A method, medium, and system for calculating a hydraulic fracture main fracture length

Abstract

The application provides a method, medium and system for calculating the propagation length of a main hydraulic fracturing fracture, and belongs to the technical field of hydraulic fracturing. The method, medium and system for calculating the propagation length of a main hydraulic fracturing fracture comprise the following steps: obtaining a water hammer wave signal at a wellhead position after hydraulic fracturing pump stopping; performing cepstrum analysis on the water hammer wave signal; calculating the minimum period of a positive pulse extreme point of a complex cepstrum curve to obtain the time for the water hammer wave to move from the wellhead to a bridge plug; calculating the average speed of the water hammer wave in the well; performing linear trend removal processing on a local signal of the water hammer wave; performing Fourier transform on the local signal after linear trend removal processing to obtain a water hammer wave local signal spectrum; 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 fracture; calculating the propagation time of the water hammer wave in the main fracture according to the response frequency in the main fracture; and calculating the propagation length of the main fracture.

Description

Technical Field

[0001] This invention belongs to the field of hydraulic fracturing technology, and specifically relates to a method, medium, and system for calculating the extension length of the main fracture in hydraulic fracturing. Background Technology

[0002] Hydraulic fracturing, as an important oil and gas production enhancement technique, has been widely applied globally. This technology injects high-pressure fluids into the formation, creating a complex network of fractures to improve the permeability and production capacity of oil and gas reservoirs. During hydraulic fracturing, the main fracture is one of the most important fluid channels, and its extension length is crucial for reservoir development. Assessing the main fracture extension length directly affects fracture stability and production capacity, making it essential for optimizing fracturing design and increasing oil and gas production. Furthermore, it indirectly determines the amount of proppant required, avoiding unnecessary proppant waste and the cost of refracking, thus maximizing the protection of groundwater resources and the ecological environment, and achieving sustainable development in oil and gas extraction.

[0003] Currently, methods for assessing the propagation length of the main fracture primarily include microseismic monitoring and electromagnetic detection techniques. Microseismic monitoring tracks fracture propagation by recording minute seismic events generated during fracturing on the surface or in the well. However, this method is limited by environmental noise, formation conditions, and the placement of monitoring equipment, and it is also costly. Electromagnetic detection involves charging underground fluids through the wellbore to generate an electromagnetic field within the fracture, thus detecting the fracture. However, its detection resolution is low, making it difficult to capture the complete propagation information of the main fracture in real time and accurately. Furthermore, the propagation behavior of the main fracture is influenced by various factors, including in-situ stress distribution, rock mechanical properties, and fracturing fluid properties. The complexity and uncertainty of these factors pose a significant challenge to the accurate assessment of the main fracture propagation length.

[0004] Furthermore, with the deepening development of unconventional oil and gas resources and continuous innovation in fracturing technology, traditional assessment methods are no longer sufficient to meet the demands of efficient and convenient new fracturing processes. Especially in shale gas development, the applicability of existing assessment methods is significantly limited due to the strong heterogeneity of formations and complex stress environments. Therefore, there is an urgent need to develop a new method for assessing the main fracture propagation length to improve assessment 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 in hydraulic fracturing, which can solve the problem of the lack of an accurate assessment method for the extension length of the main fracture, reduce the influence of factors such as geostress distribution, rock mechanical properties, fracturing fluid properties and monitoring equipment on traditional assessment methods, improve detection accuracy and reduce monitoring costs.

[0006] This invention is implemented as follows:

[0007] This invention provides a method for calculating the extension length of the main fracture in hydraulic fracturing. The method includes the following steps:

[0008] S10. Use a high-frequency pressure gauge to obtain the water hammer wave signal at the wellhead location after hydraulic fracturing pump shutdown.

[0009] S20. Convert the water hammer wave signal into a complex cepstrum and perform cepstrum analysis on the water hammer wave signal;

[0010] S30. Calculate the minimum period between the extreme points of the positive pulse in the complex cepstrum curve, and take half of the minimum period as the time for the water hammer wave to travel from the wellhead to the bridge plug.

