A horizontal well temporary plugging and fracture extension calculation method and device

Abstract

The application provides a horizontal well temporary plugging and fracture extension calculation method and device, and the method comprises the following steps: obtaining temporary plugging calculation parameters in temporary plugging and fracture reorientation when a horizontal well is segmented and multi-clustered; calculating effective hole numbers of each cluster and distribution flow rates of each cluster according to the temporary plugging calculation parameters; calculating fracture lengths, fracture widths, fracture heights and fracture reorientation angles of each cluster according to the temporary plugging calculation parameters, the effective hole numbers of each cluster and the distribution flow rates of each cluster; and performing three-dimensional imaging on the fracture lengths, the fracture widths, the fracture heights and the fracture reorientation angles of each cluster, so as to obtain an extension path of the fracture. The application can improve the accuracy of the prediction of the fracture lengths, the fracture widths, the fracture heights and the fracture reorientation angles of temporary plugging and fracture reorientation in a segment, and further improve the scientificity and pertinence of the design of the temporary plugging and fracture reorientation process in the horizontal well segment, so as to further tap the development potential of unconventional oil and gas reservoirs.

Description

Technical Field

[0001] This invention relates to the field of unconventional oil and gas development, and in particular, to a method and apparatus for calculating the extension of temporary plugging and diversion fractures in horizontal wells. Background Technology

[0002] Multi-cluster fracturing in horizontal wells is one of the core technologies for the efficient development of unconventional oil and gas reservoirs. However, during multi-cluster fracturing, severe non-uniform propagation of hydraulic fractures often occurs, significantly limiting the production enhancement effect of multi-cluster fracturing in horizontal wells. Currently, many scholars have proposed temporary plugging and redirection technology to reduce the difference in extension length between hydraulic fracture clusters during hydraulic fracturing, achieving uniform fracture extension and expanding the control range of the fracturing well. Practical applications have proven that in-segment temporary plugging and redirection technology has certain effects. However, due to the lack of reasonable optimization design, the effect of temporary plugging and redirection technology is currently relatively unstable.

[0003] In existing technologies, research on temporary plugging and redirection fracturing mainly focuses on the influence of factors such as rock mechanics parameters, fracturing construction parameters, and the properties of temporary plugging agents on the complexity of the fracture network. However, related numerical simulation studies are limited to qualitative examinations of the effective sealing of fractures by chemical temporary plugging agents such as fibers, only verifying the feasibility and effectiveness of temporary plugging and redirection technology in increasing fracture complexity on-site. Currently, there is a lack of quantitative research on the initiation and extension of fractures in horizontal wells using temporary plugging and redirection, especially on the quantitative study of fracture geometry parameters for temporary plugging and redirection within horizontal well sections using temporary plugging balls. There is a lack of numerical calculation methods that can accurately predict the extension length and path of hydraulic fractures in temporary plugging and redirection fracturing within a section, leading to significant blind spots in the optimization of key parameters of the temporary plugging process.

[0004] Therefore, there is an urgent need for a method to calculate the extension of temporary plugging and turning fractures in horizontal wells. This method can improve the accuracy of predicting the length, width, height, and turning angle of hydraulic fractures in the temporary plugging and turning fracturing section, thereby obtaining the fracture extension path and improving the scientific nature and pertinence of the temporary plugging and turning fracturing process design in the horizontal well section, and further tapping the development potential of unconventional oil and gas reservoirs. Summary of the Invention

[0005] The purpose of this embodiment is to provide a method and apparatus for calculating the extension of temporary plugging and turning fractures in horizontal wells, so as to improve the accuracy of predicting the length, width, height and turning angle of hydraulic fractures in the temporary plugging and turning fracturing section, thereby obtaining the extension path of the fracture, improving the scientificity and pertinence of the design of temporary plugging and turning fracturing process in horizontal well sections, and further tapping the development potential of unconventional oil and gas reservoirs.

[0006] To achieve the above objectives, this paper provides a method for calculating the extension of a temporarily plugged directional fracture in a horizontal well, including:

[0007] Obtain the temporary plugging calculation parameters during directional fracturing in multi-cluster sections of a horizontal well;

[0008] Based on the temporary plugging calculation parameters, the effective number of orifices for each cluster of orifices and the allocated flow rate for each cluster of orifices are calculated.

[0009] Based on the temporary plugging calculation parameters, the effective number of holes in each cluster of perforations, and the distribution flow rate of each cluster of perforations, the crack length, crack width, crack height, and crack turning angle of each cluster of cracks are calculated.

[0010] The crack length, crack width, crack height, and crack turning angle of each cluster of cracks are used to perform three-dimensional imaging of the cracks, thereby obtaining the extension path of the cracks.

[0011] Preferably, the temporary plugging calculation parameters include: geological reservoir parameters, rock mechanics parameters, fracturing operation parameters, wellbore perforation parameters, and temporary plugging process parameters.

[0012] Preferably, the step of calculating the effective number of apertures for each cluster of apertures and the allocated flow rate for each cluster of apertures based on the calculation parameters further includes:

[0013] Based on the calculation parameters, the effective number of perforations in each cluster is calculated using the perforation flow distribution equation, the perforation blockage probability equation, and the perforation blockage quantity equation.

[0014] Based on the calculation parameters, the distribution flow rate of each cluster of perforations is calculated using the perforation friction equation, the wellbore friction equation, the wellbore-perforation-slot pressure drop equation, and the mass conservation equation.

[0015] Preferably, the perforation flow rate distribution equation is:

[0016]

[0017] Where, q pf,i q represents the flow rate of perforation hole i; cl,j N represents the flow rate of cluster j; pf,j q represents the number of perforations in cluster j; w,i Q represents the total downstream flow rate at the location of perforation i within the horizontal wellbore; total q represents the total fracturing flow rate. w,0 This represents the total upstream flow rate at the No. 1 perforation location within the horizontal wellbore, i.e., the total fracturing flow rate.

