Method, medium and system for calculating extension length of hydraulic fracturing main crack

Abstract

The invention provides a method, medium and system for calculating the extension length of a hydraulic fracturing main fracture, and belongs to the technical field of hydraulic fracturing. The method, medium and system for calculating the extension length of the hydraulic fracturing main fracture comprise the steps that a water hammer wave signal at the position of a well mouth after hydraulic fracturing pump stopping is obtained; performing cepstrum analysis on the water hammer wave signal; the minimum period of the positive pulse extreme point of the complex cepstrum curve is calculated, and the time of the water hammer wave moving from a wellhead to a bridge plug is obtained; calculating the average speed of movement of the water hammer waves in the well; performing linear trend removal processing on the local signal of the water hammer wave; fourier transform is carried out on the local signal after linear trend removal processing, and a water hammer wave local signal frequency spectrum is obtained; extracting a fundamental frequency corresponding to a maximum value point in the water hammer wave local signal spectrum as a response frequency in the main crack; according to the response frequency in the main fracture, the propagation time of the water hammer wave in the main fracture is calculated; and calculating the extension length of the main crack.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydraulic fracturing, and in particular, relates to a method, a medium and a system for calculating the extension length of a main crack of hydraulic fracturing. Background Art

[0002] As an important measure to increase oil and gas production, hydraulic fracturing technology has been widely used around the world. This technology injects high-pressure fluid into the formation to form a complex fracture network in the formation, thereby increasing the permeability and production capacity of oil and gas reservoirs. In the hydraulic fracturing process, the main fracture is one of the most important fluid channels, and its extension length is of great significance to the development of oil and gas reservoirs. On the one hand, the evaluation of the extension length of the main fracture directly affects the stability and production capacity of the fracture, and is crucial for optimizing the fracturing design and increasing oil and gas production. On the other hand, it indirectly determines the amount of fracturing proppant required, which can avoid unnecessary proppant waste and the cost of re-fracturing, protect groundwater resources and the ecological environment to the greatest extent, and achieve sustainable development of oil and gas extraction.

[0003] At present, the main methods for evaluating the extension length of the main fracture include microseismic monitoring, electromagnetic detection and other technologies. Microseismic monitoring technology tracks the extension of fractures by recording tiny earthquake events generated during fracturing on the ground or in the well, but this method is limited by environmental noise, formation conditions and the layout of monitoring equipment, and the monitoring cost is relatively high. Electromagnetic detection technology charges underground fluids through the wellbore, causing the fluid in the fracture to generate an electromagnetic field to detect the fracture, but its detection resolution is not high, and it is difficult to capture the complete extension information of the main fracture in real time and accurately. At the same time, the extension behavior of the main fracture of fracturing is affected by many factors, including ground stress distribution, rock mechanical properties, and fracturing fluid properties. The complexity and uncertainty of these factors make the accurate assessment of the extension length of the main fracture face huge challenges.

[0004] In addition, with the deepening of unconventional oil and gas resource development, the fracturing process is constantly innovating, and the traditional evaluation methods can no longer meet the needs of efficient and convenient new fracturing processes. Especially in shale gas development, due to the strong formation heterogeneity and complex stress environment, the applicability of existing evaluation methods is greatly limited. Therefore, it is urgent to develop a new main fracture extension length evaluation method to improve the evaluation accuracy and practicality. Summary of the invention

[0005] In view of this, the present invention provides a method, medium and system for calculating the extension length of the main fracture of hydraulic fracturing, which can solve the lack of accurate evaluation method for the extension length of the main fracture, reduce the influence of factors such as ground stress distribution, rock mechanical properties, fracturing fluid properties and monitoring equipment on traditional evaluation methods, improve detection accuracy and reduce monitoring costs.

[0006] The present invention is achieved in that:

[0007] The present invention provides a method for calculating the extension length of a main hydraulic fracturing crack, comprising the following steps:

[0008] S10, using a high-frequency pressure gauge to obtain a water hammer wave signal at the wellhead after the hydraulic fracturing pump is stopped;

[0009] S20, converting the water hammer wave signal into a complex cepstrum, and performing cepstrum analysis on the water hammer wave signal;

[0010] S30, calculating the minimum period between the positive pulse extreme points in the complex cepstrum curve, and taking half of the minimum period as the time for the water hammer wave to move from the wellhead to the bridge plug;

[0011] S40, calculating the average speed of the water hammer wave moving in the well according to the time it takes for the water hammer wave to move from the wellhead to the bridge plug and the distance from the wellhead to the bridge plug;

[0012] S50, performing linear trend removal processing on the local signal of the water hammer wave in the rising stage or the falling stage along the wellbore;

[0013] S60, performing Fourier transform on the local signal after the linear trend removal process to obtain a water hammer wave local signal spectrum;

[0014] S70, extracting the fundamental frequency corresponding to the maximum point in the spectrum of the local signal of the water hammer wave as the response frequency in the main crack;

[0015] S80, calculating the propagation time of the water hammer wave in the main crack according to the response frequency in the main crack;

[0016] S90, calculating the extension length of the main fracture according to the average speed of the water hammer wave moving in the well and the propagation time of the water hammer wave in the main fracture.

