Shale fracturing three-dimensional positioning method based on high-sampling small-area multi-perception response

Abstract

The application discloses a shale fracturing three-dimensional positioning method based on high-sampling small-area multi-perception response, which comprises the following steps: step 1, selecting a suitable sensor and arranging the sensor in a small area; step 2, placing n sensors (n >= 4) on a test site according to step 1; step 3, receiving signals generated by shale fracturing by means of the sensors; step 4, high-sampling response signals of each sensor in step 3 to obtain high-sampling signals corresponding to the response signals of the sensors; step 5, extracting the time of arrival of the high-sampling signals in step 4 by means of an AIC algorithm, and calculating the time-difference of arrival of the fracturing signals received by each sensor; and step 6, obtaining a positioning equation group by combining position coordinates of each sensor with the time-difference data, and solving the equation group to obtain position coordinates of the fracturing point. The application can quickly realize positioning of shale cracks and evaluation of crack propagation trends, greatly improves positioning efficiency and positioning accuracy, and can greatly support oil, natural gas and shale gas exploitation.

Description

Technical Field

[0001] This invention relates to a three-dimensional localization method for shale fracturing based on high sampling, small-area, multi-sensor response, belonging to the field of seismic exploration technology. Background Technology

[0002] Currently, the three-dimensional localization technology for shale cracks mainly includes transverse and longitudinal wave reflection inversion technology and wave velocity-based ray tracing imaging technology, and scholars at home and abroad have conducted many studies on this.

[0003] Transverse and longitudinal wave reflection inversion techniques require establishing matrices showing the variation of reflection and transmission coefficients with the incident angle, which are mostly nonlinear problems. Linear inversion methods essentially linearize the nonlinear problem using approximate formulas before solving the matrix. Due to strong noise interference in fracturing zones, the signal-to-noise ratio of the reflected signal is very low, making it susceptible to interference from the initial wave and guided wave, hindering accurate analysis of the received transverse and longitudinal waves. Furthermore, sound waves propagating in inhomogeneous media undergo reflection and refraction along their propagation path, resulting in energy loss. Most of the methods described above rely on ideal models for shallow Earth rock identification, leading to problems such as high computational complexity and poor positioning accuracy in practical applications.

[0004] The imaging range of wave velocity-based ray tracing is much larger than the fracturing zone. However, due to the large dispersion of ground sensing points, the influence of rock distribution between the fracturing location and the sensing points, and the limitation of the number of paths, the wave velocity differences in the positioning model are significant, making velocity reconstruction difficult. While such reconstruction is suitable for stratigraphic analysis, applying this technology to positioning analysis is complex, directly affecting the time difference synchronization and work efficiency of fracturing zone experiments, and ultimately impacting the velocity field calculation and positioning accuracy of the algorithm. Therefore, wave velocity-based ray tracing technology is limited to laboratory research on rock fracturing and shallow engineering geological structures.

[0005] In summary, the current challenges in 3D shale crack localization include: First, addressing the low time-of-flight accuracy of discrete sensing point time-of-flight references covering a wide area; second, resolving the underdetermined and multi-valued issues in localization algorithms for discrete sensing points covering a wide area, thereby mitigating the uncertainty of the localization coordinates; and third, addressing the wave velocity differences among discrete sensing points covering a wide area, as existing analytical methods require pre-defined wave velocity values, which are often unknown or difficult to measure accurately in many localization systems. These issues hinder the implementation of 3D shale crack localization technology. Summary of the Invention

[0006] To address the aforementioned problems, the purpose of this invention is to provide a three-dimensional shale fracturing localization method based on small area and multi-sensor technology that can accurately predict the spatial location of fracturing sources.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a three-dimensional localization method for shale fracturing based on high sampling, small-area, multi-sensor response, comprising the following steps:

[0008] Step 1: Select suitable sensors and deploy them in a small area;

[0009] Step 2: Following Step 1, place n sensors (n>=4) at the test site;

[0010] Step 3: Receive signals generated by shale fracturing using sensors;

[0011] Step 4: High-sample the response signals of each sensor in Step 3 to obtain the high-sampled signals corresponding to each sensor response signal;

[0012] Step 5: Use the AIC algorithm to extract the arrival time of the high-sampling signals from Step 4 in pairs, and calculate the arrival time difference of the fracturing signals received by each sensor;

[0013] Step 6: By combining the position coordinates of each sensor with the time difference data, a set of positioning equations is obtained. Solving the set of equations yields the position coordinates of the fracturing point.

