Fracturing data analysis method based on water hammer effect

Abstract

The application discloses a fracturing data analysis method based on water hammer effect and relates to the technical field of reservoir reconstruction engineering. The application is based on circuit principle and establishes a water hammer model after hydraulic fracturing on the basis of a traditional water hammer model, which is used for calculating the geometric shape of a fracture. Through the established water hammer model, water hammer pressure change in a wellbore is simulated and analyzed, reasonable fracturing fracture characteristic parameters are given through an iterative method, and corresponding geometric parameters are calculated. The fracturing data analysis method based on water hammer effect is rapid in diagnosis and high in accuracy.

Description

Technical Field

[0001] This invention relates to the field of reservoir stimulation engineering technology, particularly to the field of real-time monitoring technology for hydraulic fracturing diagnosis during shale oil and gas field fracturing stimulation, and more specifically to a fracturing data analysis method based on the water hammer effect. Background Technology

[0002] Abundant unconventional oil and gas reserves are a key focus of current oil and gas development; however, unconventional resources are typically found in low-permeability, poorly connected formations. Hydraulic fracturing is currently the most effective method for improving oil recovery. The geometry of the fractures after fracturing significantly impacts the final production of unconventional reservoirs. Therefore, assessing the geometry of hydraulically fractured fractures is crucial for achieving high recovery rates after fracturing. However, since hydraulically fractured fractures form underground, their geometry cannot be directly observed. Therefore, an economical and effective method for assessing fracture geometry is needed.

[0003] Extensive research has been conducted by experts and scholars both domestically and internationally on the issue of fracture geometry diagnosis technology. Various methods exist for monitoring fractures, including microseismic monitoring and distributed optical fiber monitoring. Microseismic monitoring utilizes high-frequency seismographs, effectively avoiding near-surface noise interference and the hardware requirement of a well; however, it is costly and complex to process data (Liang Xueli, Liu Hailong, Cheng Ning, et al. Research and application of microseismic monitoring interpretation technology in unconventional oil and gas reservoirs [J]. Xinjiang Petroleum and Natural Gas, 2021, 17(3):53-58.). Distributed optical fiber monitoring is a highly sensitive and precise monitoring method capable of characterizing fracture distribution and evaluating fracturing effects; however, it still suffers from limitations such as operational difficulties, cumbersome construction, and the need for substantial investment (Wu Shaojiang, Wang Yibo, Liang Xing, et al. Distributed optical fiber monitoring of adjacent wells and imaging of source location in horizontal well fracturing of shale gas reservoirs [J]. Chinese Journal of Geophysics, 2022, 65(7):10.). Therefore, an economical and effective method is needed to assess fracture geometry.

[0004] Water hammer-based fracture geometry diagnosis is a promising method with advantages such as cost-effectiveness, ease of implementation, and real-time performance. Numerous studies have demonstrated the feasibility of using pressure waves to diagnose fracture geometry. Holzhausen (1985) estimated fracture impedance and calculated fracture geometry by artificially generating pressure waves at the wellhead and fitting them to the reflected pressure waves received at the wellhead using a trial-and-error method (Holzhausen, GR, Gooch, RP, 1985a. Impedance of hydraulic fractures: its measurement and use forestimating fracture closure pressure and dimensions. Brain Behav. E). Many researchers have conducted field-scale experiments to verify the adaptability of the Holzhausen model. Patzek and De (2000) proposed a lossy transmission line model to describe wellbore and fracture geometry, which can account for energy loss. Mondal (2010) used the characteristic method to establish a semi-analytical model for the continuity and momentum equations of wellbores containing microcompressible single-phase fluids (Patzek, TW, De, A., 2000. Lossy transmission line model of hydrofracturedwell dynamics. J. Petrol. Sci. Eng. 25(1–2), 59–77.). Mondal defined a fracture model that uses some parameters (R, C, and I) to represent single- and double-wing fractures. The characteristic method and the fracture model (RCI) were combined to simulate and match the hydraulic pressure signal. Using the Mondal model, the fracture length, height, and width under the single- and double-wing fracture assumption can be estimated (Mondal, S., 2010. Pressure Transients in Wellbores: Water Hammer Effects and Implications for Fracture Diagnostics. The University of Texas at Austin, Austin. MSthesis.).