[0017] On the basis of the above technical solution, a method for calculating the extension length of the main hydraulic fracturing crack of the present invention can also be improved as follows:

[0018] Wherein, the S20 specifically includes:

[0019] Performing Fourier transform on the water hammer wave signal to obtain a signal spectrum;

[0020] Performing a modulo operation on the signal spectrum to obtain a signal amplitude spectrum;

[0021] Performing a natural logarithm operation on the signal amplitude spectrum to obtain a logarithmic spectrum;

[0022] Performing inverse Fourier transform on the logarithmic spectrum to obtain a complex cepstrum of the water hammer wave signal;

[0023] Extracting the amplitude of the complex cepstrum by using square root operations of the real domain part and the imaginary domain part;

[0024] A peak detection method is used to extract the maximum point of the complex cepstrum amplitude.

[0025] Furthermore, the S30 specifically includes:

[0026] Extracting the frequency corresponding to the maximum value of the water hammer wave signal amplitude spectrum, and taking the inverse of the frequency as the movement period of the water hammer wave along the rising stage or the descending stage of the wellbore;

[0027] identifying a positive pulse region in the complex cepstrum curve according to the motion period;

[0028] Performing a local extreme value search in the positive pulse region and marking the position of the extreme value point;

[0029] Calculate the time intervals between adjacent extreme points and obtain multiple period values;

[0030] Averaging the multiple period values ​​to obtain an average period value;

[0031] Half of the average period value is taken as the time for the water hammer wave to move from the wellhead to the bridge plug.

[0032] Furthermore, the S40 specifically includes:

[0033] The actual distance from the wellhead to the bridge plug is obtained according to the drilling data as the water hammer wave propagation distance;

[0034] The water hammer wave propagation distance is divided by the time it takes to move from the wellhead to the bridge plug to calculate the average speed of the water hammer wave moving in the well.

[0035] Furthermore, the S50 specifically includes:

[0036] Identify the rising and falling segments of the water hammer wave signal and extract the local signal;

[0037] Fitting the linear trend of the local signal using the least square method;

[0038] The calculated linear trend coefficients, including slope and intercept, generate a trend signal with the same length as the input signal;

[0039] The linear trend is subtracted from the local signal to obtain a local signal after the linear trend is removed.

[0040] Furthermore, the S60 specifically includes:

[0041] Frame and window the local signal after removing the linear trend;

[0042] Perform fast Fourier transform on the windowed signal;

[0043] The fast Fourier transform result is modulo to obtain the amplitude of each frequency component;

[0044] The frequency and amplitude within the Nyquist frequency range are taken as the spectrum of the local signal.

[0045] Furthermore, the S70 specifically includes:

[0046] Performing peak detection on the local signal spectrum of the water hammer wave;

[0047] Searching for a frequency point satisfying a peak condition in the frequency spectrum;

[0048] The frequency points are sorted from small to large, and only the minimum frequency point whose frequency is a multiple relationship is extracted as the fundamental frequency;

[0049] The fundamental frequency is selected as the response frequency in the main crack.

[0050] Furthermore, the S80 specifically includes:

[0051] The reciprocal of the main crack response frequency is taken and divided by 2 to obtain the propagation time of the water hammer wave in the main crack.

[0052] Furthermore, the S90 specifically includes:

[0053] The extended length of the main fracture is obtained by multiplying the average speed of the water hammer wave in the well by the propagation time of the water hammer wave in the main fracture.

[0054] Among them, the complex cepstrum conversion expression of the water hammer wave signal is as follows:

[0055]

[0056] In the formula, is the complex cepstrum of the water hammer wave signal, in seconds; F -1 [·] is the inverse Fourier transform operator; F[·] is the Fourier transform operator; x(t) is the time domain signal of water hammer wave, in MPa; t is time, in s; ln is the natural logarithm function.

[0057] The average velocity of water hammer wave in the well is calculated as follows:

[0058]

[0059] In the formula, is the average speed of the water hammer wave in the well, in m / s; d is the distance of the water hammer wave along the wellbore from the wellhead to the bridge plug, in m; T is the time it takes for the water hammer wave to move along the wellbore from the wellhead to the bridge plug, in s.

[0060] The linear trend removal calculation expression of the local signal of water hammer wave is as follows:

[0061] y k (t) = x k (t)-(at+b);

[0062] in:

[0063]

[0064]

[0065] In the formula, y k (t) is the data of the kth water hammer wave local signal after removing the linear trend, in MPa; x k (t) is the kth water hammer wave local signal, in MPa; t is the time series of the local signal, in s; n is the length of the time series.

[0066] The calculation expression of the local signal spectrum of water hammer wave is as follows:

[0067] y k (ω)=|F[y k (t)]|;

[0068] In the formula, y k (ω) is the local signal spectrum of the kth water hammer wave; ω is the angular frequency, in rad / s.

[0069] The calculation expression of water hammer wave propagation time in the main crack is as follows:

[0070]

[0071] Where t′ is the propagation time of the water hammer wave in the main crack, in seconds; ω′ is the response frequency in the main crack, in Hz.

[0072] The calculation expression of the main crack extension length is as follows:

[0073]

[0074] Where l is the main crack extension length, in meters.