[0014] Furthermore, in step 1, the sensor selected has low-frequency response performance, a frequency response below 10Hz, and a sensitivity greater than 80 / (V·(m·s)). -1 ) -1 () low-frequency detector.

[0015] Furthermore, in step 2, let the coordinates of the sensor located at the center point O of the small circular region be R. o (x o ,y o ,z o The coordinates of the other sensors are R. i (x i ,y i ,z i ), i = 1, 2, ..., n; the arrangement of each sensor satisfies the following conditions:

[0016]

[0017]

[0018] Where: r is the distance from O to any sensor R i The radial distance between them, l, is the distance between the fracturing source and the sensor R. o The distance between them, v min f represents the maximum propagation velocity of the crack signal in the shale layer. s The sampling frequency; n is the total number of sensors deployed;

[0019] From the above, we can obtain the radial distance r and the distance s between the sensors. r This allows for the layout of sensors in a small circular area.

[0020] Furthermore, in step 4, the sampling pulse sequence is defined as δ. T (t) is shown in the following formula:

[0021]

[0022] Using δ T (t) Signal x generated by shale fracturing i (t), i = 1, 2, ..., n, are obtained by impulse sampling according to the following formula to obtain the high-speed sampling signal x. s (t):

[0023] x s (t)=x(t)δ T (t)

[0024] where n∈N * T s The time interval between each impulse.

[0025] Furthermore, the specific steps of the AIC algorithm are as follows:

[0026] (1) Calculate the AIC value of the high-sampling signal obtained in step 4 by traversing the entire signal, and obtain the AIC curve as follows:

[0027] AIC(k)=k·log(var(R(1,k)))+(N-1-k)·log(var(R(1+k,N)))

[0028] in:

[0029] k represents traversing all sampling points, k = 1, 2, 3...N;

[0030] var(R(1,k)), var(R(1+k,N)) — represent the variance of the data segments within the two windows;

[0031] N—Number of data points in the high-speed sampling signal;

[0032] var — the variance function of the sequence, var(R(1,k)) is the variance of the first to the kth parameter points in the time series;

[0033] (2) Take the minimum value of AIC according to the following formula:

[0034] t initial =x_arg(min(AIC))

[0035] (3) For sensor R1-Rn Repeat steps (1)-(2) above with the collected response signals to obtain the initial arrival time t of the fracturing signal sensed by each sensor. i (i = 1, 2, 3, ... n), let sensor R1 be the first sensor to receive the signal;

[0036] (4) The time differences between the sensors are as follows:

[0037]

[0038] Where i represents the sensor number, i = 1, 2, 3, ... n.

[0039] Furthermore, in step 6, let the position coordinates of each sensor be R. i (x i ,y i ,z i If a single positioning test requires m sensors, then the total number of positioning tests should be (The question mark at the end is missing in the original text). Multiple positioning and mutual correction of the fracturing position coordinates S(x,y,z); based on the initial arrival time t of the fracturing signals received by the n sensors determined in step 4. i (i=1,2,3,…n), the fracturing point S(x,y,z) is located using the positioning equation system.

[0040] Furthermore, the steps for determining the location of the fracturing source point include:

[0041] (1) The distance from the fracturing source to each sensor is:

[0042]

[0043] In the formula: t1 is the travel time from the fracturing source to the first sensor, t i The travel time from the fracturing source to the i-th sensor is represented by d1~d2. m It is the path distance from the fracturing source to the sensors numbered 1 to m, v1 to v m The speed of sound waves in this path;

[0044] (2) Difference processing; that is, subtracting the first equation from the second to the mth equation in the above formula yields a system of m-1 equations, as shown below:

[0045]

[0046] Where d i 2 -d1 2 =v i 2 t i 2 -v1 2t1 2 , i = 1, 2…m;

[0047] (3) Small-area velocity equivalence; wave velocity can be approximated as a constant, i.e., v1≈v2≈…≈v n ≈v, based on the idea of ​​wave speed equivalence, we have:

