A signal processing method for continuous mud pressure wave signals in logging-while-drilling systems

Abstract

For signal transmission of mud pressure waves in logging-while-drilling systems, as more measurement parameters are adopted, the conventional signal transmission rate of approximately 1 bps cannot meet the requirements of parameter uploading. Transmission rates greater than 10 bps are widely used by current Chinese and international enterprises in their continuous wave transmission systems. Due to the increasing transmission rates, a conventional single-channel pressure sensor cannot effectively identify the key features of an original signal with a low signal-to-noise ratio at a high transmission rate. This issue results in a low success rate for pressure wave recognition and decoding. This paper addresses a method for the collection of pressure wave signals using multi-channel pressure sensors through the analysis of the signal transmission changes of mud pressure waves with well depths and echo interference caused by drilling rod reflection. In this research, numerical simulation and experimental verification were used to calculate the cross-correlations of the multi-channel signals to effectively remove interference noises such as reflective waves and improve the signal-to-noise ratio of the original signal. The results showed that this method could effectively improve the SNR after the wave filtering of the original pressure wave. The characteristics of the continuous mud pressure wave signals were analysed using a circulation test. A corresponding band-pass filter was designed to remove pump noises to restore the sinusoidal pressure wave signal required by the original transmission rules.

Keywords

Logging while drilling continuous mud pressure wave cross-correlation multi-channel pressure sensor signal-to-noise ratio band-pass filter

1. Introduction

With the mature applications of geosteering tools, formation evaluation tools and rotary steering systems, more measurement parameters need to be uplinked. A positive mud pulse transmission system [1, 2], which is generally used at a transmission rate of approximately 1 bps, can no longer meet the requirements of parameter uploading. Many enterprises have developed continuous wave transmission systems with transmission rates greater than 10 bps [3]. In a continuous wave transmission system, the signal amplitude is greatly affected by noises and the signal-to-noise ratio is lower than that of the positive pulse signal because of its faster execution frequency [4]. To solve this problem, Schlumberger, Baker Hughes and other companies have adopted dual-channel or multi-channel sensors to achieve signal acquisition, obtain a higher signal-to-noise ratio (SNR), and improve the decoding success rate with the assistance of channel equalization and estimation technologies [5].

Yan et al. [6] from the China University of Petroleum analyzed the de-noising principle of the time-domain delay differential method based on dual pressure sensors in detail. Their simulation results showed that this method could effectively suppress the pump noise even when the fundamental frequency and amplitude of the pump noise fluctuated greatly.

Xu [7] proposed a frequency-domain processing method for continuous wave pulse signals based on dual sensors. He discussed the influence of noise on signal detection during the process of continuous wave transmission and analyzed the principle and characteristics of pump noise generation. He also described a signal processing method based on the signal acquisition method of using dual pressure sensors to examine the characteristics of continuous wave mud pulse signals.

Wu et al. [8] from China University of Petroleum proposed the adaptive mud pump noise cancellation algorithm to identify Continuous Phase-Frequency Keying (CPFK) signals based on probability analysis and PSO (Particle Swarm Optimization) algorithm. The results of simulation analysis show that the proposed CPFK modulation mode is feasible and the adaptive mud pump noise cancellation algorithm can realize the demodulation and decoding of CPFK signals.

Qiao et al. [9] from Guangdong University of Technology proposed a method for algorithm of adaptive noise cancellation In the measurement while drilling (MWD)system Simulation results show that the pump noise can be efficiently suppressed with both the adaptive noise canceller and the adaptive notch filter, and the power of useful signal with any SNRis protected. Since the method is simple, reliable and practical, it is highly valuable to improve the SNR of the mud pump signal and reduce the code error rate in MWD.

In summary, the mainly adopted signal processing method aiming at low-data-rate mud pulse signals with single-channel pressure sensor which cannot effectively identify the key features of an original signal with a low signal-to-noise ratio at a high transmission rate. It is essential to adopt the new kinds of method with multi-channel pressure sensor to get a higher processing quality.

2. Signal processing

2.1 Signal generation

As shown in Fig. 1, in this research, varying pressure wave signals were generated by controlling the relative motion of the stator and the rotor. The surface sensor received the corresponding pressure wave signals, which were decoded to obtain the true signals of the downhole drilling process. Common coding methods include frequency shift keying (FSK) and phase shift keying (PSK) [10].

