Research on optimization of conductivity of multilevel fractures in tight sandstone based on similar circuit principle

Volume fracturing technology is commonly used to develop tight sandstone reservoirs. During the fracturing process, it is important to not only focus on achieving a larger stimulation volume but also on creating a fracture network conductivity that is suitable for the tight reservoir. However, while there have been numerous studies on optimizing the conductivity of individual fractures, the optimization of fracture network conductivity is still incomplete. To address this issue, a reservoir numerical model is established to optimize the equivalent conductivity of the post‐fracturing fracture network, considering it as a high permeability zone, optimizing the equivalent conductivity to 9.7 μm2 cm. Utilizing the discrete element theory, a “pipe domain” discrete element model is developed to analyze fracture expansion. The findings indicate that the ratios of first‐level, second‐level, and third‐level fractures differ based on the number of clusters, such as 1:4:8 and 1:5:9 for three‐cluster and four‐cluster perforations. By applying the hydropower similarity principle, the fracture network is treated as a three‐level circuit to determine the conductivity of each fracture level. Finally, the model is fitted based on conductivity to determine the optimal fracture conductivity for different fracture number ratios, thereby enhancing the flow capability.


| INTRODUTION
With the rapid development of the economy and industrialization, there has been an increasing demand for fossil energy consumption.Recent research indicates that China's conventional oil and gas resources are gradually declining, 1,2 posing challenges in meeting China's energy development needs.As a result, unconventional oil and gas resources have gained significant attention and have become a crucial area for oil and gas exploration and development. 3,4Among these resources, tight sandstone reservoirs play a vital role. 5These reservoirs are characterized by low porosity and permeability, resulting in low natural productivity. 1,2][8][9][10][11] During the fracturing stimulation process, conductivity is the most important indicator for evaluating the effectiveness of the fracturing.Hence, optimizing fracture conductivity is of utmost importance.
In the realm of theoretical research on fracture conductivity, the current focus primarily revolves around a single fracture.The assumption made is that the proppant is uniformly distributed within the fracture.Guotao et al. 12 approached the proppant filling layer as a capillary model and derived the factors influencing conductivity based on the Carman-Kozeny formula.They established a computational model for conductivity by examining the relationship between permeability, porosity, and pore throat radius.Cui et al. 13 and Zhang et al. 14 conducted studies on fracture conductivity through a combination of experiments and numerical simulations.Li et al. 15 developed a novel analytical model for calculating conductivity based on experimental data fitting of proppant embedding and fracture conductivity.Research on the conductivity of channel fractures.However, Yan et al. 16 developed a calculation model for the conductivity of channel fractures based on the Darcy-Brinkman equation.Bo et al. 17 considered the fracture network as a high permeability zone and conducted simulations to determine the conductivity and geometric parameters of the fracture network based on the volume, permeability, and quantity of this zone.Guo et al. 18 improved the fracture network conductivity of the shale gas reservoir in the fifth member of the Xujiahe Formation in the Upper Triassic of the Sichuan Basin by integrating fracture geometric parameters with high permeability zone theory.Zhao et al., 19 on the other hand, obtained fracture geometric parameters through microseismic monitoring.They treated the high permeability zone as a secondary fracture and optimized the fracture network conductivity of the Longmaxi Formation shale reservoir in southeastern Sichuan.Shen et al. 20 established a new multi-fracture fracture criterion and adopted a uniform design method to obtain the calculation formula for the total double-fractures propagation length to characterize the conductivity of network fractures.Kangsheng 21 proposed to evaluate the conductivity of fractures through the variability and interaction of geometric parameters (mean density, network connectivity, the average number fractures intersecting with inlet outlet boundaries per meter).Due to the intricate nature of complex fracture networks, the seepage laws become intricate, rendering the traditional conductivity evaluation method obsolete.Presently, challenges persist in optimizing the conductivity of fracture networks: (1) Utilizing a macroscopic continuum mechanical model for simulating reservoir hydraulic fracturing necessitates predetermining the fracture interface unit.This approach tends to bias the shape of the fracture toward the ideal, leading to less accurate conductivity optimization.(2) Current research on optimizing fracture network conductivity primarily focuses on shale reservoirs.The fracture characteristics of sandstone reservoirs differ from those of shale, resulting in variations in conductivity optimization strategies. 225][26] Chen Mian 27 suggests that fracture expansion can occur in two forms under different stress conditions: main fracture multibranch fracture and radial network expansion.Lei Qun 28 introduced the concept of "fracture network fracturing" technology, which involves the occurrence of branch fractures when the net pressure in the fracture exceeds the sum of horizontal stress difference and rock tensile strength.These branch fractures extend a certain length away from the main fracture, eventually forming a vertical and horizontal "network fracture" system with the main fracture as the backbone.Ji Hongbo 29 analyzed and summarized the mechanisms of fracture initiation and propagation in fracturing fractures, as well as the influence of formation heterogeneity on post-fracturing fracture morphology.He emphasized the importance of considering multiple fractures to generate an effective fracture network composed of primary and secondary fractures during the fracturing process.The phenomenon of inter-stress interference should be taken into account, and reasonable fracturing perforation sections or section spacing can increase the probability of fracture network formation.
The commonly used finite element method and physical experiments have significant limitations. 30ocks, being composed of particles of different sizes cemented together with pores, are considered discontinuous media.Therefore, the study of hydraulic fracturing problem requires an approach that addresses discontinuous medium mechanics.The discrete element method offers significant advantages in studying such problems as it allows real-time calculation and tracking of particle interactions, accurate revelation of mechanical response at the microscopic scale, and the ability to capture fracture formation, core, initiation, extension, and complex fracture shapes. 30In light of previous research findings, the post-fracturing fracture network was found to be comparable to a high permeability zone.To optimize the equivalent conductivity of the fracture network, a reservoir numerical model was developed.The pipe domain model was implemented using discrete element theory, specifically PFC 2D .The simulation of fracture expansion after volume fracturing of tight sandstone was conducted to determine the shape and geometric parameters of the fractures.Subsequently, the equivalent conductivity of the fracture network was optimized based on the theory of high permeability zones.The similarity between the differential equations of incompressible underground fluid flow through porous media and the differential equations of charge flow through conductive materials allows us to characterize fracture networks and branch fractures. 31By applying the hydroelectric similarity principle, [32][33][34][35][36] we can equate multilevel fractures to circuits and establish a three-level circuit model.By combining the findings from numerical simulations, the conductivity of fractures at all levels of the fracture network was further optimized.

