De-noising processing method in the process of drilling-oriented parameters transfer

Abstract

Downstream transmission of the drilling-oriented parameters means that the drilling control parameter information at the surface is transmitted to the down-hole drill bit, and the drill bit is controlled to perform the construction according to the predetermined wellbore trajectory. It not only interrupts the normal drilling operation but also transfers the ground information to the underground pulse system in real time. The biggest problem affecting signal processing and signal decoding is noise interferences. Effective signal processing methods can improve the correctness and reliability of the received signal analysis and processing. To this end, a drilling fluid pulse signal processing method based on Kalman filter is proposed. First, according to the relationship between the noise of the drilling pump and the pump impulse, the harmonic frequency of the pump noise and the corresponding amplitude phase are obtained to realize the reconstruction of the pump noise, thereby achieving the removal of the pump noise. For removing the signal after the pump noise, the remaining noise can be treated as additive noise, and then the Kalman filter is used to achieve real-time signal filtering. The experimental results show that the pump noise is the main source of disturbance of the drilling fluid pulse signal. The Kalman filtering method proposed is practical and effective for filtering the drilling fluid pulse signal. The efficient and accurate real-time transmission of information is a key factor in improving drilling safety, reliability, and maximizing drilling cost.

Keywords

Drilling-oriented parameters noise processing noise characteristics

1. Mud pump noise characteristics analysis

Down-hole data transmission methods mainly include wired cable, drilling fluid pulse, acoustic wave, electromagnetic wave and fiber optic. Each method has its scope of application and limitations, among which the drilling fluid pulse method is the most widely used and has better robustness. It is difficult to replace the application in deep wells. The drilling fluid pulse method changes the fluid flow in the drill string to change the drilling fluid pressure in the drill string to form a pressure wave with a certain frequency and amplitude. The series of pressure waves is transmitted to the drill bit in the form of pulses. The pressure wave is pulsed into electrical signals for collection and processing.

The influence of noise on the drilling fluid pulse signal is very large. A reasonable detection method, de-noising method and signal processing method can effectively improve the accuracy and reliability of the received data [2]. Part of the noise affecting the drilling fluid pulse signal is caused by the down-hole tool, and the transmission direction is consistent with the direction of the upload pulse signal, such as the role of the drill bit and the bottom of the well, the effect of the drill string and the borehole wall [3], the drilling fluid pressure noise generated by the down-hole turbine generator, etc. Another part of the noise originates from ground equipment, such as mud pumps, and the transmission direction is opposite to the direction of the upload pulse signal. The most influential one is the pump noise of mud pumps [4].

Pulse position coding method is used to carry out data communication on drilling-oriented parameters; azimuth and tool face angle signals. Under specific frequency control, the drilling fluid pulse interval in the signal is 0.5 second (2–10 blank time), the signal spectrum it is 0.1–0.8 Hz. Due to the complex down-hole conditions, there are many noises and disturbances in the signal transmission process. The noise appears as broadband white noise; the disturbance appears as periodic pulses related to the pump noise characteristics [5]. However, because its amplitude will change (modulated by low-frequency noise), its spectral value tends to “stretch” to the signal spectrum range, causing great difficulties in signal filtering.

Drilling mud pumps typically use a three-cylinder plunger pump to achieve approximately constant flow control [6]. According to the principle of the three-cylinder plunger pump, the flow rate of the mud pump output fluctuates in a small range, and the pressure fluctuation caused by the flow fluctuation is the pump noise that affects the drilling fluid pulse signal. From the field data, we know that the pump noise has completely submerged the drilling fluid pulse signal, so it is very important to effectively remove the pump noise without affecting the drilling fluid pulse signal.

Figure 1.

Noise-containing drilling fluid pulse signal.

Pump noise is the main source of noise and interference. In general, when the mud pump works well, the noise generated on the riser mainly has weak pump stroke noise (negligible) and strong piston motion noise [7, 8, 9]. The noise signal collected at the wellhead and containing only high-frequency noise without interference is shown in Fig. 1. As can be seen from the analysis in Fig. 1, the signal collected at the wellhead contains a large amplitude low-frequency component and high-frequency noise. In the signal spectrum range, the noise amplitude is smaller than the signal amplitude.

