Mathematical modeling and design analysis of the power section of a positive displacement motor (PDM)

The recent increase in application of horizontal wells, and in particular slim lateral holes triggered necessity of a study to model and design an improved downhole motor for Coiled Tubing Drilling. To enhance the technology and make the system effective, a mathematical model is required to identify opportunities for the modification of motor design. This study presents a mathematical model and proposed design improvements for the performance of a positive displacement motor (Moineau type) for incompressible and compressible fluid systems. Generalized equations are developed for cross sectional areas of shaft, housing, volume generated and torque for mutlilobe motors to help identify opportunities to improve the design of the power section of PDM. An optimal relationship between the pitch of the motor and the diameter of the housing is obtained to achieve maximum motor torque. A dimensionless index called the Performance Index (PI), (a function of the configuration of the motor) is defined to generalize the various design parameters of the power section. The dimensionless performance plots establish a standard for comparison of the performance of the actual motor with that of the optimized ideal motor. The fluid leakage, torque losses, and their effects on the performance of the motor are considered in this study. Field records indicate that the life of downhole motors operating with compressible fluids is considerably reduced. One of the reasons contributing to poor performance is increased vibration. To identify the opportunities of improving performance, a detailed geometrical analysis is done for a conventional design operating with compressible fluids. A performance analysis is done for the conventional design and a hypothesis is presented to characterize any detrimental effects. Other geometrical options of the power section are studied. Energy relationships for the alternate designs presented are of great value. The ramifications of the analysis open a window of new opportunities for improved design of the power section. It has been concluded that other geometrical designs will improve the performance of the pneumatic PDM. A comprehensive simulator (incompressible and compressible fluid systems) code named as PDM-das1 has been developed for the analysis.