A method for predicting grouting slurry diffusion range in coal seam floor area

Abstract

The application provides a method for predicting the grouting slurry diffusion range of a coal seam floor area, comprising: obtaining a slurry water displacement model containing minefield stratum parameters and grouting borehole parameters of the coal seam floor area; obtaining a Brinkman equation for describing the incompressible fluid flow caused by reinforcing materials in a porous medium based on the Navier-Stokes equation and the Darcy law; wherein the Brinkman equation contains a viscosity term and a pressure gradient term; taking the grouting pressure, slurry density, dynamic viscosity, porous medium permeability, and porous medium porosity as the influencing factors of slurry diffusion, and obtaining various parameter combinations of each influencing factor and level; using the various parameter combinations, simulating the slurry diffusion process based on the slurry water displacement model by using the Brinkman equation, to obtain the optimal parameter combination and the corresponding slurry diffusion range. The method can scientifically and accurately predict the slurry diffusion range, and improve the consistency and reliability of the grouting treatment effect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of mine water disaster prevention, and particularly relates to a method for predicting the grouting slurry diffusion range of a coal seam floor area. BACKGROUND

[0002] In the northern part of China, coal seams in the Carboniferous-Permian coalfield are often deposited with 2 to 14 layers of thin coal measure interlayer limestone, and 200 to 800 meters of Ordovician or Cambrian thick-bedded limestone. These strata are one of the main water inrush sources faced by deep mining and lower group coal mining in coal mines. When the thickness of the coal seam floor aquifuge is insufficient and is in a strong runoff zone or a water-rich geological structure zone, the coal seam floor carbonate rock confined aquifer is prone to cause water inrush disasters. Such disasters usually have characteristics such as high water pressure, abundant water source, strong concealment, and great destructive power, and have become one of the main disasters faced by deep mining in the North China type coalfield. Grouting technology is the main means for preventing and controlling water disasters of the coal seam floor karst confined water, and its basic principle is to reinforce the floor aquifuge through surface area treatment or local grouting, transform the aquifer into a relative aquifuge, and seal the original fissures, faults, collapse columns and other water-conducting channels in the strata. Thus, the transformed strata meet the thickness requirement of the aquifuge, the comprehensive water-blocking capacity of the coal seam floor strata is improved, and the water inrush disaster caused by the floor is prevented.

[0003] Although Chinese scholars have carried out a large number of studies on the grouting slurry diffusion law of fissured rock mass and the regional treatment of coal seam floor water disasters, and have achieved certain theoretical and practical results, the existing technology still has deficiencies when faced with complex geological conditions such as deep complex stress, hydrodynamic force and structure. In particular, under different hydrogeological conditions, the grouting and reconstruction effect of thin-bedded limestone and Ordovician thick-bedded limestone in the complex engineering background of vertical holes, deviated holes and super-long horizontal holes is significantly different. The existing grouting technology relies more on idealized models and field experience, and the grasp of the main control factors and effective treatment range of slurry diffusion under complex conditions is still insufficient, which leads to the difficulty in accurately predicting and controlling the treatment effect, and limits its popularization and application in actual engineering. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a method for predicting the grouting slurry diffusion range of a coal seam floor area, which takes into account the macroscopic viscous effect and the pressure gradient in each pore channel, can scientifically and accurately predict the slurry diffusion range, overcome the deficiency that the traditional method mainly relies on field experience, and improve the consistency and reliability of the grouting treatment effect, thereby providing a scientific basis for efficient treatment of deep high-pressure aquifers.

[0005] The present application provides a method for predicting the grouting slurry diffusion range of a coal seam floor area, comprising:

[0006] The slurry water displacement model obtains coal seam floor area containing minefield stratum parameters and grouting borehole parameters;

[0007] Based on the Navier-Stokes equation and the Darcy law, a Brinkman equation for describing the incompressible fluid flow caused by the reinforcing material in the porous medium is obtained; wherein the Brinkman equation contains a viscosity term and a pressure gradient term;

[0008] The grouting pressure, slurry density, dynamic viscosity, porous medium permeability and porous medium porosity are taken as the influencing factors of slurry diffusion, and various parameter combinations of each influencing factor and level are obtained;

[0009] Using various parameter combinations, the slurry diffusion process is simulated based on the slurry water displacement model by using the Brinkman equation, so as to obtain the optimal parameter combination and the corresponding slurry diffusion range.

