A method for identifying fracture closure points and evaluating fracture network complexity

Abstract

This application discloses a method for identifying fracture closure points and evaluating fracture network complexity, relating to the field of oil and gas development. The method includes calculating dimensionless time and a G-function sequence based on a linear decay filtration model; constructing a pressure sequence based on wellhead pressure data, calculating the first derivative of the pressure with respect to the G-function, and constructing a superimposed derivative curve of the G-function; sequentially applying the stable linear segment criterion, inflection point significance criterion, and global fitting residual consistency criterion to automatically identify the closure point of the equivalent main fracture; determining the fitting pressure through linear regression based on the stable linear segment before the closure point to construct a theoretical baseline; calculating the additional filtration area and the baseline area respectively, calculating the branch fracture development coefficient based on their ratio, and outputting the fracture complexity classification result. Through in-depth exploration of the superimposed derivative of the G-function, a complete technical solution is established from intelligent identification of feature points to quantitative characterization of complexity, achieving a leap from qualitative observation to quantitative diagnosis.

Description

Technical Field

[0001] This application relates to the field of oil and gas development technology, and in particular to a method for identifying fracture closure points and evaluating fracture network complexity. Background Technology

[0002] Volumetric fracturing is a core technology for the efficient development of unconventional resources such as shale oil and gas. Accurately assessing the complexity of the post-fracturing fracture network (such as the development of main fractures and branch fractures) is of crucial engineering value for evaluating fracturing effectiveness, optimizing fracturing process parameters, and deploying subsequent well networks.

[0003] Among the analytical methods based on pump shutdown pressure drop data, the G-function analysis method is a classic tool in the industry. Its core logic is as follows: based on a linear elastic crack model and the power-law filtration assumption, a dimensionless G-function is introduced to characterize the cumulative filtration effect of the crack wall since its opening, mapping the pressure data that decays over time to the G-function domain. Under ideal conditions (a single simple crack, stable filtration), the net pressure during the pump shutdown stage exhibits an approximately linear relationship with the G-function. This linear relationship can be used to inversely derive the crack closure pressure and filtration parameters.

[0004] However, in volumetric fracturing practices in unconventional reservoirs such as shale, the formation is highly heterogeneous with widespread natural fractures, often resulting in a complex fracture network composed of a main fracture and multiple branch fractures after fracturing. Under these complex conditions, the actual pressure decay response deviates significantly from the single linear trajectory predicted by classical theory, and the superimposed derivative curve of the G-function often exhibits multiple local inflection points or nonlinear fluctuations. Traditional analysis methods rely on manual experience, searching for a "straight line segment" on the complex derivative curve that conforms to ideal assumptions and drawing a tangent to determine the fracture closure point (tangent method). This approach has significant drawbacks: firstly, manual point selection is highly subjective, and different operators may give different results, lacking uniqueness and repeatability; secondly, this method ignores reservoir stimulation information such as the development of branch fractures implied by the deviation of the curve from the linear segment; and thirdly, when multiple fracture clusters close asynchronously or when pressure-related filtering exists, the traditional tangent method often fails to effectively identify the true main fracture closure point.

[0005] Therefore, a new method is needed that can overcome human subjectivity, automatically identify crack closure points, and quantitatively evaluate the degree of branch crack development in complex crack networks. Summary of the Invention

[0006] The purpose of this application is to provide a method for identifying crack closure points and evaluating crack network complexity, thereby solving the aforementioned problems in the existing technology.

[0007] To achieve the above objectives, this application provides a method for identifying crack closure points and evaluating crack network complexity, comprising the following steps: S1: Obtain wellhead pressure data after pump shutdown during fracturing operations, calculate dimensionless time, and calculate the G-function sequence based on the linear decay filtration model; S2: Construct a pressure sequence based on wellhead pressure data, calculate the first derivative of pressure with respect to the G function using the numerical difference method, construct a superimposed derivative curve of the G function, and perform smoothing filtering. S3: On the superimposed derivative curve of the G function, the first-order rate of change stability linear segment criterion, the second-order rate of change inflection point significance criterion, and the global fitting residual consistency criterion are executed in sequence to automatically identify the closure point of the equivalent main crack. S4: Based on the stable linear segment before the closure point, the fitted pressure is determined by linear regression, and a theoretical baseline representing the ideal filtration behavior of a single main fracture is constructed. S5: Calculate the positive deviation area separately using the composite trapezoidal quadrature method. and theoretical baseline area ,in This represents the area of ​​the integral of the positive deviation of the measured smooth superimposed derivative curve from the theoretical baseline. The integral area of ​​the theoretical baseline within the closed-point interval is represented, and the branch crack development coefficient is defined as the ratio of the two. The crack complexity classification result is output based on the branch crack development coefficient to quantitatively evaluate the complexity of the crack network.