In [10, 11], the noise-related parameters were obtained by analyzing the original signal, and the noise was removed by using an adaptive filtering method. This method cannot implement the removal of pump noise over the entire pump noise bandwidth. In [12], the harmonic frequency close to the pump frequency is calculated based on the number of pumps, and the pump noise is removed based on this frequency. The above method is difficult to determine the position of the harmonic frequency point when other noise intensity is large [13]. The pump counter is used to estimate the instantaneous frequency. However, under the assumption that the instantaneous frequency changes linearly with the pump impulse per unit of time, this assumption is often biased, and the time interval between acquisitions of pump impulses is too large to be good. Real-time processing of high frequency signals. In addition, the above noise removal method can only be used when the pumping pressure of the short-term sampling data section is stable. Unsteady pump pressure may cause instability of the frequency of the pump pressure harmonics. Pump instability in the drilling site is a very common phenomenon. It is difficult to solve the time-varying problem of pump harmonics with the existing pump noise removal method.

2. Analysis of noise reduction in mud pump noise

For the muddy pump noise instantaneous fundamental frequency solution, due to a very short time $\Delta t$ , the crankshaft real-time speed $\omega$ (unit: r/min) is almost constant, the crankshaft every revolution of the mud pump three plungers reciprocate once [14], 3 pump flushes. Therefore, the pump base frequency can be expressed as Eq. (1).

$\displaystyle f_{1}=\omega/20$ (1)

Assuming that the pump noise signal can be constructed using the rotational speed of the crankshaft, set to PN( $\omega$ ), and set the pressure signal in this time to $x$ , the signal after removing the pump noise is expressed as Eq. (2).

$\displaystyle\tilde{x}=x-P_{N}(\omega)$ (2)

According to the flow characteristics of the mud pump, the output flow can be expressed as Eq. (3).

$\displaystyle Q(t)=\frac{a_{0}}{2}+\sum_{n=1}^{\infty}a_{n}\cos(2n\pi f_{1}t)+% \sum_{n=1}^{\infty}b_{n}\sin(2n\pi f_{1}t)$ (3)

According to the flow and pressure characteristics, the harmonic frequency of the pressure fluctuation generated by the mud pump is a positive multiple of the pump impulse frequency, fM $=$ Mf1. The pump pressure fluctuation is the pump noise and M is the harmonic order of the pump noise [15, 16, 17]. Regarding the problem of superposition and reconstruction of pump noise, the sampling frequency of the ground pressure wave signal is set to f, and the pump noise PN( $n$ , $\omega$ ) in the signal $x(n)$ can be discrete as shown in Eq. (4).

$\displaystyle P_{N}(n,\omega)=\sum_{m=1}^{M}a_{m}\cos(0.1\pi\textit{mwn}/f+% \theta_{m})$ (4)

In Eq. (4): $M$ is the harmonic frequency of the pump noise; the harmonic amplitude is in MPa; it is the corresponding harmonic phase. A fast Fourier transform is used to solve the frequency, amplitude and instantaneous phase of the solution, and then the amplitude-frequency phase-frequency characteristic table of the pump noise is constructed. The Fourier transform of the pump noise signal can be expressed as Eq. (5).

$\displaystyle X(m)=\sum_{n=0}^{N-1}x(n)\omega_{N}^{nm}$ (5)

Where $m\in[0,N]$ is the harmonic order of the signal, $\omega N=e-2\pi j/N$ . The amplitude of the pump noise harmonic signal can be expressed as Eq. (6).

$\displaystyle a_{m}=2\|X(m)\|/N$ (6)

The phase of the pump noise harmonic signal can be expressed as Eq. (7).

$\displaystyle\theta_{m}=A\tan 2(\text{Im}[X(m)],\text{Re}[X(m)])$ (7)

Therefore, the removal of pump noise can be achieved according to Eq. (2), and the signal after pump noise removal can be expressed by Eq. (8).

$\displaystyle\tilde{x}(n)=x(n)-P_{N}(n,\omega)$ (8)

The filtered drilling fluid pulse signal diagram shown in Fig. 1shows that the drilling fluid pulse signal collected at the site is completely submerged by the noise signal, in which the pump noise effect is more serious and the harmonic frequency of the pump noise is evenly distributed in the frequency domain.