[0048] d i 2 -d1 2 =v 2 (t i 2 -t1 2 )

[0049] The difference Δd between the distance from the sound source to the i-th sensor and the distance to the 1st sensor is... i,1 for:

[0050] Δd i1 =d i -d1=v×t i1

[0051] Where: t i1 This represents the difference between the time from the fracturing source to sensor i and the time to sensor R1;

[0052] Combining the above two equations, the system of equations in step (2) can be written as:

[0053]

[0054] After sorting, we can obtain:

[0055]

[0056] (4) Solving for the coordinates of the fracturing source using a matrix; the above equation can be written in matrix form as follows:

[0057] Ax=αd1+β

[0058] in:

[0059]

[0060] Solving the equation Ax=αd1+β and taking its positive root, we can obtain the location coordinates S(x,y,z) of the fracturing source point.

[0061] The beneficial effects of this invention are:

[0062] (1) The present invention can greatly support the exploration of oil, natural gas, shale gas and other resources by locating shale cracks and studying crack propagation state and trend. It is of great significance to alleviate my country’s energy shortage problem.

[0063] (2) This invention studies only the relationship between the fracturing point and the sensor location, overcoming the limitations of traditional three-dimensional positioning methods based on the wave velocity distribution of shallow rocks, and effectively distinguishes itself from previous analytical positioning techniques. Because this patent solves the three major difficulties in the background technology, it can quickly realize the positioning of shale cracks and the assessment of crack propagation trends, greatly improving positioning efficiency and accuracy.

[0064] (3) The positioning technology proposed in this invention does not require studying the influence of geological structure on positioning. It has the characteristics of targeted research in positioning technology, which can improve the market competitiveness of geophysical companies and bring huge economic and social benefits to the company. Attached Figure Description

[0065] Figure 1 This is a sensor layout diagram of the present invention;

[0066] Figure 2 For this invention, the radial direction r, the distance l between the source S and the center O, and the high sampling frequency f are... s Distribution relationship diagram;

[0067] Figure 3 This is a diagram showing the initial arrival results of fracturing signals obtained by the AIC method of this invention;

[0068] Figure 4 This is a flowchart illustrating the positioning process of this invention. Detailed Implementation

[0069] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0070] One embodiment of the present invention provides a shale fracturing three-dimensional localization method based on high-sampling small-area multi-sensor response, which includes the following steps:

[0071] Step 1: Sensor selection;

[0072] Step 2: Sensor arrangement in a small area;

[0073] Step 3: Following Step 2, place n sensors (n>=4) at the test site;

[0074] Step 4: Receive signals generated by shale fracturing using sensors;

[0075] Step 5: High-sample the response signals of each sensor in Step 4 to obtain the high-sampled signals corresponding to each sensor response signal;

[0076] Step 6: Use the AIC algorithm to extract the arrival time of the high-sampling signals from Step 5 in pairs, and calculate the arrival time difference of the fracturing signals received by each sensor;

[0077] Step 7: By combining the position coordinates of each sensor with the time difference data, a set of positioning equations is obtained. Solving the set of equations yields the position coordinates of the fracturing point.

[0078] The following is a detailed description of each step:

[0079] Step 1: Sensor Selection. Because the fracturing signal from the deep underground fracturing point is significantly attenuated when transmitted to the surface sensor, a sensor with low-frequency response, typically below 10Hz, and sensitivity greater than 80 / (V·(m·s)) is selected. -1 ) -1 () low-frequency detector.

[0080] Step 2: The sensors are arranged in a small circular area with radial distance r and a number of sensors n. To achieve this small area arrangement, the radial distance r of each sensor R from the center O needs to be calculated. Since high sampling frequencies of 1M-10MHz are commonly used for high sampling of the response signal in fracturing tests, this high sampling rate makes small-area testing and positioning techniques possible. Figure 1 As shown, let the sensor located at the center point O and its coordinates be R. o (x o ,y o ,z o The coordinates of the other sensors are R. i (x i ,y i ,z i Let i = 1, 2, ..., n, and let OS be the distance from O to the fracturing point, and let v be the propagation velocity corresponding to the propagation path OS. o The propagation time is t o With sensor R o Taking R2 and R3 as examples, the propagation speed corresponding to path SR3 is v3, and the propagation time is t3. The detailed steps for arranging a small area of ​​sensors using the concept of limits are as follows:

[0081] ① Calculate the sensor's time resolution t r High sampling rate f at the megahertz level s The arrival time difference of the controllable sensor is on the order of microseconds; therefore, the resolution t of the sensor's arrival time difference is... r As shown in equation (1).

