A model construction method and system reflecting the seepage characteristics of soil improvement foaming agent

Through the discrete element model construction method, a seepage characteristic model of the slag-improved foam agent was established, which solved the problem of lack of effective prediction of foam agent permeability in the existing technology, and achieved systematic simulation and analysis of the penetration mechanism of the slag-improved foam agent, and improved the perfection of the theoretical model and numerical analysis method of the foam improved soil.

CN114611434BActive Publication Date: 2025-03-14SHANDONG UNIV
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Patent Information

Application Number
CN202210300409.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-03-25
Publication Date
2025-03-14
Estimated Expiration
2042-03-25

AI Technical Summary

Technical Problem

The prior art lacks effective theoretical models and numerical methods to predict the permeability of foam agents in slag, and it is difficult to systematically carry out simulation and analysis of the time-varying behavior of foam improved soil.

Method used

The discrete element model construction method is adopted to obtain the indoor permeability test results of the slag-improved foam, and a large-scale fluid flow pore scale grid model is established, and the macroscopic mesoporosis parameters are calibrated and adjusted by discrete element software to obtain the mesoporosis relationship model at different foam intrusion distances, so as to realize the simulation of the slag-improved foam penetration test.

Benefits of technology

The systematic simulation and analysis of the seepage characteristics of the slag-improved foam agent was realized, the penetration mechanism of the slag-improved foam agent was revealed, and the theoretical model and numerical analysis methods of the foam improved soil were improved, providing a reliable theoretical calculation model for the permeability prediction of the foam improved soil.

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Abstract

The present invention provides a model construction method and system that reflects the seepage characteristics of slag improvement foam agents, obtains the results of indoor permeability tests on slag improvement foams, and obtains the variation law of seepage velocity at different foam invasion distances; establishes a large-scale fluid flow pore-scale grid model through regular Delaunay triangulation, and fully defines the fluid exchange between pores according to the local pore geometry; according to the variation law, macroscopic and microscopic parameters are calibrated and adjusted using discrete element software, and a microscopic parameter relationship model at different foam invasion distances is obtained, and the large-scale fluid flow pore-scale grid model and the microscopic parameter relationship model are embedded in a particle contact model, and a simulation of slag improvement foam permeability test is performed to simulate the foam infiltration process in slag, and the variation law of seepage velocity at different foam invasion distances is obtained. The present invention provides a theoretical basis for systematically carrying out simulation and analysis of the time-varying behavior of foam-improved soil mechanics.
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Description

Technical Field

[0001] The invention belongs to the technical field of discrete element model construction, and specifically relates to a model construction method and system that reflects the seepage characteristics of a slag improvement foaming agent. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] In underground transportation construction, the shield method is a fully mechanized construction method in the dark excavation method. It has a high degree of automation, fast construction speed, can be completed in one go, and is not affected by the climate. It is widely used due to its economic advantages. At present, the type of shield machine used in urban subway construction is mainly the earth pressure balance shield machine. Its principle is to balance the passive earth pressure inside the cut ring of the excavation face with the active earth pressure outside the cutter head of the excavation face. Therefore, the soil and sand as the supporting medium are required to have good plastic flow to ensure the excavation efficiency. However, since general soil cannot fully meet these characteristics, it is necessary to improve the slag soil.

[0004] Muck improvement is to inject improvers into the excavation face or soil compartment through special equipment on the shield machine to adjust the cut soil into a "plastic flow state". The improved slag should have good plasticity, low permeability and small friction resistance, so as to ensure the smooth progress of shield excavation. Foaming agent, also known as foaming agent, refers to the ability to reduce the surface tension of liquid and produce a large amount of uniform and stable foam. It is widely used as a soil improver in the shield industry.

[0005] In recent years, a large number of foaming agents for domestic slag improvement have been put on the market, but the existing products still expose many shortcomings such as low foaming multiples and large application dosage. For this reason, relevant personnel have conducted a large number of experiments to improve the foaming agent in order to achieve better slag improvement effects. Studies have shown that the higher the degree of mixing between the foam and the soil, the better the improvement effect, and the foam needs to penetrate into the soil particles to a certain extent before it can be fully mixed with the soil, and these experiments are closely related to the penetration process of the foam in the slag. However, the inventors found that most of the current research on the permeability of foam-improved soil remains in the experimental analysis stage, and the existing theoretical models and numerical methods involve less permeability during the foam penetration process. There is a lack of theoretical calculation models and methods with high reliability in predicting the permeability of foam-improved soil. It is difficult to systematically carry out simulation and analysis of the mechanical time-varying behavior of foam-improved soil, and there is still room for improvement in the theoretical model and numerical analysis method of foam-improved soil. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a model construction method and system that reflects the seepage characteristics of soil modification foaming agent. The present invention provides a theoretical basis for systematically carrying out simulation and analysis of the time-varying mechanical behavior of foam-modified soil.

