Deep shale horizontal well segmented multi-cluster fracturing optimization design method

Abstract

The present application provides a kind of deep shale horizontal well segmented multi-cluster fracturing optimization design method, comprising: collecting fracturing parameters;Establish shale reservoir natural fracture model;Establish the fluid-structure coupling model of horizontal well segmented multi-cluster fracturing stress field and flow field;Establish the inter-cluster flow distribution model of multiple fractures simultaneously expanding;Establish the intersection interaction model of hydraulic fracture and natural fracture;Establish segmented multi-cluster fracturing multi-fracture simultaneous expansion model;Establish the mathematical model of horizontal well segmented multi-cluster fracturing multi-fracture dynamic expansion considering the effect of natural fracture, inter-fracture stress interference and complex flow distribution;Based on the established mathematical model and combined with the collected parameters, the completion parameters and construction parameters of deep shale horizontal well segmented multi-cluster fracturing are optimized.The present application overcomes the defect that the average value is used for branch flow under fracturing fracture bifurcation in the prior art, and simultaneously makes up for the deficiency that the intersection interaction criterion of hydraulic fracture and natural fracture under the influence of multiple fractures does not consider inter-fracture stress interference.

Description

Technical Field

[0001] This invention relates to the field of unconventional oil and gas reservoir production enhancement and stimulation technology, and more specifically, to an optimized design method for multi-cluster fracturing in deep shale horizontal wells. Background Technology

[0002] With the deepening development of unconventional oil and gas resources (tight oil and gas, shale oil and gas, and coalbed methane), reservoir depths are increasing and geological conditions are becoming more complex, leading to greater development difficulties. my country has a wide distribution of deep shale gas resources with abundant reserves and enormous development potential. However, deep shale formations are characterized by low porosity, low permeability, high stress differentials, and strong heterogeneity. Effective production enhancement through hydraulic fracturing technology is necessary to achieve substantial economic productivity, realize industrial-scale extraction, fill the domestic natural gas supply gap, and ensure energy security.

[0003] Horizontal well staged multi-cluster fracturing technology is a crucial technique for deep shale gas extraction. By creating artificial fractures in the reservoir through fracturing, a high-speed flow channel is established between the horizontal wellbore and the reservoir. This increases the exposed area of ​​the reservoir, reduces the pressure differential required for shale gas flow, and shortens the seepage distance of shale gas within the reservoir, thereby achieving production enhancement. In the horizontal well staged multi-cluster fracturing process, the horizontal wellbore in the reservoir is perforated in stages, followed by pumping fracturing fluid to perform multi-cluster fracturing within each stage until all stages are fracturing, at which point the fracturing operation is complete. The fracturing effect affects the morphology of the artificial fractures, the spatial distribution of the artificial fractures influences sand conveying and proppant placement, and the proppant placement in the sand-filled fractures affects gas well production. Effective and uniform propagation of multiple fractures is key to horizontal well staged multi-cluster fracturing, requiring optimization of relevant parameters in the hydraulic fracturing design.

[0004] Currently, numerical simulation is widely used for optimizing fracturing construction design parameters. However, most models use sequential coupling between stress field and flow field, do not consider the dynamic distribution process of flow between clusters, and fail to accurately describe the interaction between hydraulic fractures and natural force fractures. For bifurcated fractures, the flow is evenly distributed, which cannot accurately simulate the propagation of multi-cluster fracturing in horizontal wells, thus affecting the optimization of fracturing design parameters. Summary of the Invention

[0005] The present invention aims to provide an optimized design method for segmented multi-cluster fracturing in deep shale horizontal wells, in order to solve the problems existing in the numerical simulation used for fracturing construction design parameter optimization in the existing methods.

[0006] This invention provides an optimized design method for multi-cluster fracturing in deep shale horizontal wells, comprising the following steps:

[0007] S100 collects geological parameters, well completion parameters, and construction parameters during fracturing;

[0008] S200, a shale reservoir natural fracture model is established based on the basic parameters of natural fractures in the reservoir;

[0009] S300, a fluid-structure interaction model of stress field and flow field of segmented multi-cluster fracturing in horizontal wells is established based on boundary element method and finite volume method;

[0010] S400 utilizes the pressure balance principle to establish a multi-crack simultaneous expansion cluster flow distribution model;

[0011] S500, based on the principle of stress superposition, establishes a model of the interaction between hydraulic fractures and natural fractures;

[0012] S600, using the equivalent stress intensity factor to establish a segmented multi-cluster fracturing model with simultaneous expansion of multiple fractures;

[0013] S700, combined with steps S200 to S600, establishes a mathematical model for the dynamic propagation of multiple fractures in a horizontal well segmented multi-cluster fracturing operation, taking into account the effects of natural fractures, stress interference between fractures, and complex flow distribution.

[0014] S800, based on the mathematical model established in step S700 and combined with the parameters collected in step S100, simulates and calculates the fracture morphology and flow distribution results of multi-cluster fracturing in deep shale horizontal wells under different parameters, and then optimizes the completion parameters and construction parameters of multi-cluster fracturing in deep shale horizontal wells.

[0015] Furthermore, the geological parameters, completion parameters, and construction parameters collected in step S100 during fracturing are as follows:

[0016] (1) Geological parameters include the maximum horizontal principal stress, the minimum horizontal principal stress, Young's modulus of reservoir rock, Poisson's ratio of reservoir rock, fracture toughness of reservoir rock, tensile strength of reservoir rock, reservoir filtration coefficient, reservoir thickness, inherent shear strength of natural fractures, friction coefficient of natural fracture wall, azimuth of natural fractures, average length of natural fractures and density of natural fractures.

[0017] (2) Completion parameters include the number of perforations, perforation diameter, perforation cluster spacing, and number of perforation clusters;

[0018] (3) Construction parameters include fracturing fluid density, fracturing fluid viscosity, construction flow rate and construction scale.