| High permeability zone principle
After volume fracturing of horizontal wells in tight sandstone reservoirs, a complex fracture system is formed around each perforation section (Figure 1).According to the equivalent seepage theory, the flow process in the wellbore can be divided into two parts: matrix seepage into the wellbore and fracture network seepage into the wellbore.The fracture system can be considered as a high permeability zone, and the characteristics of the equivalent fracture network system can be described by its volume and permeability.A reservoir numerical simulation software is used to create a numerical model for optimizing the conductivity of the target reservoir.This involves adjusting the half length and permeability of the high permeability zone, as well as optimizing the fracture permeability and volume of the high permeability zone in the target reservoir with production as the objective.By analyzing the relationship between the equivalent fracture network permeability and the permeability, volume, matrix permeability, and equivalent fracture volume of the high permeability zone using Equation (1), we can determine the relationship between the equivalent fracture network permeability and the fracture network volume.
Among them, K m , K f , and K represent the permeability of the matrix, the supporting fracture permeability, and the average permeability of the high permeability zone, respectively, measured in 10 −3 μm 2 .V f and V represent the supporting fracture (sand volume), and the high permeability zone, respectively, measured in m 3 .
In the Chang 7 reservoir section of Well Hua H1-4, the horizontal section of 1575 m was encountered during drilling.To simulate this, a square control unit of (Table 1) and PVT data (Table 2), the geology is changed.The model simulates 27 high permeability zones using the local unit permeability method, as shown in Figure 2.