[0008] Preferably, S1 specifically includes: Let the data sampling time interval be . The instant the pump stops is Any sampling time after pump shutdown is The wellhead pressure collected at the corresponding time is ; Dimensionless time is represented as: ; Where, θ i The dimensionless time for the i-th sampling point has no unit. For the first i The absolute time of each sampling point, in seconds; The instantaneous time of pump shutdown is expressed in seconds (s). Select the filtration rate index The linear decay filtering model; the analytical expression of the G function is: ; Among them, G i Let G be the dimensionless value of the G function at the i-th sampling point.

[0009] Preferably, S2 specifically includes: The pressure sequence is numerically differentiated using the central difference method, yielding the first derivative of pressure with respect to the G function, which is expressed as: ; in, Let G be the derivative of the pressure at the i-th sampling point with respect to G; , The wellhead pressures at the (i+1)th and (i-1)th sampling points; , The values ​​of the G function at the (i+1)th and (i-1)th sampling points are given; for boundary points i=1 or i=N, forward difference or backward difference is used. Constructing the superposition of derivatives of the G function: ; in, Let be the superposition derivative of the i-th sampling point, in MPa; The Savitzky-Golay filter is used to smooth the superimposed derivative sequence, as shown below: ; in, The summation derivative of the i-th sampling point after smoothing; represents the Savitzy-Golay filter coefficients; m is the half-width of the window.

[0010] Preferably, the criteria for the stable linear segment of the first-order rate of change in S3 specifically include: Calculate the first-order discrete rate of change of the superimposed derivative point by point along the G-axis: ; in, Let be the rate of change of the superimposed derivative at the i-th point; , The smoothed superposition derivatives of the (i+1)th and ith points; Set a linear segment fluctuation threshold ε1, with a value range of 0.01~0.05MPa; starting from the initial data of pump shutdown and searching backwards, when the absolute value of the first-order discrete rate of change of M consecutive sampling points is less than or equal to the threshold, i.e., |ΔD i When |≤ε1, activate the linear segment determination; denote the index of the first sampling point that satisfies the condition as the starting point s of the stable linear segment; denote the index of the last sampling point that satisfies the condition as the ending point e of the stable linear segment. The interval [s,e] is defined as the stable linear ideal filtering segment of the equivalent main crack.

[0011] Preferably, the significance criteria for the inflection point of the second-order rate of change in S3 specifically include: After the stable linear segment, calculate the second-order discrete change of the superimposed derivative: ; in, The smoothed superimposed derivative at the (i-1)th point; Set a threshold ε2 for the significance of inflection point mutation, with a value ranging from 0.1 to 0.3 MPa; within the region i>e, if a sampling point satisfies C i >ε2, and C at that point i It belongs to a local maximum point, that is, it satisfies C i >C i-1 And C i >C i+1 If a point is found to be a candidate closure point, then that point is considered a candidate closure point. All sampling points that satisfy the conditions constitute the set of candidate closure points, denoted as K={k1,k2,…,k...}. m}, where k is the sampling point index of the candidate point.

[0012] Preferably, the global fitting residual consistency criterion mentioned in S3 specifically includes: For each candidate closure point index k∈K in the candidate closure point set K, the measured pressure data in the interval [s,k] are subjected to least squares linear fitting with the G function. The fitting model is as follows: ; ; ; Among them, a k b is the slope of the fitted line; k P is the intercept of the fitted line; i For the interval [G] s G k The pressure value at the i-th point within the [ ]; , They are the intervals [G] s G k The arithmetic mean of the internal G-value and pressure value; The sum of squared global fit residuals of the linear regression model for measured pressure within this interval is calculated and expressed as: ; Among them, J(G k ) as G k Under the assumption of a closure point, the degree of deviation of the pressure data before closure from the linear model, in MPa. 2 ; Iterate through all candidate closure points in set K, and select the candidate point that minimizes the sum of squared residuals of the global fit as the final true crack closure point, denoted as: ; The index of the sampling point corresponding to the final closure point is determined as c, and its corresponding G-function value is the G-function value of the crack closure point. The wellhead pressure at the corresponding moment is the fracture closure pressure. .

[0013] Preferably, S4 specifically includes: Index of stable linear segments identified in S3 to Within this model, a linear regression is performed on the superposition derivative D(G), and the regression model is expressed as: ; Where β0 is the regression intercept, in MPa; β1 is the regression slope, dimensionless. According to the least squares method, the regression slope That is, the fitting pressure : ; in, The arithmetic mean of the G values ​​within the stable linear segment is dimensionless. The arithmetic mean of the superimposed derivatives within a stable linear segment, in MPa; With the crack closure point As boundary constraints, according to slope Constructing a theoretical superposition derivative baseline representing the ideal filtration behavior of a single principal fracture , is represented as: ; in, Let C be the superimposed derivative of the smoothed G function at the crack closure point c.