[0019] Furthermore, the shale reservoir natural fracture model established in step S200 based on the basic parameters of the reservoir's natural fractures is as follows:

[0020] The formula for calculating the number of natural cracks is:

[0021]

[0022] The formula for calculating the location of natural cracks is:

[0023]

[0024]

[0025]

[0026] Where: N nf The number of natural cracks, in L; x To simulate the length of the reservoir region along the x-direction, m; L y To simulate the length of the reservoir region in the y-direction, m; D nf The density of natural cracks, i.e., the length of natural cracks per unit area, in meters (m). -1 L nf x is the average length of a natural crack, in meters. nf With y nf X1 and Y1 are the coordinates of the midpoint of the natural crack, in meters; X2 and Y2 are the coordinates of one end point of the natural crack, in meters; R represents a random number between 0 and 1; θ nf The azimuth angle of the natural crack is °.

[0027] Furthermore, the methods used in S300 to establish fluid-structure interaction models of stress and flow fields in segmented multi-cluster fracturing of horizontal wells based on the boundary element method and the finite volume method include:

[0028] S301, The relationship between stress and displacement during fracturing is obtained using the special boundary element method—the displacement discontinuity method:

[0029]

[0030]

[0031] γ=β i -β j (7)

[0032]

[0033]

[0034] Where: σ i s With σ i n The tangential and directional stresses acting on crack element i are given in Pa; N is the total number of discrete crack elements; D i s With D i nLet x be the tangential and directional displacement discontinuity of crack element i, in m; and let x and y be the coordinates of the midpoint of the crack element in the global rectangular coordinate system, in m. and Let m be the coordinates of the midpoint of the crack element in the local rectangular coordinate system; β be the coordinates of the midpoint of the crack element. i With β j γ is the angle between fracture element i and fracture element j in a rectangular coordinate system, °; γ is the angle between fracture element i and fracture element j, °; G represents the shear modulus of the reservoir rock, Pa; v is the Poisson's ratio of the reservoir rock, dimensionless; b j The length of crack element j is represented in meters.

[0035] S302, considering the influence of seam height in the two-dimensional model, a seam height correction factor is introduced into the stress-displacement relationship:

[0036]

[0037]

[0038] In the formula: T is the seam height correction coefficient, which is dimensionless; d ij is the distance between the midpoints of fracture element i and fracture element j, in meters; h is the reservoir thickness, in meters.

[0039] S303, the formula for calculating the pressure drop of fracturing fluid in a hydraulic fracture is:

[0040]

[0041] In the formula: p f ρ is the fluid pressure in the hydraulic fracture, Pa; s is the distance, m; μ is the viscosity of the fracturing fluid, Pa·s; q is the fracturing fluid flow rate in the hydraulic fracture, m³ / s. 3 / s; w is the width of the hydraulic fracture, in meters;

[0042] S304, the formula for calculating the frictional resistance of fracturing fluid at the perforation orifice is:

[0043]

[0044] In the formula: p pf For the frictional resistance of the perforation hole, Pa; q p The flow rate of fracturing fluid flowing through the perforation orifice is m. 3 / s; ρ is the density of the fracturing fluid, kg / m³ 3 ;n p d represents the number of perforations; p C is the diameter of the perforation hole, in meters (m). p is the flow rate coefficient of the perforation orifice, which is dimensionless;

[0045] S305, the continuity equation for the fracturing fluid flow process is:

[0046]

[0047] In the formula: q inj For fracturing fluid injection, m / s; C leak The fracturing fluid loss coefficient is given by ms. -0.5 ; t is the current simulated fracturing time, s; τ is the fracture element opening time, s;

[0048] S306, using the finite volume method to discretize the flow field, the fluid-structure interaction model of the stress field and the flow field is established as follows:

[0049] For a discrete scheme without bifurcation and with two crack elements connected to the intermediate crack element, the following is true:

[0050]

[0051] The discrete scheme with bifurcations and three crack elements connected to the middle crack element is as follows:

[0052]

[0053] The discrete scheme with bifurcations and four crack elements connected to the intermediate crack element is as follows:

[0054]

[0055] S307, the fluid-structure interaction model of stress field and flow field is as follows:

[0056]

[0057]

[0058] w t+Δt =ΔtF(w t+Δt )p f +ΔtQ i +w t (20)

[0059] In the formula: Δt is the time increment, in seconds; w t+Δt,i w t,i The crack widths, m and b, are the crack widths of crack element i at the current time step and the previous time step, respectively. j-1 b j+1 Let m be the lengths of elements j-1 and j+1 adjacent to crack element j, respectively; p f,j-1 p f,j+1 These are the fluid pressures inside the fracture elements j-1 and j+1, respectively.

[0060] Furthermore, the method for establishing a multi-fracture simultaneous expansion inter-cluster flow distribution model using the pressure balance principle in step S400 includes:

[0061] S401, ignoring the influence of wellbore friction, the formula for calculating the fluid pressure at the bottom of the well for each cluster of fractures is as follows:

[0062]

[0063] In the formula: q i Let m be the inlet flow rate of the i-th cluster of cracks. 3 / s;p b,i The bottom hole pressure calculated for the i-th cluster of fractures, in MPa; p pf,i Let p be the perforation friction of the i-th cluster of cracks, MPa; f,i is the inlet fluid pressure of the i-th fracture cluster, in MPa; m is the number of fracture clusters;

[0064] S402, based on the principle of pressure balance, the formula for calculating dynamic flow rate using Newton's iterative method is as follows:

[0065]

[0066]

[0067] q1+q2+…+q m =Q all (twenty four)

[0068] In the formula: Let m be the inlet flow rate of the i-th cluster of cracks in the n-th iteration step. 3 / min; Let m be the inlet flow rate of the i-th cluster of cracks in the (n-1)-th iteration step. 3 / min; Q all m represents the total flow rate in the simulation. 3 / min; n is the number of iterations.

[0069] Furthermore, the method for establishing the interaction model between hydraulic fractures and natural fractures based on the stress superposition principle in step S500 includes:

[0070] S501, the formula for calculating the stress field at the tip of a hydraulic fracture is:

[0071]

[0072]

[0073]

[0074] Where: K I Type I stress intensity factor, MPa.m0.5 ;K II Type II stress intensity factor, MPa.m 0.5 L t The length of the crack tip element is in meters (m). denoted by and respectively, representing the discontinuity of normal and tangential displacement of the element at the crack tip, m; r represents the critical radius, m; α is the angle between the hydraulic crack and the natural crack, °; The stress field generated at the crack tip, MPa;

[0075] The formula for calculating the induced stress field generated by multiple hydraulic fractures in S502 is as follows:

[0076]

[0077] In the formula: The induced stress field generated by multiple hydraulic fractures, MPa;

[0078] S503, based on the principle of stress superposition, the formula for calculating the composite stress field is as follows:

[0079]

[0080]

[0081] In the formula: θ is the polar angle in the polar coordinate system; σ h σ H These are the minimum and maximum horizontal principal stresses, respectively, in MPa; The composite stress field is in a rectangular coordinate system, measured in MPa. The composite stress field is defined in polar coordinates with the tip of the hydraulic crack as the origin, in MPa.