[0005] In the process of implementing the embodiments of the present invention, at least one technical problem in the background art was found: although the feasibility of using pressure waves to diagnose the geometry of cracks has been proven, no specific model and simulation method for the analysis of fracturing data of water hammer effect has been proposed. Summary of the Invention

[0006] To overcome the deficiencies and shortcomings of the existing technologies, this invention provides a fracturing data analysis method based on the water hammer effect. The purpose of this invention is to provide a rapid, accurate, and low-cost fracture diagnosis model and method, addressing the lack of methods in the existing technologies for calculating fracture size using fracturing data based on the water hammer effect. Based on circuit principles, this invention establishes a post-hydraulic fracturing water hammer model on top of the traditional water hammer model to calculate the fracture geometry. Through the established water hammer model, the changes in water hammer pressure within the wellbore are simulated and analyzed. Reasonable fracturing fracture characteristic parameters are given through an iterative method, and the corresponding geometric parameters are calculated. This invention's fracturing data analysis method based on the water hammer effect offers rapid and accurate diagnosis.

[0007] To address the problems existing in the prior art, the present invention is achieved through the following technical solution.

[0008] This invention provides a fracturing data analysis method based on the water hammer effect, the method comprising the following steps:

[0009] S1. Obtain the water hammer curve of the pump stoppage and the geological data of the fractured well;

[0010] S2. Based on the characteristics of pump shutdown, the water hammer curve of pump shutdown, and the geological data of the fractured well, establish a water hammer pressure model that considers the fractured fractures; the basic equations required to establish the water hammer pressure model that considers the fractured fractures are the water hammer continuity equation and the motion equation.

[0011] When establishing the bottom-hole fracture boundary, the electrical parameters in the equivalent circuit matching the pump shutdown water hammer curve are determined. The electrical parameters include resistance R, capacitance C, and inductance I. Resistance R represents resistance, capacitance C defines weakness, which is the ratio of fracture volume to pressure potential, and inductance I is inertia, which is related to the mass of the fluid. Resistance R, capacitance C, and inductance I are connected in series to describe the bottom-hole fracture boundary, and the relationship between head difference and electrical parameters is established.

[0012] S3. Based on the established water hammer pressure model considering fracturing fractures, the electrical parameter values ​​are calculated iteratively using the method of characteristics and the Macquarie iteration.

[0013] S4. Calculate the fracture size based on the electrical parameter values ​​obtained from the iteration.

[0014] In a further preferred embodiment, in step S2, the resistance R represents the resistance, expressed as... The capacitance C defines weakness as the ratio of crack volume to pressure potential, expressed as: Inductance I is inertia, which is related to the mass of the fluid, and is expressed as... By connecting a resistor, capacitor, and inductor in series to describe the bottom-hole fracture boundary, the formula for calculating the pressure difference at the bottom of the well is:

[0015] In the formula, Q is the liquid flow rate, in meters per second (m³). 3 / s; ΔP is the pressure difference required to maintain the flow state, in Pa; ΔV is the crack volume change, in m³. 3 ; The pressure difference required to accelerate or decelerate the fluid discharge is expressed in Pa; ΔH is the pressure difference at the bottom of the well, also in Pa; ρ is the fluid density, expressed in kg / m³. 3 g is the acceleration due to gravity, in m / s². 2 .

[0016] Furthermore, in step S2, the water hammer pressure model considering fracturing fractures includes the water hammer continuity equation:

[0017] Equations of motion:

[0018] The pressure wave velocity inside the wellbore is expressed as:

[0019] Pressure difference at the bottom of the well

[0020] In the formula, A is the cross-sectional area of ​​the pipe, in meters. 2 H is the piezometric head, in meters (m); t is time, in seconds (s); Q is the liquid flow rate, in cubic meters per second (m³). 3 / s; x is the pipe length coordinate, in meters; θ is the inclination; a is the pressure wave velocity, in meters per second; g is the acceleration due to gravity, in meters per second. 2 λ is the Darcy friction coefficient; D is the pipe inner diameter (m); E is the fluid elastic modulus (Pa); ρ is the fluid density (kg / m³). 3 E0 is the pipe elasticity coefficient, in Pa; e is the pipe wall thickness, in mm; υ is the pipe Poisson's ratio. The pressure difference required to accelerate or decelerate the fluid discharge is expressed in Pa; ΔH is the pressure difference at the bottom of the well, also expressed in Pa.

[0021] In a further preferred embodiment, in step S3, the numerical solution of the water hammer pressure model considering fracturing fractures established in step S2 is calculated using the method of characteristics. The differential equation is transformed into a total differential equation along the characteristic lines of the differential equation, and then approximately transformed into a difference equation before numerical calculation is performed.