| Volume and permeability optimization in high permeability zones
According to geological data, the production conditions of different fracture half lengths (130, 180, 230, 280, and 330 m) are simulated, and the simulation time is 3 years.The relationship between cumulative production and fracture length is shown in Figure 3.
The figure reveals that the cumulative production rises with an increase in fracture half length.However, the rate of increase in cumulative production slows down when the fracture half length reaches 230 m.Therefore, it is suggested that the optimal half-length of the fracture should be set at 230 m.In addition, the high permeability width should be fixed at 20 m, resulting in a volume of the high permeability zone of 138,000 m 3 .
The figure demonstrates that as the permeability of the high permeability zone increases, the cumulative production also increases gradually.However, it is observed that when the permeability of the high permeability zone reaches 5 × 10 −3 μm 2 , the rate of increase in cumulative production slows down.Hence, the optimal permeability for the high permeability zone is determined to be 5 × 10 −3 μm 2 .
By substituting the optimization results of the optimal permeability of the high permeability zone of 5 × 10 −3 μm 2 and the volume of the high permeability zone of 138,000 m 3 into Equation ( 1), we can obtain the relationship curve between the equivalent fracture volume and the equivalent fracture permeability, as shown in Figure 5.
According to Figure 5, there is a clear concave point in the change curve of equivalent fracture volume with equivalent fracture permeability.On the right side of the concave point, a small reduction in equivalent fracture volume leads to a sharp increase in equivalent fracture permeability, making it challenging to add sand during the process.On the left side of the concave point, a small reduction in equivalent fracture permeability results in a significant increase in the required equivalent fracture volume, making the on-site process joint creation more difficult.To achieve the optimal balance between adding sand and creating joints, the most economical option is to set the optimized equivalent fracture permeability at 8.2 × 10 −3 μm 2 and the equivalent fracture volume at 81.96 m 3 .Consequently, the optimal conductivity of the equivalent fracture is 9.7 μm 2 cm.

| Establishment of particle flow discrete element model
The process of hydraulic fracturing involves fluid-solid coupling, which is achieved through the particle flow discrete element fluid-solid coupling algorithm known as the "pipe-domain" model (Figure 6).Pierce 37 proposed an algorithm for numerical simulation of fluid-solid coupling using PFC2D.In this model, a closed area surrounded by particles acts as a "domain" to contain the fluid, and fluid exchange occurs between adjacent areas through "pipes."The flow within the pipes is characterized as laminar flow, and the flow rate (q) of the flow channel per unit time can be determined using the Hagen-Poiseuille law.(2) Among them, μ represents the viscosity of the fluid; a represents the opening of the flow pipe; L represents the sum of the radii of the two particles forming the "pipeline"; P 2 and P 1 represent the fluid pressures in the two "fluid domains," respectively; t represents the value of the numerical model sample thickness, where for two-dimensional numerical simulation, t is set to 1; q represents the flow rate transferred between the two "fluid domains" per unit time.
Using the Chang 7 reservoir as an example, the numerical simulation model has a size of 400 m × 400 m.Particles are generated within this range, and those within a circular area with a diameter of 139.7 mm and centered on the specimen are removed.In their place, particles with a diameter of 124 mm are generated.The circular wall represents the stainless steel casing in the simulation, and the calculation model reaches equilibrium conditions.Table 3 presents the essential input parameters for the discrete element numerical simulation of hydraulic fracturing in the Chang 7 reservoir.respectively.The maximum principal stress direction is specified as the y direction.The model matrix is assumed to be relatively homogeneous.

| Validation of particle flow discrete element model
In particle flow programs, mesoscopic parameters are commonly used for calibration as macroscopic parameters of real materials are not suitable for numerical simulation.A two-dimensional numerical model was created to simulate compression tests on standardsized rock columns with fracture angles of 45°and 60°u nder a constant confining pressure of 23 MPa (Figure 8).The results were compared with actual core compression test results to verify the calibration.If the calibrated microscopic parameters match reality, fracture expansion simulation can proceed.Figure 9 illustrates the comparison between axial loading test and numerical simulation results under constant confining pressure conditions, showing a strong alignment between the two.This indicates that the numerical simulation model accurately reflects real-world conditions, enabling further simulation.

| Numerical simulation result analysis
The hydraulic fracture numerical model was used to simulate the expansion patterns of fractures under different cluster numbers, as illustrated in Figure 10.Since the initial minimum in-situ stress is parallel to the horizontal well, each fracture expands vertically along the wellbore.Initially, hydraulic fractures originate from the perforation position, leading to the formation of numerous micro-fractures around the wellbore.As time progresses, the number of micro-fracture branches increases, along with the widening of the fractures.Figure 10 shows the fracture extension patterns under different shot hole clusters, from which it can be seen that the ratios of primary, secondary and tertiary fractures under three, four, and five clusters of shot holes are 1:4:8, 1:5:9, and 1:6:10, respectively.