Figure 2.

Drilling fluid pulse signal pump noise before and after comparison.

Using the method proposed in this paper to achieve the removal of pump noise, the comparison of drilling fluid signal before and after removal of mud pump noise is shown in Fig. 2. It can be seen that the signal strength is increased, the signal to noise ratio is increased, and the signal characteristics after noise removal are also very obvious. Therefore, using the method proposed in this paper can effectively remove mud pump noise.

3. Drilling fluid pulse based on Kalman filtering method

Approximation of nonlinear functions mainly uses polynomial expansion. This type of nonlinear Kalman filtering method mainly includes extended Kalman filter (EKF) [18, 19] and differential filter (DDF), Various polynomial Kalman filters [20].

3.1 EKF algorithm

In the EKF algorithm, the nonlinear functions $f(x_{k-1})$ and $h(x_{k})$ in the state space model are approximated as $\hat{x}_{k}$ and $\hat{x}_{k|k-1}$ first-order Taylor polynomials are shown in Eqs (9) and (10).

$\displaystyle f(x_{k-1})\approx f\left(\hat{x}_{k-1}\right)+F_{k-1}\left(x_{k-% 1}-\hat{x}_{k-1}\right)$ (9) $\displaystyle h(x_{k})\approx h\left(\hat{x}_{k|k-1}\right)+H_{k}\left(x_{k}-% \hat{x}_{k|k-1}\right)$ (10)

Where $F_{k-1}$ and $H_{k}$ are the following Jacobi matrices (Eqs (11) and (12)).

$\displaystyle F_{k-1}=\left.\frac{\partial f(x_{k-1})}{\partial x}\right|_{x=% \hat{x}_{k-1}}$ (11) $\displaystyle H_{k}=\left.\frac{\partial h(x_{k})}{\partial x}\right|_{x=\hat{% x}_{k|k-1}}$ (12)

Therefore, Eqs (9) and (10) are introduced into the nonlinear discrete state space models Eqs (13) and (14), respectively, to obtain a linear state space model approximated by a first-order Taylor polynomial Eqs (15) and (16).

$\displaystyle x_{k}=f(x_{k-1})+w_{k-1}$ (13) $\displaystyle z_{k}=h(x_{k})+v_{k}$ (14) $\displaystyle x_{k}=F_{k-1}x_{k-1}+f\left(\hat{x}_{k-1}\right)-F_{k-1}\hat{x}_% {k-1}+w_{k-1}$ (15) $\displaystyle z_{k}=H_{k}x_{k}+h\left(\hat{x}_{k|k-1}\right)-H_{K}\hat{x}_{k|k% -1}+v_{k}$ (16)

Substituting the state estimation at time $k-1$ into Eq. (15) yields a state prediction in a nonlinear system as shown in Eq. (17).

$\displaystyle\hat{x}_{k|k-1}=F_{k-1}\hat{x}_{k-1}+f\left(\hat{x}_{k-1}\right)-% F_{k-1}\hat{x}_{k-1}=f\left(\hat{x}_{k-1}\right)$ (17)

Similarly, based on the new information calculation method of the linear Kalman filter algorithm, the state prediction at time $k$ is substituted into Eq. (16), and the new information in the nonlinear system is obtained as Eq. (18).

$\displaystyle i_{k}=z_{k}-\left(H_{k}\hat{x}_{k|k-1}+h\left(\hat{x}_{k|k-1}% \right)-H_{k}\hat{x}_{k|k-1}\right)=z_{k}-h\left(\hat{x}_{k|k-1}\right)$ (18)

Further simplification gives the state estimation under the nonlinear system as Eq. (19).

$\displaystyle\hat{x}_{k}=\hat{x}_{k|k-1}+G_{k}(z_{k}-h(\hat{x}_{k|k-1}))$ (19)

In addition, the error covariance matrix and Kalman gain of the state prediction and state estimation of the EKF algorithm are the same as the linear Kalman filter algorithm.

3.2 DDF algorithm

The differential filter is divided into a divided difference one (DD1) and a divided difference two (DD2). Unlike the EKF, the differential filter uses a multi-dimensional stirling interpolation approximation nonlinear function. DD1 represents a differential filtering algorithm using a first-order interpolation polynomial, and DD2 represents a differential filtering algorithm using a second-order interpolation polynomial [21]. The nonlinear function in the state space model Eq. (13) can be approximated as Eq. (20) using a second-order interpolation formula.