[0082] S504, the crossing criterion after the intersection of a hydraulic fracture and a natural fracture is:

[0083] When the tip of the hydraulic fracture reaches the interface of the natural fracture:

[0084]

[0085] When the fracturing fluid reaches the junction of the hydraulic fracture and the natural fracture:

[0086] p tip >σ h +T (32)

[0087] In the formula: The normal stress acting on the wall of the natural crack is expressed in MPa. The stress is the tangential stress acting on the wall of a natural crack, expressed in MPa and T. rockτ0 is the tensile strength of the rock, MPa; τ0 is the inherent shear strength of the natural fracture, MPa; K nf p is the coefficient of friction of the natural crack wall, dimensionless. tip The fluid pressure at the junction of the hydraulic fracture and the natural fracture is expressed in MPa.

[0088] Furthermore, the method for establishing a segmented multi-cluster fracturing multi-fracture simultaneous propagation model using the equivalent stress intensity factor in step S600 includes:

[0089] S601, Crack propagation criterion based on equivalent stress intensity factor:

[0090]

[0091] Where: K e The equivalent stress intensity factor at the crack tip, in MPa.m 0.5 ;K IC For the fracture toughness of reservoir rocks, MPa.m 0.5 θ is the crack deflection angle, in degrees.

[0092] S602, Calculation of hydraulic fracture propagation direction based on maximum circumferential stress theory:

[0093]

[0094] S603, Corrected multi-crack propagation step size:

[0095]

[0096] In the formula: Δx i The step size for expanding the i-th crack tip is m; K e,i Let be the equivalent stress intensity factor at the i-th crack tip, in MPa.m 0.5 ;Δx max Let m be the maximum expansion step size.

[0097] Furthermore, in step S700, in conjunction with steps S200 to S600, the method for establishing a dynamic mathematical model of multi-fracture propagation in a horizontal well segmented multi-cluster fracturing operation that considers the effects of natural fractures, inter-fracture stress interference, and complex flow distribution includes:

[0098] S701, the iterative format and convergence condition for solving fluid-structure interaction problems are as follows:

[0099]

[0100] In the formula: α is the iteration factor, dimensionless; ε is the iteration convergence tolerance, dimensionless; N is the total number of crack elements; w i n Let m be the crack width value of crack element i in the nth iteration step;

[0101] S702, the iterative format and convergence condition for dynamic traffic allocation are as follows:

[0102]

[0103] In the formula: m is the number of crack clusters; Let m be the flow rate value entering crack cluster i in the nth iteration step. 3 / s;

[0104] 3) Based on the law of conservation of mass, the condition for the simulation of hydraulic fracturing crack propagation to end is:

[0105]

[0106] In the formula: V frac Let m be the volume of the hydraulic fracture. 3 V leak The volume of fracturing fluid lost is m. 3 V max For fracturing operation scale, m 3 t represents the current fracturing simulation time, in seconds.

[0107] Furthermore, in step S800, based on the mathematical model established in step S700 and combined with the parameters collected in step S100, the simulation calculation of fracture morphology and flow distribution results of multi-cluster fracturing in deep shale horizontal wells under different parameters, and the subsequent optimization of completion and construction parameters for multi-cluster fracturing in deep shale horizontal wells, include:

[0108] S801, input the natural fracture azimuth angle, average natural fracture length, and natural fracture density into the shale reservoir natural fracture model obtained in step S200 to generate natural fractures.

[0109] In step S802, the geological parameters such as the maximum horizontal principal stress, the minimum horizontal principal stress, the Young's modulus of the reservoir rock, the Poisson's ratio of the reservoir rock, the fracture toughness of the reservoir rock, the tensile strength of the reservoir rock, the reservoir filtration coefficient, the reservoir thickness, the inherent shear strength of the natural fracture, and the friction coefficient of the natural fracture wall are input into the horizontal well segmented multi-cluster fracturing multi-fracture dynamic expansion mathematical model established in step S700.

[0110] In step S803, the completion parameters such as the number of perforations, perforation diameter, perforation cluster spacing, and number of perforation clusters, as well as the construction parameters such as fracturing fluid density, fracturing fluid viscosity, construction flow rate, and construction scale, are input into the horizontal well segmented multi-cluster fracturing dynamic expansion mathematical model established in step S700 to simulate the fracture morphology and flow distribution results of deep shale horizontal well segmented multi-cluster fracturing.

[0111] S804, with the goal of optimizing fracture morphology and uniform fracture extension, changes the completion parameters and construction parameters, repeats step S803, and compares and analyzes the fracture morphology and flow distribution results under different completion parameters and construction parameters to achieve optimization of segmented multi-cluster fracturing parameters for deep shale horizontal wells.

[0112] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0113] This invention overcomes the deficiency of existing technologies that use average values ​​for branch flow rates under fracture bifurcation, and also compensates for the lack of consideration for inter-fracture stress interference in the interaction criteria between hydraulic fractures and natural fractures under the influence of multiple fractures. This invention is more conducive to guiding the optimization design of multi-cluster fracturing parameters in deep shale horizontal wells. This invention is applied in the field of unconventional oil and gas reservoir enhancement technology, and has broad application prospects for the optimization design of multi-cluster fracturing parameters in deep shale horizontal wells. Attached Figure Description

[0114] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0115] Figure 1 This is a flowchart of the segmented multi-cluster fracturing optimization design method for deep shale horizontal wells in an embodiment of the present invention.

[0116] Figure 2 This is a schematic diagram of natural fractures in a reservoir.

[0117] Figure 3 This is a schematic diagram of hydraulic fracture discretization.

[0118] Figure 4 This is a schematic diagram of the crack bifurcation pattern.