[0011] S40. Calculate the average velocity of the water hammer wave in the well based on the time it takes for the water hammer wave to travel from the wellhead to the bridge plug and the distance from the wellhead to the bridge plug.

[0012] S50. Perform linear trend removal processing on the local signal of the water hammer wave during the rising or falling phase along the wellbore.

[0013] S60. Perform Fourier transform on the local signal after the linear trend removal process to obtain the local signal spectrum of the water hammer wave;

[0014] S70. Extract the fundamental frequency corresponding to the maximum point in the local signal spectrum of the water hammer wave, and use it as the response frequency in the main crack.

[0015] S80. Calculate the propagation time of the water hammer wave in the main crack based on the response frequency in the main crack;

[0016] S90. Calculate the main fracture extension length based on the average velocity of the water hammer wave in the well and the propagation time of the water hammer wave in the main fracture.

[0017] Based on the above technical solution, the method for calculating the propagation length of the main fracture in hydraulic fracturing according to the present invention can be further improved as follows:

[0018] Specifically, S20 includes:

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

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

[0021] Perform a natural logarithmic operation on the amplitude spectrum of the signal to obtain the logarithmic spectrum;

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

[0023] The amplitude of the complex cepstrum is extracted by taking the square root of the sum of the squares of the real and imaginary parts.

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

[0025] Furthermore, S30 specifically includes:

[0026] Extract the frequency corresponding to the maximum value of the amplitude spectrum of the water hammer wave signal, and take the reciprocal of the frequency as the motion period of the water hammer wave during the rising or falling phase along the wellbore.

[0027] Identify the positive pulse region in the complex cepstral curve based on the motion period;

[0028] Perform a local extremum search within the positive pulse region and mark the extremum point locations;

[0029] Calculate the time interval between adjacent extreme points to obtain multiple periodic values;

[0030] The average of the multiple periodic values ​​is used as the average periodic value.

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

[0032] Furthermore, S40 specifically includes:

[0033] The actual distance from the wellhead to the bridge plug is obtained from the drilling data and used as the propagation distance of the water hammer wave.

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

[0035] Furthermore, S50 specifically includes:

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

[0037] The linear trend of the local signal is fitted using the least squares method;

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

[0039] Subtracting the linear trend from the local signal yields the local signal after removing the linear trend.

[0040] Furthermore, S60 specifically includes:

[0041] Framing and windowing are performed on the local signal after removing linear trends;

[0042] Perform a Fast Fourier Transform on the windowed signal;

[0043] The amplitude of each frequency component is obtained by taking the modulus of the Fast Fourier Transform result;

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

[0045] Furthermore, S70 specifically includes:

[0046] Peak detection is performed on the local signal spectrum of the water hammer wave;

[0047] Search the frequency points in the spectrum that satisfy the peak condition;

[0048] The frequency points are sorted from smallest to largest, and only the smallest frequency point that is a multiple of the previous frequency point is extracted as the fundamental frequency.

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

[0050] Furthermore, S80 specifically includes:

[0051] The propagation time of the water hammer wave in the main fracture is obtained by taking the reciprocal of the main fracture response frequency and dividing it by 2.

[0052] Furthermore, S90 specifically includes:

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

[0054] The complex cepstral transform expression for the water hammer wave signal is as follows:

[0055]

[0056] In the formula, 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 water hammer wave time-domain signal, in MPa; t is time, in s; ln is the natural logarithm function.

[0057] The expression for calculating the average velocity of the water hammer wave moving in the well is as follows:

[0058]

[0059] In the formula, d is the average velocity of the water hammer wave moving 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 travel along the wellbore from the wellhead to the bridge plug, in s.

[0060] The expression for removing the linear trend of local signals from water hammer waves is as follows:

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

[0062] in:

[0063]

[0064]

[0065] In the formula, y k (t) represents the data of the k-th local signal of the water hammer wave after delinearization, in MPa; x k (t) represents the local signal of the k-th water hammer wave, in MPa; t represents the time series of the local signal, in seconds; n represents the length of the time series.