[0018] The perforation blockage probability equation is as follows:

[0019]

[0020]

[0021] Among them, fblock,i Let ξ be the probability that the i-th perforation hole is blocked by a temporary plugging ball; divert ρ is the temporary damming ball deflection coefficient, characterizing the ease with which the temporary damming ball deflects at the perforation point, and its value ranges from 0 to 1; divert , where is the density of the temporary blocking ball; ρ fluid , where is the density of the fracturing fluid;

[0022] The equation for the number of perforations plugged is as follows:

[0023]

[0024] Among them, M divert,j M represents the number of temporary plugging balls remaining at cluster j within the horizontal wellbore; block,j M represents the number of perforations in cluster j within the horizontal wellbore that were blocked; total M represents the total number of temporary plugging balls pumped in; eff,j M represents the number of remaining effective perforations in cluster j after the temporary plugging ball is used for sealing; ini,j M represents the number of apertures in cluster j; divert,0 This represents the number of temporary plugging balls remaining before the location of cluster 1 in the horizontal wellbore, i.e., the total number of temporary plugging balls pumped in.

[0025] Preferably, the perforation friction equation is:

[0026]

[0027] Where, Δp pf,i q represents the frictional pressure drop at the perforation hole of the i-th fracture; i The fluid flow rate allocated to the i-th fracture perforation cluster; n pf,i d represents the number of perforations in the i-th crack; pf,i α is the diameter of the perforation hole in the i-th crack; pf,i ρ is the flow rate coefficient of the i-th fracture perforation, ranging from 0.8 to 0.85; ρ is the density of the fracturing fluid.

[0028] The wellbore friction equation is:

[0029]

[0030] in:

[0031]

[0032] Where, Δp w,j C represents the pressure drop along the j-th horizontal well section; w L is the wellbore flow friction coefficient; w,j q is the length of the j-th horizontal well segment; w,j d represents the flow rate of the horizontal well in segment j; wn′ represents the diameter of the horizontal wellbore; n′ represents the rheological index of the fracturing fluid; k′ represents the consistency coefficient of the fracturing fluid.

[0033] The wellbore-perforation-slotted joint pressure drop equation is as follows:

[0034]

[0035] Where, p heel For horizontal wellhead pressure; p fi,i The pressure within the first element of the i-th crack;

[0036] The mass conservation equation is:

[0037]

[0038]

[0039] q w,j＝1 =q T ;

[0040] Where, q T This represents the total flow rate of the fracturing fluid.

[0041] Preferably, the step of calculating the crack length, crack width, crack height, and crack turning angle of each cluster crack based on the temporary plugging calculation parameters, the effective number of each cluster perforation, and the distribution flow rate of each cluster perforation further includes:

[0042] Based on the temporary plugging calculation parameters, the effective number of perforations in each cluster, and the distribution flow rate of each cluster, the fracture length and fracture height of each cluster fracture are calculated using the finite difference method through the hydraulic fracture material balance equation, fracturing fluid loss equation, fracture internal flow equation, fracture height propagation equation, fracture propagation initial conditions, and fracture propagation boundary conditions.

[0043] The crack width of each cluster of cracks is calculated based on the temporary plugging calculation parameters.

[0044] Based on the temporary plugging calculation parameters, the crack length, crack width, and crack height of each cluster of cracks, the crack turning angle is calculated using the crack turning angle equation.

[0045] Preferably, the step of calculating the crack width of each cluster of cracks based on the temporary plugging calculation parameters further includes:

[0046] Based on the temporary plugging calculation parameters, the discrete crack width of each cluster of cracks is calculated using the multi-crack stress balance equations and stress boundary conditions.

[0047] Based on the discrete crack widths of each crack cluster, the crack width of each crack cluster is calculated using the linear interpolation method.

[0048] On the other hand, this embodiment provides a calculation device for the extension of a temporarily plugged directional fracture in a horizontal well, the device comprising:

[0049] The acquisition module is used to acquire the temporary plugging calculation parameters during temporary plugging and diversion fracturing in multi-cluster sections of a horizontal well.

[0050] The first calculation module is used to calculate the effective number of apertures and the allocated flow rate of each cluster aperture based on the calculation parameters.

[0051] The second calculation module is used to calculate the crack length, crack width, crack height and crack turning angle of each cluster crack based on the temporary plugging calculation parameters, the effective number of each cluster perforation hole and the distribution flow rate of each cluster perforation hole.

[0052] The imaging module is used to perform three-dimensional imaging of the cracks, including crack length, crack width, crack height, and crack turning angle, thereby obtaining the crack extension path.

[0053] In another aspect, embodiments of this document also provide a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the computer program, when executed by the processor, performs instructions of any of the methods described above.

[0054] In another aspect, the embodiments herein also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor of a computer device, performs instructions for any of the methods described above.

[0055] As can be seen from the technical solutions provided in the embodiments above, the method described herein is specifically designed for the characteristics of temporary plugging and redirection fracturing processes within multi-cluster sections of horizontal wells. It performs three-dimensional imaging of the fractures based on the fracture length, width, height, and redirection angle of each cluster. It comprehensively considers the influence of injecting temporary plugging balls into the downhole perforation holes on the extension behavior of multi-cluster hydraulic fractures, thus solving the problem of highly non-uniform hydraulic fracture extension behavior within sections and the difficulty in accurately predicting the extension path of each cluster of fractures.

[0056] To make the above and other objects, features and advantages of this document more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments or prior art described herein, the accompanying drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this article. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 A flowchart illustrating a method for calculating the extension of a temporary plugging and redirecting fracture in a horizontal well, as provided in the embodiments of this paper, is shown.

[0059] Figure 2 This document illustrates a flowchart illustrating the calculation of the effective number of apertures for each cluster orifice and the allocated flow rate for each cluster orifice, as provided in the embodiments herein.

[0060] Figure 3 This document illustrates a flowchart of the process for calculating the crack length, crack width, crack height, and crack turning angle of each crack cluster, as provided in the embodiments herein.

