A method for simulating the fragmentation of a population of deep shale proppant particles

Abstract

The present application belongs to the technical field of shale gas development, and particularly relates to a deep shale proppant particle group crushing simulation method, which comprises the following steps: constructing a single particle numerical model by using parallel bonding contact; introducing a Weibull statistical theory to construct a strength distribution model considering the particle size effect; establishing an octahedral shear stress particle crushing judgment criterion to calculate the octahedral shear stress characteristic value of the particle; calculating the crushing strength of each particle with different particle sizes, comparing the crushing strength of the single particle with the critical crushing strength threshold of the particle, and if the particle crushing criterion is triggered, using an Apollo filling replacement mechanism to replace the parent particle in situ dynamically; and obtaining the number of particles that crush when the target stress is reached, the particle size grading evolution characteristics and the macro crushing rate from the particle endless crushing termination condition. The present application can effectively characterize the gradual failure evolution law of the deep shale proppant under high closure stress, and provides some insights for the parameter design and optimization of fracturing execution.

Description

Technical Field

[0001] This invention relates to a method for simulating the fragmentation of deep shale support particle groups, belonging to the field of shale gas development technology. Background Technology

[0002] In recent years, as exploration and development have progressed to deeper levels, deep reservoirs have exhibited characteristics of high temperature, high pressure, and high geostress. During hydraulic fracturing, the effective closure stress of the fractures is relatively large, leading to severe mutual compression between proppant particles, which easily deforms or even breaks. Particle breakage not only generates a large number of tiny fragments that block seepage channels, but also causes macroscopic volume compression of the proppant layer and a reduction in fracture width. This results in an exponential decrease in the conductivity of the hydraulic fractures after fracturing, severely restricting the production and stable production period of deep shale gas wells.

[0003] Currently, research on the fracture mechanics of proppant particle groups mainly relies on macroscopic indoor compression fracture experiments. While physical experiments can obtain macroscopic load-displacement curves and final fracture rate data of proppant materials under specific pressures, they cannot reveal the initiation and propagation paths of internal cracks within particles at the microscopic scale, and are even less capable of dynamically characterizing the complex force chain evolution and redistribution mechanisms of particle groups during compaction. To overcome the limitations of physical experiments, the discrete element method (DEM) has been widely used to study the contact mechanics between particles and the energy dissipation mechanisms during the fracture process. Currently, there are three main methods for characterizing breakable particles: 1. Particle bonding method, which aggregates microscale particles into macroscopic aggregates through bonding bonds. 2. Particle replacement method, which replaces crushed particles with smaller particles of equal mass. 3. Damage modeling based on theories such as peri-field dynamics. Among these, while the particle bonding method has good morphological adaptability, the computational resource consumption increases exponentially with the increase in model size and particle number. In contrast, the particle replacement method has high computational efficiency and shows significant advantages in simulating large-scale continuous fracture processes.

[0004] However, existing particle replacement methods still have significant limitations in practical applications, making it difficult to accurately characterize the real fragmentation process in deep and complex environments. Existing models often use a single tensile stress or contact force threshold as the criterion, resulting in inaccurate determination of the fragmentation triggering condition. Furthermore, most existing models assign a constant fragmentation strength to particles, failing to adequately consider the influence of size effects on the critical fragmentation strength.

[0005] Therefore, it is urgent to establish a simulation method for the fragmentation of deep shale support particle groups to overcome the shortcomings of existing numerical models, accurately characterize the evolution law of fragmentation behavior of particle groups under high closure stress, and provide a theoretical basis for efficiently supporting hydraulic fractures, maintaining high oil and gas conductivity channels, and extending the stable production period of deep shale gas wells. Summary of the Invention

[0006] The purpose of this invention is to address the problems existing in the prior art by providing a method for simulating the fragmentation of deep shale proppant particles. This method can effectively characterize the progressive failure evolution of deep shale proppant under high closure stress, and provides some insights for the parameter design and optimization of fracturing operations.