[0022] Furthermore, based on the water hammer pressure model considering fracturing fractures established in step S2, a pair of eigenvalues ​​are introduced to linearly combine the first-order quasi-linear hyperbolic partial differential equations, resulting in ordinary differential equations, denoted as C+ and C- respectively:

[0023]

[0024]

[0025] In the formula, A is the cross-sectional area of ​​the pipe, in meters. 2 H is the piezometric head, in meters (m); t is time, in seconds (s); Q is the liquid flow rate, in cubic meters per second (m³). 3 / s; x is the pipe length coordinate, in meters; θ is the inclination; a is the pressure wave velocity, in meters per second; g is the acceleration due to gravity, in meters per second. 2 λ is the Darcy friction coefficient; D is the pipe inner diameter, in meters.

[0026] Integrating the ordinary differential equation along the characteristic line transforms it into a finite difference scheme as follows:

[0027]

[0028]

[0029] In the formula, Let i be the water head at point i in the wellbore at time t+Δt; Let i be the flow rate at point i inside the wellbore at time t+Δt; Let i be the water head at point i inside the wellbore at time t. Let be the flow rate at point i inside the wellbore at time t; subscript i represents any grid intersection point; subscript i-1 represents the grid point corresponding to grid intersection point i on the C+ characteristic line, and subscript i+1 represents the grid point corresponding to grid intersection point i on the C- characteristic line; coefficient C p C m All are known constants;

[0030] Solve the above two equations simultaneously to find the head and flow rate at every point in the wellbore at any given time:

[0031]

[0032]

[0033] This allows for the evolution of the pump shutdown pressure.

[0034] In a further preferred embodiment, in step S3, the values ​​of the corresponding electrical parameters R, C, and I are obtained based on the conventionally statistical crack size, and these values ​​are used as initial values. Then, the estimated values ​​of electrical parameters R, C, and I are obtained by using the Macquarie iteration method and the relative error between the simulated water hammer pressure curve and the actual field data as the evaluation standard.

[0035] In a further preferred embodiment, in step S4, the crack half-length L is calculated by inverting the values ​​of the electrical parameters R, C, and I obtained through iteration. f Seam height h f and seam width

[0036] The difference between the average pressure within a fracture and the horizontal stress is called the average net pressure. Represented as:

[0037]

[0038] In the formula, P BH S is the bottom hole pressure. Hmin Minimum horizontal ground stress; ΔP nwf Here, R represents the near-wellbore frictional pressure drop, and Q0 represents the average pressure within the fracture, which is the difference between the bottom-hole pressure and the near-wellbore frictional pressure drop.

[0039] By relating the average net pressure to the crack volume change, the following relationship is obtained:

[0040]

[0041] In the formula, L is the crack width. f For half the length of the seam, h f Let be the seam height; υ be Poisson's ratio; E(m) be the elliptic integral of the second kind, and m is calculated as follows:

[0042] When 2L f / h f When ≥1, it indicates that the crack is a long crack; when 2L f / h f When the value is less than 1, it indicates that the crack is a short crack;

[0043] If the change in crack volume caused by crack flexibility is only a change in crack width, then the capacitance C can be rewritten as:

[0044]

[0045] Substituting the relationship between average net pressure and crack volume change into the capacitance expression, we get:

[0046] In the formula, E′ is the plane strain elastic modulus. E0 is Young's modulus;

[0047] Similarly, the formula for inertia I is:

[0048]

[0049] By combining the expressions for capacitance C and inertia I, the formula for crack size is derived:

[0050]

[0051]

[0052]

[0053] In a further preferred embodiment, the boundary conditions of multiple crack clusters are considered as a parallel circuit, and the inverse crack size is:

[0054]

[0055]

[0056] In the formula, L fE For multi-cluster cracks, the equivalent crack half-length is I; T Where n is the inductance value; n is the number of clusters; C i Let be the capacitance value of the i-th crack; L represents the average net pressure of the i-th crack; fi Let be the half length of the i-th crack. The equivalent crack width for multiple clusters of cracks; Let be the width of the i-th crack.