[0061] Figure 4 A schematic diagram of the process for calculating the crack width of each cluster of cracks provided in the embodiments of this article is shown;

[0062] Figure 5 This document shows a graph illustrating the variation in the number of effective perforations in each cluster during the temporary plugging and diversion fracturing process within a multi-cluster section of a horizontal well, as provided in the embodiments herein.

[0063] Figure 6 This document shows a graph illustrating the flow rate variation of each fracture cluster during the temporary plugging and diversion fracturing process within a multi-cluster section of a horizontal well, as provided in the embodiments herein.

[0064] Figure 7 This document shows a diagram illustrating the variation in half-length of each fracture cluster during temporary plugging and diversion fracturing in a horizontal well segmented multi-cluster section, as provided in the embodiments herein.

[0065] Figure 8 This document shows a three-dimensional extension path diagram of each cluster of fractures in a horizontal well segmented by fracturing before temporary plugging, as provided in the embodiments herein.

[0066] Figure 9 This document shows a three-dimensional extension path diagram of each cluster of fractures in a segmented, multi-cluster horizontal well after temporary plugging, provided in the embodiments described herein.

[0067] Figure 10 This document shows a schematic diagram of the module structure of a horizontal well temporary plugging and diversion fracture propagation calculation device provided in an embodiment of the invention;

[0068] Figure 11 A schematic diagram of the structure of the computer device provided in the embodiments of this article is shown.

[0069] Explanation of symbols in the attached drawings:

[0070] 100. Acquisition Module;

[0071] 200. First Calculation Module;

[0072] 300. Second Calculation Module;

[0073] 400. Imaging module;

[0074] 1102. Computer equipment;

[0075] 1104. Processor;

[0076] 1106. Memory;

[0077] 1108. Drive mechanism;

[0078] 1110. Input / output module;

[0079] 1112. Input devices;

[0080] 1114. Output devices;

[0081] 1116. Presentation device;

[0082] 1118. Graphical User Interface;

[0083] 1120. Network interface;

[0084] 1122. Communication link;

[0085] 1124. Communication bus. Detailed Implementation

[0086] The technical solutions in the embodiments described below will be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments described herein, and not all of the embodiments. Based on the embodiments described herein, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this document.

[0087] In existing technologies, research on temporary plugging and redirection fracturing mainly focuses on the influence of factors such as rock mechanics parameters, fracturing construction parameters, and the properties of temporary plugging agents on the complexity of the fracture network. However, related numerical simulation studies are limited to qualitative examinations of the effective sealing of fractures by chemical temporary plugging agents such as fibers, only verifying the feasibility and effectiveness of temporary plugging and redirection technology in increasing fracture complexity on-site. Currently, there is a lack of quantitative research on the initiation and extension of fractures in horizontal wells using temporary plugging and redirection, especially on the quantitative study of fracture geometry parameters for temporary plugging and redirection within horizontal well sections using temporary plugging balls. There is a lack of numerical calculation methods that can accurately predict the extension length and path of hydraulic fractures in temporary plugging and redirection fracturing within a section, leading to significant blind spots in the optimization of key parameters of the temporary plugging process.

[0088] To address the aforementioned issues, this paper presents a method for calculating the extension of temporary plugging and diversion fractures in horizontal wells. Figure 1 This is a schematic diagram illustrating the steps of a method for calculating the extension of a horizontal well temporary plugging and redirection fracture, as provided in the embodiments herein. This specification provides the operational steps of the method described in the embodiments or flowcharts, but based on conventional or non-inventive labor, more or fewer operational steps may be included. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only possible execution order. In actual system or device products, the methods shown in the embodiments or accompanying drawings can be executed sequentially or in parallel.

[0089] Reference Figure 1 A method for calculating the extension of a temporarily plugged directional fracture in a horizontal well, comprising:

[0090] S101: Obtain the temporary plugging calculation parameters during temporary plugging and diversion fracturing in multi-cluster sections of a horizontal well;

[0091] S102: Based on the temporary plugging calculation parameters, calculate the effective number of orifices for each cluster of perforations and the allocated flow rate for each cluster of perforations;

[0092] S103: Based on the temporary plugging calculation parameters, the effective number of holes in each cluster of perforations, and the distribution flow rate of each cluster of perforations, the crack length, crack width, crack height, and crack turning angle of each cluster of cracks are calculated.

[0093] S104: Perform three-dimensional imaging of the cracks by measuring the crack length, crack width, crack height, and crack turning angle of each cluster of cracks, thereby obtaining the extension path of the cracks.

[0094] Compared with existing technologies, the method described in this paper is specifically designed for the characteristics of temporary plugging and redirection fracturing processes within multi-cluster sections of horizontal wells. It performs three-dimensional imaging of the fractures based on the fracture length, width, height, and redirection angle of each cluster. It comprehensively considers the influence of the injection of temporary plugging balls into the downhole sealing perforation holes on the extension behavior of multi-cluster hydraulic fractures, thus solving the problem of highly non-uniform hydraulic fracture extension behavior within sections and the difficulty in accurately predicting the extension path of each cluster of fractures.

[0095] The temporary plugging calculation parameters include: geological reservoir parameters, rock mechanics parameters, fracturing operation parameters, wellbore perforation parameters, and temporary plugging process parameters.

[0096] Furthermore, geological reservoir parameters include, but are not limited to, formation vertical principal stress, formation maximum horizontal principal stress, formation minimum horizontal principal stress, stress difference between caprock and producing layer, stress difference between base layer and producing layer, reservoir thickness, and filtration coefficient; rock mechanics parameters include, but are not limited to, Poisson's ratio, Young's modulus, and fracture toughness; fracturing operation parameters include, but are not limited to, fracturing flow rate, fracturing fluid volume, fracturing duration, fracturing fluid density, and fracturing fluid viscosity; wellbore perforation parameters include, but are not limited to, wellbore inner diameter, number of perforation clusters, number of perforations, and perforation inner diameter; and temporary plugging process parameters include, but are not limited to, number of temporary plugging balls, temporary plugging ball density, and timing of temporary plugging.

