1. © 2010 Aspen Technology, Inc. All rights reserved Brian Hanley, Principal Engineer March 23, 2010 Packed Column Hydraulics and Continuous Phase Transitions AIChE 2010 Spring Meeting San Antonio, TX

2. © 2010 Aspen Technology, Inc. All rights reserved | 2 Introduction  Packed columns undergo a transition from vapor- to liquid- continuous operation.  The transition is a “second order” (continuous).  Examples include: –Percolation threshold in random resistor networks –Paramagnetic/ferromagnetic transition at the Curie point  Phase transitions exhibit universal behavior. –Universality classes  These observations can be can be used as a basis for correlating pressure drops/flood point in packed columns.

3. © 2010 Aspen Technology, Inc. All rights reserved | 3 Packed Columns and Resistor Networks Two Characteristic Resistances in Each Problem R1R1 R2R2

4. © 2010 Aspen Technology, Inc. All rights reserved | 4

5. 5 Phase Transitions & Renormalization I P-V-T Behavior of Pure Fluids – “Corresponding States” © J.M. Yeomans, Statistical Mechanics of Phase Transitions, Oxford University Press, 1993

6. © 2010 Aspen Technology, Inc. All rights reserved | 6 Phase Transitions & Renormalization II Ferromagnetic/Paramagnetic Transition © J.M. Yeomans, Statistical Mechanics of Phase Transitions, Oxford University Press, 1993

7. © 2010 Aspen Technology, Inc. All rights reserved | 7 Is There a Phase Transition for Packed Columns?

8. © 2010 Aspen Technology, Inc. All rights reserved | 8 Renormalization Procedure  Every liquid load curve contains a flood point  Assume all curves belong to the same universality class

9. © 2010 Aspen Technology, Inc. All rights reserved | 9 Flooding & Renormalization I. Hydraulic Behavior of Glitsch Grid EF-25A

10. © 2010 Aspen Technology, Inc. All rights reserved | 10 Flooding & Renormalization II. Hydraulic Behavior of Intalox Structured Packing 3T

11. © 2010 Aspen Technology, Inc. All rights reserved | 11 Flooding & Renormalization III. Hydraulic Behavior of 1” Ceramic Raschig Rings

12. © 2010 Aspen Technology, Inc. All rights reserved | 12 Flooding & Renormalization IV. Nutter Ring #2 and Plastic Snowflake Packings

13. © 2010 Aspen Technology, Inc. All rights reserved | 13 “Corresponding States” for Packings I. Pressure Drop/Flood for FLEXIPAC Structured Packings

14. © 2010 Aspen Technology, Inc. All rights reserved | 14 “Corresponding States” for Packings II. Pressure Drop/Flood for ISP and Raschig Super Rings

15. © 2010 Aspen Technology, Inc. All rights reserved | 15 “Corresponding States” for Packings III. Pressure Drop/Flood for Several Different Packings

16. © 2010 Aspen Technology, Inc. All rights reserved | 16 “Corresponding States” for Packings IV. Pressure Drop/Flood for Several Different Packings

17. © 2010 Aspen Technology, Inc. All rights reserved | 17 “Corresponding States” for Packings V. Pressure Drop/Flood for Several Different Packings

18. © 2010 Aspen Technology, Inc. All rights reserved | 18 Some p Data Do Not Collapse Curves for different liquid loads do not belong to the same universality class

19. © 2010 Aspen Technology, Inc. All rights reserved | 19  The Wallis equation can be used to correlate flood data.  The parameters “m” and “c” are known to depend on the physical properties of the liquid.  Dimensional analysis can be used to show that: Extending Results to Other Systems Wallis Flood Correlation and Dimensional Analysis I.

20. © 2010 Aspen Technology, Inc. All rights reserved | 20 Extending Results to Other Systems Wallis Flood Correlation and Dimensional Analysis II.

21. © 2010 Aspen Technology, Inc. All rights reserved | 21 Comparison to Experiment I.

22. © 2010 Aspen Technology, Inc. All rights reserved | 22 Comparison to Experiment II.

23. © 2010 Aspen Technology, Inc. All rights reserved | 23 Correlation Available in Aspen Plus

24. © 2010 Aspen Technology, Inc. All rights reserved | 24 Conclusions  Packed columns undergo a transition from vapor- to liquid- continuous operation.  The transition is a “second order” (continuous).  Packed column hydraulics exhibit universal behavior. –Universality classes –“Corresponding hydraulic states”  Hydraulics for a given system “near” flood are dependent on a small number of features –Dimensionality –Symmetry –Connectivity but are otherwise insensitive to the underlying geometric and topological properties of the packing.