Petroleum & Coal
ISSN 1337-7027
Available online at www.vurup.sk/petroleum-coal
Petroleum & Coal 55 (4) 311-321, 2013
EXPERIMENTAL MEASUREMENT OF DIFFERENT FLUIDIZATION
PARAMETERS
Amir Farshi
Refining Technology Development Division, Research Institute of Petroleum Industry,
Azadi Sport Complex West Boulevard,Tehran ,Iran , Farshia@ripi.ir
Received August 5, 2013, Accepted November 11, 2013
Abstract
The minimum fluidization velocity and height are the important hydrodynamic parameters of
fluidized bed which required primary data for mathematically modeling of fluidized bed reactor.
Minimum fluidized velocity for particles can be obtained through existing theoretical and experimental
equations, but the minimum bed height can be only achieved via experiments. The minimum
fluidized velocity is a function of physical properties of particles, gas and porosity of bed(εmf) in
the minimum fluidized velocity. The minimum fluidized height is a function of catalyst weight,
bed diameter, gas distributor, and fluidized bed hydrodynamic. In order to run the experiments,
an experimental system including glass column (fluidized bed) with gas distributor and manometer is
made. The dropping pressure in fluidized bed, gas distributor with variation of particle height in the
column is measured versa entering gas velocity. Diagram of dropped pressure versus velocity
(ΔP-U) is drawn in the log-log and linear scales, and where direction of the curve is changed
the minimum of fluidized velocity will be obtained. Using the curve of catalyst height versus
velocity (H-U), the minimum fluidized height (Hmf) is obtained where is the minimum of fluidized
velocity (Umf).
Key Words: Minimum Fluidization Velocity; Minimum Fluidized Height; Fluidized Bed; Hydrodynamic; Minimum
Fluidized Porosity.
1. Introduction
Literature survey in fluidization area and minimum fluidization measurement shows
that in searched literatures measurement method for minimum fluidization velocity
and height were not reviewed also researcher in this area will nor review of all applicable
minimum fluidization velocity in one point . This manuscript will review best equation
for calculating of minimum fluidization and compare it with experimental data.
The contribution of this manuscript will be summarized as following:
- A reference manuscript for find all equation for minimum fluidization velocity calculating
- Predicting a experimental method for measurement minimum fluidization velocity
- Predicting different method for measurement of minimum voidage
- Predicting experimental method for measurement minimum fluidization height
1.1. Fluidization phenomena
[4,5,9]
Whenever a fluid is entered a packed column with a low velocity, the occluded particles
in fluid do not have any movement then there is a fixed bed condition. When the fluid
velocity is going up, the particles take the distance from each other and many of them
start rotating in a limited space. In this case, the bed will be expanded to provide an
Expanded Bed and the porosity and pressure drop will be increased versa Fixed Bed.
Beginning this status, it starts moving from point A to reach the point B on the curve
A. Farshi/Petroleum & Coal 55(4) 311-321,2013
Figure 3, bed still is in Loasent status in this situation and there is still the contact
among the solid particles. With increasing the velocity of entering fluid, all solid
particles in gas and liquid phases are floating up. At this situation, friction force
between solid particles and fluid is equal with particles’ weight force, vertical vector of
existing pressure force among adjacent particles are eliminated and pressure drop of
every sections of bed is almost equal with weight of fluid and occluded particles in
that fluid section. In this case, the bed is fluidized and named primary fluidized bed or
minimum fluidization state. In liquid-solid systems, increasing of fluid flow at higher than
minimum fluidization state terminates to a gently expanding state, but permanently
bed is developing. Instability of flow pretends toward a limited expansion and will be
reached a constant value at a fixed quantity, and generally, large bubbles and
heterogeneity are not observed. The bed with these characteristics is called particle
fluidized bed; homogeneous fluidized bed, permanent fluidized bed, or smoothly
fluidized bed.
Behavior in the gas-liquid systems is often different from above behavior. With
increasing the velocity of fluid after the minimum fluidization, high instability is observed
like forming bubbles and channeling of gas flow. At even higher velocity, highly disturbance
is observed and the movement of solid particles are more complicated. Generally, the
expanding of bed concerning of its volume is not noticeable at minimum of fluidization.