[0119] Figure 5 This is a schematic diagram of flow distribution among multiple crack propagation clusters.

[0120] Figure 6 This is a schematic diagram illustrating the interaction between hydraulic fractures and natural fractures.

[0121] Figure 7a This is a diagram showing the results of simulation of the fracture morphology in a segmented multi-cluster hydraulic fracturing operation in a deep shale horizontal well according to Scheme 1.

[0122] Figure 7b This is a diagram showing the simulation results of multi-cluster fracturing fracture morphology in a deep shale horizontal well according to Scheme 2.

[0123] Figure 7c This is a diagram showing the simulation results of the multi-cluster fracturing fracture morphology in a segmented horizontal well of deep shale in Scheme 3.

[0124] Figure 7d This is a diagram showing the simulation results of multi-cluster fracturing fracture morphology in a segmented horizontal well of deep shale, as shown in Scheme 4.

[0125] Figure 8a This is a diagram showing the fluid distribution in each fracture cluster during multi-cluster fracturing in a deep shale horizontal well, as shown in Scheme 1.

[0126] Figure 8b This is a diagram showing the distribution of fluid injection into each fracture cluster in a multi-cluster fracturing operation in a deep shale horizontal well, as shown in Scheme 2.

[0127] Figure 8c This is a diagram showing the fluid distribution in each fracture cluster during multi-cluster fracturing in a deep shale horizontal well, as described in Scheme 3.

[0128] Figure 8d This is a diagram showing the fluid distribution in each fracture cluster during multi-cluster fracturing in a deep shale horizontal well, as shown in Scheme 4. Detailed Implementation

[0129] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0130] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0131] Example

[0132] like Figure 1 As shown in the figure, this embodiment proposes a segmented multi-cluster fracturing optimization design method for deep shale horizontal wells, including the following steps:

[0133] S100 collects geological parameters, completion parameters, and construction parameters during fracturing; specifically:

[0134] (1) Geological parameters include the maximum horizontal principal stress, the minimum horizontal principal stress, Young's modulus of reservoir rock, Poisson's ratio of reservoir rock, fracture toughness of reservoir rock, tensile strength of reservoir rock, reservoir filtration coefficient, reservoir thickness, inherent shear strength of natural fractures, friction coefficient of natural fracture wall, azimuth of natural fractures, average length of natural fractures, and density of natural fractures.

[0135] (2) Completion parameters include the number of perforations, perforation diameter, perforation cluster spacing and number of perforation clusters, etc.

[0136] (3) Construction parameters include fracturing fluid density, fracturing fluid viscosity, construction flow rate and construction scale.

[0137] S200, establish a shale reservoir natural fracture model based on the basic parameters of natural fractures in the reservoir; such as Figure 2 As shown, the established model of natural fractures in shale reservoirs is as follows:

[0138] The formula for calculating the number of natural cracks is:

[0139]

[0140] The formula for calculating the location of natural cracks is:

[0141]

[0142]

[0143]

[0144] Where: N nf The number of natural cracks, in L; x To simulate the length of the reservoir region along the x-direction, m; L y To simulate the length of the reservoir region in the y-direction, m; D nf The density of natural cracks, i.e., the length of natural cracks per unit area, in meters (m). -1 L nf x is the average length of a natural crack, in meters. nf With y nf X1 and Y1 are the coordinates of the midpoint of the natural crack, in meters; X2 and Y2 are the coordinates of one end point of the natural crack, in meters; R represents a random number between 0 and 1; θ nf The azimuth angle of the natural crack is °.

[0145] S300, a fluid-structure interaction model of stress field and flow field in segmented multi-cluster fracturing of horizontal wells is established based on the boundary element method and the finite volume method; specifically:

[0146] S301, such as Figure 3The schematic diagram of hydraulic fracture discretization shown is used to derive the relationship between stress and displacement during the fracturing process using a special boundary element method—the displacement discontinuity method.

[0147]

[0148]

[0149] γ=β i -β j (7)

[0150]

[0151]

[0152] In the formula: σ i s With σ i n The tangential and directional stresses acting on crack element i are given in Pa; N is the total number of discrete crack elements; D i s With D i n β represents the tangential and directional displacement discontinuities of crack element i, in m; x and y are the coordinates of the midpoint of the crack element in the global rectangular coordinate system, in m; x and y are the coordinates of the midpoint of the crack element in the local rectangular coordinate system, in m; i With β j γ is the angle between fracture element i and fracture element j in a rectangular coordinate system, °; γ is the angle between fracture element i and fracture element j, °; G represents the shear modulus of the reservoir rock, Pa; v is the Poisson's ratio of the reservoir rock, dimensionless; b j The length of crack element j is represented in meters.

[0153] S302, considering the influence of seam height in the two-dimensional model, a seam height correction factor is introduced into the stress-displacement relationship:

[0154]

[0155]

[0156] In the formula: T is the seam height correction coefficient, which is dimensionless; d ij is the distance between the midpoints of fracture element i and fracture element j, in meters; h is the reservoir thickness, in meters.

[0157] S303, the formula for calculating the pressure drop of fracturing fluid in a hydraulic fracture is:

[0158]

[0159] In the formula: p fρ is the fluid pressure in the hydraulic fracture, Pa; s is the distance, m; μ is the viscosity of the fracturing fluid, Pa·s; q is the fracturing fluid flow rate in the hydraulic fracture, m³ / s. 3 / s; w is the width of the hydraulic fracture, in meters;

[0160] S304, the formula for calculating the frictional resistance of fracturing fluid at the perforation orifice is:

[0161]

[0162] In the formula: p pf For the frictional resistance of the perforation hole, Pa; q p The flow rate of fracturing fluid flowing through the perforation orifice is m. 3 / s; ρ is the density of the fracturing fluid, kg / m³ 3 ;n p d represents the number of perforations; p C is the diameter of the perforation hole, in meters (m). p is the flow rate coefficient of the perforation orifice, which is dimensionless;

[0163] S305, the continuity equation for the fracturing fluid flow process is:

[0164]

[0165] In the formula: q inj For fracturing fluid injection, m / s; C leak The fracturing fluid loss coefficient is given by ms. -0.5 ; t is the current simulated fracturing time, s; τ is the fracture element opening time, s;