[0057] Compared with the prior art, the beneficial technical effects of the present invention are as follows:

[0058] 1. This invention, based on circuit principles, establishes a post-hydraulic fracturing water hammer model on top of the traditional water hammer model to calculate the fracture geometry. Through the established water hammer model, it simulates and analyzes the water hammer pressure changes within the wellbore, and uses an iterative method to provide reasonable fracturing fracture characteristic parameters and calculate the corresponding geometric parameters. This invention addresses the deficiency in existing technologies that lack methods for calculating fracture size using fracturing data based on the water hammer effect. This invention's fracturing data analysis method based on the water hammer effect offers rapid diagnosis and high accuracy.

[0059] 2. This invention introduces circuit principles when establishing the bottom-hole fracture boundary, facilitating model calculations and fracture parameter inversion. Connecting R, C, and I in series satisfies the conditions for describing downhole fractures because, during the duration of water hammer, the volume of fluid and fracture dominates pressure and flow behavior due to the linear flow state within the fracture. In a series circuit, current flows into the circuit until the capacitor is fully charged; at this point, current only flows into the circuit when the potential difference increases or the resistance decreases, similar to the fluid motion state in a hydraulic fracture. This invention utilizes the principle of similarity to introduce the electrical parameters of the equivalent circuit of the bottom-hole fracture into the model, establishing a connection between the electrical parameters and the hydraulic system. Furthermore, a simulation calculation method is established based on a water hammer pressure model of the fractured area; after determining the electrical parameter values, the fracture size is inverted, resulting in rapid and highly accurate diagnosis. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of the crack boundary;

[0061] Figure 2 A feature line grid diagram;

[0062] Figure 3 This is a schematic diagram of multiple clusters of cracks;

[0063] Figure 4 This is a schematic diagram of the equivalent circuit for multiple clusters of cracks.

[0064] Figure 5 This is a flowchart of the fracturing data analysis method based on the water hammer effect of the present invention;

[0065] Figure 6 This is a fracturing operation curve diagram in an example of the present invention;

[0066] Figure 7 According to the present invention Figure 6 Water hammer pressure curve obtained from fracturing operation data simulation;

[0067] Figure 8 This is a comparison diagram of the fracture height obtained from microseismic events and simulations. Detailed Implementation

[0068] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] Example 1

[0070] As a preferred embodiment of the present invention, please refer to the appendix to the specification. Figure 4 As shown in the figure, this embodiment discloses a fracturing data analysis method based on the water hammer effect, which includes the following steps:

[0071] S1. Obtain the water hammer curve of the pump stoppage and the geological data of the fractured well;

[0072] S2. Based on the characteristics of pump shutdown, the water hammer curve of pump shutdown, and the geological data of the fractured well, establish a water hammer pressure model that considers the fractured fractures; the basic equations required to establish the water hammer pressure model that considers the fractured fractures are the water hammer continuity equation and the motion equation.

[0073] When establishing the bottom-hole fracture boundary, the electrical parameters in the equivalent circuit matching the pump shutdown water hammer curve are determined. The electrical parameters include resistance R, capacitance C, and inductance I. Resistance R represents resistance, capacitance C defines weakness, which is the ratio of fracture volume to pressure potential, and inductance I is inertia, which is related to the mass of the fluid. Resistance R, capacitance C, and inductance I are connected in series to describe the bottom-hole fracture boundary, and the relationship between head difference and electrical parameters is established.

[0074] S3. Based on the established water hammer pressure model considering fracturing fractures, the electrical parameter values ​​are calculated iteratively using the method of characteristics and the Macquarie iteration.

[0075] S4. Calculate the fracture size based on the electrical parameter values ​​obtained from the iteration.

[0076] Example 2

[0077] As another preferred embodiment of the present invention, this embodiment discloses a fracturing data analysis method based on the water hammer effect. The specific scheme is as follows: Obtain the water hammer curve from the pump shutdown site and the geological data of the fracturing well. Based on the characteristics of the pump shutdown, the water hammer curve, and other relevant data, transform the hydraulic dynamic loss form of the pipeline under water hammer after hydraulic fracturing into a circuit-like equation form. This makes the water hammer model a model that considers the rapid and constant loss of fracturing fractures, applicable to complex field analysis after hydraulic fracturing. In the transformation, circuit principles are used to replace the head boundary expression in the traditional equation. Simultaneously, the electrical parameters of the equivalent circuit of the fracture at the bottom of the well are introduced into the model to establish the connection between the electrical parameters and the hydraulic system. Then, based on a simulation calculation method considering the water hammer pressure model of the fracturing fracture, after determining the electrical parameter values, the fracture size is derived.