[0014] Preferably, the development coefficient of the branched crack is calculated by numerically integrating the superimposed derivative curve of the G function and the theoretical baseline within the closed-point interval, specifically including: Numerical integration is performed on the region of positive deviation between the superimposed derivative curve of the G function and the theoretical baseline within the closure point interval to characterize the additional filtration contribution relative to the ideal filtration model of a single main crack, expressed as: ; Where c is the index of the closure point. The value of the closure point G; The theoretical baseline area is calculated and expressed as: ; Define the branch crack development coefficient : .

[0015] Preferably, the complexity of the fracture network is quantitatively evaluated by outputting the fracture complexity classification result based on the branch fracture development degree coefficient, specifically including: Set the first threshold Second threshold ,and ; like It is determined to be a simple crack, forming a primary branch, with a small number of natural cracks opening; like The crack is classified as relatively complex, with one to two levels of branches and a moderate number of natural cracks. like It is determined to be a complex suture network with three or more branches and a high number of natural cracks.

[0016] Therefore, this application adopts the above-mentioned method for identifying crack closure points and evaluating crack network complexity. By calculating the first-order rate of change, the second-order change, and the global linear fitting residual of the superimposed derivative of the G function, a triple numerical criterion is established to automatically lock the closure point of the equivalent main crack system. On this basis, by calculating the area ratio between the measured derivative curve and the ideal baseline, a branch crack development coefficient is constructed to achieve a quantitative evaluation of the crack network complexity.

[0017] The technical solution of this application will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall process of a method for identifying crack closure points and evaluating crack network complexity in this application; Figure 2 This is a graph showing the change in wellhead pressure throughout the fracturing process of the S21 section of the MaX1 well in this embodiment of the application. Figure 3 This is a graph showing the original wellhead pressure data of the pump shutdown pressure drop in section S21 of well MaX1 in this embodiment of the application. Figure 4 This is a pressure-G function relationship curve during the pump shutdown pressure drop stage in the embodiments of this application; Figure 5 This is a graph showing the superposition derivative of the G function and the smoothing result of Savitzky-Golay filtering in the embodiments of this application; Figure 6 This is a schematic diagram of the results of automatic crack closure point identification based on triple criteria in the embodiments of this application; Figure 7 This is a schematic diagram showing the ideal filter loss baseline construction and the evaluation results of the mesh complexity in the embodiments of this application. Detailed Implementation

[0019] The following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0020] Unless otherwise defined, the technical or scientific terms used in this application shall have the ordinary meaning as understood by a person of ordinary skill in the art to which this application pertains.

[0021] The terms "comprising" or "including," as used in this application, mean that the element preceding the term encompasses the element listed after the term, and do not exclude the possibility of encompassing other elements as well. The terms "inner," "outer," "upper," and "lower," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. When the absolute position of the described object changes, the relative positional relationship may also change accordingly. In this application, unless otherwise expressly specified and limited, the term "attached," etc., should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can refer to a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication of two elements or the interaction relationship between two elements. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0022] Example 1: A method for identifying crack closure points and evaluating crack network complexity, such as Figure 1 As shown, it includes the following steps: S1: Obtain wellhead pressure data after pump shutdown during fracturing operations, calculate dimensionless time, and calculate the G-function sequence based on the linear decay filtration model; Let the data sampling time interval be . (Unit: seconds, usually) s). Record the instant the pump stops as . (Unit: seconds), any sampling time after pump shutdown is (Unit: seconds) The wellhead pressure collected at the corresponding time was (Unit: MPa). Dimensionless time is expressed as: ; Where, θ i The dimensionless time for the i-th sampling point (obtained by normalizing the absolute time after pump stop and the instantaneous time after pump stop, i.e., θ) i =t i / t p ), without unit; t i t represents the absolute time of the i-th sampling point, in seconds. p The instantaneous time of pump shutdown is expressed in seconds (s). Considering the characteristics of shale reservoirs with well-developed natural fractures and pressure-dependent filtration, a filtration rate index was selected. The linear decay filtering model; the analytical expression of the G function is: ; Among them, G i Let G be the dimensionless value of the G function at the i-th sampling point.