[0097] Where T = T A / T B ;

[0098] T represents the temporary congestion time. A The temporary plugging ball insertion time, T, is the time elapsed from the start of fracturing to the insertion of the temporary plugging ball into the well. B This refers to the fracturing time, which is the total time required for the fracturing process.

[0099] Reference Figure 2 In this embodiment, calculating the effective number of apertures and the allocated flow rate of each cluster aperture based on the calculation parameters further includes:

[0100] S201: Based on the calculation parameters, the effective number of perforations in each cluster is calculated using the perforation flow distribution equation, the perforation blockage probability equation, and the perforation blockage quantity equation.

[0101] S202: Based on the calculation parameters, the distribution flow rate of each cluster of perforations is calculated using the perforation friction equation, the wellbore friction equation, the wellbore-perforation-slot pressure drop equation, and the mass conservation equation.

[0102] Specifically, during the segmented fracturing of horizontal wells with multiple clusters, temporary plugging balls are injected downhole midway through the operation to seal the perforations of the clusters with higher flow rates. This prevents excessive extension of the outer fractures and promotes accelerated extension of the inner fractures, thereby achieving uniform extension of each cluster of fractures. The effective number of perforations in each cluster can be calculated using the perforation flow rate distribution equation, the perforation plugging probability equation, and the perforation plugging quantity equation.

[0103] The perforation flow rate distribution equation is as follows:

[0104]

[0105] Where, q pf,i q represents the flow rate of perforation hole i; cl,j N represents the flow rate of cluster j; pf,j q represents the number of perforations in cluster j; w,i Q represents the total downstream flow rate at the location of perforation i within the horizontal wellbore; total q is the fracturing displacement. w,0 This is the total upstream flow rate at the No. 1 perforation location in the horizontal wellbore, i.e., the fracturing discharge rate;

[0106] The perforation flow distribution equation utilizes fracturing construction parameters and wellbore perforation parameters.

[0107] The perforation blockage probability equation is as follows:

[0108]

[0109]

[0110] Among them, f block,i Let ξ be the probability that the i-th perforation hole is blocked by a temporary plugging ball; divert ρ is the temporary damming ball deflection coefficient, characterizing the ease with which the temporary damming ball deflects at the perforation point, and its value ranges from 0 to 1; divert, Density of the temporarily blocked ball; ρ fluid, This refers to the density of the fracturing fluid.

[0111] The perforation blockage probability equation utilizes temporary plugging process parameters.

[0112] The equation for the number of perforations plugged is as follows:

[0113]

[0114] Among them, M divert,j M represents the number of temporary plugging balls remaining at cluster j within the horizontal wellbore; block,j M represents the number of perforations in cluster j within the horizontal wellbore that were blocked; total M represents the total number of temporary plugging balls pumped in; eff,j M represents the number of remaining effective perforations in cluster j after the temporary plugging ball is used for sealing;ini,j M represents the number of apertures in cluster j; divert,0 This represents the number of temporary plugging balls remaining before the location of cluster 1 in the horizontal wellbore, i.e., the total number of temporary plugging balls pumped in.

[0115] The perforation plugging quantity equation utilizes wellbore perforation parameters and temporary plugging process parameters.

[0116] During segmented, multi-cluster fracturing in horizontal wells, the stress interference between fractures leads to varying fracture openings and unequal flow resistance of the fracturing fluid within each fracture, resulting in uneven flow distribution across the perforation clusters. Typically, the outer fractures receive a larger flow and extend further, while the inner fractures, due to compression from the outer fractures, receive a smaller flow and have limited extension. The flow distribution across each fracture can be calculated using the perforation friction equation, the wellbore friction equation, the wellbore-perforation-fracture pressure drop equation, and the mass conservation equation.

[0117] The equation for perforation friction is:

[0118]

[0119] Where, Δp pf,i q represents the frictional pressure drop at the perforation hole of the i-th fracture; i The fluid flow rate allocated to the i-th fracture perforation cluster; n pf,i d represents the number of perforations in the i-th crack; pf,i Let α be the inner diameter of the perforation hole of the i-th crack; pf,i ρ is the flow rate coefficient of the i-th fracture perforation, ranging from 0.8 to 0.85; ρ is the density of the fracturing fluid.

[0120] The perforation friction equation utilizes fracturing construction parameters and wellbore perforation parameters.

[0121] The wellbore friction equation is:

[0122]

[0123] in:

[0124]

[0125] Where, Δp w,j C represents the pressure drop along the j-th horizontal well section; w L is the wellbore flow friction coefficient; w,j q is the length of the j-th horizontal well segment; w,j d represents the flow rate of the horizontal well in segment j; w is the diameter of the horizontal wellbore; n′ represents the rheological index of the fracturing fluid; the value of Newtonian fluid fracturing fluid is 1; k′ represents the consistency coefficient of the fracturing fluid, which is the viscosity μ of the fracturing fluid in Newtonian fluid fracturing fluid.

[0126] The wellbore friction equation utilizes fracturing construction parameters and wellbore perforation parameters.

[0127] The wellbore-perforation-slotted joint pressure drop equation is as follows:

[0128]

[0129] Where, p heel For horizontal wellhead pressure; p fi,i The pressure within the first element of the i-th crack;

[0130] The mass conservation equation is:

[0131]

[0132]

[0133] q w,j＝1 =Q Total ;

[0134] Among them, Q total This refers to the fracturing displacement.

[0135] The mass conservation equation utilizes fracturing construction parameters.

[0136] Reference Figure 3 In this embodiment, the step of calculating the crack length, crack width, crack height, and crack turning angle of each cluster crack based on the temporary plugging calculation parameters, the effective number of each cluster perforation, and the distribution flow rate of each cluster perforation further includes:

[0137] S301: Based on the temporary plugging calculation parameters, the effective number of holes in each cluster of perforations, and the distribution flow rate of each cluster of perforations, the fracture length and fracture height of each cluster of fractures are calculated using the finite difference method through the hydraulic fracture material balance equation, fracturing fluid loss equation, fracture internal flow equation, fracture height propagation equation, fracture propagation initial conditions, and fracture propagation boundary conditions.