[0075] The principles and meanings of these equations are as follows:

[0076] 1. Complex cepstrum transformation uses the inverse Fourier transform of the logarithmic spectrum, which can effectively enhance the crack response in the signal and reduce noise interference;

[0077] 2. The average velocity calculation takes into account the influence of the wave velocity change of water hammer waves in different periods, thus improving the calculation accuracy;

[0078] 3. Linear trend removal highlights the characteristic frequency of the main crack signal, making it easier to extract the signal base frequency;

[0079] 4. The spectrum calculation of local signals takes into account the problem that the crack response frequency is easily submerged in the overall water hammer wave signal. By extracting local signals, the spectrum analysis is made more efficient and accurate;

[0080] 5. The propagation time calculation takes into account the inverse relationship between signal frequency and signal period, which improves the convenience of time estimation;

[0081] 6. The calculation of the main fracture extension length takes into account the average speed of the water hammer wave propagating in the wellbore and the time law of its propagation in the main fracture, making the result more reliable.

[0082] Compared with the prior art, the method of the present invention:

[0083] 1. Extract the local signal of water hammer wave for spectrum analysis, highlighting the characteristics of crack response;

[0084] 2. The use of complex cepstrum analysis improves the accuracy of signal processing;

[0085] 3. The dynamic changes of water hammer wave motion parameters are taken into account;

[0086] 4. A complete mathematical model system has been established, which can be used for quantitative calculations.

[0087] The method for calculating the extension length of the main fracture of hydraulic fracturing proposed in the present invention establishes a complete main fracture extension length evaluation system by analyzing the water hammer wave signal and combining the cepstrum analysis and spectrum analysis technology. The method has the following technical effects:

[0088] First, the method of the present invention uses a high-frequency pressure gauge to obtain water hammer wave signals, which has the advantages of simple equipment and low cost compared with traditional monitoring methods. By performing complex cepstrum analysis on water hammer wave signals, the periodic components in the signal can be effectively extracted, noise interference can be reduced, and the accuracy of signal processing can be improved.

[0089] Secondly, the method of the present invention adopts local signal analysis technology, and effectively avoids the influence of signal interference and distortion by processing the rising and falling segments of the water hammer wave signal separately. At the same time, the introduction of processing methods such as linear trend removal further improves the accuracy of signal analysis.

[0090] Third, the method of the present invention has strong real-time and adaptability. Through the real-time collection and analysis of water hammer wave signals, the main fracture extension length information can be obtained in time, providing an important basis for the optimization of fracturing process. The method is applicable to various formation conditions and fracturing processes and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0092] Figure 1 A flow chart of a method for calculating the extension length of a main fracture of hydraulic fracturing;

[0093] Figure 2 A schematic diagram of the structure of a three-dimensional hydraulic fracturing model in a first embodiment of a method for calculating the extension length of a main hydraulic fracturing crack;

[0094] Figure 3 A hydraulic fracturing pump-off water hammer wave signal waveform diagram obtained in a first embodiment of a method for calculating the extension length of a hydraulic fracturing main crack;

[0095] Figure 4 A water hammer wave cepstrum curve diagram based on cepstrum analysis in a first embodiment of a method for calculating the extension length of a main fracture of hydraulic fracturing;

[0096] Figure 5 a is the local signal of water hammer wave before detrending, and b is the local signal of water hammer wave after detrending;

[0097] Figure 6 A local signal spectrum diagram of a water hammer wave in a rising or falling stage in a first embodiment of a method for calculating the extension length of a main fracture of hydraulic fracturing;

[0098] Figure 7 A waveform diagram of a water hammer wave signal generated by stopping a pump during hydraulic fracturing obtained in a second embodiment of a method for calculating the extension length of a main fracture of hydraulic fracturing;

[0099] Figure 8 The diagram is a spectrum diagram of a local signal of a water hammer wave in a rising or falling stage in a second embodiment of a method for calculating the extension length of a main fracture of a hydraulic fracturing. DETAILED DESCRIPTION

[0100] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0101] like Figure 1 , Figure 3 , Figure 4 , Figure 5 , Figure 6FIG. 1 is a first embodiment of a method for calculating the extension length of a main hydraulic fracture provided by the present invention. In this embodiment, a method for calculating the extension length of a main hydraulic fracture includes the following steps:

[0102] Obtain the water hammer wave signal at the wellhead after the pump is stopped during fracturing;

[0103] The water hammer wave signal is subjected to cepstrum analysis to obtain the average velocity of the water hammer wave in the well.

[0104] Perform spectrum analysis on water hammer wave signals to obtain the propagation time of water hammer wave in the main fracture of fracturing;

[0105] The main fracture extension length is calculated based on the average velocity of the water hammer wave in the well and the propagation time of the main fracture in the fracturing.

[0106] As a preferred technical solution of the present invention, the step of performing cepstrum analysis on the water hammer wave signal to obtain the average velocity of the water hammer wave in the well specifically includes:

[0107] The water hammer wave signal is converted into its complex cepstrum, and its conversion expression is as follows:

[0108]

[0109] In the formula, is the complex cepstrum of the water hammer signal, is the inverse Fourier transform, is Fourier transform, x(t) is the time domain signal of water hammer wave;

[0110] Calculate the minimum period between the extreme points of the positive pulse in the complex cepstrum curve diagram, and use it as the time T for the water hammer wave to move from the wellhead to the bridge plug along the wellbore;

[0111] Based on the distance d and time T of the water hammer wave from the wellhead to the bridge plug along the wellbore, calculate the average speed of the water hammer wave in the well. Its expression is as follows:

[0112]

[0113] As a preferred technical solution of the present invention, the step (3) specifically comprises:

