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Research Papers: Gas Turbines: Structures and Dynamics

Including Housing–Casing Fluid in a Lateral Rotordynamics Analysis on Electric Submersible Pumps

[+] Author and Article Information
Clay S. Norrbin

Texas A&M Turbomachinery Laboratory,
College Station, TX 77843
e-mail: clay.norrbin@gmail.com

Dara W. Childs

Leland T. Jordan Professor
Texas A&M Turbomachinery Laboratory,
College Station, TX 77843
e-mail: dchilds@tamu.edu

Stephen Phillips

Texas A&M Turbomachinery Laboratory,
College Station, TX 77843
e-mail: sphillips@tamu.edu

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 29, 2016; final manuscript received September 2, 2016; published online February 1, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(6), 062505 (Feb 01, 2017) (12 pages) Paper No: GTP-16-1428; doi: 10.1115/1.4035358 History: Received August 29, 2016; Revised September 02, 2016

Stability and synchronous-response predictions, which were presented by Childs et al. (2014, “A Lateral Rotordynamics Primer on Electric Submersible Pumps (ESPs) for Deep Subsea Applications,” 43th International Pump Users Symposium, Texas A&M University, College Station, TX, pp. 1–18), are re-evaluated to include the effect of the fluid between the pump housing and well casing. Conclusions are made based on these new findings. The same two-line rotor–housing model is used to model the pump's rotor and its housing. The model dimensions are based on direct measurements of an ESP. The pump rotor and pump housing are only connected together at each stage by reaction forces and moments from seals and bushings. The rotor model is pinned to the housing at the rotor's ends. The housing model is pinned to ground at its ends. Synchronous response predictions are presented for: (1) relative rotor–housing motion and (2) housing velocity-response amplitudes. When handling viscosity of water, the rotor–housing model is predicted to be stable at new (centered) 1× clearances but rapidly becomes unstable with enlarged clearances (2× and 3×), primarily due to rapidly dropping rotor–housing natural frequencies. The impact of introducing effective swirl brakes for the stages' wear ring seals was investigated for a pump running at 3600 rpm. Their predicted impact on stability and synchronous response was: (1) Onset speeds of instabilities (OSIs) were elevated well above running speed and (2) synchronous response amplitudes were reduced modestly. Housing-response amplitudes varied considerably with the choice of housing-termination locations. For a pump rotor length of Lr, varying the lengths of a centered housing over 1.5 Lr, 2 Lr, and 3 Lr changes the housing's natural frequency. This natural frequency can coincide with the running speed with proper termination conditions. If the running speed and natural frequency coincide, large housing vibration amplitudes associated with resonance would exceed most vibration regulations; however, relative rotor–stator response amplitudes were a small fraction of clearances for all the cases. When handling emulsions at markedly higher viscosities, with a pump speed of 3600 rpm and new centered clearances, the predicted OSI was below 300 rpm. The OSI rapidly increased as the seals were displaced eccentrically, quickly elevating the first rotor–stator natural frequency above 1800 rpm and the OSI above 3600 rpm. With the model stabilized at 0.2 eccentricity, the synchronous relative rotor–housing amplitudes were a small fraction of seal clearances. Swirl brakes were not predicted to be effective in elevating pump OSIs for high viscosity fluids with new clearances; however, they became effective as clearances were increased. An ESP housing can contact the well casing in many possible scenarios (axial locations, contact-area length or girth, etc.). A midspan, point radial contact was examined and modeled as a stiff-spring connection from the housing to ground. For both water and oil–water emulsions, a stiff housing-to-casing contact produced major elliptical housing motion (versus circular motion without contact). However, it had a comparably minor impact on relative rotor–housing response amplitudes or rotordynamic stability.

