Dynamic Modeling and Simulation of Deep Geothermal Electric Submersible Pumping Systems

Abstract

Deep geothermal energy systems employ electric submersible pumps (ESPs) in order to lift geothermal fluid from the production well to the surface. However, rough downhole conditions and high flow rates impose heavy strain on the components, leading to frequent failures of the pump system. As downhole sensor data is limited and often unrealible, a detailed and dynamical model system will serve as basis for deeper understanding and analysis of the overall system behavior. Furthermore, it allows to design model-based condition monitoring and fault detection systems, and to improve controls leading to a more robust and efficient operation. In this paper, a detailed state-space model of the complete ESP system is derived, covering the electrical, mechanical and hydraulic subsystems. Based on the derived model, the start-up phase of an exemplary yet realistic ESP system in the Megawatt range-located at a setting depth of 950 m and producing geothermal fluid of 140 • C temperature at a rate of 0.145 m 3 s −1 -is simulated in MATLAB/Simulink. The simulation results show that the system reaches a stable operating point with realistic values. Furthermore, the effect of self-excitation between the filter capacitor and the motor inductor can clearly be observed. A full set of parameters is provided, allowing for direct model implementation and reproduction of the presented results.

Speed-sensorless state feedback control of induction machines with LC filter

“…Based on Assumptions 1, 2, 3 & 4, the dynamics of IM and LC filter can be derived in the dq-reference frame as (see [4])…”

“…denote the system matrix (A x→x ∈ R 8×8 ), input matrix (A u→x ∈ R 2×8 ), output matrix (C x ∈ R 2×8 ), resp., and J 8 ∈ R 8×8 is a block matrix with J := 0 −1 1 0 matrices as block diagonal elements. Moreover, Lm is an auxiliary inductance term (for details, see [4]).…”

“…Vector control could reduce mechanical and thermal stress on the machine components and, thereby, increase motor lifetime and efficiency. Moreover, incorporating sensorless control could make this control scheme appealing for applications, where the motor is located in hostile or rather inaccessible environments; such as electric submersible pump (ESP) systems [4].…”

Speed control of electrical submersible pumps using fuzzy logic control

“…In order to study the effects of speed change of ESP pumps, a combined fluid mechanics, electrical and  ISSN: 2088-8694 mechanical models of an ESP oil well system are needed. A dynamic model of an ESP deep geothermal well was developed by Kulick et al [10], but the speed controller was not taken into consideration. Another model was presented for controller development [11], but neither ESP electric motor nor variable speed drive were included.…”

“…𝜃 and 𝜃𝑟 are the angles between a-axis and q-axis of the stator and between a-axis of the stator and a-axis of the rotor, respectively, while, 𝛽 = 𝜃 − 𝜃𝑟. The stator and rotor voltages can be obtained in the dq0 frame [16], as in from ( 5) to (10).…”