This document summarizes research on vortex generation and mass transfer in agitated vessels. Experiments were conducted in 11-inch and 24-inch diameter tanks to measure the mass transfer coefficient (kLa) of an air-water system under varying conditions. A correlation was developed to predict kLa based on impeller type, speed, diameter, and liquid coverage. The correlation showed that kLa increases with scale when the minimum Froude number (FrMIN) and geometry are maintained. This suggests mass transfer is proportional to power input per vortex surface area. Further work is needed to validate the scale up methodology for different impeller types.
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AICHE 15 VORTEX + MASS TRANSFER
1. Vortex Generation, Gas Draw Down
and Mass Transfer in Agitated
Vessels
Jason J. Giacomelli & Richard K. Grenville
AICHE – SALT LAKE CITY - 11/9/2015
3. Motivation
• Some gas-liquid reactions require draw down of gas(es) from the vessel
head space;
– 3 phase (S-L-G) – Catalytic Hydrogenations,
– Nitration of metals Metal Nitrates
– Oxidation, Carbonylation, phosphination, chlorination
– Etc..
• Correlations relating vortex depth to agitator conditions have been
reported in the open literature and developed by PMSL (AICHE 2012 &
2013).
• In order to draw conclusions regarding process efficiency, need to relate
vortex formation to mass transfer rate achieved. very little literature
• The purpose of this work is to make the connection between the vortex
and the mass transfer and how to scale up.
3
4. • Improve efficiency of gas usage by
reincorporation of gas from head
space
• Generate surface vortex
• Trim baffles and locate impeller at
trim point
• Unbaffled region will have a higher
degree of tangential swirl
promotes vortex formation.
• Retaining baffled region promotes
axial gas/liquid circulation and solid
suspension (with additional
impellers)
Motivation – Geometry Review
5. Summary of previous experiments:
• Defined minimum speed for constant gas
induction
– Based visual and auditory observations
• Dependent variables were
– Impeller type
– Impeller diameter to tank diameter ratio (D/T)
– Liquid coverage to tank diameter ratio (IBC/T)
• Values of these parameters correspond to
industrially relevant ranges.
• Data correlated with Froude number
• Scale up for equal gassing vortex depth was
verified in the 2m scale.
• Scaling based on Froude number confirmed
Previous Work – Vortex Depth
6. • The minimum speed, NMIN, is the point at which the vortex is constantly
inducing gas without periodic oscillation of the vortex.
• Auditory helped in large tank walls not transparent.
Background
Definition: Minimum speed for constant gas induction
NMin
7. • The minimum speed for constant vortexing was measured for several
common impeller types:
• The optimum impellers were the PBT, Wide Blade HF, and Rushton
• The PBT was chosen to be best choice for vortexing as it had the
optimum flow characteristics to optimize mechanical and process
characteristics:
• PBT can run slower than Wide Blade HF for equal vortexing,
• PBT suspends solids more efficiently than Rushton
• Move forward with PBT for Mass Transfer (save MHS & RT for later)
Background – Correlation of NMIN
8. • Vortex depth was correlated to relevant geometry
– FrMIN is the minimum Froude for constant gas induction
– IBC/T: Impeller-Baffle Submergence to Tank Diameter
– D/T: Impeller to Tank Diameter
– A: Function of impeller type
– | |
– A, B, and C were found to be different for each impeller.
• * The current work on mass transfer focused on Pitched
Blade Turbine
– The Regression of FrMIN for the PBT resulted in the following
relationship with the tested variables
– ∝
Background – Vortex Depth
9. • Purpose for draw down is to consume unreacted gas from head space
• Vortex Depth correlation/prediction gives no indication of mass transfer
coefficient
• Reactor design requires mass transfer rate (kLa*Driving force) and reaction
rate
• Need a correlation for mass transfer coefficient at very least scale up
methodology
• Lots of literature on vortexing and vortex depth, however,
• Limited literature for submerged baffle – vortexing system for mass transfer
– Boerma & Lankester – 1968
– measured half baffles and full baffles,
– Radial turbine only, found that speed must be above NMIN in order to achieve mass
transfer
– No scale up methodology proposed (P/M? Λ/M?, Froude?. Gas Rate?.... etc?...)