[0007] According to some embodiments, the present invention adopts the following technical solutions:

[0008] A method for constructing a model reflecting the seepage characteristics of a soil modification foaming agent comprises the following steps:

[0009] Obtain the results of indoor permeability test of soil improvement foam and obtain the variation law of seepage velocity under different foam intrusion distances;

[0010] Through regular Delaunay triangulation, a pore-scale grid model of large-scale fluid flow is established to fully define the fluid exchange between pores based on the local pore geometry;

[0011] According to the variation law, the macroscopic and microscopic parameters are calibrated and adjusted using discrete element software to obtain a microscopic parameter relationship model under different foam invasion distances;

[0012] Based on the indoor permeability test model, the large-scale fluid flow pore-scale grid model and the microscopic parameter relationship model are embedded into the particle contact model to simulate the seepage velocity of soil-improved foam at different intrusion distances.

[0013] Based on the indoor penetration test of slag-improved foam and the model obtained after embedding, the penetration test simulation of slag-improved foam was carried out to simulate the penetration process of foam in slag and obtain the variation law of seepage velocity at different foam invasion distances.

[0014] As an optional implementation manner, the indoor penetration test result of the slag-improving foam is to conduct an indoor penetration test of the slag-improving foam on the slag to be improved and the foaming agent to be studied, and use an optical fiber sensor to record the change pattern of the seepage velocity of the slag-improving foam at different intrusion distances.

[0015] As an optional implementation, the specific process of regular Delaunay triangulation includes: generalizing the classical Delaunay triangulation to weighted points, using regular Delaunay triangulation, where the weight takes into account the radius of the sphere, the edges and faces of the Voronoi diagram of the regular triangulation are completely contained in the gaps between the spheres, and the edges and faces of the regular Voronoi diagram are straight lines and planes.

[0016] As an optional implementation method, in the process of calibrating and adjusting the macro and micro parameters using discrete element software, parameter fitting is performed on each micro parameter at different foam invasion distances to obtain the relationship between the macro parameters of the improved slag and the micro parameters of the discrete element model, and then the relationship function of the seepage velocity of the slag-improved foam at different invasion distances is obtained.

[0017] As an alternative embodiment, the different intrusion distances are achieved by removing foam particles.

[0018] As an optional implementation, the seepage velocity is calculated by using a modified Darcy's law.

[0019] As an optional implementation method, the process of simulating the penetration of foam in slag is compared with the indoor penetration test, and the accuracy of the constructed model is judged by macro and micro parameters. If the degree of agreement between the numerical simulation and the indoor test is less than the set value, the relationship function of the seepage velocity of the slag-improved foam at different intrusion distances is re-characterized; otherwise, the parameters are fine-tuned to achieve a better agreement.

[0020] A model building system reflecting the seepage characteristics of soil improvement foaming agent, comprising:

[0021] The test result acquisition module is configured to obtain the indoor permeability test results of the soil improvement foam and obtain the variation law of the seepage velocity under different foam intrusion distances;

[0022] a partitioning module configured to build a large-scale fluid flow pore-scale grid model through regular Delaunay triangulation to fully define the fluid exchange between pores based on the local pore geometry;

[0023] A parameter adjustment module is configured to calibrate and adjust the macroscopic and microscopic parameters using discrete element software according to the variation law, so as to obtain a microscopic parameter relationship model under different foam invasion distances;

[0024] The model optimization module is configured to embed the large-scale fluid flow pore-scale grid model and the mesoscopic parameter relationship model into the particle contact model based on the indoor permeability test model to simulate the seepage velocity of soil-improved foam at different intrusion distances;

[0025] The simulation module is configured to simulate the soil-improving foam penetration test based on the indoor penetration test of the soil-improving foam and the model obtained after embedding, simulate the penetration process of the foam in the soil, and obtain the change law of the seepage velocity under different foam intrusion distances.

[0026] An electronic device comprises a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps in the above method are completed.