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

[0067] y k (ω)=|F[y k (t)]|;

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

[0069] The expression for calculating the water hammer wave propagation time in the main fracture is as follows:

[0070]

[0071] In the formula, 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 formula for calculating the main crack propagation length is as follows:

[0073]

[0074] In the formula, l is the main crack extension length, in meters (m).

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

[0076] 1. Complex cepstral conversion 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 variation of water hammer waves in different periods, which improves the calculation accuracy;

[0078] 3. Linear trend removal further highlights the characteristic frequencies of the main crack signal, making it easier to extract the signal fundamental 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 reciprocal 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 velocity of the water hammer wave propagating in the wellbore and the time law of its propagation in the main fracture, making the results more reliable.

[0082] Compared with existing technologies, the method of this invention:

[0083] 1. Local signals of water hammer waves were extracted and subjected to spectral analysis, which highlighted the characteristics of the crack response;

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

[0085] 3. The dynamic changes in the motion parameters of the water hammer wave were 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 main fracture propagation length in hydraulic fracturing proposed in this invention establishes a complete evaluation system for the main fracture propagation length by analyzing water hammer wave signals and combining cepstral analysis and spectral analysis techniques. This method has the following technical advantages:

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

[0089] Secondly, the method of this invention employs local signal analysis technology, effectively avoiding the effects of signal interference and distortion by processing the rising and falling segments of the water hammer wave signal separately. Simultaneously, the introduction of linear trend removal and other processing methods further improves the accuracy of signal analysis.

[0090] Third, the method of this invention has strong real-time performance and adaptability. By acquiring and analyzing water hammer wave signals in real time, the main fracture propagation length information can be obtained promptly, providing an important basis for optimizing the fracturing process. This method is applicable to various formation conditions and fracturing processes, and has broad application prospects. Attached Figure Description

[0091] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0092] Figure 1 A flowchart of a method for calculating the propagation length of the main fracture in hydraulic fracturing;

[0093] Figure 2 This is a schematic diagram of a three-dimensional hydraulic fracturing model structure in the first embodiment of a method for calculating the main fracture propagation length in hydraulic fracturing.

[0094] Figure 3 This is a waveform diagram of the hydraulic fracturing pump shutdown water hammer wave obtained in the first embodiment of a method for calculating the main fracture extension length in hydraulic fracturing;

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

[0096] Figure 5 In the diagram, a represents the local signal of the water hammer wave before detrending, and b represents the local signal of the water hammer wave after detrending.

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

[0098] Figure 7 This is a waveform diagram of the water hammer wave signal generated by the shutdown of the hydraulic fracturing pump, obtained in the second embodiment of a method for calculating the extension length of the main fracture in hydraulic fracturing.

[0099] Figure 8 This is a local signal spectrum diagram of water hammer waves in the rising or falling phase of a second embodiment of a method for calculating the extension length of the main fracture in hydraulic fracturing. Detailed Implementation

[0100] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

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

[0102] Acquire the water hammer wave signal at the wellhead location after fracturing and pump shutdown;

[0103] Cepstral analysis was performed on the water hammer wave signal to obtain the average velocity of the water hammer wave in the well.

[0104] Spectral analysis of the water hammer wave signal was performed to obtain the propagation time of the water hammer wave in the main fracture of the hydraulic 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.