[0010] Further, the minefield stratum parameters include: regional division information of each minefield stratum and geological parameter information of each minefield stratum; wherein the geological parameter information includes: porosity, permeability and thickness;

[0011] The grouting borehole parameters include: position information and segmentation information of the grouting borehole, and drill bit diameter of each segment.

[0012] Further, in the simulation of the slurry diffusion process, the following assumptions are met:

[0013] (1) the flow of the slurry is continuous;

[0014] (2) the slurry is an isotropic and incompressible fluid, and the bulk density of the slurry remains unchanged during the flow process, and the flow rate is stable;

[0015] (3) the side wall of the slurry satisfies the no-slip boundary;

[0016] (4) the diffusion mode of the slurry is complete displacement diffusion, and the mixing of water and slurry at the slurry-water interface is not considered;

[0017] (5) the flow of the slurry belongs to laminar flow.

[0018] Further, the Brinkman equation for describing the incompressible fluid flow caused by the reinforcing material in the porous medium is obtained by the following way:

[0019] The Navier-Stokes equation is used to describe the motion of viscous incompressible fluid;

[0020] The Darcy resistance term is added to the Navier-Stokes equation to simulate the resistance of the solid skeleton to the fluid flowing in the porous medium;

[0021] porosity is introduced to modify the density term to describe the fluid flow only in the pore space of the porous medium;

[0022] With the assumption of the isotropy of the porous medium, the viscosity term and the pressure gradient term are expressed as the divergence of the viscous stress tensor and the pressure tensor, respectively, and the Brinkman equation is obtained to describe the incompressible fluid flow in the porous medium caused by the reinforcement material.

[0023] Further, the Navier-Stokes equation is expressed as:

[0024]

[0025] where ρ represents the fluid density; u represents the fluid velocity; p represents the fluid pressure; μ represents the dynamic viscosity of the fluid; f represents the external force acting on the fluid; represents the gradient operator.

[0026] Further, the Darcy resistance term f d is expressed as:

[0027]

[0028] where -μ / κ·u represents the linear resistance based on the Darcy law; -βρ|u|u represents the nonlinear resistance introduced due to the increase of the flow velocity, which is usually dominant under the condition of high flow velocity; β represents a constant related to the fluid and the porous medium, reflecting the degree of the nonlinear resistance.

[0029] Further, the fluid flow only in the pore space of the porous medium is described by the following equation:

[0030]

[0031] where ε p represents the porosity of the porous medium, represents the viscosity term, represents the pressure gradient term.

[0032] Further, the viscosity term and the pressure gradient term are expressed as the divergence of the viscous stress tensor and the pressure tensor, respectively, by the following equations:

[0033]

[0034]

[0035] where represents the velocity gradient; represents the transpose of the velocity gradient; pI represents the pressure tensor, where I is the unit tensor;

[0036] The Brinkman equation is expressed as:

[0037]

[0038]

[0039] Further, the initial grouting parameter settings of the slurry water displacement model are as follows:

[0040] The initial grouting pressure is 9 MPa, the initial slurry density is 1200 kg / m 3 , the initial slurry dynamic viscosity is 3 mPa·s, the grouting reconstruction rock permeability is 1.2E-11 m 2 , the grouting reconstruction body pore ratio is 0.05, and the fault zone permeability is 0.5 m 2 , and the fault zone porosity is 0.01.

[0041] Further, the optimal parameter combination and the corresponding slurry diffusion range are obtained by the following method:

[0042] Obtain a plurality of parameter combinations, and a plurality of parameter combinations respectively corresponding to the slurry diffusion range obtained by the multi-physical field coupling numerical simulation;

[0043] Based on the plurality of parameter combinations and the respectively corresponding slurry diffusion range, the influence characteristics of single factor on the slurry diffusion range are analyzed by using the variance analysis method, and the main factor and the secondary factor are determined;

[0044] Based on the main factor and the secondary factor, and the influence characteristics of each factor on the slurry diffusion range, the optimal parameter combination is determined, and the predicted slurry diffusion range is obtained by using the Brinkman equation and the slurry water displacement model.