[0138] S302: Calculate the crack width of each cluster of cracks based on the temporary plugging calculation parameters;

[0139] S303: Based on the temporary plugging calculation parameters, the crack length, crack width, and crack height of each cluster of cracks, the crack turning angle is calculated using the crack turning angle equation.

[0140] The steps S301-S303 described above do not have a necessary order. For step S301, during the temporary plugging and fracturing process within the multi-cluster section of the horizontal well, fracturing fluid flows into the hydraulic fracture from the perforations of each cluster, promoting continuous fracture extension. The fracture length and height can be calculated using the hydraulic fracture mass balance equation, the fracturing fluid loss equation, the fracture internal flow equation, the fracture height propagation equation, and the initial and boundary conditions for fracture extension.

[0141] In this embodiment, the width of each cluster of cracks can be calculated first, and then the crack width can be substituted into the hydraulic crack mass balance equation and the internal flow equation of the crack for further calculation to obtain the crack length and crack height.

[0142] The mass balance equation for a hydraulic fracture is:

[0143]

[0144] Where q is the flow rate within the crack; h f w is the crack height. f q represents the crack width; s represents the crack length direction coordinate; t represents time; L This represents the fracturing fluid loss rate.

[0145] The fracturing fluid loss equation is:

[0146]

[0147] Among them, C L τ is the filtration coefficient; τ is the start time of filtration.

[0148] The flow equation inside the crack is:

[0149]

[0150] Where p is the pressure inside the crack; s is the coordinate of the crack length direction; and μ is the liquid viscosity.

[0151] The flow equation inside the fracture utilizes fracturing construction parameters.

[0152] The equation for crack height propagation is:

[0153]

[0154]

[0155] h f =h u +h l ;

[0156] Among them, K uc K lcThese represent the fracture toughness of the caprock and the underlying rock, respectively; S u S l These represent the stress differences between the caprock and the producing layer, and between the basal layer and the producing layer, respectively; g v g s g p These represent the high pressure drop gradient, geostress gradient, and fluid pressure gradient, respectively; h is the reservoir height; h u h l These are the upper seam height and the lower seam height, respectively.

[0157] The crack height propagation equation utilizes rock mechanics parameters.

[0158] The initial conditions for crack propagation are:

[0159] l f | t＝0 =0;

[0160] h f | t＝0 =0;

[0161] Among them, l f The length is the crack length.

[0162] The boundary conditions for crack propagation are:

[0163]

[0164]

[0165]

[0166] q| s＝0 =q inlet ;

[0167] Where, σ c This refers to the fracture wall closure stress, i.e., the minimum horizontal principal stress of the formation; q inlet This represents the flow rate at the crack opening.

[0168] Reference Figure 4 In this embodiment, calculating the crack width of each cluster of cracks based on the temporary plugging calculation parameters further includes:

[0169] S401: Based on the temporary plugging calculation parameters, the discrete crack width of each cluster of cracks is calculated using the multi-crack stress balance equation set and stress boundary conditions.

[0170] S402: Based on the discrete crack widths of each cluster of cracks, the crack width of each cluster of cracks is calculated using the linear interpolation method.

[0171] The stress balance equations for multiple cracks are as follows:

[0172]

[0173]

[0174] in:

[0175]

[0176]

[0177]

[0178]

[0179] Among them, (σ t ) i 、(σ n ) i These represent the shear stress and normal stress experienced by element i in the local coordinate system, respectively; (u t ) j Let j be the tangential strain of element j in the local coordinate system; (u n ) j Let J be the normal strain of element j in the local coordinate system, i.e., the discrete crack width; (A tt ) ij 、(A nt ) ij 、(A tn ) ij 、(A nn ) ij Let i and n be the tangential stress components and normal stress components caused by the tangential and normal displacement discontinuities of element j, respectively, in element i. i and j take values ​​from 1 to N; G is the formation shear modulus; ν is the formation Poisson's ratio; n j The cosine of the angle between the global z-axis and the j-element local ζ-axis; j F is the cosine of the angle between the global x-axis and the local ξ-axis of element j; k Let be the partial derivative equation of the Papkovitch function, k∈{3~6}.

[0180] The stress equilibrium equations for multiple fractures utilize rock mechanics parameters.

[0181] The stress boundary conditions are:

[0182] (σ t ) i =0;

[0183] (σ n ) i =-(p-σ c ) i ;

[0184] In step S401, using the aforementioned multi-fracture stress balance equations and stress boundary conditions, the discrete fracture widths of each fracture cluster are calculated. After obtaining the discrete fracture widths, in step S402, based on the discrete fracture widths of each fracture cluster, the fracture width at any coordinate along the length direction within the hydraulic fracture, i.e., the fracture width of each fracture cluster, can be calculated using the linear difference method. This fracture width can then be substituted into the hydraulic fracture mass balance equations and the internal flow equations for further calculations.

[0185] For step S303, based on the temporary plugging calculation parameters, the crack length, crack width, and crack height of each cluster of cracks, the crack turning angle is calculated using the crack turning angle equation as follows:

[0186] When performing temporary plugging and directional fracturing in a horizontal well with multiple perforation clusters, multiple fractures initiate and extend simultaneously from each perforation cluster. During the extension process, stress interference effects exist between the fractures, resulting in non-planar directional extension behavior of the fractures. The fracture directional angle can be calculated using the fracture directional angle equation.

[0187] Specifically, the equation for the crack turning angle is:

[0188] K I sinθ HF +K II (3cosθ HF -1) = 0;

[0189] in,

[0190]

[0191]

[0192] Among them, K Ⅰ K Ⅱ These represent the first and second type stress intensity factors of the reservoir rock, respectively; G is the shear modulus of the reservoir rock; D n D s These represent the normal and tangential strains at the crack tip, respectively; a is half the length of the discrete crack element in the DDM model; θ HF This represents the crack turning angle.

[0193] The fracture orientation angle equation utilizes rock mechanics parameters.

