AICHE 15 VORTEX + MASS TRANSFER

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
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.
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AICHE 15 VORTEX + MASS TRANSFER

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