[0106] As a preferred embodiment of the present invention, the step of performing cepstral 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 the conversion expression is as follows:

[0108]

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

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

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

[0112]

[0113] As a preferred embodiment of the present invention, step (3) specifically includes:

[0114] The local signal x of the water hammer wave during the rising or falling phase along the wellbore k (t) is de-linearized, and its calculation is expressed as follows:

[0115]

[0116] In the formula, y k (t) represents the delinearized trend data of the k-th local signal of the water hammer wave in the rising or falling phase, xk (t) represents the kth local signal of the water hammer wave in the rising or falling phase, where 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 a Fourier transform to obtain a spectrum, the calculation expression of which is as follows:

[0118]

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

[0120] The fundamental frequency corresponding to the local maximum point of the water hammer wave signal spectrum is taken as the response frequency ω′ in the main fracture, and the propagation time t′ of the water hammer wave in the main fracture 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 have constructed a three-dimensional hydraulic fracturing application case, and the scenario settings are as follows: Figure 2 As shown. Specific configuration details are as follows: the inner diameter of the pipe is 0.2m; the distance from the bridge plug along the wellbore to the wellhead is approximately 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. A perforation with an inner diameter of 0.015m exists at a distance of 2900m from the wellhead along the wellbore, connecting to the main fracture. Here, the main fracture is equivalent to a cuboid fracture network with dimensions of 40m x 1cm x 10m. Fluid parameters: initial flow rate is 0.27m³ / s. 3 / s, with an initial pressure of 600 atm.

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

[0124] right Figure 3 Cepstral analysis was performed on the water hammer wave signal.

[0125] The complex cepstral spectrum of the water hammer wave signal was calculated, and the result is as follows: Figure 4 As 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 = 2.289s for the water hammer wave to travel along the wellbore from the wellhead to the bridge plug.

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

[0128] right Figure 3 Spectral analysis was performed on the water hammer wave signal.

[0129] Delinearize the local signal of the water hammer wave during its rising or falling phase along the wellbore, such as... Figure 5 As shown.

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

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

[0132] The main fracture extension length is calculated based on the average velocity of the water hammer wave in the well and its propagation time in the main fracturing fracture. The calculated value has little error compared to the actual value and can be effectively used for evaluating fracturing effects.

[0133] The following is another application scenario of this embodiment. In this scenario, we constructed a hydraulic fracturing application case with the following specific configuration details: the inner diameter of the pipe is 0.2m, the distance from the bridge plug along the wellbore to the wellhead is approximately 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. A perforation with an inner diameter of 0.015m exists at a distance of 2900m from the wellhead along the wellbore, connecting it to the main fracture. Here, the main fracture is equivalent to a cuboid fracture network with dimensions of 50m x 1cm x 10m. Fluid parameters: initial flow rate is 0.27m³ / s. 3 / s, with an initial pressure of 600 atm.

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

[0135] right Figure 3 Cepstral analysis was performed on the water hammer wave signal.

[0136] The complex cepstral spectrum of the water hammer wave signal was calculated, and the result is as follows: Figure 4 As 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 = 2.289s for the water hammer wave to travel along the wellbore from the wellhead to the bridge plug.

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

[0139] right Figure 3 Spectral analysis was performed on the water hammer wave signal.

[0140] Delinearize the local signal of the water hammer wave during its rising or falling phase along the wellbore, such as... Figure 5 As shown.

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

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

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

[0144] This invention provides a second embodiment of a method for calculating the extension length of the main fracture in hydraulic fracturing. In this embodiment, the specific implementation process of the invention is illustrated using a horizontal well fracturing operation in a shale gas block as an example. The horizontal well has a depth of 3500m, a horizontal section length of 1500m, a target layer of shale reservoir, a formation temperature of 95℃, a formation pressure of 35MPa, and a minimum horizontal principal stress of 45MPa.

[0145] This fracturing operation used slickwater fracturing fluid, with a designed injection volume of 1200m³. 3 Displacement is 12m 3 The fracturing speed was 15% per minute, with a sand filling volume fraction of 15%. During the fracturing operation, staged fracturing was performed at 11 perforation clusters, each cluster being 0.8m long with a perforation density of 16 perforations / m and a spacing of 15m between adjacent clusters. A bridge plug was installed 3200m from the wellhead to facilitate staged fracturing.

[0146] During fracturing operations, a high-frequency pressure gauge was used to collect pressure data at the wellhead. The sampling frequency was 1000 Hz, and the data acquisition time was 120 seconds after the pump was stopped. The pressure measurement range of the high-frequency pressure gauge was 0 to 100 MPa, with an accuracy of 0.01 MPa. Simultaneously, a fiber optic temperature measurement system was used to monitor the wellbore temperature, with a measurement accuracy of 0.1℃.