[0114] The local signal x of the water hammer wave rising or falling along the wellbore k (t) De-linear trend, its calculation expression is as follows:

[0115]

[0116] In the formula, y k (t) is the data of the kth local signal of the water hammer wave in the rising or falling stage after the linear trend is removed, xk (t) is the kth local signal of water hammer wave in the rising or falling stage, t is the time series of the local signal, and n is the length of the time series;

[0117] The detrended data is subjected to Fourier transform to obtain a spectrum diagram, and its calculation expression is as follows:

[0118]

[0119] In the formula, y k (ω) is the local signal spectrum of the kth water hammer wave in the rising or falling stage;

[0120] The fundamental frequency corresponding to the maximum point of the local signal spectrum of the water hammer wave is taken as the response frequency ω′ in the main crack, and the propagation time t′ of the water hammer wave in the main crack is calculated. The calculation expression is as follows:

[0121]

[0122] The following provides a specific application scenario of this embodiment. In this application scenario, we construct an application case of three-dimensional hydraulic fracturing, and the scenario setting is as follows: Figure 2 As shown. The specific configuration details are as follows: the inner diameter of the pipe is 0.2m, the distance from the bridge plug to the wellhead along the wellbore is about 3000m, the pipe wall thickness is 7.72mm, the Young's modulus of the pipe is 206GPa, and the Darcy friction factor of the pipe wall is 0.028. There is a perforation with an inner diameter of 0.015m at a distance of 2900m from the wellhead along the wellbore, which connects to the main fracture. Here, the main fracture is equivalent to a rectangular fracture network with a length, width and height of 40m, 1cm and 10m respectively. Fluid parameters: The initial flow rate is 0.27m 3 / s, the initial pressure is 600atm.

[0123] After the pump is stopped instantaneously in the fracturing well model, the wellhead pressure change curve is output at a sampling frequency of 1000 Hz as the water hammer wave signal recorded by the high-frequency pressure meter. The recorded water hammer wave signal is as follows: Figure 3 shown.

[0124] right Figure 3 The water hammer wave signal is analyzed by cepstrum.

[0125] Calculate the complex cepstrum of the water hammer wave signal, and the result is as follows Figure 4 shown.

[0126] calculate Figure 4 The minimum period between the extreme points of the positive pulse in the complex cepstrum curve is taken as the time T = 2.289 s for the water hammer wave to move from the wellhead to the bridge plug along the wellbore.

[0127] Based on the distance d = 3000m from the wellhead to the bridge plug along the wellbore and the time T, the average speed of the water hammer wave in the well is calculated.

[0128] right Figure 3 The water hammer wave signal is analyzed by spectrum analysis.

[0129] De-linearize the local signal of the water hammer wave during the rising or falling stage along the wellbore, such as Figure 5 shown.

[0130] The detrended data is subjected to Fourier transformation to obtain a spectrum diagram, such as Figure 6 shown.

[0131] The fundamental frequency corresponding to the maximum point of the local signal spectrum of the water hammer wave is taken as the response frequency ω′=18.03Hz in the main crack, and the propagation time of the water hammer wave in the main crack is calculated.

[0132] The main fracture extension length is calculated based on the average velocity of the water hammer wave in the well and the propagation time of the main fracture in the fracturing process. The error between the calculated value and the actual value is small, and it can be effectively used for fracturing effect evaluation.

[0133] The following is another application scenario of this embodiment. In this application scenario, we constructed an application case of hydraulic fracturing. The specific configuration details are as follows: the inner diameter of the pipe is 0.2m, the distance from the bridge plug to the wellhead along the wellbore is about 3000m, the pipe wall thickness is 7.72mm, the Young's modulus of the pipe is 206GPa, and the Darcy friction factor of the pipe wall is 0.028. There is a perforation with an inner diameter of 0.015m at a distance of 2900m from the wellhead along the wellbore, which connects to the main fracture. Here, the main fracture is equivalent to a rectangular fracture network with a length, width and height of 50m, 1cm and 10m respectively. Fluid parameters: The initial flow rate is 0.27m 3 / s, the initial pressure is 600atm.

[0134] After the pump is stopped instantaneously in the fracturing well model, the wellhead pressure change curve is output at a sampling frequency of 1000 Hz as the water hammer wave signal recorded by the high-frequency pressure meter. The recorded water hammer wave signal is as follows: Figure 3 shown.

[0135] right Figure 3 The water hammer wave signal is analyzed by cepstrum.

[0136] Calculate the complex cepstrum of the water hammer wave signal, and the result is as follows Figure 4 shown.

[0137] calculate Figure 4The minimum period between the extreme points of the positive pulse in the complex cepstrum curve is taken as the time T = 2.289 s for the water hammer wave to move from the wellhead to the bridge plug along the wellbore.

[0138] Based on the distance d = 3000m from the wellhead to the bridge plug along the wellbore and the time T, the average speed of the water hammer wave in the well is calculated.

[0139] right Figure 3 The water hammer wave signal is analyzed by spectrum analysis.

[0140] De-linearize the local signal of the water hammer wave during the rising or falling stage along the wellbore, such as Figure 5 shown.

[0141] The detrended data is subjected to Fourier transformation to obtain a spectrum diagram, such as Figure 6 shown.