[0078] The process involves obtaining the corresponding electrical parameters R, C, and I values ​​based on conventionally statistically derived crack sizes. These initial values ​​are then used as the initial values. The Macquarie iterative method is then employed, with the relative error between the simulated water hammer pressure curve and actual field data serving as the evaluation criterion, to estimate the electrical parameters R, C, and I. The fracturing crack size is then calculated based on the iteratively obtained electrical parameter values.

[0079] Example 3

[0080] As another preferred embodiment of the present invention, this embodiment is a description of the specific implementation of the water hammer pressure model considering fracturing fractures in Embodiments 1 and 2 above.

[0081] In this embodiment, a water hammer pressure model considering fracturing fractures is established based on the characteristics of pump shutdown, the water hammer curve of pump shutdown, and the geological data of the fracturing well. The basic equations required to establish the water hammer pressure model considering fracturing fractures are the water hammer continuity equation and the motion equation.

[0082] Water hammer continuity equation:

[0083] Equations of motion:

[0084] The pressure wave velocity inside the wellbore is expressed as:

[0085] In the formula, A is the cross-sectional area of ​​the pipe, in meters.2 H is the piezometric head, in meters (m); t is time, in seconds (s); Q is the liquid flow rate, in cubic meters per second (m³). 3 / s; x is the pipe length coordinate, in meters; θ is the inclination; a is the pressure wave velocity, in meters per second; g is the acceleration due to gravity, in meters per second. 2 λ is the Darcy friction coefficient; D is the pipe inner diameter (m); E is the fluid elastic modulus (Pa); ρ is the fluid density (kg / m³). 3 E0 is the pipe elasticity coefficient, in Pa; e is the pipe wall thickness, in mm; υ is the pipe Poisson's ratio.

[0086] When establishing the boundary of fractures at the bottom of the well, circuit principles are introduced to facilitate model calculations and fracture parameter inversion. For example... Figure 1 As shown, a fracture is defined as a closed circuit consisting of three elements connected in series: resistor R, capacitor C, and inductor I. The elements constituting the boundary of the fracture at the bottom of the well have different but corresponding physical meanings in the circuit model and the fracturing model, as shown in Table 1 below.

[0087] Table 1 shows the physical meaning of the elements.

[0088]

[0089] R, C, and I are coefficients related to pressure and velocity in the crack, while resistance R represents resistance, expressed as... The capacitance C defines weakness as the ratio of crack volume to pressure potential, expressed as: Inductance I is inertia, which is related to the mass of the fluid, and is expressed as... By connecting a resistor, capacitor, and inductor in series to describe the bottom-hole fracture boundary, the formula for calculating the pressure difference at the bottom of the well is:

[0090] In the formula, Q is the liquid flow rate, in meters per second (m³). 3 / s; ΔP is the pressure difference required to maintain the flow state, in Pa; ΔV is the crack volume change, in m³. 3 ; The pressure difference required to accelerate or decelerate the fluid discharge is expressed in Pa; ΔH is the pressure difference at the bottom of the well, also in Pa; ρ is the fluid density, expressed in kg / m³. 3 g is the acceleration due to gravity, in m / s². 2 .

[0091] In this embodiment, connecting R, C, and I in series satisfies the conditions for describing downhole fractures because, during the duration of water hammer, the volume of fluid and fracture dominates pressure and flow behavior due to the linear flow state within the fracture. In a series circuit, current flows into the circuit until the capacitor is fully charged. At this point, current will only flow into the circuit when the potential difference increases or the resistance decreases, similar to the fluid motion state in a hydraulic fracture. Using this similarity principle, a relationship between the hydraulic head and electrical parameters is established through the formula for calculating the pressure difference at the bottom of the well.

[0092] Example 4

[0093] As another preferred embodiment of the present invention, this embodiment describes a specific implementation method for numerical calculation of the water hammer pressure model considering fracturing fractures established in Embodiments 1, 2, and 3 above. Since the water hammer continuity equation and motion equation in the water hammer pressure model considering fracturing fractures cannot be directly solved and numerically calculated, this embodiment provides a numerical solution method, namely, using the method of characteristics to calculate. The method transforms the differential equation along its characteristic lines into a total differential equation, then approximates it as a difference equation, and finally performs numerical calculations.

