Study of the Transmission Attenuation Characteristics of Continuous Wave Mud Pulses Considering Unsteady Friction

With the advancement of oil and gas exploration into ultra-deep drilling and increasingly complex downhole environments, the demand for higher downhole data transmission rates has steadily increased. Continuous wave mud pulse telemetry has emerged as a promising technology with significant potential for widespread application. While considerable research has focused on techniques for downhole signal generation and noise reduction at the wellhead in continuous wave mud pulse telemetry systems, the attenuation behavior of continuous wave transmission within the wellbore remains insufficiently explored. This study integrates transient flow theory to account for unsteady friction induced by continuous wave transmission and enhances the one-dimensional mathematical model for the generation and propagation of continuous waves. The attenuation process of continuous wave transmission, influenced by coupled drilling tools within the wellbore, is analyzed in detail, along with the fluctuation patterns of steady and unsteady friction. Furthermore, the study examines the effects of various parameters—such as frequency, displacement, mud density, viscosity, and wave velocity—on attenuation characteristics. The findings reveal that continuous wave signals in the wellbore undergo exponential attenuation, with the amplitude of the bottom hole assembly (BHA) significantly diminished. This attenuation is primarily attributed to both steady and unsteady friction, which exhibit fluctuating behaviors. High-frequency continuous waves are strongly affected by unsteady friction, resulting in rapid attenuation, whereas steady friction remains constant across varying frequencies. Notably, unsteady friction intensifies with increasing frequency. These insights establish a theoretical foundation for understanding the attenuation of continuous wave transmission under varying parameters, thereby contributing to the improvement of signal transmission efficiency.