[0007] The technical solution provided by this invention to solve the above-mentioned technical problems is: a method for simulating the fragmentation of deep shale-supported particle groups, comprising the following steps: Step S1: Obtain geological parameters and proppant parameters of deep shale reservoirs; Step S2: Based on the discrete element method, a single-particle numerical model is constructed using parallel bonding contact. Step S3: The micromechanical parameters in the single-particle numerical model are calibrated through a single-particle crushing experiment; Step S4: Introduce Weibull statistical theory to construct an intensity distribution model that considers particle size effects; Step S5: Establish the octahedral shear stress particle breakage judgment criterion and calculate the octahedral shear stress characteristic value of the particles. Step S6: Based on the particle replacement method, under stress loading, calculate the crushing strength of each particle of different sizes, and compare the crushing strength of a single particle with the critical crushing strength threshold of the particle. If the particle crushing criterion is triggered, the Apollo filling replacement mechanism is used to dynamically replace the parent particle in situ. Step S7: Based on the termination condition of endless particle breakage, obtain the number of particles that break when the target stress is reached, the particle size distribution evolution characteristics, and the macroscopic breakage rate.

[0008] A further technical solution is that the formation parameters include the horizontal maximum principal stress, minimum principal stress, vertical stress, Young's modulus, Poisson's ratio, and closure stress, and the proppant parameters include proppant type, particle size, apparent density, and proppant concentration.

[0009] A further technical solution is that the microscopic parameters include particle density and damping coefficient, effective elastic modulus between particles, stiffness ratio, friction coefficient, effective elastic modulus of bonding, tensile strength of bonding, cohesion of bonding and internal friction angle, effective elastic modulus of particle-wall, stiffness ratio, and friction coefficient.

[0010] A further technical solution is that the formula for calculating the octahedral shear stress characteristic value is:

[0011] In the formula: denoted as the octahedral shear stress characteristic value of the particle, in MPa; , , These represent the first, second, and third principal stresses, respectively, in MPa.

[0012] A further technical solution is that the crushing strength The calculation formula is:

[0013]

[0014] In the formula: This represents the probability of particle survival. Weibull modulus is the particle crushing strength. Where is the particle diameter, in meters (m); For particle size The particle ultimate strength, MPa; The breaking strength is expressed in MPa.

[0015] A further technical solution is that the calculation formula for the critical fracture strength threshold is:

[0016] In the formula: The critical crushing strength threshold is expressed in MPa. The contact force between the particles is N; denoted as particle diameter, in meters (m).

[0017] A further technical solution is that the requirement for triggering the particle breakage criterion in step S6 is:

[0018] In the formula: The breaking strength is expressed in MPa. The critical crushing strength threshold is expressed in MPa.

[0019] A further technical solution is that the Apollo filling replacement mechanism in step S6 is as follows: when a single particle reaches the critical threshold condition, the Apollo filling replacement algorithm is triggered to break the parent particle into 14 non-overlapping spheres of sub-particles. During the sub-particle replacement process, the radius and position of the sub-particles are determined according to the Apollo filling mode.

[0020] A further technical solution is that the termination condition for the endless crushing of particles in step S7 is: when the particle size of the replacement particle is 0.25 times the smallest particle size in the initial particles, the crushing and replacement stops, thus preventing the endless continuous crushing of particles.

[0021] A further technical solution is that the formula for calculating the macroscopic breakage rate is:

[0022] In the formula: The breakage rate is %; This represents the total number of particles in the sample before loading. This refers to the number of particles that break after loading, i.e., the number of particles that break in the group of particles after loading.

[0023] The beneficial effects of this invention are as follows: This invention reveals the physical mechanism of particle mass failure under complex stress environment in deep shale, and forms a simulation method for particle mass fracture of deep shale support, which can provide a theoretical basis for efficient support of hydraulic fractures in deep shale. Attached Figure Description

[0024] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the particle replacement method; Figure 3 This is a schematic diagram comparing the model data and experimental results of the method of the present invention; Figure 4 This is a simulation diagram of the fragmentation evolution of the supporting particle group in a deep shale block under different closure stresses in this invention. Figure 5 This is a schematic diagram illustrating the gradation evolution of deep shale in a certain block of the present invention under different closure stresses and the subsequent fragmentation of the supporting particle group. Detailed Implementation

