Variational modal domain adaptive filtering method for NMR echo data in tight sandstone reservoirs

Abstract

The present invention relates to the technical field of oil and gas development, and particularly relates to a variational mode domain adaptive filtering method for NMR echo data of tight sandstone reservoirs, comprising the following steps: 1) performing variational mode decomposition on the NMR echo data f(t) of the tight sandstone reservoir to obtain n modes u n (t), such that the sum of the modes is equal to f(t); 2) performing adaptive least mean square filtering (LMS) on the modes u n (t) obtained by variational mode decomposition; 3) summing the modes u n processed by the LMS adaptive filter to obtain the filtered NMR echo data. The method of the present invention can effectively remove the noise in the NMR echo data of the tight sandstone reservoir, improve the signal-to-noise ratio of the NMR logging data of the tight sandstone reservoir, improve the data quality, and provide a high-quality data volume for subsequent T2 spectrum inversion.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas development, and in particular to a variational modal domain adaptive filtering method for NMR echo data of a tight sandstone reservoir. Background Art

[0002] Tight sandstone reservoirs are currently the most realistic unconventional oil and gas resources that can be developed. NMR logging technology has a natural advantage over other logging methods because it only detects fluid information in rock pores. However, due to the extremely weak signals collected by NMR logging itself and the noise interference, the signal-to-noise ratio of NMR logging data is usually low. The porosity of tight sandstone reservoirs is usually less than 12%, T 2 The spectrum often shows a morphology dominated by small pores, and the signal-to-noise ratio of NMR echo data is usually less than 15. The low signal quality seriously affects the accuracy of the inverted NMR spectrum. This in turn affects the reservoir parameters calculated based on the spectrum and the understanding of the reservoir fluid properties. At present, the mainstream method for denoising NMR echo data is the wavelet denoising method, including wavelet threshold denoising method, wavelet packet threshold denoising method, wavelet domain adaptive filtering method, wavelet packet domain adaptive filtering method, etc. These methods are applicable to conventional reservoir nuclear magnetic resonance echo data denoising, and can achieve good denoising effects when the signal-to-noise ratio is in the range of [8,15]. However, it is difficult to achieve ideal denoising effects when applied to tight sandstone reservoir NMR echo data with a signal-to-noise ratio below 8. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, an object of the present invention is to provide a variational modal domain adaptive filtering method for tight sandstone reservoir NMR echo data.

[0004] To achieve the above objectives, the present invention adopts the following technical solutions:

[0005] A variational modal domain adaptive filtering method for tight sandstone reservoir NMR echo data comprises the following steps:

[0006] 1) Perform variational modal decomposition on the tight sandstone reservoir NMR echo data f(t) to obtain n modes u n (t), so that the sum of all modes is equal to f(t);

[0007] 2) Decompose the mode u obtained by variational mode decomposition n (t) performing adaptive least mean square filtering (LMS);

[0008] 3) Mode u after LMS adaptive filter processing n The filtered NMR echo data are obtained by summing.

[0009] Furthermore, in step 1), the estimated bandwidth and the minimum of the modal component, the corresponding variational constraint model is as follows:

[0010]

[0011] Among them, δ(t) is the unit impulse function, {u n} is n modes, {u n}={u 1, u 2, … , u n}; {ω n} is the center frequency of each mode, {ω n}={ω 1, ω 2, … , ω n}.

[0012] Furthermore, in step 1), the method for determining the modal number n is: determining the modal decomposition number based on the center frequency difference of the modal separation, when the center frequency difference is less than 200 at the kth decomposition, the modal number n=k-1.

[0013] Furthermore, in step 2), the mode u n (t) Perform adaptive least mean square filtering (LMS), the specific algorithm is:

[0014] e(t)=d(t)-F

[0015] Where e(t) is the error signal between the actual output and the expected output, F = u n w n represents the output signal of the adaptive filter, d(t) is the modal expected signal d(t) obtained by denoising f(t) through the adaptive filter and then performing variational mode decomposition;

[0016] F=u n w n

[0017] Among them, u n is the signal f 0 The nth mode after variational mode decomposition, f 0 is the input signal of the filter, i.e., the input signal composed of the delayed echo signal containing noise, w n is the weight vector of the adaptive filter corresponding to the nth mode;

[0018] From the above, we can know that:

[0019] e(t)=d(t)-u n w n

[0020] From the LMS algorithm, we can know that:

[0021]

[0022] Where, μ is the step size of the adaptive filter; w n The mean square error e 2 The estimated gradient of (t), that is:

[0023]

[0024] Depend on,

[0025]

[0026] We can get:

[0027] w n (t+1)=w n (t)+2μe(t)p n (t)

[0028] Compared with the prior art, the present invention proposes a method combining variational mode decomposition and adaptive filtering, which can effectively remove noise in the NMR echo data of tight sandstone reservoirs, improve the signal-to-noise ratio of the NMR logging data of tight sandstone reservoirs, improve the data quality, and provide a reference for subsequent T 2 Spectral inversion provides high-quality data volumes, especially suitable for denoising NMR echo data of tight sandstone reservoirs with a signal-to-noise ratio of less than 8. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0030] Figure 1 It is the flow chart of adaptive filtering in variational modal domain;

[0031] Figure 2 The denoising effect of variational modal domain adaptive filtering for tight sandstone reservoir NMR echo data. DETAILED DESCRIPTION