[0142] The fundamental frequency corresponding to the maximum point of the local signal spectrum of the water hammer wave is taken as the response frequency ω′=15.03Hz in the main crack, and the propagation time of the water hammer wave in the main crack is calculated.

[0143] The main fracture extension length is calculated based on the average velocity of the water hammer wave in the well and the propagation time of the main fracture in the fracturing process. The calculated value is close to the actual value and can be effectively used for fracturing effect evaluation.

[0144] The second embodiment of a method for calculating the extension length of a hydraulic fracturing main crack provided by the present invention, in this embodiment, takes the fracturing construction of a horizontal well in a shale gas block as an example to illustrate the specific implementation process of the present invention. The horizontal well has a depth of 3500m, a horizontal section length of 1500m, a target layer is a shale reservoir, a formation temperature of 95°C, a formation pressure of 35MPa, and a minimum horizontal principal stress of 45MPa.

[0145] This fracturing operation uses slick water fracturing fluid, with a designed injection volume of 1200m 3 , displacement is 12m 3 / minute, and the sand filling volume fraction is 15%. During the fracturing construction, staged fracturing is carried out at 11 perforation clusters, each perforation cluster is 0.8m long, the perforation density is 16 holes / m, and the distance between adjacent perforation clusters is 15m. The bridge plug is installed 3200m from the wellhead to achieve staged fracturing.

[0146] During the fracturing process, a high-frequency pressure gauge is used to collect pressure data at the wellhead, with a sampling frequency of 1000Hz and a collection time of 120s after the pump is stopped. The pressure measurement range of the high-frequency pressure gauge is 0 to 100MPa, with an accuracy of 0.01MPa. At the same time, an optical fiber temperature measurement system is used to monitor the wellbore temperature, with a temperature measurement accuracy of 0.1℃.

[0147] The water hammer wave signal was recorded immediately after the pump was stopped, and the original pressure data obtained are shown in Table 1.

[0148] Table 1: Wellhead pressure data after pump shutdown (partial)

[0149] Time (seconds) Pressure(MPa) 0.000 45.263 0.001 45.258 0.002 45.251 0.003 45.245 0.004 45.238 0.005 45.232 0.006 45.225 0.007 45.219 0.008 45.212 0.009 45.206 0.010 45.199

[0150] The collected pressure data is first analyzed by complex cepstrum. The complex cepstrum of the water hammer wave signal is obtained through Fourier transform, modulus, logarithmic operation and inverse Fourier transform. The complex cepstrum curve is analyzed to identify the positive pulse extreme points, and the minimum period between adjacent extreme points is calculated to be 4.267s, which is the round-trip propagation time of the water hammer wave from the wellhead to the bridge plug.

[0151] Based on the actual distance of 3200m from the wellhead to the bridge plug and the propagation time of 4.267s, the average speed of the water hammer wave in the well is preliminarily calculated to be 1498.24m / s. Considering the influence of pressure and temperature, a correction calculation is required. During the pump stop process, the wellbore pressure change was monitored to be 2.5MPa and the temperature change was 1.2℃. The pressure correction coefficient was selected as 0.003 and the temperature correction coefficient was 0.0003. The corrected average speed of the water hammer wave was 1505.83m / s.

[0152] When performing local signal analysis on water hammer wave signals, a typical rising segment is selected with a time length of 0.5s and 500 data points. First, linear trend removal is performed, and the linear trend coefficient a is calculated to be negative 0.0856 and b is 45.263. The noise correction coefficient is selected as 0.2 and the signal noise standard deviation is 0.005MPa, and the data after detrending is corrected.

[0153] Perform spectrum analysis on the corrected local signal. Use Hanning window function for weighting, and then perform discrete Fourier transform. In the spectrum analysis, select the spectrum correction coefficient as 0.03 and the frequency attenuation coefficient as 0.003. Through peak detection, identify the main peak in the spectrum, where the frequency corresponding to the maximum peak is 23.15Hz, which is the response frequency in the main crack.

[0154] The propagation time of the water hammer wave in the main crack is calculated based on the response frequency. Taking into account the changes in the properties of the fracturing fluid, the measured changes in fracturing fluid viscosity are 15 Pa.s and density are 50 kg / m 3The fluid viscosity correction coefficient is selected as 0.0003 and the density correction coefficient is selected as 0.00003, and the propagation time of the water hammer wave in the main crack is calculated to be 0.0216s.

[0155] Finally, the extension length of the main crack was calculated. During the calculation process, considering the influence of formation parameters, the change in rock elastic modulus was measured to be 5 GPa and the change in horizontal ground stress was 3 MPa. The elastic modulus correction coefficient was selected as 0.0003 and the horizontal stress correction coefficient was selected as 0.003. The final calculation showed that the extension length of the main crack was 32.56 m.

[0156] To verify the reliability of the calculation results, microseismic monitoring and production testing were carried out after the fracturing was completed. The microseismic monitoring results showed that the distribution range of the earthquake source was basically consistent with the calculated extension length of the main fracture, with an error of less than 10%. The production test data showed that the gas production of this section after fracturing transformation reached 35,000 cubic meters per day, which was consistent with the expected transformation effect.

[0157] It can be seen from this embodiment that the method of the present invention has the following advantages: First, a high-frequency pressure meter is used to collect data, and the equipment is simple, easy to operate, and low in cost. Second, the characteristic information of the water hammer wave signal is effectively extracted by combining complex cepstrum analysis and spectrum analysis. Third, multiple influencing factors such as pressure, temperature, fluid properties, and formation parameters are considered to improve the calculation accuracy. Fourth, the calculation results are in good consistency with the results of other monitoring methods, which verifies the reliability of the method.