[0045] The coal seam floor area grouting slurry diffusion range prediction method provided in the application considers the macroscopic viscous effect and the pressure gradient in each pore channel, can scientifically and accurately predict the slurry diffusion range, overcomes the shortcomings of the traditional method mainly relying on field experience, and improves the consistency and reliability of the grouting treatment effect, provides a scientific basis for realizing efficient treatment of deep high-pressure aquifer. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 A flowchart of the coal seam floor area grouting slurry diffusion range prediction method provided in the application is shown;

[0047] Figure 2 A schematic diagram of the slurry water displacement model provided in the application is shown;

[0048] Figure 3A trend graph of the estimated boundary average value changing with grouting pressure is shown;

[0049] Figure 4 A trend graph of the estimated boundary average value changing with slurry density is shown;

[0050] Figure 5 A trend graph of the estimated boundary average value changing with slurry dynamic viscosity is shown;

[0051] Figure 6 A trend graph of the estimated boundary average value changing with porous medium permeability is shown;

[0052] Figure 7 A trend graph of the estimated boundary average value changing with porous medium porosity is shown. DETAILED DESCRIPTION

[0053] To make the objectives, technical solutions, and advantages of the present technical solution clearer, further detailed descriptions of the present technical solution are provided below in conjunction with specific embodiments. It should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present technical solution.

[0054] At the present stage, the advanced regional treatment of coal seam floor water damage mainly relies on field experience. In the face of deep complex stress, hydrodynamic force, structure, and other complex geological conditions, the grouting reconstruction effect of different hydrogeological conditions under the complex engineering background of vertical holes, deviated holes, and super-long horizontal hole combinations has great differences. The slurry diffusion law and effective treatment range are difficult to accurately predict.

[0055] In addition, under normal circumstances, during the grouting process, the displaced phase cannot be completely removed from the pores, and a layer of residual wet fluid will be left on the solid surface, maintaining two incompatible fluids on the contact interface. This two-phase percolation simulation involves the flow of slurry and groundwater, which have different volume fractions in a specific spatial region, but the sum of the volume fractions of the two is always 1. Therefore, although the ratio of slurry and groundwater changes, the total volume remains constant. That is, in the initial state, the porous medium is completely filled with water, and as the slurry displaces, the volume fraction of water gradually decreases until it is completely replaced.

[0056] In porous medium phase transmission, the complex behavior of two-phase flow needs to be described by a specific equation. The related two-phase flow equation can be expressed as formula (1) as follows:

[0057]

[0058] In the formula, ε pporosity of the porous medium; density of the respective phase; S i volume fraction of the respective phase; N i flux phase; Q Si mass source term of the respective phase; u i Darcy velocity of the respective phase; K rSi relative permeability of the respective phase; mu Si dynamic viscosity of the respective phase; K is the permeability of the porous medium; P Si pressure of the respective phase fluid; P v pressure of the phase calculated according to the volume constraint; P cSi capillary pressure provided by the phase; is the divergence operator; is the gradient operator.

[0059] When coupling free medium and porous medium flow, it is often solved by introducing Darcy's law in Navier-Stokes equation, although this method is easy to solve numerically, but it does not consider the viscous effect in free medium flow, and the effect is still important in the free-porous interface area.

[0060] Therefore, the present application provides a method for predicting the diffusion range of grouting slurry in the coal seam floor area, please refer to Figure 1 , Figure 1 The flow chart of the method for predicting the diffusion range of grouting slurry in the coal seam floor area provided by the embodiment of the present application is shown. As Figure 1 shown, the method comprises:

[0061] S101, obtaining a slurry water displacement model containing minefield stratum parameters and grouting borehole parameters in the coal seam floor area.

[0062] In this step, the slurry water displacement model is used to provide a simulation environment for the grouting process. Under the action of high pressure, the slurry displaces groundwater to form a two-phase unsteady seepage in the porous medium. The slurry and groundwater interact and flow at the same time as two incompatible fluids. By simulating the grouting process, the grouting effect and the diffusion range of the slurry can be predicted, thereby providing a scientific basis for grouting design, optimizing the design scheme, and improving the engineering quality and efficiency.

[0063] The minefield stratum parameters include: regional division information of each minefield stratum and geological parameter information of each minefield stratum; the geological parameter information includes: porosity, permeability and thickness; the grouting borehole parameters include: position information and segmentation information of the grouting borehole, and drill bit diameter of each segment.