[0194] Therefore, three-dimensional imaging of fractures can be performed based on the fracture length, width, height, and turning angle of each fracture cluster. The resulting three-dimensional fracture extension path map allows for the determination of the fracture extension path. By improving the accuracy of the predicted length, width, height, and turning angle of hydraulic fractures in the temporary plugging and turning fracturing section, the fracture extension path can be obtained, enhancing the scientific rigor and relevance of the temporary plugging and turning fracturing process design in horizontal well sections, and further unlocking the development potential of unconventional oil and gas reservoirs.

[0195] For example, after obtaining the temporary plugging calculation parameters for fracturing in a multi-cluster section of a horizontal well according to Table 1 below, the fracture extension value is calculated using the calculation method in this paper.

[0196] Table 1:

[0197] Young's modulus 43.25 GPa Poisson's ratio 0.23 Dimensionless Maximum horizontal principal stress of the formation 77 MPa Minimum horizontal principal stress of the formation 65 MPa Vertical principal stress of formation 73 MPa reservoir thickness 25 m Stress difference between caprock and producing layer 5 MPa Stress difference between the bottom layer and the producing layer 5 MPa fracture toughness of the formation 0.8 <![CDATA[MPa·m 1 / 2 ]]> fracture toughness of caprock and sublayer 1.2 <![CDATA[MPa·m 1 / 2 ]]> Fracturing fluid viscosity (Newtonian fluid) 5 mPa·s fracturing fluid density 1000 <![CDATA[kg / m 3 ]]> Filtration coefficient <![CDATA[2.0×10 -4 ]]> <![CDATA[m·s -1 / 2 ]]> fracturing displacement 16 <![CDATA[m 3 / min]]> fracturing fluid volume 1800 <![CDATA[m 3 ]]> Wellbore inner diameter 114 mm Number of perforation clusters 6 Dimensionless Cluster spacing 9.5 m Number of apertures in each cluster 8 Dimensionless Hole inner diameter 11.5 mm Number of temporarily blocked balls 26 Dimensionless Temporarily blocked ball entry time 56 min Temporary blockage density 950 <![CDATA[kg / m 3 ]]>

[0198] First, the effective number of perforations in each cluster was calculated, and the changes in the effective number of perforations in each cluster are as follows: Figure 5 As shown. Before the temporary plugging ball was inserted, each cluster had 8 effective perforations. After the temporary plugging ball was inserted, the number of perforations blocked in clusters 1 to 6 were 8, 3, 2, 2, 3, and 8, respectively, and the number of remaining effective perforations were 0, 5, 6, 6, 5, and 0, respectively.

[0199] Subsequently, the distribution flow rate of each cluster of orifices was calculated, and the changes in the distribution flow rate of each cluster of orifices are as follows: Figure 6 As shown, Figure 6 The flow rate of each cluster of fractures is the distribution flow rate of each cluster perforation. Before the temporary plugging ball is inserted, the distribution flow rate of clusters 1 and 6 on the outer side continuously increases, while the distribution flow rate of clusters 2, 3, 4, and 5 on the inner side continuously decreases. After the temporary plugging ball is inserted, the perforations of clusters 1 and 6 on the outer side are completely blocked, and the flow rate drops sharply to 0. The distribution flow rate of clusters 2, 3, 4, and 5 on the inner side all increase instantaneously.

[0200] Subsequently, the crack length, crack width, crack height, and crack turning angle of each crack cluster were calculated, and the half-length variation of each crack cluster was as follows: Figure 7As shown, before the temporary plugging ball was inserted, the fractures in clusters 1 and 6 on the outer side extended faster, while the fractures in clusters 2, 3, 4, and 5 on the inner side extended slower. After the temporary plugging ball was inserted, the perforations of clusters 1 and 6 on the outer side were completely blocked, stopping their extension, and the half-length of the fractures remained unchanged. The fractures in clusters 2, 3, 4, and 5 on the inner side extended faster. When fracturing stopped, the half-lengths of each cluster were 132.0 m, 167.9 m, 151.6 m, 151.5 m, 167.9 m, and 132.1 m, respectively. Before the temporary plugging ball was inserted, the extension of each cluster of fractures was uneven, and the fractures in clusters 1 and 6 on the inner side were significantly restricted. After the temporary plugging ball was inserted, the extension of each cluster of fractures was more uniform, and the extension length of fractures in clusters 2, 3, 4, and 5 on the inner side exceeded that of the outer fractures.

[0201] Finally, the crack length, crack width, crack height, and crack turning angle of each cluster of cracks are used to create a three-dimensional crack image, thus obtaining the crack extension path, such as... Figure 9 This is a diagram showing the extension path of fractures in each cluster of fractures within a multi-cluster segment of a horizontal well after temporary plugging. For example... Figure 8 The diagram shown illustrates the extension paths of each fracture cluster within a segmented horizontal well before temporary plugging and fracturing. This allows us to determine the fracture extension paths.

[0202] Based on the aforementioned method for calculating the extension of a temporarily plugged directional fracture in a horizontal well, this embodiment also provides a device for calculating the extension of a temporarily plugged directional fracture in a horizontal well. The device may include a system (including a distributed system), software (application), module, component, server, client, etc., using the method described in this embodiment, combined with necessary implementation hardware. Based on the same innovative concept, the devices in one or more embodiments provided in this embodiment are as described in the following embodiments. Since the implementation schemes and methods for solving the problem are similar, the implementation of the specific device in this embodiment can refer to the implementation of the aforementioned method, and repeated details will not be repeated. As used below, the terms "unit" or "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0203] Specifically, Figure 10 This is a schematic diagram of the module structure of an embodiment of a horizontal well temporary plugging and diversion fracture propagation calculation device provided in this article, with reference to... Figure 10 As shown in the embodiment of this paper, a horizontal well temporary plugging and turning fracture extension calculation device includes: an acquisition module 100, a first calculation module 200, a second calculation module 300, and an imaging module 400.

[0204] Module 100 is used to acquire the temporary plugging calculation parameters during temporary plugging and diversion fracturing in multi-cluster sections of a horizontal well.

