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The feasibility of applying delay pressure detection method to eliminate mud pump pressure interference on the downhole mud pressure signals is studied. Two pressure sensors mounted on the mud pipe in some distance apart are provided to detect the downhole mud continuous pressure wave signals on the surface according to the delayed time produced by mud pressure wave transmitting between the two sensors. A mathematical model of delay pressure detection is built by analysis of transmission path between mud pump pressure interference and downhole mud pressure signals. Considering pressure signal transmission characteristics of the mud pipe, a mathematical model of ideal low-pass filter for limited frequency band signal is introduced to study the pole frequency impact on the signal reconstruction and the constraints of pressure sensor distance are obtained by pole frequencies analysis. Theoretical calculation and numerical simulation show that the method can effectively eliminate mud pump pressure interference and the downhole mud continuous pressure wave signals can be reconstructed successfully with a significant improvement in signal-to-noise ratio (SNR) in the condition of satisfying the constraints of pressure sensor distance.

In measurement while drilling (MWD), various downhole signals will be transmitted to the surface in real time for instructing the drilling operation. One of the most common methods of transmitting the measured downhole information to the surface is through mud pressure pulses produced by mechanical modulation of a mud siren in MWD tools and transmitted at acoustic speed in the mud flow. The mud siren generates mud continuous pressure wave signals with complex modulation methods to produce higher data rates. When transmitting the mud pressure signals, there will be a lot of pressure noise and interference, among which the mud pressure fluctuation generated by the mud pump contributes to the largest influence. The mud pump pressure interference is related to the pump stoke rate which includes fundamental component and harmonic component. When the mud pump is in imbalance operation mode caused by sealing problem or in abnormal working status, some higher harmonic amplitude will become very large. Although the pressure dampers are equipped on mud pump pipe, the pressure fluctuation generated by mud pump reaches or exceeds the downhole signal strength detected in the stand pipe [

The delay pressure detection method uses two pressure sensors being some distance apart on the mud pipe to detect and process the mud pressure signal; Figure

Mud pressure detection system.

Considering the mud pipe between sensors A and B as a linear system, its frequency response can be described as

Suppose that

We can get convolution of

Equation (

Subtracting the formula in (

In (

After Fourier transform of the formula in (

According to (

Considering that the maximum frequency of mud continuous pressure wave signal in transmission will be dozens of hertz (Hz), the signal frequency is lower and limited. In limited frequency band, the signal attenuation in amplitude will keep unchangeable when mud continuous pressure wave signal passes the straight pipe between pressure sensors A and B, so the pipe can be seen as an undistorted transmission system and regarded as an ideal low-pass filter. The frequency domain transfer function of the system can be described as

After reciprocal transformation of

Then

Because transfer functions of

Substituting input function

Thus, the time-domain solution of the output function of

Converting the continuous-time system to Z-system of discrete-time and setting

According to digital filter theory,

Equations (

The straight pipe between pressure sensors A and B will cause pressure signal attenuation. According to the transmission characteristics of mud pressure wave [

Because the mud pipe forms an ideal low-pass filter in the limited band

After inverse Fourier transform of (

Suppose that the mud is water-based mud. The computational conditions are listed as follows [

When

If the maximum frequency of mud pressure signal spectrum is

Suppose that

Propagation velocity of the mud pressure wave in the mud pipe can be calculated according to the literature [

The numerical simulation takes mud pressure DPSK signal as an example. According to the mathematical model of mud pressure DPSK signal [

Therefore, the SNR of signal mixed with the pump interference is

Figure

Mud pressure DPSK signal mixed with pump interference.

Mud pressure DPSK signal without pump interference

Frequency spectrum of mud pressure DPSK signal

Mud pressure DPSK signal mixed with pump interference

Frequency spectrum of mud pressure DPSK signal mixed with pump interference

Suppose that the signal acts on the

SNR of reconstructed mud pressure DPSK signal.

Delayed time |
SNR of reconstructed mud pressure DPSK signal |
---|---|

0.98 | 72.6 |

1.95 | 72.6 |

2.93 | 72.5 |

3.91 | 72.4 |

4.89 | 72.1 |

5.86 | 70.5 |

Reconstruction of mud pressure DPSK signal.

Signal waveform after delay pressure detecting

Reconstructed signal of mud pressure DPSK signal with time-domain differential equation

Reconstructed signal of mud pressure DPSK signal based on inverse Fourier transform

Numerical simulation shows that if downhole noise is added to DPSK signal, the reconstructed signals based on the two reconstruction methods are the linear superposition of DPSK signal and downhole noise, which is consistent with theoretical analysis of (

(1) Theoretical analysis and numerical simulation show that delay pressure detection method can effectively eliminate mud pump interference and realize reconstruction or recovery of mud continuous pressure wave signals with greater SNR.

(2) To avoid the pole frequency entering into the signals frequency band in signal reconstruction, the distance between pressure sensors should be determined according to the highest signal frequency and the minimum wave velocity.

(3) According to the mathematical principle analysis of delay pressure detection method, it is only applied to eliminate special interference (mud pump pressure interference) whose transmitting direction is opposite to that of the downhole signal. For mud continuous pressure wave signal which is seriously affected by mud pump interference, this method has some inspiration effect on solving the problem of mud pump pressure interference.

This work was supported by the Project of National Natural Science Foundation of China (no. 51274236) and the Project of High-tech Research and Development Program of China (no. 2006AA06A101).