[0064] As an example, please refer to Figure 2 , Figure 2 The schematic diagram of the slurry water displacement model provided by the embodiment of the present application is shown. As Figure 2As shown, the slurry water drive model is divided into multiple minefield strata from top to bottom, including: Quaternary, upper Shihezi group, lower Shihezi group, Shanxi group, 9# coal seam, Taiyuan group, 16# coal seam, Zhuozishan group, the geological parameter information of each minefield stratum is shown in Table 1, the width, length and height of the model are 1000 meters, 1000 meters and 877.53 meters respectively, further, the area below 16# coal seam and above Zhuozishan group is determined as the position of grouting reconstruction rock layer, and the position information and segmentation information of the grouting borehole are obtained as shown in Figure 2 The position information and segmentation information of the grouting borehole are shown in the figure, which specifically includes: straight well section, build-up section and horizontal section, the length of the horizontal section is 200 meters, the drill bit diameter of the first opening straight well section is 311.15 millimeters, the drill bit diameter of the second opening build-up section is 215.9 millimeters, and the drill bit diameter of the third opening horizontal section is 152.4 millimeters.

[0065] Table 1, geological parameter information of each minefield stratum

[0066]

[0067] S102, based on Navier-Stokes equation and Darcy law, the Brinkman equation for describing the incompressible fluid flow caused by the reinforcing material in the porous medium is obtained.

[0068] Wherein, the Brinkman equation contains viscosity term and pressure gradient term.

[0069] In specific implementation, the Brinkman equation for describing the incompressible fluid flow caused by the reinforcing material in the porous medium is obtained by the following way:

[0070] Step 1021, the motion of viscous incompressible fluid is described by Navier-Stokes equation.

[0071] Specifically, the Navier-Stokes equation is expressed as:

[0072]

[0073] In the formula, ρ represents fluid density; u represents fluid velocity; p represents fluid pressure; μ represents fluid dynamic viscosity; f represents external force acting on the fluid; Gradient operator is represented.

[0074] Step 1022, Darcy resistance term is added to the Navier-Stokes equation to simulate the resistance of solid skeleton to fluid flowing in the porous medium.

[0075] Specifically, the Darcy resistance term f d is expressed as:

[0076]

[0077] In the formula, -μ / κ·u represents the linear resistance based on Darcy's law; -βρ|u|u represents the nonlinear resistance introduced due to the increase in flow velocity, which usually dominates under high flow velocity conditions; β represents a constant related to the fluid and porous medium, reflecting the degree of nonlinear resistance.

[0078] Step 1023: Porosity is then introduced to correct the density term in order to describe the fluid flowing only within the pore space of the porous medium.

[0079] Specifically, the fluid flowing only within the pore space of a porous medium is described by the following equation:

[0080]

[0081] In the formula, ε p Porosity represents the porosity of porous media. Indicates the viscosity term. This represents the pressure gradient term.

[0082] Step 1024: Based on the premise that the porous medium is isotropic, the viscosity term and pressure gradient term are expressed as divergence forms of the viscous stress tensor and pressure tensor, respectively, and the Brinkman equation is obtained to describe the incompressible fluid flow caused by the reinforcing material in the porous medium.

[0083] Specifically, the viscosity term and pressure gradient term are expressed in divergence form as the viscous stress tensor and pressure tensor, respectively, using the following equations:

[0084]

[0085] In the formula, Represents the velocity gradient; pI represents the transpose of the velocity gradient; pI represents the pressure tensor, where I is the unit tensor.

[0086] Here, we replace the viscosity and pressure gradient terms in formula (4) with formulas (5) and (6), and at the same time, we assume that the fluid flow is slow and further ignore the inertia term. The Brinkman equation was finally obtained.

[0087] The Brinkmann equation is expressed as:

[0088]

[0089] S103. Grouting pressure, grout density, dynamic viscosity, porous media permeability, and porous media porosity are taken as influencing factors of grout diffusion, and various parameter combinations of each influencing factor and level are obtained.

[0090] In this step, considering that the diffusion of grout in karst media is influenced by multiple factors, studying these factors helps to better understand and control the diffusion process, thereby improving grouting efficiency. A comprehensive analysis of the influencing factors on grout diffusion in advanced treatment of coal seam floor water hazards categorizes them into three main types: external driving forces, grout characteristics, and formation characteristics. External driving forces include grouting pressure; grout characteristics include grout density and dynamic viscosity; and formation characteristics include porous media permeability and porosity.

[0091] To comprehensively cover situations that may be encountered in actual engineering, this application's embodiments designed an orthogonal experiment. Orthogonal experiments can achieve better experimental results with fewer trials, significantly optimizing the experimental process. This orthogonal experiment includes 5 factors, each with 5 levels, the specific selection of which is shown in Table 2.