Figure 1.

Schematic diagram of continuous wave transmission.

2.2 Signal characteristics

2.2.1 Noise effect

The transmission channel of pressure wave signals is mainly affected by the drilling head vibration, ground electromagnetic noise and mud pump noise during downhole drilling [11]. The pump noise is a typical signal with a specific frequency generated by the movement of the ground mud pump’s piston. The signal can be mixed in the pressure wave signal.

2.2.2 Signal attenuation

Based on Lamb’s Law, Desbrandes [12] proposed a pressure wave transmission attenuation model in 1988. The signal’s pressure amplitude at a certain well depth can be described by the following formula:

$\displaystyle P\left(x\right)=\textit{Po}\cdot e^{-\frac{x}{L}}$ (1) $\displaystyle L=\frac{di}{2}\sqrt{\frac{2B}{\rho v\omega}}$ (2)

where $P_{o}$ is the signal source amplitude in Pa, $d_{i}$ is the inner diameter of the drilling rod in m, $B$ is the mud volume modulus in Pa, $\rho$ is the mud density in kg/cm ${}^{3}$ , $\nu$ is the kinematic viscosity in m ${}^{2}$ /s, and $\omega$ is the angular velocity frequency in Hz

2.2.3 Signal reflection [13]

When the pressure wave signal is propagated with different drilling rod sizes or joints, some pressure waves are transmitted in different directions due to signal reflection, and some pressure waves can even be reflected to the superimposed original pressure wave signal.

3. Multichannel signal processing

Figure 2 shows the interference waveform diagram of the reflected wave with respect to the original pressure wave signal. The figure shows that due to the superposition of the reflected wave, the interference with the original pressure wave signal mainly includes the following two aspects.

(1)
When signal distortion occurs, the interference is superimposed to possibly amplify the noise into a signal waveform. Similarly, the interference may cause signals to cancel each other and mistakenly generate noise signals.
(2)
When signal offset occurs, the duration of the effective pulse signal increases and the pulse variation location cannot be accurately determined, thus affecting the judgment of the position accuracy in the decoding process and leading to decoding errors

Figure 2.
Interference signal waveform of reflected wave.

3.1 Cross correlation

In the field of signal processing, cross correlation [14] is a measure used to express the similarity between two signals. It can be used to find the characteristics of unknown signals by comparison with known signals. It is a function with respect to time between two signals, sometimes called a moving dot product. Cross correlation is used in pattern recognition and cryptanalysis. It reflects the matching degree of two functions at different relative positions. Therefore, a cross correlation approach can be used to process two-channel or multi-channel sensor signals to effectively extract the original signal’s characteristics.

For two random sequences $X_{n}$ and $Y_{n}$ , their cross correlation can be calculated with Eq. (3):

$\displaystyle\textit{RR}_{xy}m=E\left\{{x_{n+m}y_{n}^{\ast}}\right\}=E\left\{{% x_{n}y_{n-m}^{\ast}}\right\}$ (3)

where $-\infty<n<\infty$ , * represents the complex conjugate, and $E$ is the expectation operator. In general, the original correlation without normalization can be given by Eq. (4):

$\displaystyle\widehat{R_{xy}}\left(m\right)=\left\{{{\begin{array}[]{l}{% \mathop{\sum}\nolimits_{n=0}^{N-m-1}x_{n+m}y_{n}^{\ast},m\geqslant 0}\hfill\\ {\widehat{R_{yx}^{\ast}}\left(m\right),m<0}\hfill\\ \end{array}}}\right.$ (4)

where $c(m)=\widehat{R_{xy}}\left({m-N}\right),m=1,2,\ldots,2N-1$ .

3.2 Echo filtering

Due to the phenomena of reflection and scattering in the signal transmission process, the effective signal is interfered with and restricted in signal extraction. Hence, it is necessary to remove the influence of reflective and scattering waves from the original signal.

Therefore, the steps to remove reflective and scattering interferences based on cross correlation are as follows.