[0205] The first calculation module 200 is used to calculate the effective number of apertures and the allocated flow rate of each cluster aperture according to the calculation parameters.

[0206] The second calculation module 300 is used to calculate the crack length, crack width, crack height and crack turning angle of each cluster crack based on the temporary plugging calculation parameters, the effective number of each cluster perforation and the distribution flow of each cluster perforation.

[0207] The imaging module 400 is used to perform three-dimensional imaging of the cracks, including crack length, crack width, crack height, and crack turning angle, thereby obtaining the extension path of the cracks.

[0208] Reference Figure 11 As shown, based on the above-described method for calculating the extension of a horizontal well temporary plugging and redirection fracture, one embodiment of this document also provides a computer device 1102, wherein the above method is run on the computer device 1102. The computer device 1102 may include one or more processors 1104, such as one or more central processing units (CPUs) or graphics processing units (GPUs), each processing unit implementing one or more hardware threads. The computer device 1102 may also include any memory 1106 for storing any kind of information such as code, settings, data, etc. In one specific embodiment, a computer program is stored on the memory 1106 and can run on the processor 1104. When the computer program is run by the processor 1104, it can execute instructions according to the above method. Non-limitingly, for example, the memory 1106 may include any type of RAM, any type of ROM, flash memory device, hard disk, optical disk, etc. More generally, any memory can use any technology to store information. Further, any memory can provide volatile or non-volatile retention of information. Further, any memory can represent a fixed or removable component of the computer device 1102. In one scenario, when processor 1104 executes associated instructions stored in any memory or combination of memories, computer device 1102 can perform any operation of the associated instructions. Computer device 1102 also includes one or more drive mechanisms 1108 for interacting with any memory, such as hard disk drive mechanisms, optical disk drive mechanisms, etc.

[0209] Computer device 1102 may further include an input / output module 1110 (I / O) for receiving various inputs (via input device 1112) and providing various outputs (via output device 1114). A specific output mechanism may include a presentation device 1116 and an associated graphical user interface 1118 (GUI). In other embodiments, the input / output module 1110 (I / O), input device 1112, and output device 1114 may be omitted, and the device may function solely as a computer device within a network. Computer device 1102 may also include one or more network interfaces 1120 for exchanging data with other devices via one or more communication links 1122. One or more communication buses 1124 couple the components described above together.

[0210] Communication link 1122 can be implemented in any way, such as via a local area network, a wide area network (e.g., the Internet), a point-to-point connection, or any combination thereof. Communication link 1122 may include any combination of hardwired links, wireless links, routers, gateway functions, name servers, etc., governed by any protocol or combination of protocols.

[0211] Corresponding to Figures 1-4 In addition to the methods described above, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, performs the steps of the above-described methods.

[0212] This embodiment also provides a computer-readable instruction, wherein when a processor executes the instruction, the program therein causes the processor to perform the following: Figures 1 to 4 The method shown.

[0213] It should be understood that in the various embodiments of this document, the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this document.

[0214] It should also be understood that, in the embodiments herein, the term "and / or" is merely a description of the relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following associated objects have an "or" relationship.

[0215] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this document.

[0216] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0217] In the embodiments provided herein, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the couplings or direct couplings or communication connections shown or discussed may be indirect couplings or communication connections through some interfaces, devices, or units, or they may be electrical, mechanical, or other forms of connection.

[0218] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments described herein, depending on actual needs.

[0219] Furthermore, the functional units in the various embodiments of this document can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0220] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this paper, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this paper. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0221] This document uses specific embodiments to illustrate the principles and implementation methods of this document. The descriptions of the embodiments above are only for the purpose of helping to understand the methods and core ideas of this document. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this document. Therefore, the content of this specification should not be construed as a limitation of this document.

Claims

1. A method for calculating the extension of a temporarily plugged diversion fracture in a horizontal well, characterized in that, include: Obtain the temporary plugging calculation parameters during directional fracturing in multi-cluster sections of a horizontal well; Based on the temporary plugging calculation parameters, the effective number of orifices for each cluster of orifices and the allocated flow rate for each cluster of orifices are calculated. Based on the temporary plugging calculation parameters, the effective number of holes in each cluster of perforations, and the distribution flow rate of each cluster of perforations, the crack length, crack width, crack height, and crack turning angle of each cluster of cracks are calculated. The crack length, crack width, crack height, and crack turning angle of each cluster of cracks are used to perform three-dimensional crack imaging, thereby obtaining the crack extension path. The step of calculating the effective number of perforations for each cluster based on the temporary plugging calculation parameters further includes: Based on the temporary plugging calculation parameters, the effective number of perforations in each cluster is calculated using the perforation flow distribution equation, the perforation blockage probability equation, and the perforation plugging quantity equation. The perforation flow rate distribution equation is as follows: ； in, q pf , i for i No. 1 perforation flow rate; q cl , j for j Cluster flow; N pf , j for j Number of perforations in cluster number 1; q w , i For horizontal wellbore i Total downstream flow at the location of the No. 1 perforation hole; Q total This represents the total fracturing flow rate. q w , 0 This represents the total upstream flow rate at the No. 1 perforation location within the horizontal wellbore, i.e., the total fracturing flow rate. The perforation blockage probability equation is as follows: ； ； in, f block , i for i The probability that the No. 1 perforation hole is blocked by a temporary plugging ball; ξ divert The temporary dam ball turning coefficient represents the ease with which the temporary dam ball turns at the perforation hole, and its value ranges from 0 to 1. ρ divert, Density of temporarily blocked balls; ρ fluid, This refers to the density of the fracturing fluid. The equation for the number of perforations plugged is as follows: ； in, M divert , j For horizontal wellbore j The number of temporarily blocked balls remaining at the cluster position; M block , j For horizontal wellbore j The number of perforations in cluster 1 were blocked; M total This represents the total number of temporary plugging balls pumped in. M eff , j After temporarily blocking the ball j The remaining effective perforation number of cluster number 1; M ini , j for j Number of perforations in cluster 1; M divert , 0 This represents the number of temporary plugging balls remaining before the location of cluster 1 in the horizontal wellbore, i.e., the total number of temporary plugging balls pumped in.