$\displaystyle f(x_{k-1})\approx f\left(\hat{x}_{k-1}\right)+\tilde{D}_{\Delta x% }f+\frac{1}{2!}\tilde{D}_{\Delta x}^{2}f$ (20)

In the Eq. (20) the difference operators and the average operator are respectively expressed as Eqs (21) and (22).

$\displaystyle\tilde{D}_{\Delta x}f=\frac{1}{h}\left(\sum_{p=1}^{M}\Delta x_{p}% u_{p}\delta_{p}\right)f\left(\hat{x}_{k-1}\right)$ (21) $\displaystyle\tilde{D}_{\Delta x}^{2}f=\frac{1}{h^{2}}\left(\sum_{p=1}^{M}% \Delta x_{p}^{2}\delta_{p}^{2}+\sum_{p=1}^{M}\sum_{q=1,q\neq p}^{M}\Delta x_{p% }\Delta x_{q}(u_{p}\delta_{p})(u_{q}\delta_{q})\right)f(\hat{x}_{k-1})$ (22)

In the above two formulas, $h$ steps. The $\delta_{p}$ and $u_{p}$ are the difference operator and the average operator, as shown in Eqs (23) and (24).

$\displaystyle\delta_{p}f\left(\hat{x}_{k-1}\right)=f\left(\hat{x}_{k-1}+\frac{% h}{2}e_{p}\right)$ (23) $\displaystyle u_{p}f\left(\hat{x}_{k-1}\right)=\frac{1}{2}\left\{f\left(\hat{x% }_{k-1}+\frac{h}{2}e_{p}\right)+f\left(\hat{x}_{k-1}-\frac{h}{2}e_{p}\right)\right\}$ (24)

In the above two equations, $e_{p}$ represents the unit vector with the $p$ position.

4. Drilling fluid pulse filter test and result analysis

4.1 Drilling fluid pulse filter test model analysis

The drilling fluid pulse signal is continuously changed, and the sequence of the drilling fluid pulse signal can be expressed by the P-order AR model as Eq. (25).

$\displaystyle\tilde{x}(n)=\sum\xi_{i}(n)\tilde{x}(n-i)+u(n)$ (25)

In the formula, $\xi_{i}(n)$ for the prediction coefficient, it is a zero mean Gaussian white noise. Therefore, the state equations and observation equations of the drilling fluid pulse signals are expressed as Eqs (26) and (27).

$\displaystyle\alpha(n)=F(n)\alpha(n-1)+Gu(n)$ (26) $\displaystyle y(n)=H\alpha(n)+v(n)$ (27)

In the formula, $\alpha(n)=\left[\tilde{x}(n-p+1),\tilde{x}(n-p+2),\ldots,\tilde{x}(n)\right]^{T}$ is a signal sequence of length; $y(n)$ is an observation value; $v(n)$ is the update coefficient of the state equation; $\xi=[\xi_{p},\xi_{p-1},\ldots,\xi_{1}]^{T}$ is a coefficient matrix; $H$ , $G$ are noise estimates and observation vectors, respectively, and can be expressed as $H=G^{T}=[00\ldots 01]_{1\times p}$ ; $\tilde{x}(n)$ is additive noise in a signal. According to the above state equations and observation equations, the recursive process of filtering can be expressed as Eqs (28)–(35).

$\displaystyle e(n)=y(n)-H\hat{\alpha}(n|n-1)-\bar{v}$ (28) $\displaystyle K(n)=P(n|n-1)H^{T}\times\left[HP(N|N-1)H^{t}+\sigma_{V}^{2}% \right]^{-1}$ (29) $\displaystyle\hat{\alpha}(n|n)=\hat{\alpha}(n|n-1)+K(n)e(n)$ (30) $\displaystyle P(n|n)=[I-K(n)H]P(n|n-1)$ (31) $\displaystyle\hat{\alpha}(n+1|n)=F(n)\hat{\alpha}(n|n)+G\bar{u}$ (32) $\displaystyle A^{T}=[\alpha(n),\alpha(n-1),\ldots,\alpha(n-p+1)]$ (33) $\displaystyle\xi(n)=(A^{T}A)^{-1}A^{T}\alpha(n)$ (34) $\displaystyle P(n+1|n)=F(n)P(n|n)F^{T}(n)+GG^{T}\sigma_{u}^{2}$ (35)