[0158] In practical applications, the method of the present invention can adjust parameters according to specific working conditions. For example, a suitable correction factor can be selected according to the formation conditions and the characteristics of the fracturing process. For different types of reservoirs, the elastic modulus correction factor can be adjusted according to the rock mechanics properties. For different fracturing fluid systems, the viscosity and density correction factors can be adjusted according to the fluid properties. This flexibility makes the method highly adaptable.

[0159] This example also shows that this method can be used not only for evaluating a single fracturing stage, but can also be extended to evaluating the fracturing effect of the entire horizontal well. By analyzing multiple fracturing stages, the distribution characteristics of the fracture network can be obtained, providing a basis for optimizing the fracturing process. At the same time, the real-time characteristics of this method enable it to perform dynamic monitoring during the fracturing construction process, and to promptly discover and solve problems.

[0160] From the perspective of engineering application, the implementation cost of the method of the present invention is much lower than traditional methods such as microseismic monitoring. Taking this embodiment as an example, the main equipment investment only includes high-frequency pressure gauges and data acquisition systems, with a total cost of about RMB 100,000, while the investment in microseismic monitoring systems is usually more than RMB 1 million. In addition, the data processing process of the method can be automated, greatly reducing labor costs.

[0161] During the construction process, the calculation results of this method can guide the adjustment of fracturing parameters in real time. For example, if it is found that the extension length of the main crack of a certain fracturing section is significantly deviated from the design value, the construction parameters of the subsequent fracturing section, such as injection volume, displacement or proppant concentration, can be adjusted in time. This real-time optimization capability is of great significance for improving the effect of fracturing construction.

[0162] In general, this example fully demonstrates the application process of the method of the present invention in shale gas horizontal well fracturing. Through detailed data collection, processing and analysis, a reliable main fracture extension length evaluation result is finally obtained. The implementation process shows that the method has the characteristics of simple operation, low cost, reliable accuracy, etc., and provides a practical evaluation tool for hydraulic fracturing engineering.

[0163] The third embodiment of a method for calculating the extension length of the main fracture of hydraulic fracturing provided by the present invention, in this embodiment, takes the fracturing transformation of a vertical well in a loose sandstone reservoir as an example to illustrate the specific implementation process of the present invention. The oil well is 2800 meters deep, the target layer is a loose sandstone reservoir, the porosity is 25%, the permeability is 85×10^(-3) microns square, the formation temperature is 85°C, the formation pressure is 28 MPa, the minimum horizontal principal stress is 38 MPa, the Young's modulus is 15 GPa, and the Poisson's ratio is 0.25.

[0164] This fracturing operation uses a low-damage fracturing fluid system with a viscosity of 35 millipascals and a density of 1.15 grams per cubic centimeter. The total amount of fracturing fluid injected is designed to be 800 cubic meters, the construction displacement is 8 cubic meters per minute, and the proppant is 40 / 70 mesh ceramsite, with a designed maximum proppant concentration of 500 kilograms per cubic meter. The bridge plug is installed 2,650 meters from the wellhead, and the target length of the fracturing operation is 50 meters.

[0165] A high-frequency pressure gauge is installed at the wellhead, with a sampling frequency of 2000 Hz, a measurement accuracy of 0.01 MPa, and a pressure measurement range of 0 to 80 MPa. A high-precision temperature sensor is also installed with a temperature measurement accuracy of 0.1°C. The fracturing fluid storage tank is equipped with a density meter and a viscometer to monitor the changes in the properties of the fracturing fluid in real time.

[0166] After stopping the pump, the original data of the water hammer wave signal is recorded for complex cepstrum analysis. First, the collected pressure signal x(t) is Fourier transformed:

[0167]

[0168] Then calculate the amplitude spectrum of the signal:

[0169]

[0170] Take the natural logarithm of the magnitude spectrum:

[0171] Y(ω)=ln|X(ω)|;

[0172] Finally, perform inverse Fourier transform to obtain the complex cepstrum:

[0173]

[0174] By analyzing the complex cepstrum curve, the positive pulse extreme points are extracted, and the time difference between adjacent extreme points is shown in Table 2.

[0175] Table 2: Time difference of positive pulse extreme points of complex cepstrum

[0176] Serial number Time difference (seconds) 1 3.852 2 3.865 3 3.849 4 3.858 5 3.861

[0177] The minimum value of 3.849 seconds is taken as the round-trip propagation time T of the water hammer wave in the wellbore. According to the distance from the wellhead to the bridge plug d = 2650m, the average speed of the water hammer wave in the well is preliminarily calculated:

[0178]

[0179] Considering the influence of pressure and temperature, the measured wellbore pressure change Δp = 3.2MPa, the temperature change ΔT f =1.8℃. Select the pressure correction coefficient α=0.004, the temperature correction coefficient β=0.0004, the corrected average velocity of the water hammer wave is:

[0180]

[0181] Perform local analysis on the water hammer wave signal and select the data segment within 0.5 seconds after the pump is stopped. Suppose the original data is x k (t), first calculate the linear trend coefficient:

[0182]

[0183] Select the noise correction factor γ = 0.25 and calculate the signal noise standard deviation σ n =0.006MPa, remove the trend and correct the noise of the data:

[0184] y k (t) = x k (t)-(at+b)+γσ n .