[0092] Table 2. Selection of various influencing factors and levels

[0093]

[0094] Furthermore, according to the orthogonal design principle, at least 21 experiments are required based on the above parameter combination. To meet the experimental requirements, the L25(56) orthogonal table is selected. This table contains 25 sets of experimental configurations, that is, 25 parameter combinations that can cover all factors and levels, to ensure experimental flexibility and data integrity. The control index of the experiment is the diffusion range of grout in the coal seam floor area.

[0095] S104. Using multiple parameter combinations, the Brinkman equation is used to simulate the slurry diffusion process based on the slurry-driven water model to obtain the optimal parameter combination and the corresponding slurry diffusion range.

[0096] In simulating the diffusion of slurry, the following assumptions are met:

[0097] (1) The flow of the slurry is continuous;

[0098] (2) The slurry is an isotropic and incompressible fluid, and the slurry density remains constant and the flow rate is stable during the flow process;

[0099] (3) The sidewalls of the slurry satisfy the no-slip boundary condition;

[0100] (4) The diffusion mode of the slurry is complete displacement diffusion, without considering the mixing of water and slurry at the slurry-water interface;

[0101] (5) The flow of the slurry is laminar flow.

[0102] Meanwhile, the initial grouting parameters of the slurry-driven water-displacement model are set as follows:

[0103] The initial grouting pressure was 9 MPa and the initial grout density was 1200 kg / m³. 3 The initial dynamic viscosity of the grout was 3 mPa·s, and the permeability of the grouting-modified rock strata was 1.2E-11m. 2 The grouting modification experience showed a porosity of 0.05 and a fault zone permeability of 0.5m. 2 The porosity of the fault zone is 0.01.

[0104] In this step, the slurry flooding model is used as the simulation environment, and the Brinkman equation is used as the solution equation for the slurry flooding model. Multiple parameter combinations are used to simulate the slurry diffusion process to complete the orthogonal experiment. By analyzing the results of the orthogonal experiment, the optimal parameter combination and the corresponding slurry diffusion range are obtained.

[0105] In practical implementation, the optimal parameter combination and the corresponding slurry diffusion range are obtained through the following methods:

[0106] Step 1041: Obtain multiple parameter combinations, and the slurry diffusion range corresponding to each of the multiple parameter combinations obtained through multi-physics field coupling numerical simulation.

[0107] As an example, the 25 parameter combinations and their corresponding slurry diffusion ranges are shown in Table 3:

[0108]

[0109] Step 1042: Based on multiple parameter combinations and their corresponding slurry diffusion ranges, the influence of single factors on the slurry diffusion range is analyzed using the analysis of variance method, and the main and secondary factors are determined.

[0110] In this step, analysis of variance (ANOVA) can distinguish experimental differences caused by factors, level variations, and errors, and provide reliable quantitative estimates. Meanwhile, SPSS statistical software is widely used in natural and social sciences and can efficiently perform data analysis. Therefore, this application embodiment uses SPSS software for ANOVA.

[0111] Here, before conducting the analysis of variance, we perform a one-way analysis by introducing an estimated marginal mean:

[0112] Estimating the marginal mean refers to estimating the average value of a specific variable while controlling for the influence of other relevant variables, for data analysis. This application calculated the estimated marginal mean values ​​for specific variables: grouting pressure, grout density, grout dynamic viscosity, porous media permeability, and porous media porosity. It also plotted the trend of the estimated marginal mean value with respect to these specific variables to analyze the influence characteristics of each factor on the grout diffusion range. Specifically:

[0113] (1) Please refer to Figure 3The diagram shown illustrates the trend of the estimated boundary average value as a function of grouting pressure, provided in the embodiments of this application. Figure 3 As shown, the grout diffusion range significantly increases with the grouting pressure from 3 MPa to 15 MPa. The increase is particularly pronounced at lower grouting pressures (A1 to A3), especially from A1 (88.189 m...). 3 ) to A2 (287.574m 3 The increase was 199.385m 3 The increase from A2 to A3 is 356.972m. 3 However, during the higher pressure phase, the increase gradually decreases: from A3 to A4, the increase decreases to 137.96m. 3 The distance from A4 to A5 is only 22.745m. 3 This trend indicates that the grout diffusion range exhibits high responsiveness at lower grouting pressures, while gradually stabilizing at higher pressures.

