Clearance-fit (side-fit) spline joints are a key component in a permanent magnet synchronous motor (PMSM) in electric submersible pumping wells. The nonuniform spline clearance affects the output performance of a PMSM. A concept for energy conservation is optimized in this study to improve the modeling accuracy of electromagnetic torque. However, most existing computation models are one-way model with a magneto-mechanical simulation. In this study, a more accurate two-way coupling method is presented for simulating the electromagnetic and mechanical characteristics of PMSM. Additionally, importance should be attached to this two-way magneto-mechanical coupling methodology in an actual simulation. The coupled power, electrical and magnetic energy, and electromagnetic torque equations are solved iteratively until convergence for PMSMs with a segmented rotor and a non-segmented rotor. The optimal electromagnetic torque is obtained for different rotor configurations with the change of temperatures and rotational speeds. The results show that the output performance and electromagnetic torque of the PMSM are seriously affected by the effects of two-way magneto-mechanical coupling and nonuniform spline clearance. The proposed two-way coupling model gives more reasonable predictions than other one-way models do, because the power transfer between the electrical and magnetic energy can be modeled more accurately. The self-centralizing performance of clearance-fit splines and the sensitivity to the radial clearance magnitude lead to the reduction of the electromagnetic torque for the PMSM. Additionally, the electromagnetic torques decrease with the enhanced rotor temperatures and rotational speeds. The best rotor temperature and rotational speed are chosen through a comparison of the experimental results, and then the optimal electromagnetic torque is provided to ensure the output performance of the PMSM in electric submersible pumping wells.

Dynamic performance on solids flow with water in deviated tubing is essential for the reliability of pump and normal operation of horizontal and directional wells. Compared with coal-water flow in vertical tubing and sand-oil flow with high production in deviated tubing, solids deposition with water shows obvious non-symmetric distributions in deviated tubing from simulations and experiments. The mathematical model of two phase flow was developed under coupling conditions of deviated tubing, low flow rate and viscosity based on the kinetic theory of granular flow and first-order discrete scheme. The results show that solid-water stratified flow in deviated tubing can be divided into two zones of suspension bed and the moving bed throughout the flow field. The solid flowing velocity with water is negative and particles slide down at the bottom of moving bed zone. The process of solids flow with water in deviated tubing will produce pressure loss and consume the kinetic energy. The thickness of deposited layer and the flowing velocity of solids flow downward with water at the moving bed zone enhance with the decreased inlet flow rate and the increased particle size, tubing inside diameter (ID) and inclination angle. Solids are easier into suspension from the upper part of moving bed zone to suspension bed zone and more solid particles flow with water towards the tubing outlet with the increase of inlet flowing velocity. The decision is made to reduce the screen width, tubing ID and inclination angle to maintain to be greater than critical deposition velocity in order to prevent solids settling. And it provides the theoretical basis and technical reserves for solid control and offers an effective approach to enhance tubing cleaning in deviated strings.