Such a this bed is named comprehensive fluidized bed, heterogeneous fluidized bed,
bubbling fluidized bed, or more simple, gas fluidized bed. In the recent situation,
pressure drop is decreased a little bit until reaches to the point C on the curve. The
velocity of fluid in the bed and among particles are more than its upper air space and
as a result, all particles are flowed towards outside of tube, but only very small particles
are carried by fluid in this position (Entrainment). With increasing velocity of fluid at
point D, all particles in the bed are carried by fluid, so that its porosity is shifted to 1.
This phenomenon causes generating two phases and the primary fluidity is called bath
fluidization because the particles out of the bed are not carried by fluid, but after that
fluidization is named continuous fluidization.
2. Explanation
2.1. Minimum velocity
It is common knowledge that the minimum fluidization velocity is the basic information
required for the design and development of fluidized bed processes; however in industrial
practice fluidized bed reactors are mostly operated at superficial gas velocities well above
the minimum fluidization velocities and, therefore, the minimum fluidization velocity is
not a quantity with a precise significance for industrial applications. From the point of
view of engineering practice even inaccuracies of up to 40% in the prediction of the
minimum fluidization velocity values are more or less acceptable (Molerus and Wirth, [16].
Despite that and many earlier works, discussion on accurate prediction of the minimum
fluidization velocity still seems to remain of much scientific interest. The best method to
determine the minimum fluidization velocity would be by measurement. In practice,
however, this is not always possible, especially at different operating conditions, such as
at elevated pressure. In the absence of the facility to carry out experiments to determine
the minimum fluidization velocity, approximate computation of this is necessary for
any design or study of the fluidized bed process and numerous correlations have been
proposed in the literature [12] .
The generally accepted approach is to estimate the effect of pressure on minimum
fluidization velocity by employing Ergun [17] equation for pressure loss through a
packed bed, which in slightly modified form as Equation (1) appears in many books on
fluidization; or its numerous simplified variations, such as the most popular Wen and
Yu [12,13 ] correlation Yang [15] noted that in the design of fluidized bed systems
312
A. Farshi/Petroleum & Coal 55(4) 311-321,2013
313
designers encounter two completely different situations: the area of interest has very
little information or it has many correlations available and their predictions give sometimes
very different results. There are numerous studies and proposed correlations on the
prediction of the minimum fluidization velocity at ambient conditions as well as a number of
comprehensive reviews comparing these correlations (Adanez and Abanades [1]; Couderc [3],
Grewal and Saxena [8]; Lippens and Mulder [10]). The great majority of the correlations
proposed in the literature are based on the Ergun equation, modified after an experimental
evaluation based on limited numbers of data and materials, and quite often they are
purely empirical. Those empirical correlations have limited value and according to
Lippens and Mulder [10 ], preference should be given to complete characterization of the
fluidized bed including determination of particle shape factor φ and voidage at minimum
fluidization εmf as described by Geldart [7]. Lippens and Mulder [10] explain the widely
accepted success of the Wen and Yu [13,14] correlation in engineering practice as a
first approximation because it simply offers the correct order of magnitude.
2.2 Pressure drop and minimum velocity at fluidized bed
[11, 9]
Many researchers (Blake [18], Carman [19, Kozeny[20] and Ergun [17]) have presented
equations for pressure drop at fluidized bed. Ergun’s equation is applied in a Wide
range of Reynold’s number for non-sphere particles. Ergun [17] presented that pressure
drop at bed is equal total energy lost because of viscosity and kinetic effects.
For low Reynold’s number (small particles and high temperature), losing of viscosity
energy is more than losing of kinetic energy and total pressure drop is explainable using
the losing of viscosity energy.
For high Reynold’s number (large particles), the kinetic energy is important and total
pressure drop is explainable using the losing kinetic energy. Ergun’s equation is presented
as the following:
ΔP/L = 150 (1- ε)2/Фs2 (ε3) . μU/d p 2 + 1.75 (1- ε) U2ρ/ ε3 Фs d p
(1)
As it is expressed previously that the solid or gas is flowing up where fluidized action
happens, the following equation is applied:Particle weight = the Drag force that is
applied by moving gas or, it can be written as following:
(solid specific gravidity) X (the fraction of solid at bed) X (bed’s volume) = (cross sectional
of column) X (pressure drop at bed)
As a result of that, the following equation can be written:
ΔPb X At = (At X Hmf) (1- εmf) (ρs – ρg) g/gc
The equation of pressure drop at bed:
ΔPb/ Hmf = (1- εmf) (ρs – ρg) g/gc
(2)
Using the equation of pressure drop at bed (Ergun’s Equation) where fluidized velocity
is minimum, pressure drop can be obtained by the following equation:
1.75 K1 Remf 2 + 150 K2 Remf = Ar
K1 = (1/Φs εmf
2
) , K2 = (1 -
εmf /Φs2
εmf )
Remf = Umf. dp. ρg / μ , Ar = dp . ρg (ρs – ρg) g / μ2
3
[13,14]
(3)
3
(4)
Wen and Yu
are the first researchers that the quantities of K1 and K2 at the
Reynold’s number range of 0.001 to 4000; while, suggested Umf has the standard deviation
+/- 34%. The Table 1 shows the values of K1 and K2 that are obtained by the other
researchers.
