Transcript Minimum Fluidizing Velocities for Various Bed Packings
Minimum Fluidizing Velocities for Various Bed Packings
By Andrew Maycock
Introduction to Fluidization Fluid flowed through bottom of a fixed bed Fluidization is the balance of gravity, drag and buoyant forces Suspended particles have larger effective surface area than a packed fixed bed The smallest velocity at which fluidization occurs is the minimum fluidization velocity
Fluidization Apparatus Figure 1: Example of fluidization bed
Overview Theoretical Approach Experimental Approach Results Method Summaries Conclusions Q&A
Theoretical Approach Bernoulli’s Equation
P
g
z
V
2 2 Correlations for friction loss terms through porous media
La
min
ar
150
V s
D
1
p
2 3 2
x
Turbulent
1 .
75
V s
2
x D p
1 3
Ergun Equation
P
x
150
V s
s D
1
p
2 2 3 1 .
75
V s
2
s D p
1 3 Sphericity term included Composed of known or obtainable parameters
Minimum Fluidizing Velocity Ergun Equation solved simultaneously with force balance.
P
x
1
p
g
May assume that flow is laminar (N Re < 20) (Equation reduces to laminar friction term)
MFV
D
2
p
p
150
g
1 3
s
2
Experimental Approach Figure 2: Example of fluidization bed
Determining MFV Change occurs in slope of pressure drop plot Figure 3: Plot of pressure drop vs. Fluid Velocity
Particle Properties Graduated cylinder for bed density Displaced volume for particle density 1
bed particle
Microscopic photos for sphericity
Experimental Procedure Glass Beads and Pulverized Coal Increase mass flowrate Measure pressure drop across bed Change temperature and repeat Determine fluid properties using correlations and equations of state
Experimental Problems Poor Distribution Faulty or imprecise pressure gauges Difficulty in determining when fluidization has been reached
Results
Pulverized Coal Results Figure 3: Microscopic photo of pulverized coal
Pulverized Coal Results (cont.) 4000 3500 3000 2500 2000 1500 1000 Data Ergun Equation 500 0 0 0.05
0.1
0.15
Vs (m/s)
0.2
0.25
0.3
Figure 4: Pressure drop data and Ergun Equation for pulverized coal at 26.2 °C
Pulverized Coal Results (cont.) 4000 3500 3000 2500 2000 1500 1000 500 0 -0.05
0 0.05
Vs (m/s)
0.1
0.15
0.2
Data Ergun Equation Figure 5: Pressure drop data and Ergun Equation for pulverized coal at 32.8 °C
Pulverized Coal Results (cont.) 6000 5000 4000 3000 2000 1000 Data Ergun Equation 0 -0.05
0 0.05
Vs (m/s)
0.1
0.15
0.2
Figure 6: Pressure drop data and Ergun Equation for pulverized coal at 39.9 °C
Pulverized Coal Results (cont.) Example of results for pulverized coal
Glass Bead Results Figure 7: Microscopic photo of glass beads
Glass Bead Results (cont.) 20000 18000 16000 14000 12000 10000 8000 6000 4000 2000 0 0 Data Ergun Equation 0.1
0.2
Vs (m/s)
0.3
0.4
0.5
Figure 8: Pressure drop data and Ergun Equation for glass beads at 30.0 °C
Glass Bead Results (cont.) 20000 15000 10000 Data Ergun Equation 5000 0 -5000 0 0.1
0.2
0.3
Vs (m/s)
0.4
0.5
0.6
Figure 9: Pressure drop data and Ergun Equation for glass beads at 37.8 °C
Glass Bead Results (cont.) 16000 14000 12000 10000 8000 6000 Data Ergun Equation 4000 2000 0 -2000 0 0.1
0.2
Vs (m/s)
0.3
0.4
0.5
Figure 10: Pressure drop data and Ergun Equation for glass beads at 42.1 °C
Glass Bead Results (cont.) Example of results for glass beads
The Laminar Assumption
The Laminar Assumption (cont.) Reported to be accurate for Particle Reynolds Numbers under 20 More accurate as Reynolds Numbers get smaller Typical values within 15-30% of Ergun Equation Has no consistent relation to experimental value
Experimental Summary Experimental determination is accurate and necessary Difficult to determining exact value for minimum fluidizing velocity Error in minimum fluidizing velocity measurement based on test interval
Correlation Summary Provide a good estimate for actual fluidizing velocity.
Require difficult estimation of bed height and void fraction for operation above minimum fluidizing velocity.
Ergun Equation can show unrealistic results, as in this case.
Decent estimation requires accurate particle property values (void fraction and particle density are difficult to determine due to adsorption).
Conclusions Correlations are useful, but not substitute for actual experimentation Experimentation necessary because of inaccurate and imprecise instrumentation Correlations are useful for industrial processes which are usually operated at two to three times the minimum fluidizing velocity
References de Nevers, Noel, Air Pollution Control Engineering , 2nd ed. Mc-Graw Hill, New York (2005).
de Nevers, Noel, Fluid Mechanics for Chemical Engineers , 3rd ed. Mc-Graw Hill, New York (2005).
Seader, J.D. and Henley, Ernest J., Separation Process Principles , 2nd ed.Wiley, Danver, Massachusetts (2006).
Wikipedia, Sphericity , http://en.wikipedia.org/wiki/Sphericity
Questions 5 Minute Question Period