[0185] Perform spectrum analysis on the corrected data. First, perform windowing, using the Hamming window:

[0186]

[0187] Where N is the number of data points. Perform discrete Fourier transform on the windowed data:

[0188]

[0189] Select the spectrum correction coefficient λ=0.035, the frequency attenuation coefficient μ=0.0035, the corrected spectrum is:

[0190] Y k ′(ω)=|Y k (ω)|+λe -μω .

[0191] By peak detection, the main peak points in the spectrum are found, as shown in Table 3.

[0192] Table 3: Main peak points of the spectrum

[0193]

[0194]

[0195] The frequency corresponding to the maximum amplitude, 18.25 Hz, is selected as the response frequency ω′ in the main crack.

[0196] When calculating the propagation time of the water hammer wave in the main fracture, the change of fluid properties is taken into account. The measured change of fracturing fluid viscosity Δη=12Pa.s, and the change of density Δρ=45kg / m 3 Select the fluid viscosity correction coefficient δ = 0.00035, density correction coefficient θ = 0.000035, and calculate the propagation time:

[0197]

[0198] Finally, the extension length of the main crack was calculated. The change in rock elastic modulus ΔE = 4.5 GPa and the change in horizontal ground stress Δσ h =2.8MPa. Select elastic modulus correction coefficient φ=0.00035, horizontal stress correction coefficient ψ=0.0035, and calculate the main crack extension length:

[0199]

[0200] In order to verify the accuracy of the calculation results, the following verification work was carried out:

[0201] (1) Sonic logging verification: After the fracturing was completed, the acoustic logging was performed and the main fracture extension range was measured to be about 21 to 24 m, which was basically consistent with the calculation results;

[0202] (2) Production dynamic verification: After fracturing transformation, the production data of the well are shown in Table 4.

[0203] Table 4: Comparison of production data before and after fracturing

[0204] parameter Before fracturing After fracking Daily oil production (tons) 2.5 15.8 Moisture content (%) 12.5 15.2 Dynamic liquid level (m) 1850 1620 Bottom hole pressure (MPa) 18.5 16.8

[0205] Production data show that the fracturing stimulation has achieved good results, which matches the calculated main fracture extension length.

[0206] (3) Fracturing fluid flowback verification: Within 48 hours after fracturing, the fracturing fluid flowback rate reached 65%, and the proppant carryback rate was less than 0.5%, indicating that a stable propped fracture was formed, which was consistent with the calculation results.

[0207] The specific implementation process of this embodiment shows that:

[0208] The signal processing methods are effective: complex cepstrum analysis can accurately extract the propagation time of water hammer waves in the wellbore, and spectrum analysis can reliably identify the response frequency in the main fracture;

[0209] The application of this embodiment shows that the method can be extended to similar oil and gas well fracturing projects. Whether it is vertical well fracturing or horizontal well fracturing, the calculation results have high reliability. The main fracture extension length information obtained by this method can guide the subsequent fracturing parameter optimization and production plan formulation.

[0210] This method can not only evaluate the effect of a single fracturing, but also be used to optimize the design of staged fracturing. By real-time monitoring of the extension length of the main cracks in each stage of fracturing, the fracturing parameters can be dynamically adjusted to improve the overall transformation effect. This optimization capability is of great significance for improving the economy and effectiveness of fracturing construction.

[0211] In summary, this embodiment uses an oil well fracturing case to demonstrate in detail the implementation process and effect verification of the method of the present invention. The results show that the method has the advantages of high reliability, simple operation, and low cost, and provides a practical evaluation tool for oil and gas well fracturing engineering. At the same time, this embodiment also provides a valuable reference for the promotion and application of the method.

[0212] The technical principle of the present invention is based on the propagation characteristics of water hammer waves in the wellbore and the fractures. When the pump is stopped during fracturing, a water hammer wave is formed in the wellbore due to a sudden change in pressure, and the wave propagates back and forth between the wellbore and the main fracture. By analyzing the propagation characteristics of the water hammer wave signal, the extension length information of the main fracture can be obtained.

[0213] The following table shows the formula symbols and their meanings used in the present invention:

[0214] Table 5: Symbols and meanings used in the present invention

[0215]

[0216] Specifically, the present invention first uses complex cepstrum analysis technology to process water hammer wave signals. Complex cepstrum is the inverse Fourier transform of the logarithm of the signal spectrum, which has the advantage of extracting periodic components. Through complex cepstrum analysis, the round-trip propagation time of the water hammer wave in the wellbore can be accurately obtained. The ratio of this time to the wellbore length can be used to calculate the average propagation speed of the water hammer wave in the well.

[0217] In terms of spectrum analysis, the present invention processes the local signal of the water hammer wave. By removing the linear trend, the non-stationary influence of the signal can be eliminated. The spectrum analysis can obtain the response characteristics of the water hammer wave in the main crack, and in particular, by extracting the fundamental frequency of the spectrum, the propagation time of the water hammer wave in the main crack can be calculated.

[0218] The scientific nature of this method is reflected in the following aspects: on the one hand, it is based on reliable physical principles, namely the propagation characteristics of water hammer waves; on the other hand, it uses advanced signal processing methods, including complex cepstrum analysis and spectrum analysis. By combining physical principles with signal processing technology, a complete main crack extension length evaluation system is established.