Chitester et. al. [26 have presented the following equation for large particles:
A. Farshi/Petroleum & Coal 55(4) 311-321,2013
314
Remf = [(28.7)2 + 0.0494 Ar]1/2 – 28.7
(5)
The following equation is also presented for small particles (Wen and Yu
[13,14]
:
1.75/εmf Φs(dp . Umf ρg/ μ) +150(1-εmf)/εmf Φs (dp.Umf ρg/ μ) =(dp ρg (ρs–ρg ) g /μ) (6)
3
2
3
2
3
Repmf = [(33.7)2 = 0.0408 Ar]1/2 – 33.7
Wen and Yu
[13,14]
(7)
have also presented the following equation for small particles:
Umf = dp2 (ρs - ρg)g/150 μ X εmf 3Φs2/1 - εmf
Repmf <20
(8)
For large particles the equation is:
Umf = dp2 (ρs - ρg)g/1.75 ρg εmf 3Φs
Repmf >1000
(9)
Using equation (3) it can be written as following:
At the equation (3) for low Reinhold’s numbers, the kinetic term is ignored and then the
following equation is obtained:
150 C2 Repmf = Ar
or
μ Umf = Constant
(10)
According to above equation with increasing the gas temperature, viscosity decreases
and Umf enhances for high Reinhold’s number. Then viscosity term is ignored and the
following equations are obtained:
1.75 C1 Repmf2 = Ar
or
ρ Umf 2= Constant
Table 1 All existing equations, which are used to calculate (Umf)
Type of equation
Ergun, 1952[17]
General equation
Wen and Yu [13]
Richardson [21]
Saxena and Vogel [22]
Babu et.al. [23]
Grace [24]
Chitester et al. [25]
Chitester et.al. [26]
Goroshko et.al. [27]
McKay and McLain [11]
Leva [28]
Davidson, Harrison .[29]
Rowe and Yacono [30]
Yacono
[31]
(11)
[9]
Theoretical an experimental equation, Umf(cm/sec)
1.75/ εmf 3 Φs Repmf + 150 [(1 - εmf)/ εmf 3 Φs2]Repmf = Ar
Repmf = (dp . Umf ρg/ μ) , Ar = dp3 (ρs - ρg)g/ μ2
For small partides: Repmf = [(33.7)2 +0.0408 Ar]1/2 – 33.7
For Umf = dp2 (ρs - ρg)g/1650 μ
For Rep >1000, Umf = dp2 (ρs - ρg)g/24.5 ρg
K1Repmf2+ K2Repmf=Ar
K1
K2
24.5
1651.96
27.39
1408.21
17.5131
886.164
15.36
777.265
24.509
1333.33
20.242
1161.94
For large particles: Remf=[(28.7)2+0.0494 Ar]1/2-28.7
Remf=Ar/(150(1/
400 [(1 - εmf)/ dp]Umf μ + 2.4 ρg Umf 2= (ρs - ρg)g εmf 3 dp
Umf = 0.0093 dp1.82 (ρs - ρg) 0.94/ μ0.88 ρg 0.06
(SI)
Umf = 0.0008 g (ρs - ρg) dp2/ μ
(SI)
Umf=0.0085[
Umf=0.000512 dp1.77Umf(cm/s); dp(
At equation (11), gas density decreases when the temperature increases and Umf also
decreases. For small particles and large particles, terms of viscosity and kinetic are
important. Table 1 presents all existing equations in literature which are used to calculate
fluidity.
