Analytical Study of the Performance of Positive Displacement Motor (PDM): Modeling for Incompressible Fluid

Abstract

Abstract Recent increases in the application of horizontal wells, in particular slim hole laterals, has triggered the need for more powerful downhole drill motors. To meet this need, motors require performance improvements which, in turn, requires development of a mathematical model. This paper presents a mathematical model for the performance of positive displacement motors (Moineu type) for incompressible fluids. Generalized equations for the cross sectional area of the shalt, housing, volume generated and torque for multilobed motors help identify design improvements. The maximum motor torque requires an optimal relationship between the pitch of the motor and the diameter of the housing. A dimensionless index called the Performance Index (PI), helps generalize the various design parameters of the power section. Dimensionless performance plots establish a standard to compare the performance of actual motors to the ideal motor. Also, common parametric curves describe the effect of various design parameters on operating parameters. Leakage and torque losses play an important role in the performance of a motor. These losses and their effects are also addressed. Numerical examples for incompressible fluids demonstrate the practical usefulness of the theory and optimal analysis. Introduction During the past two decades, extensive research and development have yielded highly efficient drilling systems to achieve cost reductions for high departure wells. The world wide acceptance of rotary drilling methods and tools made it difficult to introduce new drilling techniques. The current need to exploit low pressure oil reserves has required drilling more horizontal wells. Since many wells could probably be re-entered and completed with lateral holes, coiled tubing drilling technology (CTD) became of interest to service, major oil and gas companies. This almost mandates a downhole drill motor since coiled tubing cannot be rotated. Percussion hammer, positive displacement, turbine and electric motors can be use downhole but the positive displacement motor is currently preferred. A variety of positive displacement motors are available but all have problems when used in coiled tubing drilling. Some simulation and performance studies exist for turbines, but no mathematical model adequately addresses performance of the positive displacement motor.