[0166] S306, such as Figure 4 As shown, the flow field is discretized using the finite volume method, and a fluid-structure interaction model of the stress field and the flow field is established as follows:

[0167] For a discrete scheme without bifurcation and with two crack elements connected to the intermediate crack element, the following is true:

[0168]

[0169] The discrete scheme with bifurcations and three crack elements connected to the middle crack element is as follows:

[0170]

[0171] The discrete scheme with bifurcations and four crack elements connected to the intermediate crack element is as follows:

[0172]

[0173] S307, the fluid-structure interaction model of stress field and flow field is as follows:

[0174]

[0175]

[0176] w t+Δt =ΔtF(w t+Δt )p f +ΔtQ i +w t (20)

[0177] In the formula: Δt is the time increment, in seconds; w t+Δt,i w t,i The crack widths, m and b, are the crack widths of crack element i at the current time step and the previous time step, respectively. j-1 b j+1 Let m be the lengths of elements j-1 and j+1 adjacent to crack element j, respectively; p f,j-1 p f,j+1 These are the fluid pressures inside the fracture elements j-1 and j+1, respectively.

[0178] S400 utilizes the pressure balance principle to establish a flow distribution model among multiple fractures simultaneously expanding clusters; such as... Figure 5 As shown, specifically:

[0179] S401, ignoring the influence of wellbore friction, the formula for calculating the fluid pressure at the bottom of the well for each cluster of fractures is as follows:

[0180]

[0181] In the formula: q i Let m be the inlet flow rate of the i-th cluster of cracks. 3 / s;p b,i The bottom hole pressure calculated for the i-th cluster of fractures, in MPa; p pf,i Let p be the perforation friction of the i-th cluster of cracks, MPa; f,i is the inlet fluid pressure of the i-th fracture cluster, in MPa; m is the number of fracture clusters;

[0182] S402, based on the principle of pressure balance, the formula for calculating dynamic flow rate using Newton's iterative method is as follows:

[0183]

[0184]

[0185] q1+q2+…+q m =Q all (twenty four)

[0186] In the formula: Let m be the inlet flow rate of the i-th cluster of cracks in the n-th iteration step. 3 / min; Let m be the inlet flow rate of the i-th cluster of cracks in the (n-1)-th iteration step. 3 / min; Q all m represents the total flow rate in the simulation. 3 / min; n is the number of iterations.

[0187] S500, based on the principle of stress superposition, establishes a model of the interaction between hydraulic fractures and natural fractures; such as Figure 6 As shown, specifically:

[0188] S501, the formula for calculating the stress field at the tip of a hydraulic fracture is:

[0189]

[0190]

[0191]

[0192] Where: K I Type I stress intensity factor, MPa.m 0.5 ;K II Type II stress intensity factor, MPa.m 0.5 L t The length of the crack tip element is in meters (m). denoted by and respectively, representing the discontinuity of normal and tangential displacement of the element at the crack tip, m; r represents the critical radius, m; α is the angle between the hydraulic crack and the natural crack, °; The stress field generated at the crack tip, MPa;

[0193] The formula for calculating the induced stress field generated by multiple hydraulic fractures in S502 is as follows:

[0194]

[0195] In the formula: The induced stress field generated by multiple hydraulic fractures, MPa;

[0196] S503, based on the principle of stress superposition, the formula for calculating the composite stress field is as follows:

[0197]

[0198]

[0199] In the formula: θ is the polar angle in polar coordinates; σ h σ H These are the minimum and maximum horizontal principal stresses, respectively, in MPa; The combined stress field is in a rectangular coordinate system, measured in MPa. The composite stress field is defined in polar coordinates with the tip of the hydraulic crack as the origin, in MPa.

[0200] S504, the crossing criterion after the intersection of a hydraulic fracture and a natural fracture is:

[0201] When the tip of the hydraulic fracture reaches the interface of the natural fracture:

[0202]

[0203] When the fracturing fluid reaches the junction of the hydraulic fracture and the natural fracture:

[0204] p tip >σ h +T (32)

[0205] In the formula: The normal stress acting on the wall of the natural crack is expressed in MPa. The stress is the tangential stress acting on the wall of a natural crack, expressed in MPa and T. rock τ0 is the tensile strength of the rock, MPa; τ0 is the inherent shear strength of the natural fracture, MPa; K nf p is the coefficient of friction of the natural crack wall, dimensionless. tip The fluid pressure at the junction of the hydraulic fracture and the natural fracture is expressed in MPa.

[0206] S600, using the equivalent stress intensity factor to establish a segmented multi-cluster fracturing model with simultaneous propagation of multiple fractures; specifically:

[0207] S601, Crack propagation criterion based on equivalent stress intensity factor:

[0208]

[0209] Where: K e The equivalent stress intensity factor at the crack tip, in MPa.m 0.5 ;K IC For the fracture toughness of reservoir rocks, MPa.m 0.5 θ is the crack deflection angle, in degrees.

[0210] S602, Calculation of hydraulic fracture propagation direction based on maximum circumferential stress theory:

[0211]

[0212] S603, Corrected multi-crack propagation step size:

[0213]

[0214] In the formula: Δx i The step size for expanding the i-th crack tip is m; Ke,i Let be the equivalent stress intensity factor at the i-th crack tip, in MPa.m 0.5 ;Δx max Let m be the maximum expansion step size.

[0215] S700, combined with steps S200–S600, establishes a dynamic mathematical model for multi-fracture propagation in a horizontal well with segmented multi-cluster fracturing, considering the effects of natural fractures, inter-fracture stress interference, and complex flow distribution; specifically:

[0216] S701, the iterative format and convergence condition for solving fluid-structure interaction problems are as follows:

[0217]

[0218] In the formula: α is the iteration factor, which is dimensionless; ε is the iteration convergence tolerance, which is dimensionless; N is the total number of crack elements; Let m be the crack width value of crack element i in the nth iteration step;

[0219] S702, the iterative format and convergence condition for dynamic traffic allocation are as follows:

[0220]

[0221] In the formula: m is the number of crack clusters; Let m be the flow rate value entering crack cluster i in the nth iteration step. 3 / s;

[0222] 3) Based on the law of conservation of mass, the condition for the simulation of fracturing crack propagation to end is:

[0223]

[0224] In the formula: V frac Let m be the volume of the hydraulic fracture. 3 V leak The volume of fracturing fluid lost is m. 3 V max For fracturing operation scale, m 3 t represents the current fracturing simulation time, in seconds.