A. Farshi/Petroleum & Coal 55(4) 311-321,2013
315
3. Experimental work
3.1.Manufacturing a set-up of glass bed for measurement of Umf and Hmf [6]
A glass fluidized bed is made to measure Umf and Hmf set up is including:
A glass column is used with internal diameter 4.8 cm and the glass column has
two parts. Its top part, is a 100 cm distributor including one outer pathway and
two other pathways located at both sides of distributor to measure the pressure
drop. Down part of distributor has one pathway for entering gas and another
pathway to measure pressure drop and the height of upper part is varied from 13
to 20 Cm. Because three different sizes of distributors of porous type are used,
each of columns has a specific size.
b) The distributor of porous type which is used at the lower of column is separateable. Three different sizes of porous plates are used with 1, 2 and 3 meshes. The
mesh 1 is smaller than meshes of 2 and 3.
c) Other equipment which are used are a water manometer, a gas flowmeter, the
tygon hoses and a metal frame. The water manometer and the gas flowmeter are
used to measure pressure drop and gas flow respectively. The gas flowmeter is
calibrated using calibrating equipment with nitrogen gas. The tygon hoses are
used to measure pressure. All equipment is installed on the metal frame. Glass
fluidized bed system is shown at Figure 1.
a)
Fig.1 Glass fluidized reactor set-up for measuring Umf and Hmf of silicagel catalyst
3.2. The distributing size of silicagel particles (averaged diameter of particles),
physical properties of particles and nitrogen gas [6]
Table 2 Distributing size of particles of silicagel catalyst coupled with physical properties of catalyst
and physical properties of gas.
Particle size per
micrometer
500
Percent of
particles
0.7
Particles density, (g/cm3) ρs
1.96
Bulk density, (g/cm3) ρB
0.43
o
300
43.96
Temperature of nitrogen Gas(T), C
250
18.55
Nitrogen gas pressure(P-atm)
180
24.32
150
6.56
Gas Density(Kg/m3) ρg
125
3.45
100
2.47
Gas viscosity(kg/m.sec) μ
27
1
0.00001784
1.1421
A. Farshi/Petroleum & Coal 55(4) 311-321,2013
316
The averaged diameter of particles is calculated from the following equation:
dpAverage = 1/∑ i (X/dp)i= ¼.697 x 10
-6
= 212.88 μm = 0.21288 mm
3.3. Calculation of Umf and Hmf via experiments
400 grams of silica gel powder catalyst (silicagel is the catalyst of conversion urea
to melamine) is weighed and transfer into a column equipped with porous distributor
with porous mesh 1. Nitrogen gas is flown with flow rate in which flow meter showed
the numbers higher than 150 mm (Flow = 50 cm 3/sec.) then the pressure drop in the
bed and total are measured (pressure drop is obtained using variation of pressure
drop of bed and total). The bed height at fixed bed position is chosen zero as a baselines
and the variation of catalyst height with gas flow rate is measured (using of length
scale on the column). The value of pressure drop is measured from high velocity to
low velocity and these amounts have a little variation from measuring pressure drop
from low velocity to high velocity because of the cohesive force among particles. For
distributor with mesh size 1, the variations of total pressure drop, bed pressure drop,
and distributor pressure drop versus gas flow velocities are drawn. The experiment
for distributors with porosities of mesh sizes 2 and 3 are also drawn. The situation of
fluidized bed is studied in all above cases (fixed bed, bubbled fluidized bed, slugging
phenomena and carrying particles at high velocity).
The experiments indicate that with decreasing the porosity size of distributor, the
condition of distributing of gas flow will become better and the amount of distributing
pressure drop will be increased as Figures presented. The porosity size decreases with
enhancing number of distributors. The height of 400grams catalyst in column is measured
which is 50 cm and based on, the variation of total height versus gas flow velocity is
drawn. The experiments indicate which the variation of catalyst height (∆H) increases
with decreasing porosity size of distributor. Fluidized bed has better condition with
high catalyst height variations rather than low catalyst height variations. Diagram of
pressure drop (∆ P) is drawn versus gas velocity (U) in a logarithm scale. Consider
that Umf is velocity that the curve of P-U has been broken and the value of pressure
drop from its maximum reaches to a fixed value. The value of Umf is a function of
the type of distributor and obtained values are not identical in all states. Considering
that distributor is at the best state with the mesh size 3 and provides properly gas
distribution at the bed, the value in which third state is acceptable. U mf (3) is located
between Umf (1) and Umf (2).
Umf (1) = 3.9cm/sec, Umf (2) = 2.4 cm/sec and Umf (3) = 2.9 cm/sec
These values are obtained using the diagram of height versus velocity (H-U). The
height of catalyst (Hmf) which obtained has the following values for 400 gram of catalyst
and are valid only for a reactor with internal diameter 4.8 cm.