[0114] Therefore, it can be determined that there is a positive correlation between the grout diffusion range and the grouting pressure; that is, the higher the grouting pressure, the wider the grout diffusion range, and the lower the grouting pressure, the smaller the grout diffusion range. However, as the grouting pressure continues to increase, the grout gradually fills the pores of the porous medium. After reaching saturation, the effect of further increasing the pressure on diffusion gradually weakens, resulting in a decrease in the rate of increase.

[0115] (2) Please refer to Figure 4 The diagram shown illustrates the trend of the estimated boundary average value as a function of slurry density, provided in the embodiments of this application. Figure 4 As shown, as the slurry density increases from 1200 kg / m³... 3 Gradually increase to 1500 kg / m 3 The slurry diffusion range showed a clear decreasing trend. From B1 to B2, the slurry diffusion range decreased by 20.769m. 3 The temperature dropped by 14.394m from B2 to B3. 3 The decrease from B3 to B4 is 19.395m. 3 Finally, from B4 to B5, the descent was 3.625m. 3 Overall, as the density of the slurry increases, the rate of decrease in the slurry diffusion range gradually decreases, especially in the higher density range, where the rate of decrease slows down significantly.

[0116] Therefore, it can be determined that there is a negative correlation between the slurry diffusion range and the slurry density; that is, the lower the slurry density, the wider the slurry diffusion range; and the higher the slurry density, the smaller the slurry diffusion range.

[0117] (3) Please refer to Figure 5The diagram shown illustrates the trend of the estimated boundary average value as a function of the slurry dynamic viscosity, as provided in the embodiments of this application. Figure 5 As shown, the slurry diffusion range exhibits a significant decreasing trend as the dynamic viscosity of the slurry gradually increases from 3 mPa·s to 6 mPa·s. Specifically, from C1 to C2, the slurry diffusion range decreases by 67.079 m. 3 From C2 to C3, the reduction was 46.789m. 3 From C3 to C4, the descent was 98.925m. 3 The reduction from C4 to C5 was 18.095m. 3 Overall, as the dynamic viscosity of the slurry increases, the slurry diffusion range continuously decreases, but the magnitude of this decrease varies across different viscosity ranges. Particularly in the lower viscosity range (3 mPa·s to 4 mPa·s), the decrease is significant, while in the higher viscosity range (5 mPa·s to 6 mPa·s), the decrease is considerably smaller.

[0118] Therefore, it can be determined that there is a negative correlation between the slurry diffusion range and the slurry dynamic viscosity, that is, the lower the slurry dynamic viscosity, the wider the slurry diffusion range; the higher the slurry dynamic viscosity, the smaller the slurry diffusion range.

[0119] (4) Please refer to Figure 6 The diagram shown illustrates the trend of the estimated boundary average value as a function of the permeability of the porous medium, provided in the embodiments of this application. Figure 6 As shown, with the permeability of the porous medium increasing from 6.5 × 10⁻¹³ m⁻¹... 2 Gradually increase to 1.2 × 10⁻¹¹ m 2 The slurry diffusion range showed a clear increasing trend. Specifically, from D1 (53.869m...) 3 ) to D2 (229.176m) 3 The diffusion range increased by 175.307m. 3 This indicates that in low-permeability media, the flow resistance of the slurry is relatively large, and the diffusion range increases relatively slowly; from D2 to D3 (514.244m) 3 The diffusion range increased by 285.068m. 3 From D3 to D4 (829.202m) 3 The diffusion range increased by 314.958m. 3 This indicates that in the intermediate permeability stage (e.g., D2 to D4), increased permeability significantly enhances the diffusion capacity of the slurry; from D4 to D5 (981.575m) 3 The diffusion range increased by 152.376m. 3Although the diffusion range continues to increase, the rate of increase has slowed down. This trend indicates that when the permeability of the porous medium reaches a certain level, the diffusion capacity of the slurry tends to saturate, and the effect of further increasing the permeability of the porous medium on the diffusion range gradually weakens.

[0120] Therefore, it can be determined that there is a positive correlation between the slurry diffusion range and the permeability of the porous media; that is, the higher the permeability, the wider the slurry diffusion range, and the lower the permeability, the smaller the slurry diffusion range. However, as the permeability continues to increase, the slurry gradually fills the pores of the porous media and tends to saturate. Thereafter, the effect of further increasing the permeability on diffusion gradually weakens, and the rate of increase gradually decreases.