[0225] S800, based on the mathematical model established in step S700 and combined with the parameters collected in step S100, simulates and calculates the fracture morphology and flow distribution results of multi-cluster fracturing in deep shale horizontal wells under different parameters, and then optimizes the completion and construction parameters for multi-cluster fracturing in deep shale horizontal wells; specifically:

[0226] S801, input the natural fracture azimuth, average natural fracture length, and natural fracture density into the shale reservoir natural fracture model obtained in step S200 to generate natural fractures.

[0227] In step S802, the geological parameters such as the maximum horizontal principal stress, the minimum horizontal principal stress, the Young's modulus of the reservoir rock, the Poisson's ratio of the reservoir rock, the fracture toughness of the reservoir rock, the tensile strength of the reservoir rock, the reservoir filtration coefficient, the reservoir thickness, the inherent shear strength of the natural fracture, and the friction coefficient of the natural fracture wall are input into the horizontal well segmented multi-cluster fracturing multi-fracture dynamic expansion mathematical model established in step S700.

[0228] In step S803, the completion parameters such as the number of perforations, perforation diameter, perforation cluster spacing, and number of perforation clusters, as well as the construction parameters such as fracturing fluid density, fracturing fluid viscosity, construction flow rate, and construction scale, are input into the horizontal well segmented multi-cluster fracturing dynamic expansion mathematical model established in step S700 to simulate the fracture morphology and flow distribution results of deep shale horizontal well segmented multi-cluster fracturing.

[0229] S804, with the goal of optimizing fracture morphology and uniform fracture extension, changes the completion parameters and construction parameters, repeats step S803, and compares and analyzes the fracture morphology and flow distribution results under different completion parameters and construction parameters to achieve optimization of segmented multi-cluster fracturing parameters for deep shale horizontal wells.

[0230] Example:

[0231] The following detailed description of the invention is based on an example from a deep shale gas well in southern Sichuan, China, but does not constitute any limitation on the invention. The basic parameters used in the simulation are shown in Table 1, and the optimized parameters and schemes are shown in Table 2.

[0232] Table 1. Basic parameters used in the simulation:

[0233]

[0234] Table 2, Optimization Parameters and Schemes:

[0235] Number of perforations indivual 12 12 6 6 Perforation cluster spacing m 8 10 10 10 fracturing fluid viscosity mPa.s 5 20 10 10 Construction displacement <![CDATA[m 3 / min]]> 10 16 10 16

[0236] Therefore, the segmented multi-cluster fracturing optimization design method for deep shale horizontal wells is implemented:

[0237] Step 1: Input the geological parameters in Table 1 into the natural fracture model, and generate natural fractures in deep shale reservoirs through equations (1) to (4), such as Figure 2 As shown;

[0238] Step 2: Input the parameters in Table 1 and Table 2 into the segmented multi-cluster fracturing dynamic propagation model of deep shale horizontal wells, establish the stress field through equations (5) to (11), establish the flow field according to equations (12) to (14), and solve the fluid-structure interaction equation set (20) to obtain the normal displacement discontinuity (i.e., fracture width) w and the fluid pressure p inside the fracture. fThe distribution is determined by using equations (21) to (24) to solve for the flow rate q of each crack cluster. i Equations (36) and (37) serve as convergence conditions for solving the equations. If the results converge, proceed to the third step.

[0239] Step 3: Determine whether the tip of the hydraulic fracture intersects with the natural fracture. If the hydraulic fracture intersects with the natural fracture, use equations (25) to (32) to determine the result of the intersection. If the hydraulic fracture does not intersect with the natural fracture, the hydraulic fracture extends in the reservoir. Use equations (25), (26), (33), and (34) to determine whether the hydraulic fracture extends and calculate the extension direction. Calculate the fracture extension step based on equation (35).

[0240] Step 4: Update the fracture unit and the pressure information inside the fracture, calculate the simulated fracturing time or the amount of fracturing fluid injected based on the volume conservation equation (38), and determine whether the fracture propagation simulation has ended. If it has not ended, repeat steps 2 and 3 until the conditions are met. If it has ended, output the simulated fracture morphology and the fluid injection situation of each fracture cluster.

[0241] Step 5: Simulate and calculate the fracture morphology and fluid injection of each fracture cluster under different completion and construction parameters. Select optimized parameters based on fracture length, fracture width, and uniform extension. Using the parameters in Tables 1 and 2, repeat steps 1 to 4 to obtain the fracture morphology distribution and fluid injection distribution of each fracture cluster after fracturing under four parameter conditions (Scheme 1, Scheme 2, Scheme 3, and Scheme 4), as shown below. Figure 7a , 7b As shown in 7c, 7d and 8a, 8b, 8c, 8d. Through comparative analysis, it can be seen that the parameter settings of Scheme 2 and Scheme 4 can effectively promote uniform crack extension and uniform liquid inflow of each crack cluster. At the same time, the crack length and crack width are improved compared with Scheme 1 and Scheme 3. Therefore, the parameters in Scheme 2 and Scheme 4 can be used as optimization parameters.