[0027] A computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the steps in the above method are completed.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] (1) Starting from the microscopic scale, the present invention conducts numerical simulation research on the seepage characteristics of soil improvement foam under different foam intrusion distance conditions, explores the changes in pore water pressure in different sections, and obtains the seepage velocity calculated by the pore water pressure, thereby revealing the penetration mechanism of soil improvement foam agent and improving the theoretical model and numerical analysis method of foam-improved soil.

[0030] (2) At present, most of the research on the permeability of foam-improved soil remains in the experimental analysis stage. The existing theoretical models and numerical methods involve little permeability in the foam penetration process. The present invention can obtain the seepage characteristics under different foam agent improvement conditions by setting different improvement parameters, which provides assistance for formulating foam improvement plans, thereby providing a theoretical calculation model and method with high reliability for the prediction of foam-improved soil permeability, and providing a theoretical basis for systematically carrying out simulation and analysis of the time-varying mechanical behavior of foam-improved soil.

[0031] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0033] Figure 1 is a flow chart of model construction of the present invention;

[0034] Figure 2 is a diagram of the foam penetration process simulated by the present invention;

[0035] Figure 3 It is the sand grade distribution diagram used in the embodiment of the present invention;

[0036] Figure 4 is a two-dimensional schematic diagram of the throat volume of the model of the present invention;

[0037] Figure 5 It is a curve diagram of the change of seepage velocity with invasion distance obtained by experiments and simulations of the embodiments of the present invention. DETAILED DESCRIPTION

[0038] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0039] It should be noted that the following detailed descriptions are all illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0040] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0041] A discrete element-finite volume method model construction method that reflects the seepage characteristics of soil improvement foam agent, such as Figure 1 As shown, it mainly includes the following steps:

[0042] Step 1: Select the slag soil to be improved and the foaming agent used for slag soil improvement, carry out the indoor permeability test of slag soil improvement foam, and obtain the variation law of seepage velocity under different foam invasion distances;

[0043] Step 2: Establish a large-scale fluid flow pore-scale grid model through regular Delaunay triangulation to fully define the fluid exchange between pores based on the local pore geometry;

[0044] Step 3: Based on the variation law obtained in step 1, the discrete element software is used to simulate the soil improvement foam penetration test, and the micro-parameter relationship model under different foam intrusion distances is obtained by calibrating and adjusting the macro- and micro-parameters;

[0045] Step 4: Based on the indoor permeability test model, the models in steps 2 and 3 are embedded into the existing particle contact model to simulate the seepage velocity of soil-improved foam at different intrusion distances;

[0046] Step 5: Based on the indoor penetration test of slag-improved foam and the model obtained in step 4, a simulation of the slag-improved foam penetration test is carried out to simulate the penetration process of foam in slag and obtain the variation law of seepage velocity at different foam intrusion distances.

[0047] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0048] (1) Conduct indoor penetration test of soil improvement foam

[0049] This embodiment uses European Quartz S80 sand, and the gradation curve of the sand is as follows: Figure 2 As shown in the figure, sand that meets the test requirements is obtained by screening, and foam with a foam expansion ratio (FIR) of 15 is prepared by a foaming device. The indoor test of soil improvement foam penetration is carried out using a penetration test device. The curve of the seepage velocity versus the intrusion distance obtained in the test is shown in Figure 5 (solid line) shown.

[0050] (2) Establish a pore-scale grid model for large-scale fluid flow.

[0051] Through regular Delaunay triangulation, a large-scale fluid flow pore-scale grid model is established. The classical Delaunay triangulation is extended to weighted points, and regular Delaunay triangulation is adopted, in which the weight takes into account the radius of the sphere; contrary to the classical Delaunay triangulation, the edges and faces of the Voronoi diagram of the regular triangulation are completely contained in the gaps between the spheres. The edges and faces of the regular Voronoi diagram are straight lines and planes, where Γ and Θ represent the domains occupied by the solid and fluid, respectively, and Ω=ΓUΘ, (Θ is also called pore size).

[0052] Based on the local pore geometry, the fluid exchange between pores is fully defined, and the velocity function V of the particle is given by the divergence theorem. f The relationship between the time derivative of and the fluid velocity:

[0053]

[0054] in, is Θ i The boundary of n is perpendicular to the outward direction. Unit vector, u is the fluid velocity, v is the velocity of the outer boundary.

[0055] Define the flow flux q from tetrahedron i to the adjacent tetrahedrons j1 to j4 ij ,get:

[0056]

[0057] (3) The discrete element software is used to obtain the microscopic parameter relationship model under different foam invasion distances.

