Method of Optimizing Motor and Bit Performance for Maximum ROP
Authors: Motahhari H.R. , Hareland G. , Nygaard R. , Bond B. 
Published: March 2010

Abstract
Downhole motors are widely used to drill vertical, directional and horizontal wells in conjunction with Polycrystalline Diamond Compact (PDC) bits. When a bent housing Positive Displacement Motor (PDM) is oriented for slide drilling to manipulate a well's trajectory, the drill string does not rotate. Consequently, the rate of penetration (ROP) typically decreases. It is therefore important to optimize bottomhole assembly (BHA) performance in conjunction with PDC drill bits. This paper discusses how motor performance data, coupled with an ROP model, can predict the optimal weight-on-bit (WOB) required to derive maximum ROP for a given section of a hole to be drilled. This approach solves the ROP model and determines the ideal WOB with respect to any restrictions that PDM performance equations apply on it. Bit wear is included in the ROP model and an analysis is performed to optimize a given interval of wellbore. The optimization approach is illustrated with two examples for different formation types and one field case comparing the performance of two motors with PDC bits. The optimum WOB, maximum average ROP and differential pressure values are the outputs from the analysis. This analytical approach can be used to determine the optimum PDM/PDC bit combination to achieve maximum ROP through a wide range of operational conditions.

Introduction
Positive Displacement Motors (PDMs) have gained widespread use in vertical, directional and horizontal drilling applications. In directional and horizontal mode, bent housing PDMs are used to manipulate well trajectory (inclination and azimuth) to intersect bottomhole targets. Slide drilling occurs when the bend in the PDM is oriented in a certain direction. During slide drilling, the drill string does not rotate. In slide drilling mode, bit rotation is generated only from the motor as drilling fluid is pumped through the drill string. Drilling in this mode can significantly reduce ROP and increase well costs. Accordingly, overall performance of bit and motor combinations can have an extremely significant impact on drilling costs. In comparison to using a simple approach like mechanical specific energy (MSE) which is a relative 'local' value as a function of instantaneous operating parameters like WOB and RPM only(1), the approach herein can do a global bit run optimization in the pre-planning and follow-up phases, which include bit selection and detailed design parameters, bit wear throughout the bit run as a function of operating parameters and motor selection and performance. MSE does not consider any of these parameters and is not an overall 'global' ROP or $/m optimization tool.
In a PDM, the power section converts hydraulic energy of mud flow into mechanical rotary power ? the reverse action of the Moineau pump principle(2). Each PDM has a helical rotor assembled inside a helical stator. The rotor has one less spiral or lobe than the stator, which results in a continuous seal line between the two. Likewise, the length of helical pitch for the stator is greater than the rotor, which forms cavity spaces between them. These cavities move along the power section from the inlet to outlet by rotating the rotor.