| Analysis of fracture propagation area
During the fracture extension process, the area of at each level changes over time.The injection displacement is 10 m 3 /min.As the injection time increases, the area of fractures at all levels continues to increase.The main fracture, which is the first level fracture, occupies the largest area.It is worth noting that the increase in area of first-order fractures is greater than that of second-and third-order fractures.The fracture area of secondary and tertiary fractures increases rapidly in the early stages of fracturing, but the rate of increase slows down in the later stages.After the expansion is completed, in the case of three clusters of perforations as shown in Figure 11, the final reformed areas of first-level fractures, second-level fractures, and third-level fractures are 1194, 830, and 571 m 2 , respectively.The volume ratio of first-level fractures, second-level fractures, and third-level fractures is 4.6:3.2:2.2.In the case of four clusters of perforations, the final reformed areas of first-level fractures, second-level fractures, and third-level fractures are 1096, 908, and 668 m 2 , respectively.The volume ratio of first-level fractures, second-level fractures, and third-level fractures is 4.1:3.4:2.5.In the case of five clusters of perforations, the final reformed areas of first-level fractures, second-level fractures, and third-level fractures are 964, 991, and 798 m 2 , respectively.The volume ratio of first-level fractures, second-level fractures, and third-level fractures is 3.5:3.6:2.9.

| Analysis of fracture width characteristics
Based on the changes in fracture width during the fracture extension process, it was observed that all levels of fractures rapidly increased in width during the initial stage of fracturing.Specifically, the width of second and third-level fractures exhibited a significant increase.However, the rate of width increase for these fractures slowed down considerably during the later stage of fracturing.Figure 12 illustrates the final dynamic fracture widths for different levels of fractures in cases with three, four, and five clusters of perforations.For three clusters of perforations, the final dynamic fracture widths were measured to be 2.2, 1.64, and 0.94 cm for first-level, second-level, and third-level fractures, respectively.Similarly, for four clusters of perforations, the final dynamic fracture widths were 2.14, 1.59, and 0.91 cm for first-level, second-level, and third-level fractures, respectively.In the case of five clusters of perforations, the final dynamic fracture widths were 2.12, 1.56, and 0.88 cm for first-level, second-level, and third-level fractures, respectively.

| Optimization of flow diversion capacity
The equivalent conductivity of the fracture network refers to the average conductivity of all fractures.However, it is not possible to directly obtain the conductivity of fractures at all levels.Therefore, it is necessary to equate the seepage law (Darcy's law) in a single fracture to Ohm's law based on the similar principle of hydropower.In this analogy, the seepage pressure difference, seepage flow rate, and seepage resistance correspond to voltage, current, and resistance, respectively.This relationship is shown in Equation 3.
The fracture network can be represented as a three-level circuit, as depicted in Figure 13.
According to Ohm's law, if all resistances in the entire circuit are regarded as one resistance, then the equivalent resistance R a is: Among them, R a represents the equivalent resistance of the main fracture, R 2 represents the equivalent resistance of all subfractures, and R 3 represents the equivalent resistance of all micro-fractures.It should be noted that R 2 and R 3 are parallel resistors.
In the discrete element numerical simulation, a 1 represents the ratio of the number of secondary fractures to the main fractures, while a 2 represents the ratio of the number of micro-fractures to the main fractures.R l s denotes the equivalent resistance of the secondary fractures, and R ll s denotes the equivalent resistance of the micro-fractures.
According to the similarity principle of hydropower and combining Equations ( 4)- (6). (7) Among them, L is the length of each fracture; w is the width of each fracture; h is the reservoir height; u is the fluid viscosity.
Conductivity F e : At the same time, (11)   Then the relationship between the equivalent conductivity and the conductivity of main fractures, secondary fractures and micro-fractures is: Among them, F a , F p , F 1 , and F 2 represent the equivalent fracture conductivity, main fracture conductivity, secondary fracture conductivity, and microfracture conductivity, respectively.In addition, b 1 and b 2 denote the length of the secondary fracture and the length of the main fracture, respectively.Ratio represents the ratio of micro-fracture length to main fracture length.
According to the three-level fracture network circuit model, Figure 14 illustrates the relationship between the conductivity of first-, second-, and third-level fractures in the Chang 7 reservoir fracture network.The data reveals that the conductivity relationship of third-level fractures can be represented as a three-dimensional surface.
The conductivity within the range of the surface vertices meets the requirements in the following order: primary fractures > secondary fractures > micro-fractures.Table 4 presents the optimization results of conductivity for different number ratios of third-level fractures in the Chang 7 reservoir.