[0082]

[0083] Where f s It is the sampling rate of the fracturing response signal. If the sampling rate is 1M, the time difference resolution is 1us.

[0084] ② In triangle SOR3, the difference in distance between the propagation path SR3 and SO can be expressed as:

[0085]

[0086] ③ To ensure the sensor layout area is minimized, the time t taken for the crack signal to travel along the propagation path SO must be minimized. o The minimum time difference between SR3 and SR3 is one time difference resolution t. r Furthermore, within a small region, the wave velocities of the two paths can be approximated as equal, i.e., v o =v3=v, then we have:

[0087]

[0088] ④ The propagation speed of shale is taken as the limiting speed, i.e., v = v min r, l and f s As unknowns, r, l, and f are obtained from equation (3). s With the limit speed v min The functional relationship between them can be expressed as:

[0089]

[0090] Where: r is the distance from O to any sensor R i The radial distance between them, l, is the distance between the fracturing source and the sensor R. o The distance between them, v min f represents the maximum propagation velocity of the crack signal in the shale layer. s The sampling frequency.

[0091] ⑤ According to formula (4), the variables r, l and f are obtained. s The distribution relationship is as follows Figure 2 As shown, by Figure 2 It can be seen that when f is set s =1MHz, v min When the velocity is 3650 m / s, the radial distance of the sensor layout is calculated to be r = 5 m. This is the minimum radial distance for a small area layout under high-frequency sampling. If the distance is greater than this, the time difference accuracy that the sensor can distinguish can be met. However, considering that it is a small area layout and the minimum propagation speed fluctuates, based on engineering experience, it is recommended that the radial distance r of the sensor layout be between 5 and 35 m.

[0092] ⑥ From the radial distance r known in ⑤, calculate the distance between the sensors, i.e., OR2 = OR3 = r. For example... Figure 1 As shown in △OR2R3, let R2R3=s r If ∠R²OR³ is γ, then we have:

[0093]

[0094] in n represents the total number of sensors deployed.

[0095] Therefore, based on the above 6 sub-steps, we can obtain the radial distance as r and the distance between the sensors as s. r The sensor layout is in a small circular area.

[0096] Step 3: Following the sensor arrangement distance designed in Step 2, place n sensors (n>=4) at the test site, such as... Figure 1 The image shows a sensor arrangement model, with the position coordinates of each sensor being R. i (x i ,y i ,z i ), i = 1, 2, ..., n.

[0097] Step 4: Receive the signal x generated by shale fracturing using sensors. i (t), i = 1, 2, ..., n. Fracturing tests were conducted at the test site, and each sensor collected signals generated at the fracturing points.

[0098] Step 5: High-sample the response signals of each sensor from Step 4 to obtain the high-sampled signal corresponding to each response signal. Define the sampling pulse sequence as δ. T (t) As shown in formula (6), using δ T (t) for signal x i (t) The high-speed sampling signal x is obtained by impulse sampling according to formula (7). s (t).

[0099]

[0100] x s (t)=x(t)δ T (t) (7)

[0101] where n∈N * T s The time interval between each impulse.

[0102] Step 6: Use the AIC algorithm to extract the arrival times of the high-sampling signals from Step 5 in pairs, and calculate the arrival time difference of the fracturing signals received by each sensor. The specific steps of the AIC algorithm are as follows:

[0103] ① The AIC value is calculated by traversing the entire high-sampling signal obtained in step 5, and the AIC curve is obtained, which can be expressed as shown in formula (8):

[0104] AIC(k)=k·log(var(R(1,k)))+(N-1-k)·log(var(R(1+k,N))) (8)

[0105] in:

[0106] k represents traversing all sampling points, k = 1, 2, 3...N;

[0107] var(R(1,k)), var(R(1+k,N)) — represent the variance of the data segments within the two windows;

[0108] N—Number of data points in the high-speed sampling signal;

[0109] var — the variance function of the sequence, var(R(1,k)) is the variance of the first to the kth parameter points in the time series.