[0023] S2: Construct a pressure sequence based on wellhead pressure data, calculate the first derivative of pressure with respect to the G function using the numerical difference method, construct a superimposed derivative curve of the G function, and perform smoothing filtering. Specifically, after the pump is shut down, the fracturing operation flow rate drops to zero, and the friction along the wellbore and the perforation friction essentially disappear. Therefore, the wellhead pressure can directly reflect the pressure attenuation characteristics inside the fracture system without the need for additional friction correction. This application directly uses the wellhead pressure after the pump is shut down as the analysis pressure sequence.

[0024] To characterize the dynamic response of the fracture system to filtration loss after pump shutdown, it is necessary to construct the derivative relationship of pressure with respect to the G function. Since the field pressure data is a discrete sampling sequence, the numerical difference method is used to calculate the first derivative of pressure with respect to the G function, and further, a superimposed derivative curve of the G function is constructed to characterize the time-varying characteristics of the fracture filtration behavior.

[0025] To describe the dynamic response characteristics of pressure as a function of G after pump shutdown, it is necessary to calculate the rate of change of pressure with respect to the G function. Since the pressure data collected in the field is a discrete sequence, the central difference method is used to numerically differentiate the pressure sequence, obtaining the first derivative of pressure with respect to the G function, expressed as: ; Wherein, (dP / dG) i P is the derivative of the pressure at the i-th sampling point with respect to G, in MPa; i+1 P i-1 G represents the wellhead pressure at the (i+1)th and (i-1)th sampling points, in MPa. i+1 G i-1 The values ​​of the G function at the (i+1)th and (i-1)th sampling points are dimensionless; for boundary points i=1 or i=N, forward difference or backward difference is used. To enhance the identifiability of crack filtration behavior characteristics, after obtaining the first derivative of the G function with respect to pressure, a superposition derivative of the G function is constructed: ; in, The superposition derivative of the i-th sampling point is expressed in MPa. The superposition derivative can more sensitively reflect the changing characteristics of the filtration mechanism during crack closure, which is beneficial for subsequent closure point identification and complex crack network evaluation.

[0026] Since the pressure derivative is calculated using numerical difference, it is easily affected by on-site sampling noise and discretization errors, leading to local high-frequency oscillations in the superimposed derivative curve. This noise fluctuation interferes with subsequent identification of closure points and inflection points, as well as the determination of stable linear segments. Therefore, smoothing of the superimposed derivative sequence is necessary. This application uses a Savitzky-Golay filter to smooth the superimposed derivative sequence, as shown below: ; in, The summation derivative of the i-th sampling point after smoothing; denoted by Savitzy-Golay, and m is the half-width of the window. Compared to traditional moving average filtering methods, the Savitzy-Golay filter can better preserve the local peaks, inflection points, and curvature changes of the curve while suppressing high-frequency noise, making it more suitable for derivative curve processing in crack closure point identification. S3: On the superimposed derivative curve of the G function, the first-order rate of change stability linear segment criterion, the second-order rate of change inflection point significance criterion, and the global fitting residual consistency criterion are executed in sequence to automatically identify the closure point of the equivalent main crack. Specifically, during the pump shutdown pressure drop process, as the main fracture gradually closes, the filtration mechanism of the fracture system changes, and the superimposed derivative curve gradually deviates from a stable linear response, exhibiting a clear inflection point characteristic. Therefore, the fracture closure point essentially corresponds to the position where the superimposed derivative curve transitions from a stable linear segment to a nonlinear segment. Based on the above physical response laws, this application sequentially constructs a stable linear segment existence criterion, an inflection point significance criterion, and a global fitting residual consistency criterion on the smoothed superimposed derivative curve, achieving automatic identification of the fracture closure point through multiple numerical constraints.

[0027] The first-order rate of change stability linear segment criterion determines the starting point s and ending point e of the ideal filtering interval. Specifically, it includes: Calculate the first-order discrete rate of change of the superimposed derivative point by point along the G-axis: ; in, The rate of change of the superimposed derivative at the i-th point is expressed in MPa. , The smoothed superposition derivative of the (i+1)th and ith points is expressed in MPa. Set a linear segment fluctuation threshold ε1, with a value range of 0.01~0.05MPa; starting from the initial data of pump shutdown and searching backwards, when the absolute value of the first-order discrete rate of change of M consecutive sampling points (M≥10) is less than or equal to the threshold, i.e., |ΔD iWhen |≤ε1, activate the linear segment determination; denote the index of the first sampling point that satisfies the condition as the starting point s of the stable linear segment; denote the index of the last sampling point that satisfies the condition as the ending point e of the stable linear segment. The interval [s,e] is defined as the stable linear ideal filtering segment of the equivalent main crack.