[0058] According to the pore grid division method in step 2, the interpore gradient is introduced, which is defined as the pressure difference p between two connected tetrahedral units. i -p j With the correlation length L ij Since it is linear, q ij The relationship between the pore gradient and the local conductivity factor g with an ij scale can be expressed as ij express:

[0059]

[0060] Similar to the Hagen-Poiseuille relation, by introducing the pore throat The hydraulic radius (HR) and its cross-sectional area A ij To define g ij, the throat shape is reflected by the dimensionless conductivity factor α which reflects the throat shape (Hagen-Poiseuille for radius The circular cross section is obtained with α = 1 / 2):

[0061]

[0062] Define a hydraulic radius (HR) As the throat volume (two-dimensional diagram of the throat volume is shown in Figure 4 The ratio of the solid-liquid interface area, HR Denoted as:

[0063]

[0064] Among them, Φ ij Represents Θ ij The volume, γ ij express The area of ​​the contour that is in contact with the sphere.

[0065] Among them, L ij , and A ij It is a geometric quantity that describes the geometry of the throat.

[0066] Based on the macroscopic mechanical parameters at different intrusion distances during the foam penetration process, the macroscopic and mesoscopic parameters are calibrated by continuously adjusting the mesoscopic parameters in the above numerical simulation, ultimately ensuring that the failure mode and macroscopic mechanical parameters of the model are basically consistent with those of the indoor test.

[0067] (4) Carry out simulation of foam penetration test on improved soil slag.

[0068] Based on the indoor permeability test model, the models in steps 2 and 3 are embedded into the existing particle contact model. By removing the foam particles to achieve different foam invasion distances, the seepage velocity of the soil-improved foam at different invasion distances is simulated. The simulated seepage velocity curve with invasion distance is shown in Figure 5 The results are shown in (dashed line) and compared with the test results to verify the correctness of the model in simulating the relationship between the seepage velocity of soil-improved foam and the intrusion distance.

[0069] Total permeability k of foam-invaded sand f Determined by Darcy's law:

[0070]

[0071] Where μ is the correction factor, Q is the flow rate (m 3 / s); x is the thickness of the foam penetration sand (or the foam penetration depth) (m); Δφ fis the water head difference of the piezometer in the permeable foam sand layer (m); A is the cross-sectional area of ​​the cylinder where the sand is located (m 2 ).

[0072] The above is a detailed introduction to the discrete element-finite volume method model construction method of the present invention that reflects the seepage characteristics of the slag improvement foam agent. Based on the test results, the present invention elaborates on the construction process of the permeability model and the calibration method of the mesoscopic parameters, and verifies the correctness of the relationship between the seepage velocity of the slag improvement foam in the model and the intrusion distance through simulation. The above description is only used to help understand the method of the present invention and its core idea; at the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0073] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0074] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0075] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0076] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0077] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for constructing a model that reflects the seepage characteristics of a soil modification foaming agent, characterized in that: The following steps are involved: Obtain the results of indoor permeability test of soil improvement foam and obtain the variation law of seepage velocity under different foam intrusion distances; Through regular Delaunay triangulation, a pore-scale grid model of large-scale fluid flow is established to fully define the fluid exchange between pores based on the local pore geometry; According to the variation law, the macroscopic and microscopic parameters are calibrated and adjusted using discrete element software to obtain a microscopic parameter relationship model under different foam invasion distances; Based on the indoor permeability test model, the large-scale fluid flow pore-scale grid model and the microscopic parameter relationship model are embedded into the particle contact model to simulate the seepage velocity of soil-improved foam at different intrusion distances. Based on the indoor penetration test of soil-improving foam and the model obtained after embedding, the soil-improving foam penetration test simulation was carried out to simulate the penetration process of foam in soil and obtain the variation law of seepage velocity under different foam invasion distances. According to the variation law, the macroscopic and microscopic parameters are calibrated and adjusted using discrete element software to obtain the microscopic parameter relationship model under different foam invasion distances. The specific process includes: according to the pore grid division method, the interpore gradient is introduced, which is defined as the pressure difference between two connected tetrahedral units. With the relevant length ratio, flow flux The relationship between the pore gradient and Local conductivity factor of the scale express: By introducing pore throat The hydraulic radius and cross-sectional area To define , through the dimensionless conductance factor reflecting the throat shape Reflect the shape of the throat: is the correction factor, defining the hydraulic radius As the ratio of throat volume HR to solid-liquid interface area, HR Denoted as: Among them, express The volume of Represents the part of the contour that is in contact with the sphere The area of , and It is a geometric quantity that describes the geometry of the throat.