| Proppant recommendations
According to the numerical simulation results, it has been observed that secondary and third-level fractures primarily occur in the initial stage of fracturing, while main extension fractures dominate in the later stages.To minimize construction risks and provide effective support for fractures at all levels, it is essential to optimize the order of adding different particle sizes.The specific approach is as follows: during the early stage of fracturing, if tiny branch fractures (third-level fractures) appear in the wellbore, small-particle size proppant can be added for support.As the pumping time increases, the number of branch fractures further increases and the fracture width continues to expand (secondary fractures), indicating the need for medium-sized proppant for support.In the middle and late stages of fracturing, the growth of branch fractures slows down, with the main fracture extension becoming the primary focus.Consequently, large particle size proppant should be added for support.Therefore, a combination of particle sizes, such as 70/140 mesh + 40/70 mesh + 20/40 mesh, can be utilized to effectively support fractures at all levels.
Based on the optimization results of multi-stage fracture conductivity, the determination of the target reservoir proppant sand spreading concentration is possible.However, this sand spreading concentration cannot be directly applied in the design of fracturing construction.It needs to be converted into parameters that are readily available on site, particularly during construction pump injection procedures.The commonly used parameter for proppant on site is the sand concentration.The on-site sand concentration can be obtained by establishing the relationship between dynamic joint width, sand spreading concentration, and sand concentration.
Among them, C p is the sand concentration, kg/m 3 ; S is the sand spreading concentration, kg/m 2 ; w is the dynamic fracture width, mm, ρ p is the proppant density, kg/m 3 .The relationship between the conductivity of various levels of fractures and the proppant particle size under different levels of fracture number ratios obtained based on the circuit principle is shown in Figure 15.
Assuming that proppant with different particle sizes provides equal support for fractures of corresponding levels, the proportion of proppant dosage of different particle sizes should be the same as the volume ratio of fractures at each level.Therefore, in the case of three cluster perforations, the volume ratio of on-site proppant usage is 20/40 mesh:40/70 mesh:70/140 mesh = 4.6:3.2:2.2.In the case of four-cluster perforation, the proppant volume ratio used in the target reservoir is 20/40 mesh:40/70 mesh:70/140 mesh = 4.1:3.4:2.5.In the case of fivecluster perforation, the volume ratio of on-site proppant usage in the target reservoir is 20/40 mesh:40/70 mesh:70/140 mesh = 3.5:3.6:2.9.
Based on the conductivity prediction model 38 and the proppant particle size, this study calculated the sand spreading concentrations needed for different fracture number ratios.The results are presented in Figure 16.To make it easier for practical application, the sand concentration commonly used in the field was derived from the sand spreading concentration, as shown in Figure 17.The analysis revealed that the sand concentration required for proppants of various particle sizes decreases as the number of second-and third-level fractures increases.The order of proppant concentration is as follows: first-level > secondlevel > third-level.Moreover, the sand concentration needed for second-level and third-level fractures is relatively similar and significantly lower than that required for first-level fractures.

| EXAMPLE ANALYSES
Take Hua H6-1 well in Qincheng oilfield as an example, the horizontal section length of Hua H6-4 well is 1200 m, with 15 sections, and each section has an average of three clusters.The thickness of the reservoir is 30 m, the average porosity is 8.83%, the average permeability is 0.15 × 10 −3 μm 2 , the burial depth is 2105 m, and it is fractured before production.The construction parameters of the well are shown in Table 5, and the production data simulated by the model is compared with the actual production data of the oilfield, as shown in Figure 18, and it is found that the actual production fits well with the simulated production.1. Secondary and third-level fractures primarily occur during the initial stage of fracturing, while in the later stage, main fractures are predominantly extended.As the number of perforation clusters increases, the number of branch fractures also increases, resulting in a decrease in the proportion of first-level fracture area and an increase in the proportion of second-and third-level fractures.Throughout the fracture extension process, the area of fractures at each level changes over time.With increasing injection time, the area of fractures at all levels continues to grow.The area of first-level fractures is the largest, and their increase in area surpasses that of second-and thirdlevel fractures.In the early stage of fracturing, the width of fractures at all levels increases rapidly, with second-and third-level fractures exhibiting a particularly rapid width expansion.However, in the later stage of fracturing, the width growth of second-and third-level fractures slows down significantly.2. The sand concentration required for proppant of various particle sizes decreases as the number of perforation clusters and second-and third-level fractures increases.The proppant concentration is in the order of first-level > second-level > third-level fractures.The sand concentration required for second-level and third-level fractures is relatively close and much lower than the concentration required for first-level fractures.3. The proppant utilizes a combination of small, medium, and large particle sizes (70/140 mesh + 40/ 70 mesh + 20/40 mesh) to effectively achieve multilevel fracture support.As the number of perforation clusters increases, the number of branch fractures also increases, resulting in a decrease in the area proportion of first-order fractures and an increase in the area proportion of second-and third-order fractures.4. A three-level fracture network conductivity optimization method was developed using the equivalent seepage theory and the circuit principle.This method aims to optimize the conductivity of each level of fractures considering different fracture number ratios.
The study revealed that an increase in branch fractures leads to a decrease in the conductivity of each level of fractures.
1575 × 1575 m was established.The grid step size in the X and Y directions is set to 10 m, and the reservoir thickness is 30 m.As a result, the longitudinal grid is divided into one section with a grid step size of 30 m.The total number of grids in the model is 105 × 105 × 1 = 11,025.Considering that the fracture design parameters of Well H1-4 in Chang 7 are 27 sections, based on the basic parameters of Chang 7 F I G U R E 1 Schematic diagram of the fracture network equivalent to a high permeability zone.(A) Hydraulic fracture propagation pattern.(B) Equivalent high permeability zone.

