Including Housing-Casing Fluid in a Lateral Rotordynamics Analysis on Electric Submersible Pumps
Authors: Norrbin Clay S. , Childs Dara W. , Phillips Stephen 
Published: September 2016

Stability and synchronous-response predictions, which were presented in the paper “A Lateral Rotordynamics Primer on Electric Submersible Pumps (ESPs) for Deep Subsea Applications” [1], are reevaluated 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) 1X clearances but rapidly becomes unstable with enlarged clearances (2X, 3X), 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 were: (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 1.5Lr, 2Lr, and 3Lr changes the housing’s natural frequency. This natural frequency can coincide with the running speed with proper termination conditions. If the running speed coincided 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 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 1st 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 mid-span, 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.