2. A method for constructing a model reflecting the seepage characteristics of a soil modification foaming agent as claimed in claim 1, characterized in that: The indoor penetration test result of the slag improvement foam is to conduct an indoor penetration test of the slag improvement foam on the slag to be improved and the foaming agent to be studied, and use an optical fiber sensor to record the change pattern of the seepage velocity of the slag improvement foam at different intrusion distances.

3. A method for constructing a model reflecting the seepage characteristics of a soil modification foaming agent as claimed in claim 1, characterized in that: The specific process of regular Delaunay triangulation includes: generalizing the classical Delaunay triangulation to weighted points, using regular Delaunay triangulation, where the weight considers the radius of the sphere, the edges and faces of the Voronoi diagram of the regular triangulation are completely contained in the gaps between the spheres, and the edges and faces of the regular Voronoi diagram are straight lines and planes.

4. A method for constructing a model reflecting the seepage characteristics of a soil modification foaming agent as claimed in claim 1, characterized in that: In the process of calibrating and adjusting the macro and micro parameters using discrete element software, parameter fitting is performed on each micro parameter at different foam invasion distances to obtain the relationship between the macro parameters of improved slag and the micro parameters of the discrete element model, and then the relationship function of the seepage velocity of slag-improved foam at different invasion distances is obtained.

5. The method for constructing a model reflecting the seepage characteristics of a soil modification foaming agent according to claim 1, characterized in that: The different intrusion distances are achieved by removing foam particles.

6. A method for constructing a model reflecting the seepage characteristics of a soil modification foaming agent as claimed in claim 1, characterized in that: The seepage velocity is calculated by using the modified Darcy's law.

7. A method for constructing a model reflecting the seepage characteristics of a soil modification foaming agent as claimed in claim 1, characterized in that: In the process of simulating the penetration of foam in slag, the simulation results are compared with the indoor penetration test, and the accuracy of the constructed model is judged by macro and micro parameters. If the agreement between the numerical simulation and the indoor test is less than the set value, the relationship function of the seepage velocity of the slag-improved foam at different invasion distances is re-characterized; otherwise, the parameters are fine-tuned to make the agreement better.

8. A model building system that reflects the seepage characteristics of soil improvement foaming agent, characterized in that: include: The test result acquisition module is configured to obtain the indoor permeability test results of the soil improvement foam and obtain the variation law of the seepage velocity under different foam intrusion distances; a partitioning module configured to build a large-scale fluid flow pore-scale grid model through regular Delaunay triangulation to fully define the fluid exchange between pores based on the local pore geometry; A parameter adjustment module is configured to calibrate and adjust the macroscopic and microscopic parameters using discrete element software according to the variation law, so as to obtain a microscopic parameter relationship model under different foam invasion distances; The model optimization module is configured to embed the large-scale fluid flow pore-scale grid model and the mesoscopic parameter relationship model into the particle contact model based on the indoor permeability test model to simulate the seepage velocity of soil-improved foam at different intrusion distances; The simulation module is configured to simulate the soil improvement foam penetration test based on the soil improvement foam indoor penetration test and the model obtained after embedding, simulate the penetration process of foam in the soil, and obtain the variation law of seepage velocity under different foam invasion distances; According to the variation law, the macroscopic and microscopic parameters are calibrated and adjusted using discrete element software to obtain the microscopic parameter relationship model under different foam invasion distances. The specific process includes: according to the pore grid division method, the interpore gradient is introduced, which is defined as the pressure difference between two connected tetrahedral units. With the relevant length ratio, flow flux The relationship between the pore gradient and Local conductivity factor of the scale express: By introducing pore throat The hydraulic radius and cross-sectional area To define , through the dimensionless conductance factor reflecting the throat shape Reflect the shape of the throat: is the correction factor, defining the hydraulic radius As the ratio of throat volume HR to solid-liquid interface area, HR Denoted as: Among them, express The volume of Represents the part of the contour that is in contact with the sphere The area of , and It is a geometric quantity that describes the geometry of the throat.

9. An electronic device, characterized in that: The method comprises a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the steps in the method according to any one of claims 1 to 7 are completed.

10. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the steps of the method according to any one of claims 1 to 7.

Citation Information

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