[0094] As one implementation method of this embodiment, based on the water hammer pressure model considering fracturing fractures established in step S2, a pair of eigenvalues ​​are introduced to linearly combine the first-order quasi-linear hyperbolic partial differential equations to obtain ordinary differential equations, represented as C+ and C- respectively:

[0095]

[0096]

[0097] In the formula, A is the cross-sectional area of ​​the pipe, in meters. 2 H is the piezometric head, in meters (m); t is time, in seconds (s); Q is the liquid flow rate, in cubic meters per second (m³). 3 / s; x is the pipe length coordinate, in meters; θ is the inclination; a is the pressure wave velocity, in meters per second; g is the acceleration due to gravity, in meters per second. 2 λ is the Darcy friction coefficient; D is the pipe inner diameter, in meters.

[0098] However, these ordinary differential equations are not valid everywhere in the xt plane; they are only valid on lines with slopes of 1 / a and -1 / a, which are called characteristic lines, such as... Figure 2 As shown.

[0099] In this embodiment, integrating the ordinary differential equation along the characteristic line transforms it into a finite difference scheme as follows:

[0100]

[0101]

[0102] In the formula, Let i be the water head at point i in the wellbore at time t+Δt; Let i be the flow rate at point i inside the wellbore at time t+Δt; Let i be the water head at point i inside the wellbore at time t. Let be the flow rate at point i inside the wellbore at time t; subscript i represents any grid intersection point; subscript i-1 represents the grid point corresponding to grid intersection point i on the C+ characteristic line, and subscript i+1 represents the grid point corresponding to grid intersection point i on the C- characteristic line; coefficient C p C m All are known constants;

[0103] Solve the above two equations simultaneously to find the head and flow rate at every point in the wellbore at any given time:

[0104]

[0105]

[0106] Since the parameters on the right side of the above equation are only related to the head and flow rate of the previous time step, the evolution of the pump shutdown pressure can be quickly calculated, thereby allowing for the evolution of the pump shutdown pressure.

[0107] In this embodiment, the values ​​of electrical parameters R, C, and I are obtained based on the crack size obtained through conventional statistics. These values ​​are used as initial values. Then, the estimated values ​​of electrical parameters R, C, and I are obtained by using the Macquarie iteration method and the relative error between the simulated water hammer pressure curve and the actual field data as the evaluation standard.

[0108] Example 5

[0109] As another preferred embodiment of the present invention, this embodiment is a description of the specific implementation of calculating the size of the hydraulic fracturing crack in the above embodiments 1 and 2. The implementation of this embodiment is further proposed based on the above embodiments 3 and 4.

[0110] In this embodiment, the electrical parameter values ​​are iteratively obtained to calculate the fracturing fracture size according to the implementation method of Embodiment 4.

[0111] Based on the values ​​of the electrical parameters R, C, and I obtained through iteration, the crack half-length L can be deduced. f Seam height h f and seam width The difference between the average pressure within a fracture and the horizontal stress is called the average net pressure. Represented as:

[0112]

[0113] In the formula, PBH S is the bottom hole pressure. Hmin Minimum horizontal ground stress; ΔP nwf Here, R represents the near-wellbore frictional pressure drop, and Q0 represents the average pressure within the fracture, which is the difference between the bottom-hole pressure and the near-wellbore frictional pressure drop.

[0114] By relating the average net pressure to the crack volume change, the following relationship is obtained:

[0115]

[0116] In the formula, L is the crack width. f For half the length of the seam, h f Let be the seam height; υ be Poisson's ratio; E(m) be the elliptic integral of the second kind, and m is calculated as follows:

[0117] When 2L f / h f When ≥1, it indicates that the crack is a long crack; when 2L f / h f When the value is less than 1, it indicates that the crack is a short crack;

[0118] Assuming that the change in crack volume caused by crack flexibility is only a change in crack width, then the capacitance C can be rewritten as:

[0119]

[0120] Substituting the relationship between average net pressure and crack volume change into the capacitance expression, we get:

[0121] In the formula, E′ is the plane strain elastic modulus. E0 is Young's modulus;

[0122] Similarly, the formula for inertia I is:

[0123]

[0124] By combining the expressions for capacitance C and inertia I, the formula for crack size is derived:

[0125]

[0126]

[0127]

[0128] In practical engineering, staged fracturing is typically used for shale gas wells, with each stage containing more than one cluster of fractures. If these multiple fracture clusters are approximated as a single biplane fracture, the calculated fracture parameters are equivalent to the dimensions of the actual fracture network. For example... Figure 3 and Figure 4 As shown, if the boundary conditions of multiple crack clusters are considered as a parallel circuit, the inverted crack size is as follows:

[0129]

[0130]

[0131] In the formula, L fE For multi-cluster cracks, the equivalent crack half-length is I; T Where n is the inductance value; n is the number of clusters; C i Let be the capacitance value of the i-th crack; L represents the average net pressure of the i-th crack; fi Let be the half length of the i-th crack. The equivalent crack width for multiple clusters of cracks; Let be the width of the i-th crack.

