Over the last few years, use of downhole motors have increased dramatically to meet the challenges of horizontal wells and in particular, extended reach drilling, deep and ultra-deep water wells. With these wells pushing the limits of rigs and equipment it is imperative that motors be utilized optimally in the system. More often downhole motor pressure loss calculations are not explicitly included in the overall hydraulic optimization and bit nozzle selection with the available pump power. Generally a motor pressure loss is specified in the optimization calculation and the optimized nozzle sizes are selected. To enhance the method of optimization and make the system more effective, hydraulic optimization is required by taking into consideration various motor and drilling parameters. The key to an improved drilling system is a unified system approach that encompasses motor and bit. This paper presents a new approach to hydraulic optimization by including both the motor and bit. It enables us not only to calculate the optimal flowrate and optimal horsepower of the motor as a function of configuration of the motor but also to select the correct motor configuration. In addition, calculations are made for hydraulic horsepower per square inch encompassing bit and motor. The practical usefulness of the theory, backed by the fundamental and optimal analysis is demonstrated with numerical examples.


The optimum utilization of the mud pump power has become more significant in present day, challenging drilling environments. There exist well defined guidelines for hydraulic optimization using maximization techniques. Although the drill bit hydraulic optimization is not new to the industry, the extensive use of downhole motors underscores the analytical evaluation of a downhole motor with the system. In drilling operations, the mud pump horsepower is consumed as hydraulic horsepower inside the drillstring, drillcollars, and downhole motor, at bit nozzles and in the annulus. The determination of the proper jet nozzle size is important because significant increases in penetration rate can be achieved through proper choice of nozzle sizes. More often, the jet nozzle optimization is carried out by assuming pressure drop across the motor irrespective of weight on bit. For true optimization of jet bit hydraulics an accurate downhole motor model must be incorporated including motor configuration, dimension. weight on bit, etc.. Current well planning practice for bit hydraulic design quantifies the selection of optimum flowrate and corresponding optimum nozzle flow area using 1. bit hydraulic horsepower 2. jet impact force and 3. jet nozzle velocity. Present study involves the selection of bit nozzle sizes that will cause the one of the following parameters to be a maximum: 1. bit hydraulic horsepower 2. bit jet Impact force 3. rate of penetration.

Optimization Methodology

In drilling operations, the total pump pressure needed is equal to the summation of the frictional pressure losses in the surface equipment, frictional pressure losses in the drillstring and collars, pressure loss in the downhole motor, pressure loss due to the acceleration of drilling fluid through the jet bit nozzles and the frictional pressure losses in the annulus. Back in the 1950's it was pointed out that the effectiveness of the jet bits could be improved by increasing the hydraulics power of the mud pumps. Shortly after that, several authors pointed out that due to the frictional pressure loss in the system bit horsepower is more important rather than pump horsepower.

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