[0025] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] like Figure 1 As shown, the present invention provides a method for simulating the fragmentation of deep shale-supported particle groups, which specifically includes the following steps: Step S1: Obtain geological parameters and proppant parameters of deep shale reservoirs; The geological parameters mentioned above include elastic modulus, Poisson's ratio, in-situ stress, and closure stress; The crack parameters include crack length and crack width, and the proppant parameters include sand concentration, particle size, apparent density, Young's modulus, and Poisson's ratio. Step S2: Based on the discrete element method, a single-particle numerical model is constructed using parallel bonding contact. The normal and tangential components of the contact surface in the parallel bond model are as follows: (1) The strength failure criteria for tension and shear force around parallel bond bonds are as follows: (2) (3) (4) In the formula: Normal stress; It is the tangential stress; Normal intensity; Tangential strength; The bonding radius is [value]. For torque contribution coefficient; Step S3: The micromechanical parameters in the single-particle numerical model are calibrated through a single-particle crushing experiment; The particle density is 2650 kg / m³. 3 The damping coefficient is 0.7, the effective elastic modulus between particles is 14 GPa, the stiffness ratio is 1.0, the friction coefficient is 0.5, the effective elastic modulus of bonding is 14 GPa, the bond tensile strength is 6 MPa, the bond cohesion is 8 MPa, the internal friction angle is 45°, the effective elastic modulus between particles and the wall is 14 GPa, the stiffness ratio is 1.0, and the friction coefficient is 0.5.

[0027] Step S4: Introduce Weibull statistical theory to construct an intensity distribution model that considers particle size effects; Step S5: Establish the octahedral shear stress particle breakage judgment criterion and calculate the octahedral shear stress characteristic value of the particles. (5) In the formula: denoted as the octahedral shear stress characteristic value of the particle, in MPa; , , These represent the first, second, and third principal stresses, respectively, in MPa. Step S6: Based on the particle replacement method, calculate the crushing strength of each particle with different particle sizes under stress loading; The crushing strength of a single particle is: (6) In the formula: This represents the probability of particle survival. The Weibull modulus is the particle crushing strength. The larger the particle size, the more concentrated the crushing strength of the particles; the size effect of particle crushing strength is achieved through… reflect; Where is the particle diameter, in meters (m); For particle size The particle ultimate strength, MPa; The breaking strength is expressed in MPa. This implementation selects = 10, characteristic particle size = 1.5mm and characteristic crushing strength = 28 MPa.

[0028] The fragmentation strength distribution of the granular material exhibits typical Weibull probability characteristics: (7) In the formula: σ e denoted as the octahedral shear stress characteristic value of the particle, in MPa; Then, the crushing strength of a single particle is compared with the critical crushing strength threshold of the particle. The formula for calculating the critical breaking strength threshold is: (8) In the formula: The critical crushing strength threshold is expressed in MPa. The contact force between the particles is N; Where is the particle diameter, in meters (m); When the crushing strength of a single particle reaches 0.9 times the critical crushing strength threshold, that is: (9) If the particle breakage criterion is triggered, the Apollo filling and replacement mechanism is used to dynamically replace the parent particles in situ. Specifically, the Apollo filling and replacement algorithm is used to break the parent particle into 14 non-overlapping spheres. During the sub-particle replacement process, the radius and position of the sub-particles are determined according to the Apollo filling mode. That is, the particle size and spatial position parameters of the proppant after the replacement sphere are broken are obtained from Table 1 below. Represents the radius of the sub-particle. Represents the radius of the parent particle. Representing sub-particles Axis coordinates Representing the master particles Axis coordinates shaft and The way axes are represented and Same axis.

[0029] Table 1 Apollo Filling and Replacement Patterns

[0030] Step S7: Based on the termination condition of endless particle breakage, obtain the number of particles that break when the target stress is reached, the particle size distribution evolution characteristics, and the macroscopic breakage rate. The condition for stopping the endless crushing of particles is that the replacement particle size is 0.25 times the smallest particle size in the initial particles, thus preventing the endless continuous crushing of particles.

[0031] The formula for calculating the macroscopic breakage rate is: (10) In the formula: Breakage rate, representing the degree of particle breakage, %; This represents the total number of particles in the sample before loading. This refers to the number of particles that break after loading, i.e., the number of particles that break in the group of particles after loading.

[0032] Example Taking the reservoir geological parameters of a deep shale fractured well in China as an example, using the basic fracturing parameter table shown in Table 2, according to... Figure 1 The process can simulate the fragmentation and gradation evolution of deep shale-supported particle communities. Following the steps described above, the example calculations are performed, the model's calculated fragmentation rate is output, and the results are compared under the same experimental test conditions (e.g., ...). Figure 3 As shown in Table 2), the simulation diagrams of the fragmentation evolution of deep shale supported particle groups under different closure stresses and the gradation evolution curves were plotted using the parameters in Table 2 (as shown in Table 2). Figure 4 , Figure 5 (As shown).