Current Work - Mass Transfer Rate
10. • Measured mass transfer at two scales –
– 11.44”/11” and 24” diameter tanks
– partially baffled
– and impeller centered with baffle
– (same geometry as original vortex depth testing)
• Simple Air/Water system:
– Liquid Water, Turbulent flow regime
– Gas Air, ambient conditions (open tank)
• Varied Geometry D/T, Impeller Coverage or Submergence (C/D or
IBC/T)
• Varied liquid coverage on impeller Simulates changing liquid level
during semi-batch process
• Varied Speed Increasing power input
• Correlated data taken at Fr > FrMIN
Experimental
11. Experimental –
Mass Transfer Rate
• 0.291m (T) Diameter Vessel
(12” Scale)
• 0.121m (D) Impeller (0.43D/T)
• Sub Surface Terminated baffles,
Baffle width = T/10
• Oxygen Probe located behind baffle
(low pressure side) so as to
not disturb flow due to size of Probe
relative to Tank internals
12. • 0.610m (T) Diameter Vessel
(24” Scale)
• 0.263m (D) Impeller (0.43D/T)
• Sub Surface Terminated baffles,
Baffle width = T/10
Experimental – Mass Transfer Rate
13. Measurement of kLa
• Catalyzed Sulfite oxidation method is utilized.
• Despite issues with this method, it is well suited for larger scale testing
• Experiments are randomized such that any effect of TDS on kLa is absorbed into
the statistics.
• The re-oxygenation process is recorded with a YSI optical probe which the
response time has been measured to be ~5s.
• Data is acquired at 1 second intervals.
0%
20%
40%
60%
80%
100%
120%
0 5 10 15 20 25
DissolvedOxygenConcentration[%C*]
Time [min]
Sulfite Charge
90%C*
10%C*
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∗
14. Data Analysis
• The data is filtered to isolate the 10%C* to 90%C* portion and then
regressed determine the mass transfer coefficient
– Compensate for lag time of probe:
– TauP = 1/kla (process time constant), Tau0 is probe time constant (5s).
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-2.50
-2.00
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
2.50
3.00
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
0 20 40 60 80 100 120
ln[C*-C(t)]
DissolvedOxygen[mg/L]
Time [s]
Model 1
Model 2
Measured Data
Data
Model 1
Model 2
Slope = kLa
15. Results – Constant Speed
Semi-Batch Process – Increasing Liquid Level
15
Radial splashing C/D < 0.25 - 0.5 Vortexing C/D > 0.5
0
20
40
60
80
100
120
140
160
0.00 0.20 0.40 0.60 0.80 1.00 1.20
MassTransferCoef.[hr-1]
Impeller Coverage to Diameter Ratio
Mass Transfer vs.
