Abstract
In this study, the friction model in non-Newtonian drilling fluid is developed to evaluate the signal attenuation in the information transmission with the continuous wave. A model of transient non-Newtonian power- law pipe flow is developed by assuming a steady viscosity varied only with the radius and the solution is derived analytically in complex domain and time domain. The frequency-dependent friction is developed based on the solution in the time domain and is used in the pressure wave transmission. And the analysis results show that the highest pressure amplification with resonant frequency increases with the power-law index n increase and the resonant frequency increases with the n decrease.
Highlights
Mud pulse telemetry has been the global standard for real time data transmission in the Measurement While Drilling/Logging While Drilling (MWD/LWD) technology for the past thirty years (Klotz et al, 2008a)
The data rate of the mud pulse telemetry had reached to 6bits per second in the 1990s (Martin et al, 1994), this technology reached mature and the data rate is up to 20 bps (Klotz et al, 2008a, b)
The theoretical analysis of data rate limit for the mud pulse telemetry has not been found in the relevant literature
Summary
Mud pulse telemetry has been the global standard for real time data transmission in the Measurement While Drilling/Logging While Drilling (MWD/LWD) technology for the past thirty years (Klotz et al, 2008a). The attenuation models of the pressure wave cited above have been limited to the Newtonian fluid which cannot fully reflect the transmission characteristics of a pressure wave transmitted in the non-Newtonian fluid flowing. The frequency-dependent attenuation model for the non-Newtonian power-law fluid is developed based on the approach developed by Zielke (1968) for Newtonian laminar flows. By assuming the fluid motion of the power-law fluid inside the drill string as incompressible and laminar, the motion equation for the unsteady-state flow can be written as:. For the information transmission, the amplitude of the pressure wave is small, so that the velocity disturbance and shear rates caused by the pressure wave are smaller than that of the steady-state flow. In this study the shear rate in steady power-law flow is used in the apparent viscosity a. Boundary conditions: The following equations represent the boundary conditions for all time which must be applied to solving the governing equation: U s, y
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