[0033] Table 2 Basic parameters for fracturing in a deep shale reservoir

[0034] The above description is not intended to limit the present invention in any way. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention are still within the scope of the present invention.

Claims

1. A method for simulating the fragmentation of deep shale-supported particle groups, characterized in that, Includes the following steps: Step S1: Obtain geological parameters and proppant parameters of deep shale reservoirs; Step S2: Based on the discrete element method, a single-particle numerical model is constructed using parallel bonding contact. Step S3: The micromechanical parameters in the single-particle numerical model are calibrated through a single-particle crushing experiment; Step S4: Introduce Weibull statistical theory to construct an intensity distribution model that considers particle size effects; Step S5: Establish the octahedral shear stress particle breakage judgment criterion and calculate the octahedral shear stress characteristic value of the particles. Step S6: Based on the particle replacement method, under stress loading, calculate the crushing strength of each particle of different sizes, and compare the crushing strength of a single particle with the critical crushing strength threshold of the particle. If the particle crushing criterion is triggered, the Apollo filling replacement mechanism is used to dynamically replace the parent particle in situ. Step S7: Based on the termination condition of endless particle breakage, obtain the number of particles that break when the target stress is reached, the particle size distribution evolution characteristics, and the macroscopic breakage rate.

2. The method for simulating the fragmentation of deep shale-supported particle groups according to claim 1, characterized in that, The formation parameters include the maximum and minimum horizontal principal stress, vertical stress, Young's modulus, Poisson's ratio, and closure stress. The proppant parameters include proppant type, particle size, apparent density, and proppant concentration.

3. The method for simulating the fragmentation of deep shale-supported particle groups according to claim 1, characterized in that, The microscopic parameters include particle density and damping coefficient, effective elastic modulus between particles, stiffness ratio, friction coefficient, effective elastic modulus of bond, tensile strength of bond, cohesion of bond and internal friction angle, effective elastic modulus of particle-wall, stiffness ratio, and friction coefficient.

4. The method for simulating the fragmentation of deep shale-supported particle groups according to claim 1, characterized in that, The formula for calculating the characteristic value of the octahedral shear stress is as follows: In the formula: denoted as the octahedral shear stress characteristic value of the particle, in MPa; , , These represent the first, second, and third principal stresses, respectively, in MPa.

5. The method for simulating the fragmentation of deep shale-supported particle groups according to claim 4, characterized in that, The crushing strength The calculation formula is: In the formula: This represents the probability of particle survival. Weibull modulus is the particle crushing strength. Where is the particle diameter, in meters (m); For particle size The particle ultimate strength, MPa; The breaking strength is expressed in MPa.

6. The method for simulating the fragmentation of deep shale supported particle groups according to claim 1, characterized in that, The formula for calculating the critical fracture strength threshold is: In the formula: The critical crushing strength threshold is expressed in MPa. The contact force between the particles is N; denoted as particle diameter, in meters (m).

7. The method for simulating the fragmentation of deep shale-supported particle groups according to claim 1, characterized in that, The requirement for triggering the particle breakage criterion in step S6 is as follows: In the formula: The breaking strength is expressed in MPa. The critical crushing strength threshold is expressed in MPa.

8. The method for simulating the fragmentation of deep shale-supported particle groups according to claim 1, characterized in that, The Apollo filling and replacement mechanism in step S6 is as follows: when a single particle reaches the critical threshold condition, the Apollo filling and replacement algorithm is triggered to break the parent particle into 14 non-overlapping spheres of sub-particles. During the sub-particle replacement process, the radius and position of the sub-particles are determined according to the Apollo filling mode.

9. The method for simulating the fragmentation of deep shale supported particle groups according to claim 1, characterized in that, The termination condition for the endless crushing of particles in step S7 is: when the particle size of the replacement particle is 0.25 times the smallest particle size in the initial particles, the crushing and replacement will stop to prevent the endless continuous crushing of particles.

10. The method for simulating the fragmentation of deep shale-supported particle groups according to claim 1, characterized in that, The formula for calculating the macroscopic breakage rate is as follows: In the formula: The breakage rate is %; This represents the total number of particles in the sample before loading. This refers to the number of particles that break after loading, i.e., the number of particles that break in the group of particles after loading.

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