[0028] The significance criteria for the inflection point of the second-order rate of change specifically include: After the stable linear segment, i.e., the index Calculate the second-order discrete change of the superimposed derivative: ; in, The summation of the smoothed derivative at point i-1 is expressed in MPa. Set a threshold ε2 for the significance of inflection point mutation, with a value ranging from 0.1 to 0.3 MPa; within the region i>e, if a sampling point satisfies C i >ε2, and C at that point i It belongs to a local maximum point, that is, it satisfies C i >C i-1 And C i >C i+1 If a point is found to be a candidate closure point, then that point is considered a candidate closure point. All sampling points that satisfy the conditions constitute the set of candidate closure points, denoted as K={k1,k2,…,k...}. m}, where k is the sampling point index of the candidate point.

[0029] Traditional tangent methods rely solely on local geometric features and are susceptible to interference from the asynchronous closure of multiple crack clusters. This application introduces a global fitting residual consistency criterion, specifically including: For each candidate closure point index k∈K in set K, assuming it is a true closure point, then within the interval [s,k], the pressure data and the G function should exhibit the best overall linear mapping relationship. The least-squares linear fit is performed on the measured pressure data within the interval [s,k] and the G function; the fitting model is as follows: ; ; ; Among them, a k b is the slope of the fitted line, in MPa. k G is the intercept of the fitted line, in MPa; i For the interval [G] s G k The value of the G function at the i-th point within the range is dimensionless; P i For the interval [G] s G k The pressure value at the i-th point within the [input range], in MPa; , They are the intervals [G] s G k The arithmetic mean of the internal G-value and pressure value; The sum of squared global fit residuals of the linear regression model for measured pressure within this interval is calculated and expressed as: ; Among them, J(G k ) as G k Under the assumption of a closure point, the degree of deviation of the pressure data before closure from the linear model, in MPa. 2 ; Iterate through all candidate closure points in set K and compare their corresponding global fitting residual sums of squares J(G) k Candidate points that minimize the sum of squared global fitted residuals are selected as the final true crack closure points, expressed as: ; The index of the sampling point corresponding to the final closure point is determined as c, and its corresponding G-function value is the G-function value of the crack closure point. The wellhead pressure at the corresponding moment is the fracture closure pressure. .

[0030] By employing three numerical criteria—first-order stability constraint, second-order mutation constraint, and global residual minimization constraint—the subjectivity of manual interaction is eliminated, enabling intelligent and fully automatic locking of closure points.

[0031] S4: Based on the stable linear segment before the closure point, the fitted pressure is determined by linear regression, and a theoretical baseline representing the ideal filtration behavior of a single main fracture is constructed. Index of stable linear segments identified in S3 to Within this model, a linear regression is performed on the superposition derivative D(G), and the regression model is expressed as: ; Where β0 is the regression intercept, in MPa; β1 is the regression slope, dimensionless. According to the least squares method, the regression slope That is, the fitting pressure : ; in, The arithmetic mean of the G values ​​within the stable linear segment is dimensionless. The arithmetic mean of the superimposed derivatives within a stable linear segment, in MPa; With the crack closure point As boundary constraints, according to slope Constructing a theoretical superposition derivative baseline representing the ideal filtration behavior of a single principal fracture In the superposition derivative domain, the theoretical baseline equation is expressed as: ; in, The sum of the derivatives of the smoothed G function at the crack closure point c is given. This baseline characterizes the theoretical superimposed derivative response curve of the pump shutdown pressure drop under ideal conditions where there are no branch cracks, natural cracks are not activated, and only the main crack matrix is ​​lost.

[0032] S5: Calculate the positive deviation area separately using the composite trapezoidal quadrature method. and theoretical baseline area ,in This represents the area of ​​the integral of the positive deviation of the measured smooth superimposed derivative curve from the theoretical baseline. The integral area of ​​the theoretical baseline within the closed-point interval is represented, and the branch crack development coefficient is defined as the ratio of the two. The crack complexity classification result is output based on the branch crack development coefficient to quantitatively evaluate the complexity of the crack network.

[0033] Numerical integration is performed on the region of positive deviation between the superimposed derivative curve of the G function and the theoretical baseline within the closure point interval to characterize the additional filtration contribution relative to the ideal filtration model of a single main crack, expressed as: ; Where c is the index of the closure point; The theoretical baseline area is calculated and expressed as: ; Define the branch crack development coefficient : .

[0034] The crack complexity classification results are output based on the branch crack development degree coefficient, and the complexity of the crack network is quantitatively evaluated, specifically including: Set the first threshold Second threshold ,and ; like It is determined to be a simple crack, forming a primary branch, with a small number of natural cracks opening; like The crack is classified as relatively complex, with one to two levels of branches and a moderate number of natural cracks. like It is determined to be a complex suture network with three or more branches and a high number of natural cracks.

