Mathematical model and optimum design approach of sinusoidal pressure wave generator for downhole drilling tool

- A model is proposed for the structure of sinusoidal pressure wave generator.
- An optimum design for the generator is proposed based on CFD analysis.
- Optimum generator design can reduce the risks of clogging and generate sinusoidal wave.
- Simulation and experimental results validate the effectiveness of the method.

Mud pulse generators have been widely used for the real-time transmission of valuable directional and formation data from downholes with depths of thousands of meters. There have been numerous studies on the design of mud pulse generators in which the pressure waves were typically nonsinusoidal. Sinusoidal waves provide improved long-distance data transmission and signal noise suppression compared with nonsinusoidal waves. Although sinusoidal pressure wave generators have been studied in the published literature, the influence of the risks of clogging on the design of the generator for producing sinusoidal pressure waves has rarely been considered. To generate sinusoidal pressure waves and to reduce the risks of clogging, a mathematical model for the design of a sinusoidal pressure wave generator is developed in this paper. The effects of the axial and radial clearances between the rotor and stator on the design of the generator are considered in the model. An optimum design method for the generator is provided by combining the developed model and a computational fluid dynamics analysis. Finally, an experimental platform was built and experiments at frequencies 2 Hz and 10 Hz were conducted to validate the design result. The simulation and experimental results show that the optimized pressure waves closely approximate sine waves. Therefore, the developed mathematical model and optimization approach can be used to design a sinusoidal pressure wave generator.