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Research Papers

Modeling Oscillatory Behavior of Electrical Submersible Pump Wells Under Two-Phase Flow Conditions

[+] Author and Article Information
Rinaldo Antonio de Melo Vieira

Petrobras,
Salvador, BA 41820-021, Brazil

Mauricio Gargaglione Prado

The University of Tulsa,
Tulsa, OK 74104

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received August 9, 2013; final manuscript received July 14, 2014; published online November 6, 2014. Assoc. Editor: Andrew K. Wojtanowicz.

J. Energy Resour. Technol 136(4), 041001 (Nov 06, 2014) (8 pages) Paper No: JERT-13-1232; doi: 10.1115/1.4028271 History: Received August 09, 2013; Revised July 14, 2014

The effect of free gas on electrical submersible pump (ESP) performance is well known. At a constant rotational speed and constant liquid flow rate, a small amount of gas causes a mild head reduction when compared to the single phase liquid head. However, at higher gas rates, a drastic reduction in the head is observed. This critical condition, known as the surging point, is a combination of liquid and gas flow rates that cause a maximum in the head performance curve. The first derivative of the head with respect to the liquid flow rate changes sign as the liquid flow rate crosses the surging point. In several works on ESP two-phase flow performance, production conditions to the left of the surging region are described or reported as unstable operational conditions. This paper reviews basic concepts on stability of dynamical systems and shows through simulation that ESP oscillatory behavior may result from two-phase flow conditions. A specific drift flux computation code was developed to simulate the dynamic behavior of ESP wells producing without packers.

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References

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Strogatz, S. H., 2001, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 1st ed., Westview Press, Boulder, CO.
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Delhaye, J. M., Giot, M., and Riethmuller, M. L., 1981, Thermohydraulics of Two-Phase System for Industrial Design and Nuclear Engineering, Hemisphere Publishing Corporation, Managua, Nicaragua.
Zuber, N., and Findlay, J. A., 1965, “Average Volumetric Concentration in Two-Phase Flow Systems,” ASME J. Heat Transfer, 87(4), pp. 453–468. [CrossRef]
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Ishii, M., and Hibiki, T., 2005, “One-Dimensional Drift-Flux Model for Various Flow Conditions,” The 11th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics, Avignon, France, April 8–12, 2013.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, New York.
Sachdeva, R., 1984, “Two-Phase Flow Through Chokes,” MS thesis, The University of Tulsa, Tulsa, OK.
Alhanati, F. J. S., 1993, “Bottomhole Gas Separation Efficiency in Electrical Submersible Pump Installations,” Ph.D. dissertation, The University of Tulsa, Tulsa, OK.
Duran, J., 2003, “Pressure Effects on ESP stages Air-Water Performance,” MS thesis, The University of Tulsa, Tulsa, OK.
Carvalho, P. C. G., Prado, M. G., Blanco, J. G., Morooka, C., and Estevam, V., 2009, “Multiphase Performance of ESP Stage Part II – Case Study,” Technical Report, The University of Tulsa, Tulsa, OK.

Figures

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Fig. 1

Phase portrait–stable node

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Fig. 2

Equilibrium solutions stability—linear 2D problems (adapted from Ref. [2])

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Fig. 3

Possible phase portrait in a 2D nonlinear system

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Fig. 4

Strange attractor [3]—Lorenz attractor

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Fig. 5

Horizontal pumping system

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Fig. 6

Typical nodal analysis graph

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Fig. 7

Nodal analysis graph: unstable and stable points

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Fig. 8

Reservoir-casing-tubing-annular space model

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Fig. 9

Natural casing-annulus separation efficiency—pumped well

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Fig. 10

Generic rotary separator efficiency curve

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Fig. 11

Two-phase pump performance curve

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Fig. 12

Nodal analysis—example 1

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Fig. 13

Transient solution—example 1—liquid flow rates

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Fig. 14

Attractor—example 1

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Fig. 15

Transient solution—example 2—tubing and reservoir liquid flow rates

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Fig. 16

Transient solution—example 2—annular space and reservoir liquid flow rates

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Fig. 17

Nodal analysis—example 3

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Fig. 18

Transient solution—example 3—tubing and reservoir liquid flow rates

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Fig. 19

Transient solution—example 3—annular space and reservoir liquid flow rates

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