2. The method for calculating the extension of a temporarily plugged diversion fracture in a horizontal well according to claim 1, characterized in that, The temporary plugging calculation parameters include: geological reservoir parameters, rock mechanics parameters, fracturing operation parameters, wellbore perforation parameters, and temporary plugging process parameters.

3. The method for calculating the extension of a temporarily plugged diversion fracture in a horizontal well according to claim 1, characterized in that, The step of calculating the effective number of orifices and the allocated flow rate of each cluster perforation based on the temporary plugging calculation parameters further includes: Based on the temporary plugging calculation parameters, the distribution flow rate of each cluster of perforations is calculated using the perforation friction equation, the wellbore friction equation, the wellbore-perforation-slot pressure drop equation, and the mass conservation equation.

4. The method for calculating the extension of a temporary plugging and redirecting fracture in a horizontal well according to claim 3, characterized in that, The equation for perforation friction is: ； Where, Δ p pf , i For the first i Frictional pressure drop at the perforation hole of the crack; q i For the first i The fluid flow rate distributed by the perforation cluster with cracks; n pf , i For the first i Number of perforations in the crack; d pf , i For the first i Diameter of the perforation hole in the crack; α pf , i For the first i The flow rate coefficient of the perforated section is taken as 0.8~0.85; ρ This refers to the density of the fracturing fluid. The wellbore friction equation is: ； in: ； Where, Δ p w , j For the first j Pressure drop along the horizontal section of the well; C w The coefficient of friction for wellbore flow; L w , j For the first j Length of horizontal well section; q w , j For the first j Horizontal well flow rate; d w The diameter of the horizontal wellbore; Represents the rheological index of fracturing fluid; Represents the consistency coefficient of the fracturing fluid; The wellbore-perforation-slotted joint pressure drop equation is as follows: ； in, p heel For horizontal wellhead pressure; p fi , i For the first i Pressure within the first unit of the crack; The mass conservation equation is: ； ； ； in, q T This represents the total flow rate of the fracturing fluid.

5. The method for calculating the extension of a temporarily plugged diversion fracture in a horizontal well according to claim 1, characterized in that, The step of calculating the fracture length, fracture width, fracture height, and fracture turning angle of each cluster fracture based on the temporary plugging calculation parameters, the effective number of each cluster perforation, and the distribution flow rate of each cluster perforation further includes: Based on the temporary plugging calculation parameters, the effective number of perforations in each cluster, and the distribution flow rate of each cluster, the fracture length and fracture height of each cluster fracture are calculated using the finite difference method through the hydraulic fracture material balance equation, fracturing fluid loss equation, fracture internal flow equation, fracture height propagation equation, fracture propagation initial conditions, and fracture propagation boundary conditions. The crack width of each cluster of cracks is calculated based on the temporary plugging calculation parameters. Based on the temporary plugging calculation parameters, the crack length, crack width, and crack height of each cluster of cracks, the crack turning angle is calculated using the crack turning angle equation.

6. The method for calculating the extension of a temporarily plugged diversion fracture in a horizontal well according to claim 5, characterized in that, The step of calculating the crack width of each cluster of cracks based on the temporary plugging calculation parameters further includes: Based on the temporary plugging calculation parameters, the discrete crack width of each cluster of cracks is calculated using the multi-crack stress balance equations and stress boundary conditions. Based on the discrete crack widths of each crack cluster, the crack width of each crack cluster is calculated using the linear interpolation method.

7. A calculation device for the extension of a temporarily plugged diversion fracture in a horizontal well, characterized in that, The device includes: The acquisition module is used to acquire the temporary plugging calculation parameters during temporary plugging and diversion fracturing in multi-cluster sections of a horizontal well. The first calculation module is used to calculate the effective number of orifices and the allocated flow rate of each cluster of perforations based on the temporary blocking calculation parameters. The second calculation module is used to calculate the crack length, crack width, crack height and crack turning angle of each cluster crack based on the temporary plugging calculation parameters, the effective number of each cluster perforation hole and the distribution flow rate of each cluster perforation hole. The imaging module is used to perform three-dimensional imaging of the cracks, including crack length, crack width, crack height, and crack turning angle, thereby obtaining the extension path of the cracks. The first calculation module is also used to calculate the effective number of perforations in each cluster based on the temporary plugging calculation parameters, through the perforation flow distribution equation, the perforation blockage probability equation, and the perforation plugging quantity equation. The perforation flow rate distribution equation is as follows: ； in, q pf , i for i No. 1 perforation flow rate; q cl , j for j Cluster flow; N pf , j for j Number of perforations in cluster number 1; q w , i For horizontal wellbore i Total downstream flow at the location of the No. 1 perforation hole; Q total This represents the total fracturing flow rate. q w , 0 This represents the total upstream flow rate at the No. 1 perforation location within the horizontal wellbore, i.e., the total fracturing flow rate. The perforation blockage probability equation is as follows: ； ； in, f block , i for i The probability that the No. 1 perforation hole is blocked by a temporary plugging ball; ξ divert The temporary dam ball turning coefficient represents the ease with which the temporary dam ball turns at the perforation hole, and its value ranges from 0 to 1. ρ divert, Density of temporarily blocked balls; ρ fluid, This refers to the density of the fracturing fluid. The equation for the number of perforations plugged is as follows: ； in, M divert , j For horizontal wellbore j The number of temporarily blocked balls remaining at the cluster position; M block , j For horizontal wellbore j The number of perforations in cluster 1 were blocked; M total This represents the total number of temporary plugging balls pumped in. M eff , j After temporarily blocking the ball j The remaining effective perforation number of cluster number 1; M ini , j for j Number of perforations in cluster 1; M divert , 0 This represents the number of temporary plugging balls remaining before the location of cluster 1 in the horizontal wellbore, i.e., the total number of temporary plugging balls pumped in.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, When the computer program is run by the processor, it executes the instructions of the method according to any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor of the computer device, it executes the instructions of the method according to any one of claims 1-6.

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