[0242] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimized design of multi-cluster fracturing in deep shale horizontal wells, characterized in that, Includes the following steps: S100 collects geological parameters, well completion parameters, and construction parameters during fracturing; S200, a shale reservoir natural fracture model is established based on the basic parameters of natural fractures in the reservoir; S300, a fluid-structure interaction model of stress field and flow field of segmented multi-cluster fracturing in horizontal wells is established based on boundary element method and finite volume method; S400 utilizes the pressure balance principle to establish a multi-crack simultaneous expansion cluster flow distribution model; S500, based on the principle of stress superposition, establishes a model of the interaction between hydraulic fractures and natural fractures; S600, using the equivalent stress intensity factor to establish a segmented multi-cluster fracturing model with simultaneous expansion of multiple fractures; S700, combined with steps S200~S600, establish a mathematical model for the dynamic propagation of multiple fractures in a horizontal well segmented multi-cluster fracturing, taking into account the effects of natural fractures, inter-fracture stress interference, and complex flow distribution. S800, based on the mathematical model established in step S700, combined with the parameters collected in step S100, simulates and calculates the fracture morphology and flow distribution results of segmented multi-cluster fracturing in deep shale horizontal wells under different parameters, and then optimizes the completion parameters and construction parameters of segmented multi-cluster fracturing in deep shale horizontal wells. The methods for establishing fluid-structure interaction models of stress and flow fields in segmented multi-cluster fracturing of horizontal wells based on the boundary element method and the finite volume method in S300 include: S301, The relationship between stress and displacement during fracturing is obtained using the special boundary element method—the displacement discontinuity method: (5) (6) (7) (8) (9) In the formula: σ i s and σ i n For action on crack elements i Tangential and directional stresses, Pa; N This represents the total number of discrete crack elements. D i s and D i n For crack elements i The tangential and directional displacement discontinuities, in meters; x and y Let m be the coordinates of the midpoint of the crack element in the global rectangular coordinate system. and The coordinates of the midpoint of the crack element in the local rectangular coordinate system are in meters (m). β i and β j For crack elements i With crack unit j Angle in a rectangular coordinate system, °; γ For crack elements i With crack unit j The angle between them, °; G This represents the shear modulus of the reservoir rock, in Pa. v is the Poisson's ratio of the reservoir rock, which is dimensionless; b j Represents crack element j The length, in meters; S302, considering the influence of seam height in the two-dimensional model, a seam height correction factor is introduced into the stress-displacement relationship: (10) (11) In the formula: T This is a dimensionless correction factor for seam height. d ij For crack elements i Midpoint and Crack Elements j The distance between the midpoints, in meters (m). h Let be the reservoir thickness, in meters (m). S303, the formula for calculating the pressure drop of fracturing fluid in a hydraulic fracture is: (12) In the formula: p f The fluid pressure in the hydraulic fracture is expressed in Pa. s The distance is in meters (m). μ Here is the viscosity of the fracturing fluid, in Pa·s; q The flow rate of fracturing fluid in a hydraulic fracture is given in m. 3 / s; w Width of the hydraulic fracture, in meters (m); S304, the formula for calculating the frictional resistance of fracturing fluid at the perforation orifice is: (13) In the formula: p pf The frictional resistance of the perforation hole is measured in Pa. q p The flow rate of fracturing fluid flowing through the perforation orifice is m. 3 / s; ρ The density of the fracturing fluid is kg / m³. 3 ; n p This refers to the number of perforations; d p The diameter of the perforation hole is in meters (m). C p is the flow rate coefficient of the perforation orifice, which is dimensionless; S305, the continuity equation during fracturing fluid flow is: (14) In the formula: q inj For fracturing fluid injection, m / s; C leak The fracturing fluid loss coefficient is given by ms. -0.5 t represents the current simulated fracturing time, in seconds. τ The crack element opening time is in seconds. S306, using the finite volume method to discretize the flow field, the fluid-structure interaction model of the stress field and the flow field is established as follows: For a discrete scheme without bifurcation and with two crack elements connected to the intermediate crack element, the following is true: (15) The discrete scheme with bifurcations and three crack elements connected to the middle crack element is as follows: (16) The discrete scheme with bifurcations and four crack elements connected to the intermediate crack element is as follows: (17) S307, the fluid-structure interaction model of stress field and flow field is as follows: (18) (19) (20) In the formula: Δ t The time increment is s; w t+Δt,i , w t,i These are the crack elements for the current time step and the previous time step, respectively. i The seam width, in meters; b j-1 , b j+1 They are respectively related to crack elements j Adjacent units j -1 and unit j +1 is the length, in meters; p f,j-1 , p f,j+1 They are crack units. j -1 and crack element j +1 fluid pressure inside the crevice.

2. The method for optimized design of multi-cluster fracturing in deep shale horizontal wells according to claim 1, characterized in that, The geological parameters, completion parameters, and construction parameters collected in step S100 during fracturing are as follows: (1) Geological parameters include the maximum horizontal principal stress, the minimum horizontal principal stress, Young's modulus of reservoir rock, Poisson's ratio of reservoir rock, fracture toughness of reservoir rock, tensile strength of reservoir rock, reservoir filtration coefficient, reservoir thickness, inherent shear strength of natural fractures, friction coefficient of natural fracture wall, azimuth of natural fractures, average length of natural fractures and density of natural fractures. (2) Completion parameters include the number of perforations, perforation diameter, perforation cluster spacing, and number of perforation clusters; (3) Construction parameters include fracturing fluid density, fracturing fluid viscosity, construction discharge rate and construction scale.

3. The method for optimized design of multi-cluster fracturing in deep shale horizontal wells according to claim 2, characterized in that, The shale reservoir natural fracture model established in step S200 based on the basic parameters of the reservoir's natural fractures is as follows: The formula for calculating the number of natural cracks is: (1) The formula for calculating the location of natural cracks is: (2) (3) (4) In the formula: N nf The number of natural cracks; L x To simulate the reservoir region along x Length in the direction, in meters; L y To simulate reservoir region research y Length in the direction, in meters; D nf The density of natural cracks, i.e., the length of natural cracks per unit area, in meters (m). -1 ; L nf The average length of a natural crack, in meters; x nf and y nf Let the coordinates of the midpoint of the natural crack be m; X 1 and Y 1 represents the coordinates of one end point of the natural crack, in meters. X 2 and Y 2 represents the coordinates of the other end point of the natural crack, in meters (m). R Represents a random number between 0 and 1; θ nf The azimuth angle of the natural crack is °.

4. The method for optimized design of multi-cluster fracturing in deep shale horizontal wells according to claim 3, characterized in that, The method for establishing a multi-fracture simultaneous propagation inter-cluster flow distribution model using the pressure balance principle in step S400 includes: S401, ignoring the influence of wellbore friction, the formula for calculating the fluid pressure at the bottom of the well for each cluster of fractures is as follows: (21) In the formula: q i For the first i Inlet flow rate of cluster fracture, m 3 / s; p b,i For the first i Bottomhole pressure calculated from cluster fractures, MPa; p pf,i For the first i Perforation friction of clustered fractures, MPa; p f,i It is the first i Inlet fluid pressure of the cluster fracture, MPa; m It is the number of crack clusters; S402, based on the principle of pressure balance, the formula for calculating dynamic flow rate using Newton's iterative method is as follows: (22) (23) (24) In the formula: For the first n The next iteration step i Inlet flow rate of cluster fracture, m 3 / min; For the first n -1st iteration step i Inlet flow rate of cluster fracture, m 3 / min; Q all m represents the total flow rate in the simulation. 3 / min; n This represents the number of iteration steps.