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

[0148] Table 1: Partial Wellhead Pressure Data After Pump Shutdown

[0149] Time (seconds) Pressure (megapascals) 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 were first subjected to complex cepstrum analysis. Through Fourier transform, modulus taking, logarithmic operation, and inverse Fourier transform, the complex cepstrum of the water hammer wave signal was obtained. Analyzing the complex cepstrum curve, the extreme points of the positive pulse were identified, and the minimum period between adjacent extreme points was calculated to be 4.267 s, 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 initial calculation yielded an average water hammer wave velocity of 1498.24m / s in the well. Considering the effects of pressure and temperature, a correction calculation is required. During the pump shutdown process, a wellbore pressure change of 2.5MPa and a temperature change of 1.2℃ were monitored. Using a pressure correction factor of 0.003 and a temperature correction factor of 0.0003, the corrected average water hammer wave velocity is 1505.83m / s.

[0152] When performing local signal analysis on the water hammer wave signal, a typical rising segment with a duration of 0.5 s and containing 500 data points was selected. First, linear trend removal was performed, and the calculated linear trend coefficients a and b were -0.0856 and 45.263, respectively. A noise correction factor of 0.2 and a signal noise standard deviation of 0.005 MPa were selected to correct the detrended data.

[0153] Spectral analysis was performed on the corrected local signal. A Hanning window function was used for weighting, followed by a Discrete Fourier Transform. In the spectral analysis, a spectral correction coefficient of 0.03 and a frequency attenuation coefficient of 0.003 were selected. Peak detection identified the main peaks in the spectrum, with the maximum peak corresponding to a frequency of 23.15 Hz, which is the response frequency in the main crack.

[0154] The propagation time of the water hammer wave in the main fracture was calculated based on the response frequency. Considering the changes in fracturing fluid properties, the viscosity change was measured to be 15 Pa·s, and the density change to be 50 kg / m³. 3With a fluid viscosity correction factor of 0.0003 and a density correction factor of 0.00003, the propagation time of the water hammer wave in the main crack was calculated to be 0.0216 s.

[0155] Finally, the main fracture extension length was calculated. During the calculation, considering the influence of formation parameters, the measured change in rock elastic modulus was 5 GPa, and the change in horizontal stress was 3 MPa. An elastic modulus correction factor of 0.0003 and a horizontal stress correction factor of 0.003 were selected, and the final calculated main fracture extension length was 32.56 m.

[0156] To verify the reliability of the calculation results, microseismic monitoring and production tests were conducted after fracturing. Microseismic monitoring results showed that the distribution range of the seismic sources basically matched the calculated main fracture extension length, with an error within 10%. Production test data indicated that the gas production of this section after fracturing reached 35,000 cubic meters per day, consistent with the expected modification effect.

[0157] As can be seen from this embodiment, the method of the present invention has the following advantages: First, it uses a high-frequency pressure gauge to collect data, which is simple, easy to operate, and low in cost. Second, by combining complex cepstral analysis and spectral analysis, the characteristic information of the water hammer wave signal is effectively extracted. Third, it considers multiple influencing factors such as pressure, temperature, fluid properties, and formation parameters, thus improving the calculation accuracy. Fourth, the calculation results show good consistency with the results of other monitoring methods, verifying the reliability of the method.

[0158] In practical applications, the method of this invention can be adjusted according to specific working conditions. For example, appropriate correction coefficients can be selected based on formation conditions and fracturing process characteristics. For different types of reservoirs, the elastic modulus correction coefficient can be adjusted based on rock mechanical properties. For different fracturing fluid systems, the viscosity and density correction coefficients can be adjusted based on fluid properties. This flexibility makes the method highly adaptable.