In the formula, $\hat{\alpha}(n|n-1)$ represents a priori estimate, $\hat{\alpha}(n|n)$ represents a posterior estimate, $P(n|n-1)$ represents priori variance, $P(n|n)$ represents a posterior variance, $\sigma_{u}^{2}$ represents an input process variance, $\sigma_{r}^{2}$ represents an observation noise equation, and $I$ represents identity matrix.

Figure 3.

Noisy drilling fluid pulse signal.

Figure 4.

Noise filtered drilling fluid pulse signal.

4.2 Drilling fluid pulse filtering results analysis

The drilling fluid communication signal collected at the site is shown in Fig. 3. The drilling pump adopts a three-cylinder piston mud pump, in which the pump stroke is approximately 82/min. The filtering algorithm for the drilling fluid pulse signal is shown in Fig. 4. This is because the drilling pump has a small change in the working speed. If only using the pump to solve the fundamental frequency signal, it will be slightly different from the actual harmonic frequency, so the calculation needs to be based on sampling the spectrum analysis of the signal section, in the vicinity of the pump impulse frequency to find large harmonic energy. If the length of the sample analysis data segment is smaller, the pump speed variation will be smaller and the harmonic frequency will be more accurately reflected. Therefore, when the drilling pump noise is removed, a signal is intercepted as analysis data, which is also favorable for real-time data analysis.

Figure 5.

Threshold filtered back wave signal.

Using the above method to directly remove noise, the effect after removal is shown in Fig. 5, and the signal to noise ratio is greatly improved. However, there is still a small part of the pump noise that is not completely removed. There is still a low-noise noise signal near the higher harmonic frequency point, which may also be due to pump noise. After the pump noise is removed, the Kalman filter method is used to further process the signal that removes the pump noise and the waveform in Fig. 5 is obtained. The waveform has obvious characteristics and can directly implement feature recognition. The data collected at the measurement site was processed using the flat top elimination threshold method. The results show that the method can obtain all dynamic sync words, static sync words and data including down-hole information within the allowable error range. Preliminary statistical results show that the bit error rate is lower than 3%, and the process is simple and effective, and meet the requirements of engineering applications. The specific experimental results are summarized as the following three points.

(1)

The theoretical analysis and experimental results show that the pump noise is the main noise source affecting the drilling fluid pulse signal. The noise is composed of multiple harmonics. The harmonic spectrum is an integer multiple of the fundamental harmonic, and the fundamental frequency is harmonic. The wave is equal to the number of pump strokes per unit time.

(2)

The Kalman filter method is used to achieve further processing of the signal after removing the pump noise, and a good filtering effect is obtained.

(3)

Scanning along a certain width of the data window, using the proposed drilling fluid pulse signal processing method, the real-time filtering of the drilling fluid pulse signal is realized.

5. Conclusion

Because of the special conditions of drilling, the measurement signal while drilling between the bottom of the well and the ground is difficult to transmit through the wired method. Currently, the wireless transmission method based on pulse position code modulation of drilling fluid is mainly used in the project. However, because the channel transmission characteristics such as mud pressure, well depth, and pump pressure may affect the signal, the drilling fluid pulse signal collected at the wellhead during the measurement while drilling often contains various noises and interferences, which directly affects the correct decoding result of the ground signal. This paper analyzes the method of pulse wave filtering of drilling fluid, noise and interference. According to the characteristics of interference and noise, the Kalman filter method is used to restore the pulse signal, and the EKF method is used to process the signal collected in the field. A comprehensive comparison with the results of the linear filtering method shows that this method can effectively remove the drilling pump noise and other disturbances. The field application results show that this method has little effect on the position restoration error of the pulse signal, and the filtering process is simple and practical. It has the characteristics of low error rate and high reliability.

Footnotes

Acknowledgments

This study was supported by the Scientific Research Project of Hubei Provincial Department of Education (No: B2018029).

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