U = Umf (3) = 2.9 cm/s H = Hmf (3) = 54
Related Figures of the experiments are drawn as figures 2,3,4, 5,6,7,8,9 and 10.
Pressure drop distributor and pressure drop of bed have the following relationship:
ΔP(Distributor) = ΔP(bed) x (0.2 to 0.4)
(12)
Therefore the averaged distributor pressure drop is 30% of bed pressure drop where
distributor with porosity of type 3 is used. All experiments result were shown at following
figures:
A. Farshi/Petroleum & Coal 55(4) 311-321,2013
Fig. 2 Pressure drop and different height of
catalyst vs gas velocity were measured.(for
distributor mesh size1)-dr=4.8cm,w=400gr, h-1
20cm
Fig. 4 Different height of catalyst vs gas
velocity for distributor mesh size1
Fig. 6 Bed pressure drop vs gas velocity for
distributor mesh size2
317
Fig. 3 Bed pressure drop vs gas velocity for
distributor mesh size1
Fig. 5 Pressure drop and different height of
catalyst vs gas velocity were measured.(for
distributor
mesh
size2)-dr=4.8cm,w=400gr,h-1
20cm
Fig. 7 Different height of catalyst vs gas velocity
for distributor mesh size2
A. Farshi/Petroleum & Coal 55(4) 311-321,2013
Fig. 8 Pressure drop and different height of catalyst
vs gas velocity were measured.(for distributor
mesh size3)-dr=4.8cm,w=400gr,h-1 20cm
Fig. 9 Bed pressure drop vs gas velocity for
distributor mesh size3
Fig. 10 Different height of catalyst vs gas velocity for
distributor mesh size
4. Calculation of Umf Via the Equations and The Comparison of Obtained Values
with Experimental Values [4,5,9]
Table 3 Calculation Umf according different equation is given.
Type of Equation
Wen and Yu [13]
Richardson [21]
Saxena and Vogel [22]
Babu et.al. [23]
Grace [24]
Chitester et.al.[25]
Gorosho et.al. [27]
Ergun [17]
Leva [28]
Davidson and Harrison
Rowe and Yacono [30]
Yacono [31]
McKay and McLain [11]
[29]
318
Umf(cm/sec)
2.915
3.4089
5.388
6.13
3.6
4.1284
14.3095, εmf=0.4151
3.9443, εmf=0.41516
3.6509
3.8982
3.0604, εmf=0.4149
6. 7574
1.493
A. Farshi/Petroleum & Coal 55(4) 311-321,2013
5. The Values of εmf at Fluidized Bed
319
[2,9]
In order to calculate the value of εmf , there are two following methods: The first
method is the use of equation of Broadhurst and Becker and second method is based
on the amounts of K1 and K2 in the equation which presented by Wen and Yu [13]. K2 / K1
is obtained with using the following equation:
K2 / K1 = 85.714 (1- εmf )/ Φs
(13)
εmf (K2) < εmf < εmf (K1)
(14)
Φs is spherical factor which is equal 1 for spherical particles. Φs is defined as following:
Φs = Sphere Surface/ Particle Surface which has the Same Volume as Sphere ; Φs for
Sharp Sand, Round Sand and for Fischer Tropsch Catalyst is 0.67, 0.86 and 0.58 resp.
The values of εmf for spherical particles with presented K2 / K1 for K1 and K2 with εmf
is calculateable. Table 4 presents the values which are calculated for different states
of εmf. The calculated value of εmf based on K2/ K1 is a little smaller than the calculated
values based on two separated values obtained using the equations of K 1 and K2. The
calculated values of εmf at Table 4 and the obtained values using equations of K 1 and
K2 are nearly closed, and εmf between two values obtained from K1 and K2 is varied.
Table 4 Values which are calculated for different states of εmf
Type of
Equation
K2/K1
1- εmf
εmf
K2
K1
1/
εmf
1εmf
(k1)
(k2)
Wen and
Yu, [13]
67.4
0.7863
0.2137
1651.96
24.5
Richardson
57.4
0.5996
0.4004
1408.21
27.39
Saxena &
Vogel [22]
50.6
0.59
0.41
886.16
17.51
Babu
et.al.[23]
50.6
0.59
0.41
777.26
17.51
54.4
0.6346
0.3654
1333.3
24.5
Chitester
et.al. [25]
57.4
0.6696
0.331
1161.94
20.242
14
15.655
10.007
10.007
14.005
11.566
0.4149
0.3997
0.4646
0.4646
0.4149
0.4421
11.013
9.388
5.9077
5.9077
8.888
7.7462
0.3827
0.3998
0.4525
0.4525
0.4058
0.421193
[21]
Grace,
[24]
If the value of εmf from equation of Broadhrst and Becker
for silicagel catalyst
regarding of catalyst physical properties is calculated, ε mf will be calculated using the
following equation:
[2]
εmf = 0.586 (μ
2
/ ρg g (ρg – ρs ) d p 3)
(ρg / ρs )
0.029
0.021
(15)
The following value is obtained for nitrogen gas and silicagel catalyst: εmf = 0.41516.