[0159] This embodiment also demonstrates that this method can be used not only for evaluating individual fracturing sections but also for evaluating the fracturing effect of the entire horizontal well. By analyzing multiple fracturing sections, the distribution characteristics of the fracture network can be obtained, providing a basis for optimizing the fracturing process. Furthermore, the real-time nature of this method allows for dynamic monitoring during fracturing operations, enabling timely detection and resolution of problems.

[0160] From an engineering application perspective, the implementation cost of the method of this invention is far lower than that of traditional methods such as microseismic monitoring. Taking this embodiment as an example, the main equipment investment includes only a high-frequency pressure gauge and a data acquisition system, with a total cost of approximately RMB 100,000, while the investment in a microseismic monitoring system typically exceeds RMB one million. Furthermore, the data processing of this method can be automated, significantly reducing labor costs.

[0161] During construction, the calculation results of this method can guide the adjustment of fracturing parameters in real time. For example, if the main fracture length of a certain fracturing segment deviates significantly from the design value, the construction parameters of subsequent fracturing segments, such as injection volume, displacement, or proppant concentration, can be adjusted promptly. This real-time optimization capability is of great significance for improving the effectiveness of fracturing operations.

[0162] In summary, this embodiment fully demonstrates the application process of the present invention's method in shale gas horizontal well fracturing. Through detailed data acquisition, processing, and analysis, reliable assessment results of the main fracture propagation length were obtained. The implementation process shows that this method is simple to operate, low in cost, and reliable in accuracy, providing a practical assessment tool for hydraulic fracturing engineering.

[0163] This invention provides a third embodiment of a method for calculating the extension length of the main fracture in hydraulic fracturing. In this embodiment, the specific implementation process of the invention is illustrated using the fracturing stimulation of a vertical well in a loose sandstone oil reservoir as an example. The well is 2800 meters deep, the target layer is a loose sandstone reservoir with a porosity of 25%, a permeability of 85 × 10^(-3) micrometers squared, a formation temperature of 85℃, a formation pressure of 28 MPa, a minimum horizontal principal stress of 38 MPa, a Young's modulus of 15 GPa, and a Poisson's ratio of 0.25.

[0164] This fracturing operation employed a low-damage fracturing fluid system with a viscosity of 35 mPa·s and a density of 1.15 g / cm³. The designed total injection volume of fracturing fluid was 800 cubic meters, with a flow rate of 8 cubic meters per minute. 40 / 70 mesh ceramsite was used as proppant, with a designed maximum proppant concentration of 500 kg / m³. The bridge plug was installed 2650 meters from the wellhead, and the target fracturing section length was 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℃. The fracturing fluid storage tank is equipped with a densitometer and a viscometer to monitor changes in the fracturing fluid properties in real time.

[0166] After the pump was stopped, the raw data of the water hammer wave signal were recorded and subjected to complex cepstral analysis. First, a Fourier transform was performed on the acquired pressure signal x(t):

[0167]

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

[0169]

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

[0171] Y(ω) = ln|X(ω)|;

[0172] Finally, an inverse Fourier transform is performed to obtain the complex cepstral:

[0173]

[0174] By analyzing the complex cepstral curves, the extreme points of the positive pulses were extracted, and the time difference between adjacent extreme points is shown in Table 2.

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

[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. Based on the distance d from the wellhead to the bridge plug being 2650m, the average velocity of the water hammer wave in the well is preliminarily calculated:

[0178]

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

[0180]

[0181] A local analysis of the water hammer wave signal was performed, selecting the data segment within 0.5 seconds after the pump stopped. Let the original data be x. k (t), first calculate the linear trend coefficient:

[0182]

[0183] Selecting a noise correction factor γ = 0.25, calculate the signal-to-noise standard deviation σ. n =0.006MPa, performing trend removal and noise correction on the data:

[0184] y k (t)=x k (t)-(at+b)+γσ n .