[0132] Example 6

[0133] As an example of the present invention, this example uses data from a fractured horizontal well for simulation. The purpose of this example is to verify whether the water hammer pressure model considering the fractures proposed in this application is effective. The microseismic monitoring data of the horizontal well in the field is used and compared with the model calculation results.

[0134] The fractured well is a horizontal well. Its basic parameters are: length 157 meters, pipe inner diameter 0.025 meters.

[0135] Relevant parameters for fracturing operation: The main fracturing section is the 2946–4496 meter well section, using soluble bridge plugs as the fracturing tool. The operation pressure is 57–67 MPa, and the average fracturing flow rate is 14 m³ / s. 3 The total fluid volume used in the fracturing layer was 2353.0t of 100-mesh quartz sand and 734.7t of 40 / 70-mesh ceramsite, with a total fluid volume of 23568.85m³. 3 (Slippery water 22828.82m) 3 Linear adhesive volume 740m 3 The average pump stop pressure was 45.4 MPa. Figure 6 This is a pressure construction curve for one segment.

[0136] The water hammer pressure model considering fracturing fractures established in this application was initialized with an initial calculation time step of dt = 1 s, and a total calculation time of 250 s. By continuously changing the values ​​of R, C, and I in the iterations, a better fitting result was obtained. Figure 7 The simulated water hammer pressure curve is shown.

[0137] After the numerical simulation, the crack size formula was derived using the method described in Example 5:

[0138]

[0139]

[0140] Invert the crack size.

[0141] After processing, the corresponding half-length of the hydraulic fracturing fracture can be obtained, as shown in Table 2.

[0142] Table 2 Comparison of Simulated Crack Size and Microseismic Results

[0143]

[0144] Figure 8 The image shows a comparison between the crack height obtained from microseismic monitoring and the simulated crack height. The simulated crack size is basically consistent with the crack size obtained from microseismic monitoring, with an average accuracy of over 80%.

Claims

1. A fracturing data analysis method based on water hammer effect, characterized in that, The method includes the following steps: S1. Obtain the water hammer curve of the pump stoppage and the geological data of the fractured well; S2. Based on the characteristics of pump shutdown, the water hammer curve of pump shutdown, and the geological data of the fractured well, establish a water hammer pressure model that considers the fractured fractures; the basic equations required to establish the water hammer pressure model that considers the fractured fractures are the water hammer continuity equation and the motion equation. When establishing the bottom-hole fracture boundary, the electrical parameters in the equivalent circuit matching the pump shutdown water hammer curve are determined. The electrical parameters include resistance R, capacitance C, and inductance I. Resistance R represents resistance, capacitance C defines weakness, which is the ratio of fracture volume to pressure potential, and inductance I is inertia, which is related to the mass of the fluid. Resistance R, capacitance C, and inductance I are connected in series to describe the bottom-hole fracture boundary, and the relationship between head difference and electrical parameters is established. The resistance R represents the resistance, expressed as: The capacitance C defines weakness as the ratio of crack volume to pressure potential, expressed as: Inductance I is inertia, which is related to the mass of the fluid, and is expressed as... ; By connecting resistors, capacitors, and inductors in series to describe the bottom-hole fracture boundary, the established water hammer pressure model considering the fracturing fracture includes the water hammer continuity equation: ； Equations of motion: ; The pressure wave velocity inside the wellbore is expressed as: ; Pressure difference at the bottom of the well ; In the formula, Liquid flow rate, unit: m 3 / s; P The pressure difference required to maintain the flow state, in Pa; This represents the change in crack volume, in meters (m). 3 ; The pressure difference required to accelerate or decelerate the discharge rate, in Pa; The pressure difference at the bottom of the well is expressed in Pa. Fluid density, unit: kg / m³ 3 ; Acceleration due to gravity, unit: m / s² 2 A represents the cross-sectional area of ​​the pipe, in meters (m²). 2 H represents the piezometric head, in meters (m); t represents time, in seconds (s). These are coordinates representing the pipe length, in meters (m). Indicates the degree of inclination; Pressure wave velocity, in m / s; D is the Darcy friction coefficient; E is the pipe inner diameter in meters; E is the fluid elastic coefficient in Pa; E0 is the pipe elastic coefficient in Pa; e is the pipe wall thickness in millimeters. The pipeline's Poisson's ratio.