[0110] ②Then take the minimum value of AIC according to formula (9), such as Figure 3 As shown, the horizontal axis corresponding to the black dashed line represents the initial arrival time t of the signal. initial .

[0111] t initial =x_arg(min(AIC)) (9)

[0112] ③ For sensor R1-R n Repeating steps ① and ② above with the acquired response signals, the initial arrival time t of the fracturing signal sensed by each sensor can be obtained. i (i = 1, 2, 3, ..., n), where sensor R1 is the first sensor to receive the signal. The method proposed above can solve the problem of low time difference accuracy based on a discrete sensing point time difference reference covering a wide area.

[0113] ④ The time differences between the sensors are as follows:

[0114]

[0115] Where i represents the sensor number, i = 1, 2, 3, ... n.

[0116] Step 7: By combining the position coordinates of each sensor with the time difference data, a set of positioning equations is obtained. Solving the equations yields the position coordinates of the fracturing point. Let the position coordinates of each sensor be R. i (x i ,y i ,z i If a single positioning test requires m sensors, then the total number of positioning tests should be (The question mark at the end is missing in the original text). The fracturing position coordinates S(x,y,z) are cross-corrected through multiple positioning operations. Based on the initial arrival time t of the fracturing signals received by the n sensors determined in step 6... i (i = 1, 2, 3, ... n), taking sensors numbered 1 to m as an example, the location of the fracturing point S(x, y, z) is completed using the positioning equation system. The main steps include:

[0117] ① The distance from the fracturing source to each sensor is:

[0118]

[0119] In the formula: t1 is the travel time from the fracturing source to the first sensor, t i The travel time from the fracturing source to the i-th sensor is represented by d1~d2. m It is the path distance from the fracturing source to the sensors numbered 1 to m, v1 to v m The velocity of the sound waves in this path.

[0120] ② Difference processing, that is, subtracting the first equation from the second to the mth equation in equation (11), yields a system of m–1 equations, as shown in equation (12):

[0121]

[0122] Where d i 2 -d1 2 =v i 2 t i 2 -v1 2 t1 2 , i = 1, 2…m.

[0123] ③ Small-area velocity equivalence. Since the discrete sensing point area is small, the crack response can be essentially considered as having the same rock distribution characteristics along its propagation path. Therefore, the wave velocity can be approximated as a constant, i.e., v1≈v2≈…≈v n ≈v, which can solve the problem of wave velocity differences among discrete sensing points caused by wide-area deployment in existing methods. Based on the idea of ​​wave velocity equivalence:

[0124] d i 2 -d1 2 =v 2 (t i 2 -t1 2 (13)

[0125] The difference Δd between the distance from the sound source to the i-th sensor and the distance to the 1st sensor is... i,1 for:

[0126] Δd i1 =d i -d1=v×t i1 (14)

[0127] Where: t i1 This represents the difference between the time from the fracturing source to sensor i and the time to sensor R1.

[0128] Combining equations (13) and (14), equation (12) can be written as equation (15):

[0129]

[0130] After sorting, we can obtain:

[0131]

[0132] ④ Solving for the fracturing source coordinates using a matrix. The above equation can be written in matrix form as follows:

[0133] Ax=αd1+β (17)

[0134] in:

[0135]

[0136] Solving equation (17) and taking its positive root will yield the location coordinates S(x,y,z) of the fracturing source point. This method can solve the underdetermined and multi-valued problems of discrete sensing point localization algorithms with a wide area.

[0137] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the scope of protection of the present invention in any way, and all technical solutions obtained by equivalent substitution or other means fall within the scope of protection of the present invention.

[0138] All parts not covered in this invention are the same as or can be implemented using existing technologies.