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References

Childs, D. , Norrbin, C. , and Phillips, S. , 2014, “ A Lateral Rotordynamics Primer on Electric Submersible Pumps (ESPs) for Deep Subsea Applications,” Proceedings of the 30th International Pump Users Symposium, Texas A&M University, College Station, TX, pp. 1–18.
Scarsdale, K. , 2012, “ Panel Session, ESP Qualification and Reliability, Multiphase Pump User Roundtable (MPUR),” Houston, TX.
Durham, M. , 1990, “ Effect of Vibration on Electric-Submersible Pump Failures,” SPE J. Pet. Technol., 42(2), pp. 186–190. [CrossRef]
Corbo, M. , Stefanko, D. , and Leishear, R. , 2002, “ Practical Use of Rotordynamic Analysis To Correct a Vertical Long Shaft Pump's Whirl Problem,” 19th International Pump Users Symposium, Houston, TX, pp. 107–120.
Massey, I. , 1985, “ Subsynchronous Vibration Problems in High-Speed Multistage Centrifugal Pumps,” 14th Turbomachinery Symposium, Texas A&M University, College Station, TX, pp. 11–16.
Valantas, R. , and Bolleter, U. , 1988, “ Solutions to Abrasive Wear-Related Rotordynamic Instability Problems in Prudhoe Bay Injection Pumps,” 5th International Pump Users Symposium, Turbomachinery Laboratory at Texas A&M University, College Station, TX, pp. 3–10.
Forsberg, M. , 2013, “ Evaluation of ESP Vibration: Technical Process Versus Black Magic,” Society of Petroleum Engineers (SPE), ESP Workshop, Houston, TX.
Bolleter, U. , Wyss, A. , Welte, I. , and Stürchler, R. , 1987, “ Measurement of Hydrodynamic Interaction Matrices of Boiler Feed Pump Impellers,” ASME J. Vib. Acoust. Stress Reliab. Des., 109(151), pp. 144–151. [CrossRef]
Childs, D. , 2013, Turbomachinery Rotordynamics With Case Studies, Minter Spring Publishing, Wellborn, TX.
Rivera, R. , 2013, Kinetic Pump Innovations, LP, Houston, TX, personal communication.
Lomakin, A. , 1958, “ Calculation of Critical Number of Revolutions and the Conditions Necessary for Dynamic Stability of Rotors in High-Pressure Hydraulic Machines When Taking Into Account Forces Originating in Sealings,” Power and Mechanical Engineering, (in Russian), pp. 1–5.
Zirkelback, N. , and San Andrés, L. , 1996, “ Bulk-Flow Model for the Transition to Turbulence Regime in Annular Seals,” STLE Tribol. Trans., 39(4), pp. 835–842. [CrossRef]
Black, H. , 1979, “ Effects of Fluid-Filled Clearance Spaces on Centrifugal Pump and Submerged Motor Vibrations,” 8th Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX, pp. 29–34.
Blevins, R. D. , 2001, Formulas for Natural Frequency and Mode Shape, Krieger Publishing, Malabar, FL.
Semanate, J. , and San Andrés, L. , 1993, “ Thermal Analysis of Locked Multi-Ring Oil Seals,” Tribol. Int., 27(3), pp. 197–206. [CrossRef]
Bolleter, U. , Liebungut, E. , Stürchler, R. , and McCloskey, T. , 1989, “ Hydraulic Interaction and Excitation Forces of High Head Pump Impellers,” Third Joint ASCE/ASME Pumping Machinery Symposium, San Diego, CA, pp. 187–193.
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Figures

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Fig. 1

Synchronous (right peak) and subsynchronous (left peak) motion amplitudes versus frequency in rpm after Valantas and Bolleter [6]

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Fig. 2

Swirl brake used to solve Massey's pump instability problem [5]

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Fig. 3

ESP stage with balance holes showing annular and axial seals

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Fig. 4

The Lomakin effect, Childs [9]

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Fig. 5

Model of ESP pump cross section. Added damping and mass to the housing are not shown.

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Fig. 6

Predictions of the damping and added-mass for a viscosity of water between the pump housing and well casing: (a) Black's damping coefficient and (b) Black's and Blevins's added-mass coefficient

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Fig. 7

Effect of including the fluid interaction of the housing-to-casing cavity for (a) relative response versus speed and (b) housing vibration versus speed

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Fig. 8

Forsberg's measured housing assembly response (from accelerometer output) at 3600 rpm [13]

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Fig. 9

Predicted pump housing response amplitude at 3600 rpm

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Fig. 10

Impeller dimensions for hydraulic imbalance definition, Childs [9]

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Fig. 11

Predicted synchronous response due to mechanical imbalance, hydraulic imbalance, and bent-shaft excitation for the base-line ESP model with water: (a) midrotor, relative rotor–housing response amplitude (mil) and (b) housing velocity amplitude (in./s)

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Fig. 12

Impact of varying seal offset on (a) relative rotor–housing amplitudes and (b) housing vibration levels

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Fig. 13

The impact on predicted synchronous response due to changing the seal clearances: (a) relative rotor–housing amplitudes and (b) housing vibration levels

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Fig. 14

Impact of changing the housing-termination location for new clearances on (a) predicted relative rotor–housing motion and (b) housing vibration amplitudes

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Fig. 15

Predicted impact of a stiff elastic connection from midspan of the pump housing to midspan of the housing: (a) relative rotor housing response orbit amplitudes, (b) housing velocity amplitudes in the X (connection) direction, and (c) housing velocity amplitudes in the Y (transverse-to-connection) direction

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Fig. 16

Emulsion, no swirl brakes: OSI versus ε0; 1×, 2×, and 3× clearances

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Fig. 17

Impact on predicted synchronous response due to changing the seal static eccentricity ratios; new clearances, water–oil emulsion: (a) relative rotor–housing amplitudes and (b) housing-vibration levels

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Fig. 18

Emulsion predictions for WFR versus ω with and without swirl brake at 1×, 2×, and 3× clearances

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Fig. 19

Response with and without housing–casing contact, new clearances, ε0 = 0.2

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Fig. 20

Comparison of adding moment coefficients to the interstage seal with a viscosity similar to water: (a) relative rotor–housing amplitudes and (b) housing vibration levels

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