[0185] Spectral analysis was performed on the corrected data. First, windowing was applied using a Hamming window:

[0186]

[0187] Where N is the number of data points. Perform a Discrete Fourier Transform on the windowed data:

[0188]

[0189] With a spectral correction coefficient λ = 0.035 and a frequency attenuation coefficient μ = 0.0035, the corrected spectrum is as follows:

[0190] Y k ′(ω)=|Y k (ω)|+λe -μω .

[0191] Peak detection identifies the main peak points in the spectrum, as shown in Table 3.

[0192] Table 3: Main Peak Points in the Spectrum

[0193]

[0194]

[0195] The frequency corresponding to the maximum amplitude, 18.25 Hz, was 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, changes in fluid properties are considered. The measured viscosity change of the fracturing fluid is Δη = 12 Pa·s, and the density change is Δρ = 45 kg / m³. 3 Using a fluid viscosity correction factor δ = 0.00035 and a density correction factor θ = 0.000035, the propagation time is calculated as follows:

[0197]

[0198] Finally, the main fracture propagation length was calculated. The change in rock elastic modulus ΔE = 4.5 GPa and the change in horizontal geostress Δσ were measured. h =2.8MPa. Selecting the elastic modulus correction factor φ = 0.00035 and the horizontal stress correction factor ψ = 0.0035, calculate the main crack propagation length:

[0199]

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

[0201] (1) Verification by acoustic logging: After fracturing, acoustic logging was performed, and the main fracture extension range was measured to be approximately 21 to 24 m, which is basically consistent with the calculation results.

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

[0203] Table 4: Comparison of Production Data Before and After Fracturing

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

[0205] Production data shows that the fracturing stimulation achieved good results, matching the calculated main fracture extension length.

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

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

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

[0209] The application of this embodiment demonstrates that this method can be extended to similar oil and gas well fracturing projects. The calculation results show high reliability for both vertical and horizontal well fracturing. The main fracture propagation length information obtained through this method can guide subsequent fracturing parameter optimization and production plan formulation.

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

[0211] In summary, this embodiment demonstrates in detail the implementation process and effect verification of the method of the present invention through an oil well fracturing case. The results show that the method has advantages such as high reliability, simple operation, and low cost, providing a practical evaluation tool for oil and gas well fracturing engineering. Furthermore, this embodiment also provides valuable reference for the widespread application of the method.

[0212] The technical principle of this invention is based on the propagation characteristics of water hammer waves in the wellbore and fractures. When the fracturing pump is shut down, a sudden pressure change generates a water hammer wave in the wellbore, which 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 of the main fracture can be obtained.

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

[0214] Table 5. Formula symbols used in this invention and their meanings.

[0215]

[0216] Specifically, this invention first utilizes complex cepstrum analysis to process water hammer wave signals. The complex cepstrum is the inverse Fourier transform of the logarithm of the signal spectrum, offering the advantage of extracting periodic components. Through complex cepstrum analysis, the round-trip propagation time of the water hammer wave within the wellbore can be accurately obtained. The ratio of this time to the wellbore length allows for the calculation of the average propagation velocity of the water hammer wave within the well.

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

[0218] The scientific merit of this method lies in two aspects: firstly, it is based on reliable physical principles, namely the propagation characteristics of water hammer waves; secondly, it employs advanced signal processing methods, including complex cepstrum analysis and spectral analysis. By combining physical principles with signal processing techniques, a complete system for evaluating the propagation length of the main crack has been established.

[0219] The technical solution of this invention is logically sound. It begins with signal acquisition, proceeds through signal processing and parameter extraction, and ultimately obtains the main crack propagation length. Each step has a solid theoretical basis and practical foundation, forming a complete technical chain. This method not only considers the complexity of the physical process but also takes into account the feasibility of engineering applications, thus effectively solving the technical problem of assessing the main crack propagation length.