Claims

1. A three-dimensional localization method for shale fracturing based on high-sampling, small-area, multi-sensor response, characterized in that... Includes the following steps: Step 1: Select a device with low-frequency response performance, a frequency response below 10 Hz, and a sensitivity greater than 80 V·(m·s). -1 ) -1 Low-frequency detectors were installed and deployed in a small area. Step 2: Following Step 1, place n sensors (n>=4) at the test site; let the coordinates of the sensors located at the center O of the circular area be R. o (x o ,y o , z o The coordinates of the other sensors are... , i = 1,2,…n; the arrangement of each sensor satisfies the following conditions: Where: r is the distance from O to any sensor R i The radial distance between them, l, is the distance between the fracturing source and the sensor R. o The distance between them, v min f represents the maximum propagation velocity of the crack signal in the shale layer. s The sampling frequency; , where n is the total number of sensors deployed; From the above, we obtain the radial distance r and the distance s between the sensors. r This allows for the layout of sensors in a small circular area. Step 3: Receive signals generated by shale fracturing using sensors; Step 4: High-sample the response signals of each sensor in Step 3 to obtain the high-sampled signals corresponding to each sensor response signal; Step 5: Use the AIC algorithm to extract the arrival time of the high-sampling signals from Step 4 in pairs, and calculate the arrival time difference of the fracturing signals received by each sensor; Step 6: By combining the position coordinates of each sensor with the time difference data, a set of positioning equations is obtained. Solving the set of equations yields the position coordinates of the fracturing point.

2. The shale fracturing three-dimensional localization method based on high-sampling small-area multi-sensor response according to claim 1, characterized in that, In step 4, the sampling pulse sequence is defined as follows: As shown in the following formula: use Signal x generated by shale fracturing i (t), i = 1,2,…n, are obtained by impulse sampling according to the following formula to obtain the high-speed sampling signal. : in T s The time interval between each impulse.

3. The shale fracturing three-dimensional localization method based on high-sampling small-area multi-sensor response according to claim 1, characterized in that, The specific steps of the AIC algorithm are as follows: (1) Calculate the AIC value of the high-sampling signal obtained in step 4 by traversing the entire signal, and obtain the AIC curve as follows: in: k — represents traversing all sampling points, k=1,2,3…N; , —This represents the variance of the data segments within the two windows; —Number of data points for high-speed acquisition signals; var — the variance function of the sequence. This represents the variance of the first to the kth parameter points in the time series. (2) Take the minimum value of AIC according to the following formula: (3) For sensor R1-R n The collected response signals are subjected to the above steps (1)-(2) repeatedly to obtain the initial arrival time t of the fracturing signal sensed by each sensor. i Let i = 1, 2, 3, ..., n, and let sensor R1 be the first sensor to receive a signal; (4) The time differences between the sensors are as follows: Where i represents the sensor number, i=1,2,3,…n.

4. The shale fracturing three-dimensional localization method based on high-sampling small-area multi-sensor response according to claim 1, characterized in that, In step 6, let the position coordinates of each sensor be... A single positioning requires If each sensor completes the task, then the total number of positioning tests should be: Multiple positioning and mutual correction of fracturing position coordinates ; Based on the initial arrival time t of the fracturing signals received by the n sensors determined in step 4. i For i=1,2,3,…n, the fracturing points are determined using the location equations. Positioning.

5. The shale fracturing three-dimensional localization method based on high-sampling small-area multi-sensor response according to claim 4, characterized in that, The steps to determine the location of the fracturing source point include: (1) The distance from the fracturing source to each sensor is: In the formula: t1 is the travel time from the fracturing source to the first sensor. The travel time from the fracturing source to the i-th sensor is represented by d1~d2. m It is the path distance from the fracturing source to the sensors numbered 1~m, v1~v m The speed of sound waves in this path; (2) Difference processing; that is, subtracting the first equation from the second to the mth equation in the above equation yields a system of m-1 equations, as shown below: in , i=1,2…m; (3) Small-area velocity equivalence; wave velocity can be approximated as a constant, i.e. Based on the idea of ​​wave velocity equivalence, there are: The difference between the distance from the sound source to the i-th sensor and the distance to the 1st sensor. for: Where: t i1 This represents the difference between the time from the fracturing source to sensor i and the time to sensor R1; Combining the above two equations, the system of equations in step (2) can be written as: After sorting, we can obtain: (4) Solve for the coordinates of the fracturing source using a matrix; the above equation can be written in matrix form as follows: in: ， ， ， Solve the equation Taking its positive root, we can obtain the location coordinates of the fracturing source point. .

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