5. The method for optimized design of multi-cluster fracturing in deep shale horizontal wells according to claim 4, characterized in that, The method for establishing the interaction model between hydraulic fractures and natural fractures based on the stress superposition principle in step S500 includes: S501, the formula for calculating the stress field at the tip of a hydraulic fracture is: (25) (26) (27) In the formula: K I Type I stress intensity factor, MPa.m 0.5 ; K II Type II stress intensity factor, MPa.m 0.5 ; L t The length of the crack tip element is in meters (m). , denoted by m, representing the discontinuities in normal and tangential displacement of the element at the crack tip; r Represents the critical radius, in meters (m). α The angle between the hydraulic fracture and the natural fracture, in °; , , The stress field generated at the crack tip, MPa; The formula for calculating the induced stress field generated by multiple hydraulic fractures in S502 is as follows: (28) In the formula: , , The induced stress field generated by multiple hydraulic fractures, MPa; S503, based on the principle of stress superposition, the formula for calculating the composite stress field is as follows: (29) (30) In the formula: θ The polar angle in polar coordinates; σ h , σ H These are the minimum and maximum horizontal principal stresses, respectively, in MPa; , , The composite stress field is in a rectangular coordinate system, measured in MPa. , , The composite stress field is defined in polar coordinates with the tip of the hydraulic crack as the origin, in MPa. S504, the crossing criterion after the intersection of a hydraulic fracture and a natural fracture is: When the tip of the hydraulic fracture reaches the interface of the natural fracture: (31) When the fracturing fluid reaches the junction of the hydraulic fracture and the natural fracture: (32) In the formula: The normal stress acting on the wall of the natural crack is expressed in MPa. The stress is the tangential stress acting on the wall of a natural crack, expressed in MPa. T rock The tensile strength of the rock is given in MPa. τ 0 represents the inherent shear strength of the natural crack, in MPa; K nf is the friction coefficient of the natural crack wall, dimensionless; p tip The fluid pressure at the junction of the hydraulic fracture and the natural fracture is expressed in MPa.

6. The method for optimized design of multi-cluster fracturing in deep shale horizontal wells according to claim 5, characterized in that, The method for establishing a segmented multi-cluster fracturing multi-fracture simultaneous propagation model using the equivalent stress intensity factor in step S600 includes: S601, Crack propagation criterion based on equivalent stress intensity factor: (33) In the formula: K e The equivalent stress intensity factor at the crack tip, in MPa.m 0.5 ; K IC For the fracture toughness of reservoir rocks, MPa.m 0.5 ; θ The crack deflection angle is expressed in degrees. S602, Calculation of hydraulic fracture propagation direction based on maximum circumferential stress theory: (34) S603, Corrected multi-crack propagation step size: (35) In the formula: Δ x i For the first i The crack tip expansion step length is m; K e,i For the first i The equivalent stress intensity factor at the crack tip, MPa.m 0.5 ;Δ x max Let m be the maximum expansion step size.

7. The method for optimized design of multi-cluster fracturing in deep shale horizontal wells according to claim 6, characterized in that, Step S700, in conjunction with steps S200~S600, establishes a mathematical model for the dynamic propagation of multiple fractures in a horizontal well segmented multi-cluster fracturing operation, taking into account the effects of natural fractures, inter-fracture stress interference, and complex flow distribution. This model includes: S701, the iterative format and convergence condition for solving fluid-structure interaction problems are as follows: (36) In the formula: α The iteration factor is dimensionless. ε Dimensionless for iterative convergence tolerance; N This represents the total number of crack elements. For the first n The crack width value of crack unit i in each iteration step, m; S702, the iterative format and convergence condition for dynamic traffic allocation are as follows: (37) In the formula: m The number of crack clusters; For the first n Each iteration step enters the crack cluster i The flow rate value, m 3 / s; 3) Based on the law of conservation of mass, the condition for the simulation of fracturing crack propagation to end is: (38) In the formula: V frac Let m be the volume of the hydraulic fracture. 3 ; V leak The volume of fracturing fluid lost is m. 3 ; V max For fracturing operation scale, m 3 ; t The current fracturing simulation time is in seconds.

8. The method for optimized design of multi-cluster fracturing in deep shale horizontal wells according to claim 7, characterized in that, The method for optimizing the completion and construction parameters of deep shale horizontal well multi-cluster fracturing based on the mathematical model established in step S700 and the parameters collected in step S100 in step S800 includes: S801, input the natural fracture azimuth, average natural fracture length, and natural fracture density into the shale reservoir natural fracture model obtained in step S200 to generate natural fractures. In step S802, the geological parameters such as the maximum horizontal principal stress, the minimum horizontal principal stress, the Young's modulus of the reservoir rock, the Poisson's ratio of the reservoir rock, the fracture toughness of the reservoir rock, the tensile strength of the reservoir rock, the reservoir filtration coefficient, the reservoir thickness, the inherent shear strength of the natural fracture, and the friction coefficient of the natural fracture wall are input into the horizontal well segmented multi-cluster fracturing multi-fracture dynamic expansion mathematical model established in step S700. In step S803, the completion parameters such as the number of perforations, perforation diameter, perforation cluster spacing, and number of perforation clusters, as well as the construction parameters such as fracturing fluid density, fracturing fluid viscosity, construction flow rate, and construction scale, are input into the horizontal well segmented multi-cluster fracturing dynamic expansion mathematical model established in step S700 to simulate the fracture morphology and flow distribution results of deep shale horizontal well segmented multi-cluster fracturing. S804, with the goal of optimizing fracture morphology and uniform fracture extension, changes the completion parameters and construction parameters, repeats step S803, and compares and analyzes the fracture morphology and flow distribution results under different completion parameters and construction parameters to achieve optimization of segmented multi-cluster fracturing parameters for deep shale horizontal wells.

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