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I G U R E 2 Numerical simulation model of Hua H1-4 well after pressure.F I G U R E 3 The relationship between cumulative output and fracture length.F I G U R E 4 Cumulative production curve changes with permeability of high permeability zone.

Figure 7
illustrates the setup of three clusters, four clusters, and five clusters of perforations.Each section has a length of 20 m, with a cluster spacing of 5 m.The hole diameter is 25 mm, and the distance between the holes is 100 mm, evenly distributed.Constant ground stresses δx and δy are applied along the x direction (left and right walls) and y direction (upper and lower walls),

F I G U R E 5
Curve of equivalent fracture volume with equivalent fracture permeability in Chang 7 reservoir.F I G U R E 6 Schematic diagram of the pipe domain model.T A B L E 3 Chang 7 reservoir discrete element input parameters.

F I G U R E 7
Hydraulic fracturing numerical simulation model.F I G U R E 8 Core specimens with different fracture angles and numerical models under corresponding conditions: (A) the numerical simulation verification when the fracture angle is 45°; (B) the numerical simulation verification when the fracture angle is 60°.

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I G U R E 9 Comparison of strain-stress curves between numerical simulation results and experimental results: (A) the comparison result when the fracture angle is 45°; (B) the comparison result when the fracture angle is 60°.F I G U R E 10 The expansion morphology of multilevel fractures at different times: (A) the expansion morphology of three clusters of perforation fractures; (B) the expansion morphology of four clusters of perforation fractures; (C) the expansion morphology of five clusters of perforation fractures.The black line represents the first-level fracture; the yellowline represents the second-level fracture; the red line represents the third-level fracture.

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I G U R E 11 The changes in the fracture expansion area at all levels with time, (A) the change in the fracture expansion area over time when three clusters of perforations are used; (B) the change in the fracture expansion area over time when four clusters of perforations are used; (C) the fracture expansion area when there are five clusters of perforations changes over time.MULTI-LEVEL FRACTURE CONDUCTIVITY

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I G U R E 12 Changes in fracture width at all levels with time.(A) The change of fracture width with time when three clusters of perforation are used; (B) the change of fracture width with time when four clusters of perforation are used; (C) the change of fracture width with time when five clusters of perforation are used.
The fracture network is equivalent to a schematic diagram of a three-level circuit.F I G U R E 14 The relationship curve of fracture conductivity under different fracture number ratios: (A) the surface diagram of the fracture conductivity relationship when the number ratio of cracks is 1:4:8; (B) the relationship between the fracture conductivity when the number ratio of cracks is 1:5:9 surface diagram; (C) the surface diagram of the fracture conductivity relationship when the fracture number ratio is 1:6:10.

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I G U R E 16 Optimization results of sand concentration under different number ratios of fractures at all levels.

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I G U R E 17 Optimization results of sand concentration under different number ratios of fractures at all levels.T A B L E 5 Chang 7 basic parameter table.
T A B L E 1 T A B L E 4 Optimization results of conductivity under different ratios of third-level fractures in Chang 7 reservoir.
F I G U R E 15 Conductivity under different number ratios of fractures at all levels.
Table of construction parameters for well H6-1.