[0035] In this embodiment, the first threshold is determined based on statistical calibration of field data from 13 wells in the Ma51X well area. Set it to 0.5, the second threshold. Set the value to 1.0; other blocks can be adjusted appropriately based on actual production data.

[0036] Example 2: This embodiment takes the shale oil reservoir in the Mabei block as the research object, and selects the horizontal shale oil well MaX1 in the block for field application. The average daily oil production of MaX1 well reaches 60.33 t / d, and its production performance is significantly better than other adjacent wells in the block. This well underwent 23 fracturing operations covering different geological conditions and engineering parameters, making it highly representative of engineering applications. This embodiment selects S21, a representative section of MaX1 well, as a typical analysis object. The wellhead pressure data throughout the entire fracturing process are as follows: Figure 2 As shown, the original wellhead pressure data obtained after pump shutdown is as follows: Figure 3 As shown.

[0037] Step 1: Convert absolute time to dimensionless time. Considering the physical characteristics of shale reservoirs with well-developed natural fractures and a linear decay filtration model after pump shutdown (selecting a filtration rate exponent). The corresponding dimensionless G-function sequence is calculated. The traditional "pressure-time" response is transformed into a "pressure-G function" response, forming a curve showing the relationship between wellhead pressure P and the G function. For example... Figure 4 As shown.

[0038] Step 2: Since the fracturing operation flow rate drops to zero instantaneously after pump shutdown, the friction along the wellbore and the orifice friction essentially disappear completely. Therefore, the measured pressure at the wellhead can directly reflect the pressure attenuation characteristics inside the fracture system. In this embodiment, the wellhead pressure after pump shutdown is directly used as the analysis pressure sequence without additional friction correction. To accurately characterize the dynamic response of the fracture system after pump shutdown, the central difference method is used to numerically differentiate the discrete pressure sequence to obtain the first derivative of the pressure with respect to the G function. After obtaining the first derivative, a sequence of superimposed derivatives of the G function corresponding to each sampling point is further constructed. To enhance the identifiability of the filtration mechanism changes during crack closure; finally, to suppress local high-frequency oscillations caused by numerical difference and high-pressure sensor sampling noise, a Savitzky-Golay filter was used to smooth the superimposed derivative sequence to obtain a smoothed superimposed derivative sequence. like Figure 5 As shown, while effectively suppressing high-frequency noise, the peak value, inflection point and curvature change characteristics of the curve are well preserved.

[0039] Step 3: Utilize the smoothed superimposed derivative curve A three-tiered numerical constraint criterion is constructed sequentially to achieve intelligent, fully automatic locking of the crack closure point through multiple numerical constraints. First, criterion one (existence criterion of stable linear segment) is executed, and the first-order discrete rate of change of the superimposed derivative is calculated point by point along the G-axis. Set the fluctuation threshold for the linear segment. Starting from the initial data of the pump shutdown and proceeding backwards, when the conditions are met (M=12 sampling points are satisfied)... The absolute values ​​of the first-order discrete rates of change are all less than or equal to this threshold (i.e. When the linear segment determination is activated, the index of the first sampling point that meets the condition is locked as the starting point s, and the index of the last sampling point that meets the condition is locked as the ending point e. The interval [s, e] is defined as the stable linear ideal filtering segment of the equivalent main crack. Then, the second criterion (inflection point significance criterion) is executed to calculate the second-order discrete change of the superimposed derivative in the region i>e. Set a threshold for the significance of inflection point mutation. Filter out those that simultaneously meet the requirements And at that point It belongs to a local maximum point (i.e., satisfies) and All sampling points are used to form a candidate closure point set K; finally, criterion three (global linear fitting residual consistency criterion) is executed. For each candidate closure point index k in set K, the pressure data in the interval [s,k] is subjected to least squares linear fitting with the G function, and the sum of squared global fitting residuals of the measured pressure to the linear regression model in that interval is calculated. Finally, iterate through all candidate points in set K and compare the residuals to solve the corresponding mathematical objective function. The candidate points that minimize the sum of squared residuals of the global fit are identified as the final true crack closure points. The sampling point index c corresponding to the final closure point is automatically determined, and its corresponding G-function value is the G-function value of the crack closure point. (like Figure 6 The location of the closure point indicated by the red dot corresponds to the automatically acquired wellhead pressure at that moment. This value is confirmed as the true closure pressure of the fracture system in that stratum.

[0040] Step 4: Within the stable linear segment (index s to e) automatically identified in Step 3, perform linear regression on the superimposed derivative D(G) to construct the regression model; calculate the slope of this regression model using the least squares method, and this slope value is defined as the fitting pressure. (Calculated in this example) for This is used to quantify the equivalent pressure drop rate under matrix filtration in a single main fracture; subsequently, using the fracture closure point precisely locked in step 3 as the boundary constraint, the pressure drop rate is determined according to the slope. Working backward from the initial moment, a theoretical superposition derivative baseline equation representing the ideal filtration behavior of a single principal fracture is constructed (corresponding to...). Figure 7 (As shown by the black dashed line in the image) GdP / dG=3.05*G.