Claims

1. A method for calculating the extension length of the main fracture in hydraulic fracturing, comprising the following steps: S10. Use a high-frequency pressure gauge to obtain the water hammer wave signal at the wellhead location after hydraulic fracturing pump shutdown. S20. Convert the water hammer wave signal into a complex cepstrum and perform cepstrum analysis on the water hammer wave signal; S30. Calculate the minimum period between the extreme points of the positive pulse in the complex cepstrum curve, and take half of the minimum period as the time for the water hammer wave to travel from the wellhead to the bridge plug. S40. Calculate the average velocity of the water hammer wave in the well based on the time it takes for the water hammer wave to travel from the wellhead to the bridge plug and the distance from the wellhead to the bridge plug. S50. Perform linear trend removal processing on the local signal of the water hammer wave during the rising or falling phase along the wellbore. S60. Perform Fourier transform on the local signal after the linear trend removal process to obtain the local signal spectrum of the water hammer wave; S70. Extract the fundamental frequency corresponding to the maximum point in the local signal spectrum of the water hammer wave, and use it as the response frequency in the main crack. S80. Calculate the propagation time of the water hammer wave in the main crack based on the response frequency in the main crack; S90. Calculate the main fracture extension length based on the average velocity of the water hammer wave in the well and the propagation time of the water hammer wave in the main fracture.

2. The method for calculating the propagation length of the main fracture in hydraulic fracturing according to claim 1, characterized in that, S20 specifically includes: Perform a Fourier transform on the water hammer wave signal to obtain the signal spectrum; Perform a modulo operation on the signal spectrum to obtain the signal amplitude spectrum; Perform a natural logarithmic operation on the amplitude spectrum of the signal to obtain the logarithmic spectrum; Perform an inverse Fourier transform on the logarithmic spectrum to obtain the complex cepstrum of the water hammer wave signal; The amplitude of the complex cepstrum is extracted by taking the square root of the sum of the squares of the real and imaginary parts. The peak detection method is used to extract the maximum points of the complex cepstrum amplitude.

3. The method for calculating the propagation length of the main fracture in hydraulic fracturing according to claim 2, characterized in that, S30 specifically includes: Extract the frequency corresponding to the maximum value of the amplitude spectrum of the water hammer wave signal, and take the reciprocal of the frequency as the motion period of the water hammer wave during the rising or falling phase along the wellbore. Identify the positive pulse region in the complex cepstral curve based on the motion period; Perform a local extremum search within the positive pulse region and mark the extremum point locations; Calculate the time interval between adjacent extreme points to obtain multiple periodic values; The average of the multiple periodic values ​​is used as the average periodic value. Half of the average period value is taken as the time it takes for the water hammer wave to travel from the wellhead to the bridge plug.

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

5. The method for calculating the propagation length of the main fracture in hydraulic fracturing according to claim 4, characterized in that, S50 specifically includes: Identify the rising and falling segments of the water hammer wave signal and extract the local signal; The linear trend of the local signal is fitted using the least squares method; The calculated linear trend coefficients, including the slope and intercept, generate a trend signal with the same length as the input signal; Subtracting the linear trend from the local signal yields the local signal after removing the linear trend.

6. The method for calculating the propagation length of the main fracture in hydraulic fracturing according to claim 5, characterized in that, S60 specifically includes: Framing and windowing are performed on the local signal after removing linear trends; Perform a Fast Fourier Transform on the windowed signal; The amplitude of each frequency component is obtained by taking the modulus of the Fast Fourier Transform result; The frequency and amplitude within the Nyquist frequency range are taken as the spectrum of the local signal.

7. The method for calculating the propagation length of the main fracture in hydraulic fracturing according to claim 6, characterized in that, The S70 specifically includes: Peak detection is performed on the local signal spectrum of the water hammer wave; Search the frequency points in the spectrum that satisfy the peak condition; The frequency points are sorted from smallest to largest, and only the smallest frequency point that is a multiple of the previous frequency point is extracted as the fundamental frequency. The fundamental frequency was selected as the response frequency in the main crack.

8. The method for calculating the propagation length of the main fracture in hydraulic fracturing according to claim 7, characterized in that, S80 specifically includes: The propagation time of the water hammer wave in the main fracture is obtained by taking the reciprocal of the main fracture response frequency and dividing it by 2.

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

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

Images