钻井液连续压力波信号的延迟差动检测及信号重构

Delay differential detection and signal reconstruction of continuous pressure-wave signals of drilling fluid

根据钻井泵产生的泵干扰与钻井液压力信号的传输路径分析,建立了信号延迟差动检测数学模型;根据检测管路的传输函数分析,建立了短距离直管路传输有限频带信号的理想低通滤波器数学模型;以数学分析为基础,分别在时域和频域研究了钻井液连续压力波信号的数学重构方法。基于无限冲击响应(IIR)理论,通过时域差分方程建立了信号重构数学模型;基于延迟差动检测信号的傅里叶正、逆变换建立了从频域实现信号重构的数学模型。通过频域重构数学模型的极点频率与信号传输延迟之间的理论关系,建立了压力传感器间距的约束条件,为传感器的合理布置提供了理论依据。理论计算与数值仿真表明,信号延迟差动检测方法可以有效地消除泵干扰的影响,通过时域和频域的数学模型均可实现钻井液压力相移键控信号的重构与恢复,信号的信噪比(SNR)大幅提高,在测量直管路长度符合压力传感器间距的约束条件下,两种重构方法均可获得满意的信号质量。

A mathematical model for delay differential detection of signals was built based on analyzing pump interference induced by a drill pump and transmission paths of drilling-fluid pressure signals.A functional analysis on transmission of detection conduits was applied to build an ideal low-pass filter mathematical model for limited frequency band signals in short-distance straight-conduit transmission.A mathematical reconstruction approach of continuous pressure-wave signals of drilling liquid was studied in time domain and frequency domain,respectively,based on mathematical analysis.A mathematical model for signal reconstruction was established with a differential equation in time domain based on infinite impulse response（IIR） theory and so was a mathematical model for signal reconstruction in frequency domain established with Fourier forward and inverse transform based on the delay differential detection of signals.Therefore,constraint conditions for space between pressure sensors were defined according to theoretical relationship between pole frequencies of the reconstruction mathematical model in frequency domain and signal transmission delay,which lays a theoretic basis for rational arrangement of sensors.Theoretical calculation and numerical simulation showed that the delay differential detection method of signals can effectively eliminate influence of pump interference.The reconstruction and recovery of pressure phase-shift and keying signals of drilling fluid can be successfully achieved with mathematical models in both time and frequency domains,in which signal to noise ratio（SNR） of signals can be increased significantly.Therefore,qualified signals can be obtained with both reconstruction methods so long as length of measuring straight conduits accords with the constraint condition of the space between pressure sensors.