Speed
NMIN at C/D = 0.5
Surface Aeration -
No Vortexing
> NMIN < NMIN
16. Mass Transfer Coefficient:
Effect of Scale & Geometry
• Only Correlate Data Above Minimum Froude Number
• KLa trend changes below FrMIN as gassing rate becomes
periodic
• Model chosen to regress mass transfer data to establish
effect of scale:
– ′|
• Range of Variables:
– 0.25 < C/D < 1.0
– 0.3 < D/T < 0.5
– N ≥ NMIN
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17. Results: Regression of Data
• Empirical Model:
′
• Refined Model:
′
• N & D have matching exponent of 3
Tip speed Cubed
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0
25
50
75
100
125
150
175
200
225
0 25 50 75 100 125 150 175 200 225
CALCULATEDKLA[HR-1]
MEASURED KLA [HR-1]
Y=X +20%
-20% 0.5D/T, 24"Scale
0.4D/T, 24"Scale 0.4D/T, 24"Scale
0.43D/T, 24"Scale 0.43D/T, 11.44"Scale
0.3D/T, 24"Scale 0.4D/T, 24"Scale
0.5D/T, 24"Scale 0.45D/T, 11"Scale
Regression Statistics
Multiple R 0.98
R Square 0.95
Adjusted R Square 0.95
Standard Error 0.12
Observations 44
Coefficients
Standard
Error t Stat P‐value
Lower
95%
Upper
95%
A’ 5.44 0.167 32.66 6.14E‐30 5.11 5.78
N 2.99 0.209 14.29 4.31E‐17 2.57 3.41
D 3.03 0.130 23.37 1.52E‐24 2.77 3.29
C/D ‐1.16 0.153 ‐7.60 3.26E‐09 ‐1.47 ‐0.85
D/T 1.90 0.156 12.21 6.79E‐15 1.59 2.22
18. Results - Physical Explanation of Correlation
• Mass Transfer is a function of power input
per vortex surface area.
– The vortex surface area is proportional to the
tank diameter squared.
• The mass transfer rate is dependent on the
impeller type and liquid coverage
Scaling up maintaining FrMIN & Geometry:
• Tip speed and power/area increase
• mass transfer coefficient increases on
scale up
• ∝
• ∝ ∙ ∙
• Surface Area of Vortex ∝
•
• ∝ ∙
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19. • Measured kLa and related to vortex depth and geometry
• Provided Fr > FrMIN mass transfer increases with scale
• Exponents on D/T and C/D (IBC/T) are the same for FrMIN
and kLa
• is constant for a given geometry
• P Tau is Energy Energy/Length² is Force/Length (or
Interfacial tension)
• Describes more general mechanism?
• Is this impeller specific?
Conclusions
20. Future Work
• Test Mass Transfer Rate in 6 ft vessel
– Adds third scale
• Test Different impeller types
– Wide Blade Hydrofoil
– Rushton Turbine
• Goal:
– Confirm scale up metric of power/surface
area.
– Most Efficient Impeller ? …Flow vs. Shear ?
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21. References
[1] E. L. Paul, V. A. Atieno‐Obeng and S. M. Kresta, Handbook of Industrial Mixing, Hoboken : Wiley & Sons, INC,
2004.
[2] S. Bhattacharya, D. Hebert and S. M. Kresta, "Air Entrainment in Baffled Stirred Tanks," I Chem E, vol. 85, pp.
654‐664, 2007.
[3] O. Khazam and M. S. Kresta, "A novel geometry for solids drawdown in stirred tanks," Chemical Engineering
Research and Design, pp. 280‐290, 2009.
[4] J. Markopoulos and E. Kontogeorgaki, "Vortex Depth in Unbaffled Single and Multiple Impeller Agitated
Vessels," Chemical Engineering Technology, pp. 68‐74, 1995.
[5] G. Özcan‐Taskin and G. McGrath, "Draw down of light particles in stirred tanks," Trans IChemE, vol. 79, 2001.
[6] G. Özcan‐Taskin, "Effect of scale on the drawdown of floating solids," Chemical Eng Sci, pp. 2871‐2879, 2006.
[7] G. Özcan‐Taskin and H. Wei, "The effect of impeller‐to‐tank diameter ratio on draw down of solids," Chem.
Eng. Sci., pp. 2011‐2022, 2003.
[8] A. Patwardhan and J. Joshi, "Hydrodynamics of a Stirred Vessel Equipped with a Gas‐Inducing Impeller," Ind.
Eng. Chem. Res., vol. 36, pp. 3904‐3914, 1997.
[9] R. H. Perry and D. W. Green, Perry's Chemical Engineers' Handbook, New York: McGraw‐Hill, 2008.
[10] H. Boerma and J. H. Lankester, "The Occurrence of Minimum Stirring Rates in Gas‐Liquid Reactors," Chem.
Eng. Sci., pp. 799‐801, 1968.
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