The values of εmf for spherical particles with presented K 2 / K1 for K1 and K2 with εmf is
calculatable.
6. Results and Discussion
The distributor pressure drop at distributor with mesh size 3 is maximum 5.5 cmH2O which is almost 30% of bed pressure drop (17.5 cm- H2O). Regarding that distributor
pressure drop is appropriate and this distributor is appropriate for fluidized bed and
the obtained value of Umf (Umf = 2.9 cm/sec) is acceptable.
1. The value of Umf is calculated using the equations which presented in articles and
books. The calculations indicate that for silicagel catalyst with averaged diameter
212 micrometer and solid density 1.96 g/cm3, the equation presented with maximum
14.3 cm/sec (Gorosho et al., [27]), the equation presented with minimum 1.493
cm/sec (McKay and McLain [11]) and the equations presented with Umf 2.915
cm/sec (Wen and Yu [14]), 3.0 cm/sec (Rowe and Yacono [30]) and 3.6 cm/sec are
more appropriate respectively. Then the only equation for silicagel catalyst which
A. Farshi/Petroleum & Coal 55(4) 311-321,2013
320
predicts real Umf is equation of Wen and Yu [14] and the equation presented by
Rowe and Yacono for Umf has a small variation from real Umf.
2. Considering fluidization, fluidized bed with very small porousity of distributor is
appropriate which distributor bed has proper pressure drop and the variations of
catalyst height at the bed also are more in comparison with the others cases of
catalyst height. In third status, distributor pressure drop is higher than first and
second statuses.
3. The minimum value of fluidized height is obtained using U mf = 2.9 cm/sec while the
variation of catalyst height versus velocity for bed with diameter 4.8 cm, distributor
type of porous and 400 gr of catalyst are measured. This value is only applicable
for the above condition and they have to obtain for the other states (diameter, type of
distributor and catalyst weight through experiments.)
4. The porosity values in condition of minimum of fluidization (εmf ) is calculated using
Broadhurst and Becker [2] equation and presented values of K 1 and K2 in general
equation of Remf for different states are based on the values of K1 and K2. Maximum
and minimum of εmf are 0.48 and 0.41 based on the values of K1 and K2 respectively.
Basically, based on the ratio of K2 to K1 (K2/ K1), minimum and maximum of εmf are
0.21 and 0.41. In order to calculate Umf, the value of εmf which is resulted from
Broadhurst and Becker equation is used.
Symbols
Ar , (dp3 ρg (ρs - ρg)/μ,2
K1 (1/Φs εmf 3 )
K2, (1 - εmf /Φs εmf 3 )
dp, m
g ,m/s2
ΔP, N/m2
Hmf, cm
Re, U. dp. ρg / μ
Remf, Umf.dp.ρg / μ
U, m/s
Umf, m/s
Arschmides number
A function of porosity and the figure factor in general equation
A function of porosity and figure factor in general equation
Particle diameter
Accelerative gravity
Pressure drop
The height of bed at the condition of minimum of fluidized height
Reynolds number based on particle diameter
Reynolds number in the state of minimum of fluidized velocity
Nominal velocity of fluid
Minimum of velocity of fluid
Greek Alphabets
ε
εmf
Φs
Μ
ρ
ρs
Porosity which is dimensionless
Porosity in minimum of fluidized velocity which is dimensionless
Figure Factor (Spherical) which is dimensionless
N/Sm2 Viscosity of Fluid
Kg/m3Density of Fluid
Kg/ m3 Density of Particles
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[2]
[3]
[4]
[5]
Adanez, J., and Abanades, J. C. (1991) Minimum fluidization velocities of
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London, 1-46.
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Press, London, 1-46.
Fogler, H. S. and Brown, L. F.(1981.Prediction of Fluidized Bed Operation
Under Two Limiting Condition. American Chemical Society.
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