1. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Phase portrait–stable node

2. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Equilibrium solutions stability—linear 2D problems (adapted from Ref. [2])

3. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Possible phase portrait in a 2D nonlinear system

4. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Strange attractor [3]—Lorenz attractor

5. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Horizontal pumping system

6. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Typical nodal analysis graph

7. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Nodal analysis graph: unstable and stable points

8. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Reservoir-casing-tubing-annular space model

9. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Natural casing-annulus separation efficiency—pumped well

10. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Generic rotary separator efficiency curve

11. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Two-phase pump performance curve

12. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Nodal analysis—example 1

13. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Transient solution—example 1—liquid flow rates

14. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Attractor—example 1

15. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Transient solution—example 2—tubing and reservoir liquid flow rates

16. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Transient solution—example 2—annular space and reservoir liquid flow rates

17. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Nodal analysis—example 3

18. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Transient solution—example 3—tubing and reservoir liquid flow rates

19. Date of download: 12/26/2017
Copyright © ASME. All rights reserved.
From: Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions
J. Energy Resour. Technol. 2014;136(4): doi: /
Figure Legend:
Transient solution—example 3—annular space and reservoir liquid flow rates