2. The fracturing data analysis method based on water hammer effect as described in claim 1, characterized in that: In step S3, the numerical solution of the water hammer pressure model considering fracturing fractures established in step S2 is calculated using the method of characteristics. The differential equation is transformed into a total differential equation along the characteristic lines of the differential equation, and then approximately transformed into a difference equation before numerical calculation is performed.

3. The fracturing data analysis method based on water hammer effect as described in claim 2, characterized in that: Based on the water hammer pressure model considering fracturing fractures established in step S2, a pair of eigenvalues ​​are introduced to linearly combine the first-order quasi-linear hyperbolic partial differential equations, resulting in ordinary differential equations, expressed as C. + C - : ； ； Integrating the ordinary differential equation along the characteristic line transforms it into a finite difference scheme as follows: ； ； Solve the above two equations simultaneously to find the head and flow rate at every point in the wellbore at any given time: ； ； This allows for the evolution of the pump shutdown pressure; In the formula, A is the cross-sectional area of ​​the pipe, in meters. 2 H represents the piezometric head, in meters (m). t is time, in seconds; Q is liquid flow rate, in cubic meters per second. 3 / s; Pressure wave velocity, in m / s; The angle of inclination is denoted by g; g is the acceleration due to gravity, in m / s². 2 ; D is the Darcy friction coefficient; D is the pipe inner diameter, in meters. for The water head at point i in the well shaft at any given moment; for The flow rate at point i inside the wellbore at time i; Let i be the water head at point i inside the wellbore at time t. Let i be the flow rate at point i inside the wellbore at time t; the subscript i represents any grid intersection point. The subscript i-1 indicates that the grid intersection point i is in C. + The grid points corresponding to the feature lines, with index i+1 indicating the grid intersection point i in C. - Grid points corresponding to feature lines; coefficients , x represents the pipe length coordinate, in meters (m). , All of these are known constants.

4. The fracturing data analysis method based on water hammer effect as described in claim 2, characterized in that: In step S3, the values ​​of the corresponding electrical parameters R, C, and I are obtained based on the crack size obtained through conventional statistics. These values ​​are used as initial values. Then, the estimated values ​​of electrical parameters R, C, and I are obtained by using the Macquarie iteration method and the relative error between the simulated water hammer pressure curve and the actual field data as the evaluation standard.

5. The fracturing data analysis method based on water hammer effect as described in claim 1, characterized in that: In step S4, the crack half-length L is calculated by using the values ​​of electrical parameters R, C, and I obtained through iteration. f Seam height h f and seam width ; The difference between the average pressure within a crack and the horizontal ground stress is called the average static pressure. , represented as ； ； In the formula, For the bottom hole pressure, Minimum horizontal ground stress; Here, R represents the near-wellbore frictional pressure drop, and the average pressure within the fracture is the difference between the bottom-hole pressure and the near-wellbore frictional pressure drop. Net flow; By relating the average static pressure to the crack volume change, the following relationship is obtained: ； In the formula, The width of the crack. For half the length of the seam, To make the seam higher, The pipeline's Poisson's ratio; For the complete elliptic integral of the second kind, m is calculated as follows: ,when When, it indicates that the crack is a long crack, when When the time is right, it indicates that the crack is a short crack; If the change in crack volume caused by crack flexibility is only a change in crack width, then the capacitance C can be rewritten as: ； Substituting the relationship between average static pressure and crack volume change into the capacitance expression, we get: In the formula, For plane strain elastic modulus, , Young's modulus; Similarly, the formula for inertia I is: ； By combining the expressions for capacitance C and inertia I, the formula for crack size is derived: ； ； 。 6. The fracturing data analysis method based on water hammer effect as described in claim 5, characterized in that: The boundary conditions of multiple crack clusters are considered as a parallel circuit, and the inverse crack size is: ； ； In the formula, The equivalent crack half-length for multiple clustered cracks; Here, n is the inductance value, and n is the number of clusters. Let be the capacitance value of the i-th crack; Let be the average static pressure of the i-th crack; Let be the half length of the i-th crack. The equivalent crack width for multiple clusters of cracks; Let be the width of the i-th crack.

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