[0032] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several variations and improvements may be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0033] Example 1

[0034] A variational modal domain adaptive filtering method for tight sandstone reservoir NMR echo data comprises the following steps:

[0035] 1) Perform variational modal decomposition on the tight sandstone reservoir NMR echo data f(t) to obtain n modes u n (t), so that the sum of each mode is equal to f(t), the estimated bandwidth and modal component are minimized, and the corresponding variational constraint model is as follows:

[0036]

[0037] Among them, δ(t) is the unit impulse function, {u n} is n modes, {u n}={u 1, u 2 ,…,u n}; {ω n} is the center frequency of each mode, {ω n}={ω 1 ,ω 2 ,…,ω n}.also, It represents partial derivative; st is a common abbreviation in mathematics, namely subject to, which indicates constraint condition; j is the imaginary number symbol, and e is the base of natural logarithm.

[0038] To perform variational modal decomposition, the modal number n must be determined. Whether the modal number is reasonable directly affects the accuracy and efficiency of the algorithm. If the modal number is too large, false components and modal aliasing will be generated, resulting in over-decomposition; if the modal number is too small, some inherent modal components of limited bandwidth cannot be decomposed, resulting in under-decomposition. In order to determine a reasonable modal number n, the present application proposes a method for determining the modal decomposition number based on the center frequency difference of modal separation. When the kth decomposition is performed, the center frequency difference is less than 200, then the modal number n = k-1. That is, the modal number is determined with the center frequency difference not exceeding 200 as the limit.

[0039] 2) Decompose the mode u obtained by variational mode decomposition n (t) Adaptive least mean square filtering (LMS) is performed. The specific algorithm flow is as follows Figure 1 As shown in the figure, f(t) is the input signal of the filter, i.e., the echo signal containing noise. 0 is the input signal formed by delaying f(t); u n is the signal f 0 The nth mode after variational mode decomposition. n is the weight vector of the adaptive filter corresponding to the nth mode; F = u n w n represents the output signal of the adaptive filter, F = u nw n d(t) is the expected signal. The present invention performs denoising on f(t) through an adaptive filter and then performs variational mode decomposition. The mode thus obtained is the expected signal d(t). e(t) = d(t) - F is the error signal between the actual output and the expected output. e(t) = d(t) - F,

[0040] From the above, we can know that:

[0041] e(t)=d(t)-u n w n

[0042] From the LMS algorithm, we can know that:

[0043]

[0044] Where, μ is the step size of the adaptive filter; w n The mean square error e 2 The estimated gradient of (t), that is:

[0045]

[0046] Depend on,

[0047]

[0048] We can get:

[0049] w n (t+1)=w n (t)+2μe(t)p n (t)

[0050] 3) The mode u processed by the LMS adaptive filter n The filtered NMR echo data are obtained by summing.

[0051] Example 2

[0052] The actual NMR logging data of a tight sandstone reservoir in an oil field is denoised. The denoising effect of NMR echo data at a certain depth point is as follows: Figure 2 As shown. The horizontal axis is time, in ms. The vertical axis is amplitude. The blue line in the figure is the noisy NMR echo data before denoising, and the red line is the NMR echo data after denoising using the variational mode domain adaptive filtering method. After calculation, the signal-to-noise ratio before denoising is 6.0290. After denoising by variational mode domain adaptive filtering, its signal-to-noise ratio is improved to 17.2405. Here, the signal-to-noise ratio is defined as:

[0053]

[0054] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A variational mode domain adaptive filtering method for NMR echo data of tight sandstone reservoirs, Characterized in that, It includes the following steps: 1) Perform variational modal decomposition on the tight sandstone reservoir NMR echo data f(t) to obtain n modes u n (t), so that the sum of all modes is equal to f(t); 2) Decompose the mode u obtained by variational mode decomposition n (t) performing adaptive least mean square filtering (LMS); 3) Mode u after LMS adaptive filter processing n The filtered NMR echo data are obtained by summing; In the said step 1), the estimated bandwidth of the modal component is the smallest, and the corresponding variational constraint model is as follows: Among them, δ(t) is the unit impulse function, {u n } is n modes, {u n }={u 1 ,u 2 ,…,u n }; {ω n } is the center frequency of each mode, {ω n }={ω 1 ,ω 2 ,…,ω n }; In step 1), the method for determining the number of modes n is: determine the number of mode decompositions based on the center frequency difference of mode separation. When the k-th decomposition is performed, if the center frequency difference is lower than 200, then the number of modes n = k - 1; In step 2), the mode u n (t) Perform adaptive minimum mean square filtering, the specific algorithm is: e(t) = d(t) - F Where e(t) is the error signal between the actual output and the expected output, F = u n w n represents the output signal of the adaptive filter, d(t) is the modal expected signal obtained by denoising f(t) through the adaptive filter and then performing variational mode decomposition; F=u n w n Among them, u n is the signal f 0 The nth mode after variational mode decomposition, f 0 is the input signal of the filter, i.e., the input signal composed of the delayed echo signal containing noise, w n is the weight vector of the adaptive filter corresponding to the nth mode; As can be seen from the above: e(t)=d(t)-u n w n As can be seen from the LMS algorithm: Where, μ is the step size of the adaptive filter; w n The mean square error e 2 The estimated gradient of (t), that is: From, It can be obtained: w n (t+1)=w n (t)+2μe(t)p n (t)。

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