[0041] Step 5: Superimpose the measured derivative curve D(G) and the ideal baseline. Numerical integration was performed over the entire interval from pump shutdown to main fracture closure. Using the composite trapezoidal quadrature method, the positive deviation of the measured smooth superimposed derivative curve from the theoretical baseline within the closure interval was numerically integrated to calculate the corresponding total area. for The theoretical filtration area under the ideal baseline equation is obtained by analytical integration. for The branch fracture development coefficient of the fracturing section was calculated. This is used to quantify the physical ratio between the additional excess filtration effect caused by the opening of branch fractures and the activation of natural fractures and the baseline filtration effect; finally, the system calculates the... Automatic comparison with preset grading standards, because this coefficient meets... The system automatically determines that the crack modification morphology of the construction section reaches the "simple crack" level (indicating that the section has formed a first-level branch and the number of natural cracks is relatively small), and directly outputs the quantitative classification result for comprehensive evaluation of post-pressure effects and dynamic optimization of subsequent pumping parameters.

[0042] Therefore, this application adopts the above-mentioned method for identifying crack closure points and evaluating crack network complexity. By calculating the first-order rate of change, the second-order change, and the global linear fitting residual of the superimposed derivative of the G function, a triple numerical criterion is established to automatically lock the closure point of the equivalent main crack system. On this basis, by calculating the area ratio between the measured derivative curve and the ideal baseline, a branch crack development coefficient is constructed to achieve a quantitative evaluation of the crack network complexity.

[0043] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of this application, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of this application.

Claims

1. A method for identifying crack closure points and evaluating crack network complexity, characterized in that, Includes the following steps: S1: Obtain wellhead pressure data after pump shutdown during fracturing operations, calculate dimensionless time, and calculate the G-function sequence based on the linear decay filtration model; S2: Construct a pressure sequence based on wellhead pressure data, calculate the first derivative of pressure with respect to the G function using the numerical difference method, construct a superimposed derivative curve of the G function, and perform smoothing filtering. S3: On the superimposed derivative curve of the G function, the first-order rate of change stability linear segment criterion, the second-order rate of change inflection point significance criterion, and the global fitting residual consistency criterion are executed in sequence to automatically identify the closure point of the equivalent main crack. S4: Based on the stable linear segment before the closure point, the fitted pressure is determined by linear regression, and a theoretical baseline representing the ideal filtration behavior of a single main fracture is constructed. S5: Calculate the positive deviation area separately using the composite trapezoidal quadrature method. and theoretical baseline area ,in This represents the area of ​​the integral of the positive deviation of the measured smooth superimposed derivative curve from the theoretical baseline. It represents the integral area of ​​the theoretical baseline within the closed-point interval, and defines the branch crack development coefficient as the ratio of the two. Based on the branch crack development coefficient, the crack complexity classification result is output to quantitatively evaluate the complexity of the crack network.

2. The method for identifying crack closure points and evaluating crack network complexity according to claim 1, characterized in that, S1 specifically includes: Let the data sampling time interval be . The instant the pump stops is Any sampling time after pump shutdown is The wellhead pressure collected at the corresponding time is ; Dimensionless time is represented as: ； Where, θ i Let be the dimensionless time of the i-th sampling point; For the first i The absolute time of each sampling point; This refers to the instantaneous time it takes for the pump to stop. Select the filtration rate index The linear decay filtering model; the analytical expression of the G function is: ； Among them, G i Let be the G function value at the i-th sampling point.

3. The method for identifying crack closure points and evaluating crack network complexity according to claim 2, characterized in that, S2 specifically includes: The pressure sequence is numerically differentiated using the central difference method, yielding the first derivative of pressure with respect to the G function, which is expressed as: ； in, Let G be the derivative of the pressure at the i-th sampling point with respect to G; , The wellhead pressures at the (i+1)th and (i-1)th sampling points; , The values ​​of the G function at the (i+1)th and (i-1)th sampling points are given; for boundary points i=1 or i=N, forward difference or backward difference is used. Constructing the superposition of derivatives of the G function: ； in, The superposition derivative of the i-th sampling point; The Savitzky-Golay filter is used to smooth the superimposed derivative sequence, as shown below: ； in, The summation derivative of the i-th sampling point after smoothing; represents the Savitzy-Golay filter coefficients; m is the half-width of the window.