(1)
The correlation between the two signals is calculated based on the unbiased estimation of the cross correlation and the correlation coefficient is determined.
(2)
The number of terms greater than zero in the correlation coefficient is determined.
(3)
The delay time of the reflective and scattering waves is determined using the judgment of the abrupt point based on the threshold
(4)
Based on the IIR system [15], $y\left(n\right)=w\left(n\right)+\alpha w\left({n-\Delta}\right)$ the original signal is obtained from the superimposed signal, where $y(n)$ is the superimposed signal, $w(n)$ is the original signal, $\alpha$ is the reflective wave attenuation factor, and $\Delta$ is the delay time.

Figure 3 shows the waveform of the original pressure wave signal superimposed by a reflective signal with an attenuation factor of 0.5 and a delay time of 0.23 s.

Figure 3.
Original signal’s waveforms after delayed reception.

The cross-correlation operation based on unbiased estimation is given by

$\displaystyle\widehat{R_{xy}(m)}_{\textit{unbiased}}=\frac{1}{N-|m|}\widehat{R% _{xy}(m)}$ (5)

Signal delay removal was carried out in this research. The calculation result is shown in Fig. 4.

The calculation result of the correlation coefficient in Fig. 4 shows that the correlation coefficient had a great change at 0.23 s, which enabled the accurate positioning of the generation time of the echo delay. The signal waveform after echo removal was consistent with the original waveform. The autocorrelation calculation result was 1.

Figure 4.
Waveform comparison between received signal and original signal after delay removal.

4. Signal recovery

As shown in Fig. 5, an experimental test was carried out with a mud pump circulation system. The filtering processing method was studied by testing the response characteristics of the pressure wave signals at different output frequencies.

Figure 5.

Schematic diagram of the mud circulation system.

The output waveform of the mud pump’s background signal in the time domain and the frequency domain is shown in Fig. 6. The fundamental frequency of the pump signal was 1.06 Hz.

Figure 6.

Time-domain and frequency-domain waveforms of the mud pump’s background signal.

Figure 7 shows the frequency characteristic curve of the pressure wave signals at different frequencies obtained from the test. The figure also shows that the signal frequency domain and the mud pump noise frequency were intermixed.

Empirical Mode Decomposition (EMD) decomposes signals based on the time scale characteristics of the data itself, without the need to set any basis functions in advance. This is fundamentally different from the Fourier decomposition and wavelet decomposition methods based on prior harmonic and wavelet basis functions. Due to this characteristic, the EMD method can theoretically be applied to the decomposition of any type of signal. Therefore, it has significant advantages in processing non-stationary and nonlinear data, suitable for analyzing nonlinear and non-stationary signal sequences, and has a high signal-to-noise ratio. Therefore, a pressure wave signal filtering processing method was proposed based on empirical mode decomposition (EMD) [16] and a band-pass filter [17].

Figure 7.

Pressure wave signal response characteristics at different frequencies.

Figure 8 shows the data processing result of the 1.59 Hz pressure wave signal. The frequency range of the band-pass filter was 1.49 Hz to 1.69 Hz. The characteristic curve after time-frequency domain filtering showed that the proposed method could successfully restore the signal characteristics of the original pressure wave to obtain a high-quality response curve for the sinusoidal pressure wave.

Figure 8.

Comparison of waveforms before and after 1.59 Hz pressure wave signal processing.

4.1 Conclusions

This paper proposed a method for processing continuous mud pressure signal of acquired by dual-channel or multi-channel standpipe pressure sensors through theoretical analysis and numerical simulation based on the cross-correlation and EMD $+$ band-pass filter. The advantages could be drawn below:

(1)

The method could remove the signal distortion caused by sampling delay and reflection interference in high-data-rate transmission pressure wave signal processing.

(2)

Through the utilizing of circulation test. The interference of the mud pump noise was effectively recovered with frequency domain characteristics analysis. The signal characteristics of the original pressure wave were successfully restored.

Footnotes

Acknowledgments

The authors acknowledge the Science and technology projects of China National Petroleum Corporation: “Research on key technologies of continuous wave transmission and power supply based on integrated LWD system (2021DQ0409)”.

Limitations and next steps

The flow circulation test result showed the feasibility of above method. However, the response relationship between key parameters and echo attenuation that affected by sensor’s installation distance, delay coefficient, and different pump frequency characteristics has not been fully achieved. Field applications should be carried out to improve this method.

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