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Vortex Generation, Gas Draw Down
and Mass Transfer in Agitated
Vessels
Jason J. Giacomelli & Richard K. Grenville
AICHE – SALT LAKE CITY - 11/9/2015
AGENDA
• Motivation
• Correlation for Vortex Depth
• Mass transfer Measurements and Analysis
• Conclusions
• Future Work
2
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
• 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
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
• 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
• 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
• 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
• 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
• 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
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
• 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
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*
13
∗
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).
14
-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
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
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
16
Results: Regression of Data
• Empirical Model:
′
• Refined Model:
′
• N & D have matching exponent of 3
 Tip speed Cubed
17
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
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	∝
• 	 	
• 	∝ ∙
18
• 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
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 ?
20
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. 
21

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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
  • 2. AGENDA • Motivation • Correlation for Vortex Depth • Mass transfer Measurements and Analysis • Conclusions • Future Work 2
  • 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* 13 ∗
  • 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). 14 -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 16
  • 17. Results: Regression of Data • Empirical Model: ′ • Refined Model: ′ • N & D have matching exponent of 3  Tip speed Cubed 17 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 ∝ • • ∝ ∙ 18
  • 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 ? 20
  • 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.  21