Housing Shape's Impact on Electric Submersible Pump's Equilibrium Position and Rotordynamics
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Electric Submersible Pumps (ESPs) are a subgroup of pumps designed to have small diameters to accommodate tight working environments. The long length of an ESP (5-100 stages) requires a large amount of annular seals. Each seal provides a lateral reaction force for the rotor. Lateral loading caused by gravity and housing curvature changes the running position of the rotor in these seals. The running position of the rotor with respect to the housing is the Static Equilibrium Position (SEP). The SEP is important in determining the rotordynamic coefficients for the bearings/seals. An SEP analysis suitable for ESPs is shown. The analysis predicts the equilibrium position due to gravity and/or curvature loading in the well casing as well as for surface applications. The analysis can accept seals with eccentricity-dependent reaction forces. The code also interfaces with response codes to predict the rotordynamic characteristics of motion around the equilibrium position. The rotor or housing can be set to any prescribed position, and the remaining stations can be solved for. A static and rotordynamic analysis is presented for an ESP model. This model is of a Baker Hughes G400 ESP pump. This study first finds the SEP and then shows 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 of: (1) Viscosity of 1 cP and interstage seal clearances of 127 µm (2) Viscosity of 1 cP and interstage seal clearances of 381 µm (3) Viscosity of 30 cP and interstage seal clearances of 127 µm (4) Viscosity of 30 cP and interstage seal clearances of 381 µm. The appropriate shorthand notations are: 1X 1cP, 3X 1cP, 1X 30cP, and 3X 30cP respectively. In a horizontal, straight-housing position, the model includes gravity and buoyancy on the shaft. At 1X 1cP, the horizontal statics show a moderate eccentricity ratio of 0.53 for the shaft with respect to the housing. With 3X 1cP, the static eccentricity ratio is increased to 0.76. With 1X 30cP, the predicted static eccentricity ratio is low at 0.08. Increasing the clearance to 3X 30cP, the predicted eccentricity ratio increases to 0.33. No horizontal case is expected to rub. With the housing is supported at five different housing positions instead of fixed straight, the static position had relatively no change. Predictions for a vertical case of the same model are also presented. The curvature of the housing is varied until rub or close-to-wall rub is expected. The curvature needed for a rub with a 1cP-1X fluid is 7.5 Degrees of Curvature (DOC). The DOC is a metric for curvature. It is defined as the amount of degrees which pass around a constant curve of 33.3 m in length. The stability of the system with changing curvature is presented, and curvature is shown to have a minor impact. With 3X 1cP, there is a decrease in maximum eccentricity, but with more seals loaded than with 1X 1cP. With 1X 30cP, a smaller length of shaft that deviates from the housing centerline’s position. The maximum curvature for a static rub with 1X 30cP is greater than 25 DOC. Both 1X 30cP and 3X 30cP are unstable. No dynamic data predictions are shown for 30 cP since the model is unstable. The static position for 3D housing shape with 1 cP fluid is lastly presented. A helix as the housing shape is used due to constant curvature. With respect to a curvature in only the Y direction, the helix static shape differed from the Y-Z plane curvature in attitude angle.
electric submersible pump
Norrbin, Clay Sven (2016). Housing Shape's Impact on Electric Submersible Pump's Equilibrium Position and Rotordynamics. Master's thesis, Texas A & M University. Available electronically from