The Mathematical Modeling Of Drilling Fluid Pressure MPSK Signals Based On PWM And PPM And The Signal Characteristic Analysis

The drilling fluid pressure telemetry in MWD (Measurement While Drilling) is the most common down-hole tool that transmits data by drilling fluid pressure modulation technology, and the multiple phase shift keying (MPSK) modulation is the effective method to improve the data transmission rate.In this paper, a transmission characteristics analysis of drilling fluid pressure MPSK signals based on PWM (Pulse Width Modulation) and PPM (Pulse Position Modulation) in a directional well is introduced. With the control logic analysis of a rotary valve in a drilling fluid pressure generator, a logical control signal is built and a phase-shift function is obtained from integral function of the logical control signal with Fourier and inverse transform operation along with numeric communication theory. A mathematic model of drilling fluid pressure MPSK signals based on PWM and PPM is built by acting the phase-shift function to a carrier wave. With short-term Fourier transform of MPSK signal's mathematic model, the signal frequency spectrum is analyzed. The numerical calculation result shows that the average power spectra of MPSK signal based on PPM is better than that based on PWM, owning to the narrow width of baseband control pulse, the process of modulating signal is momentary, the signal's power in routine bandwidth after the modulation of MPSK signals is better relatively and the power is concentrated, so PPM is in favor of the frequency-band transmission of the signals. Compared with BPSK (Binary Phase Shift Keying) signal, in the same bandwidth, the information transmission rate and utilization ratio of trequency-band of MPSK signals based on PWM and PPM is enhanced once, but the signal's power in routine bandwidth after modulated is less than BPSK, in addition, the control demand for rotary wave is high. As the consequence, the modulation means of PWM and PPM is still not used in drilling fluid pressure MPSK. By means of numerical simulation of MPSK signal, the modulation rule reflected by signal wave verifies the exactitude of built mathematic model.Considering the theory of fluid mechanics and ideal gas state equation, associated with drillingpipe pressure and drilling fluid temperature, the change of volume fraction of gas in drilling fluids along the directional drillpipe is analyzed. Through the transmission characteristics analysis of MPSK signal in drilling fluid channel and adoption of numerical simulation , the impact of propagation distance, drilling size, carrier frequency, drilling fluids viscosity and volume fraction of gas is studied. The numerical simulation result shows that the impact of drilling fluid viscosity and volume fraction of gas in drilling fluid on the signal transmission is more notable than the others.According to the mathematical model and transmission characteristics analysis of drilling fluid pressure MPSK signals based on PWM and PPM, the limitation is theoretically explained of adopting those modulations as a method of down-hole data transmission. This research presents considerable reference merit in terms of down-hole information telemetry technology adopting more feasible modulation of MPSK.