – Health Hazard Data
No Acute Hazards Known
Section V – Reactivity Data
Stability:
Incompatibility (Materials to avoid)
Stable
None
30
Hazardous Polymerization:
None
Section VI – Health Hazards (Acute and Chronic)
None Known Section VII – Precautions for safe handling and use
Steps to be taken if material is released or spilled:
Sweep, Shovel up, or Vacuum
Waste Disposal Methods:
No special requirements
Precautions to be take in handling and storing:
None
Other Precautions:
None
Section VIII – Control Measures
Ventilation: Local Exhaust
Nuisance Dust Levels
Protective clothing, gloves, or equipment:
Not required
Eye Protection:
Not required – Safety goggles recommended
Ground English Walnut Shell
PROPERTIES:
Dual Screen Aggregates have the following characteristics
SPECIFIC GRAVITY
1.2 – 1.4
pH VALUE AT 25ºC (IN WATER)
4-6
FREE MOISTURE (80ºC FOR 15HRS)
3-9%
FLASH POINT (CLOSED CUP)
380º
HARDNESS -VICKERS NO
25-30
MOHS SCALE
3-4
DRY PACKING DENSITY (LBS PER CU. FT.)
22-74
GSA Specification:
AA-1722
Type 2
Military Specification:
MIL-G-5634
Type 3
CHEMICAL ANALYSIS
Nitrogen
Cellulose
Lignin
Toluene Solubility
Methoxyl
Chlorine
Ash
Cutin
0.10
40/60
20/30
0.5/1.0
6.5
0.10
1.5
1.0
31