4. The method for identifying crack closure points and evaluating crack network complexity according to claim 3, characterized in that, The criteria for determining the stable linear segment of the first-order rate of change in S3 specifically include: Calculate the first-order discrete rate of change of the superimposed derivative point by point along the G-axis: ； in, Let be the rate of change of the superimposed derivative at the i-th point; , The smoothed superposition derivatives of the (i+1)th and ith points; Set a linear segment fluctuation threshold ε1, with a value range of 0.01~0.05MPa; starting from the initial data of pump shutdown and searching backwards, when the absolute value of the first-order discrete rate of change of M consecutive sampling points is less than or equal to the threshold, i.e., |ΔD i When |≤ε1, activate the linear segment determination; denote the index of the first sampling point that satisfies the condition as the starting point s of the stable linear segment; denote the index of the last sampling point that satisfies the condition as the ending point e of the stable linear segment, and the interval [s,e] is defined as the stable linear ideal filtering segment of the equivalent main crack.

5. The method for identifying crack closure points and evaluating crack network complexity according to claim 4, characterized in that, The significance criteria for the inflection point of the second-order rate of change in S3 specifically include: After the stable linear segment, calculate the second-order discrete change of the superimposed derivative: ； in, The smoothed superimposed derivative at the (i-1)th point; Set a threshold ε2 for the significance of inflection point mutation, with a value ranging from 0.1 to 0.3 MPa; within the region i>e, if a sampling point satisfies C i >ε2, and C at that point i It belongs to a local maximum point, that is, it satisfies C i >C i-1 And C i >C i+1 If a point is found to be a candidate closure point, then that point is considered a candidate closure point. All sampling points that satisfy the conditions constitute the set of candidate closure points, denoted as K={k1,k2,…,k...}. m }, where k is the sampling point index of the candidate point.

6. The method for identifying crack closure points and evaluating crack network complexity according to claim 5, characterized in that, The global fitting residual consistency criterion described in S3 specifically includes: For each candidate closure point index k∈K in the candidate closure point set K, the measured pressure data in the interval [s,k] are subjected to least squares linear fitting with the G function. The fitting model is as follows: ； ； ； Among them, a k b is the slope of the fitted line; k P is the intercept of the fitted line; i For the interval [G] s G k The pressure value at the i-th point within the range; , They are the intervals [G] s G k The arithmetic mean of the internal G-value and pressure value; The sum of squared global fit residuals of the linear regression model for measured pressure within this interval is calculated and expressed as: ； Among them, J(G k ) as G k Under the assumption of a closure point, the degree of deviation of the pressure data from the linear model before closure; Iterate through all candidate closure points in set K, and select the candidate point that minimizes the sum of squared residuals of the global fit as the final true crack closure point, denoted as: ； The index of the sampling point corresponding to the final closure point is determined to be c, and its corresponding G-function value is the G-function value of the crack closure point. The wellhead pressure at the corresponding moment is the fracture closure pressure. .

7. The method for identifying crack closure points and evaluating crack network complexity according to claim 6, characterized in that, S4 specifically includes: Index of stable linear segments identified in S3 to Within this model, a linear regression is performed on the superposition derivative D(G), and the regression model is expressed as: ； in, The regression intercept; The regression slope; According to the least squares method, the regression slope That is, the fitting pressure : ； in, The arithmetic mean of the G values ​​within the stable linear segment; The arithmetic mean of superimposed derivatives within a stable linear segment; With the crack closure point As boundary constraints, according to slope Constructing a theoretical superposition derivative baseline representing the ideal filtration behavior of a single principal fracture , is represented as: ； in, Let C be the superimposed derivative of the smoothed G function at the crack closure point c.

8. The method for identifying crack closure points and evaluating crack network complexity according to claim 7, characterized in that, Numerical integration is performed on the superimposed derivative curve of the G function and the theoretical baseline within the closure interval to calculate the branch crack development coefficient, specifically including: Numerical integration is performed on the region of positive deviation between the superimposed derivative curve of the G function and the theoretical baseline within the closure point interval to characterize the additional filtration contribution relative to the ideal filtration model of a single main crack, expressed as: The theoretical baseline area is calculated and expressed as: ； Define the branch crack development coefficient : 。 9. The method for identifying crack closure points and evaluating crack network complexity according to claim 8, characterized in that, The crack complexity classification results are output based on the branch crack development degree coefficient, and the complexity of the crack network is quantitatively evaluated, specifically including: Set the first threshold Second threshold ,and ; like It is determined to be a simple crack, forming a primary branch, with a small number of natural cracks opening; like The crack is classified as relatively complex, with one to two levels of branches and a moderate number of natural cracks. like It is determined to be a complex suture network with three or more branches and a high number of natural cracks.

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