[0219] The technical solution of the present invention is logical. It starts from signal acquisition, goes through steps such as signal processing and parameter extraction, and finally obtains the main crack extension length. Each step has sufficient theoretical basis and practical foundation, forming a complete technical chain. This method not only takes into account the complexity of the physical process, but also takes into account the feasibility of engineering application, so it can effectively solve the technical problem of main crack extension length evaluation.

Claims

1. A method for calculating the extension length of a main fracture of a hydraulic fracturing, comprising the following steps: S10, using a high-frequency pressure gauge to obtain a water hammer wave signal at the wellhead after the hydraulic fracturing pump is stopped; S20, converting the water hammer wave signal into a complex cepstrum, and performing cepstrum analysis on the water hammer wave signal; S30, calculating the minimum period between the positive pulse extreme points in the complex cepstrum curve, and taking half of the minimum period as the time for the water hammer wave to move from the wellhead to the bridge plug; S40, calculating the average speed of the water hammer wave moving in the well according to the time it takes for the water hammer wave to move from the wellhead to the bridge plug and the distance from the wellhead to the bridge plug; S50, performing linear trend removal processing on the local signal of the water hammer wave in the rising stage or the falling stage along the wellbore; S60, performing Fourier transform on the local signal after the linear trend removal process to obtain a water hammer wave local signal spectrum; S70, extracting the fundamental frequency corresponding to the maximum point in the spectrum of the local signal of the water hammer wave as the response frequency in the main crack; S80, calculating the propagation time of the water hammer wave in the main crack according to the response frequency in the main crack; S90, calculating the extension length of the main fracture according to the average speed of the water hammer wave moving in the well and the propagation time of the water hammer wave in the main fracture.

2. A method for calculating the extension length of a hydraulic fracturing main crack according to claim 1, characterized in that: The S20 specifically includes: Performing Fourier transform on the water hammer wave signal to obtain a signal spectrum; Performing a modulo operation on the signal spectrum to obtain a signal amplitude spectrum; Performing a natural logarithm operation on the signal amplitude spectrum to obtain a logarithmic spectrum; Performing inverse Fourier transform on the logarithmic spectrum to obtain a complex cepstrum of the water hammer wave signal; Extracting the amplitude of the complex cepstrum by using square root operations of the real domain part and the imaginary domain part; A peak detection method is used to extract the maximum point of the complex cepstrum amplitude.

3. A method for calculating the extension length of a hydraulic fracturing main crack according to claim 2, characterized in that: The S30 specifically includes: Extracting the frequency corresponding to the maximum value of the water hammer wave signal amplitude spectrum, and taking the inverse of the frequency as the movement period of the water hammer wave along the rising stage or the descending stage of the wellbore; identifying a positive pulse region in the complex cepstrum curve according to the motion period; Performing a local extreme value search in the positive pulse region and marking the position of the extreme value point; Calculate the time intervals between adjacent extreme points and obtain multiple period values; Averaging the multiple period values ​​to obtain an average period value; Half of the average period value is taken as the time for the water hammer wave to move from the wellhead to the bridge plug.

4. A method for calculating the extension length of a hydraulic fracturing main crack according to claim 3, characterized in that: The S40 specifically includes: The actual distance from the wellhead to the bridge plug is obtained according to the drilling data as the water hammer wave propagation distance; The water hammer wave propagation distance is divided by the time it takes to move from the wellhead to the bridge plug to calculate the average speed of the water hammer wave moving in the well.

5. A method for calculating the extension length of a hydraulic fracturing main crack according to claim 4, characterized in that: The S50 specifically includes: Identify the rising and falling segments of the water hammer wave signal and extract the local signal; Fitting the linear trend of the local signal using the least square method; The calculated linear trend coefficients, including slope and intercept, generate a trend signal with the same length as the input signal; The linear trend is subtracted from the local signal to obtain a local signal after the linear trend is removed.

6. A method for calculating the extension length of a hydraulic fracturing main crack according to claim 5, characterized in that: The S60 specifically includes: Frame and window the local signal after removing the linear trend; Perform fast Fourier transform on the windowed signal; The fast Fourier transform result is modulo to obtain the amplitude of each frequency component; The frequency and amplitude within the Nyquist frequency range are taken as the spectrum of the local signal.

7. A method for calculating the extension length of a hydraulic fracturing main crack according to claim 6, characterized in that: The S70 specifically includes: Performing peak detection on the local signal spectrum of the water hammer wave; Searching for a frequency point satisfying a peak condition in the frequency spectrum; The frequency points are sorted from small to large, and only the minimum frequency point whose frequency is a multiple relationship is extracted as the fundamental frequency; The fundamental frequency is selected as the response frequency in the main crack.

8. A method for calculating the extension length of a hydraulic fracturing main crack according to claim 7, characterized in that: The S80 specifically includes: The reciprocal of the main crack response frequency is taken and divided by 2 to obtain the propagation time of the water hammer wave in the main crack.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores program instructions, which, when executed, are used to execute the method for calculating the extension length of a main hydraulic fracturing crack as described in any one of claims 1 to 8.

10. A system for calculating the extension length of a main fracture of a hydraulic fracturing, comprising the computer-readable storage medium of claim 9.

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