The long length of sub-sea Electric Submersible Pumps (ESPs) requires a large amount of annular seals. Loading caused by gravity and housing curvature changes the Static Equilibrium Position (SEP) of the rotor in these seals. This analysis predicts the SEP due to gravity and/or well curvature loading. The analysis also interfaces displays the rotordynamics around the SEP.
A static and rotordynamic analysis is presented for a previously studied ESP model. This study differs by first finding the SEP and then performing a rotordynamic analysis about the SEP. Predictions are shown in a horizontal and a vertical orientation. In these two configurations, viscosities and clearances are varied through 4 cases: 1X 1cP, 3X 1cP, 1X 30cP, and 3X 30cP.
In a horizontal, straight-housing position, the model includes gravity and buoyancy on the shaft. At 1cP-1X and 1cP-3X, the horizontal statics show a moderate eccentricity ratio for the shaft with respect to the housing. With 30cP-1X, the predicted static eccentricity ratio is low at 0.08. With 30cP-3X, the predicted eccentricity ratio increases to 0.33.
Predictions for a vertical case of the same model are also presented. The curvature of the housing is varied in the Y-Z plane until rub or close-to-wall rub is expected. The curvature needed for a rub with a 1X 1cP fluid is 7.5 degrees of curvature. Curvature has little impact on stability. With both 1X 30cP and 3X 30cP, the maximum curvature for a static rub are over 25 degrees of curvature. Both 1X 30cP and 3X 30cP remain unstable with increasing curvature.