[0121] (5) Please refer to Figure 7 The diagram shown illustrates the trend of the estimated boundary average value as a function of the porosity of the porous medium, provided by the embodiments of this application. Figure 7 As shown, the slurry diffusion range exhibits a significant decreasing trend as the porosity of the porous medium gradually increases from 0.05 to 0.4. Specifically, from E1 (813.526m)... 3 ) to E2 (72.984m 3 The slurry diffusion range was reduced by 40.542m. 3 From E2 to E3 (471.799m) 3 This reduced the length by 301.185m. 3 From E3 to E4 (385.196m) 3 This reduced the size by 86.603m. 3 From E4 to E5 (164.563m) 3 This reduced the amount by 220.633m. 3 Overall, as the porosity of the porous medium increases, the slurry diffusion range gradually decreases, but the rate of decrease varies across different ranges. Particularly in the higher porosity stage (e.g., E4 to E5), the increase in porosity significantly restricts slurry diffusion, indicating that the pore structure of the medium significantly hinders slurry penetration and diffusion.

[0122] Therefore, it can be determined that there is a negative correlation between the slurry diffusion range and the porosity of the porous medium: the smaller the porosity, the wider the slurry diffusion range; the larger the porosity, the smaller the slurry diffusion range.

[0123] Furthermore, one-way analysis was performed using analysis of variance:

[0124] Table 4. Analysis of Variance Table

[0125]

[0126]

[0127] Table 4 shows that the significance levels of grout density and dynamic viscosity are 0.965 and 0.253 (both greater than 0.05), respectively, indicating no significant impact on the experimental results. However, the significance levels of grouting pressure, porous media permeability, and porous media porosity are 0.010, 0.003, and 0.006 (all less than 0.05), respectively, indicating that they have a significant impact on the experimental results. Based on the significance analysis results of each factor, it can be determined that porous media permeability, porous media porosity, and grouting pressure are the main factors affecting the variation of grout diffusion range, while grout dynamic viscosity and grout density have relatively small effects.

[0128] Step 1043: Based on the main and secondary factors, and the influence characteristics of each factor on the slurry diffusion range, determine the optimal parameter combination, and use the Brinkman equation and the slurry water displacement model to obtain the predicted slurry diffusion range.

[0129] In this step, different levels of different factors have different effects on the test results. Based on the above analysis of the influence of single factors on the slurry diffusion range, the optimal parameter combination can be determined.

[0130] As an example, the grouting pressure is 15 MPa and the grout density is 1200 kg / m³. 3 The dynamic viscosity of the slurry is 3 MPa·s, and the permeability of the porous medium is 1.2 × 10⁻¹¹ m³. 2 The parameter combination with a porosity of 0.05 in porous media has the greatest impact on the variation of slurry diffusion range. Therefore, the above parameter combination is determined as the optimal parameter combination. Furthermore, using the optimal parameter combination, the slurry diffusion process is simulated based on the slurry water-drive model using the Brinkman equation to obtain the predicted slurry diffusion range.

[0131] The above content is only a preferred embodiment of the present invention. For those skilled in the art, many changes can be made in the specific implementation and application scope based on the ideas of the present invention. As long as these changes do not depart from the concept of the present invention, they all fall within the protection scope of this patent.

Claims

1. A method for predicting the diffusion range of grout in the coal seam floor area, characterized in that, The method includes: A slurry-driven water model for the coal seam floor region, including coalfield strata parameters and grouting borehole parameters, was obtained. Based on the Navier-Stokes equations and Darcy's law, the Brinkman equation is derived to describe the incompressible fluid flow caused by reinforcing materials in porous media; wherein the Brinkman equation includes viscosity terms and pressure gradient terms. Grouting pressure, grout density, dynamic viscosity, porous media permeability, and porous media porosity were used as influencing factors for grout diffusion, and various parameter combinations of each influencing factor and level were obtained. Using multiple parameter combinations and the Brinkman equation, the slurry diffusion process is simulated based on the slurry flooding model to obtain the optimal parameter combination and the corresponding slurry diffusion range. The following assumptions are met during the simulation of slurry diffusion: (1) The flow of the slurry is continuous; (2) The slurry is an isotropic and incompressible fluid, and the slurry density remains constant and the flow rate is stable during the flow process; (3) The sidewalls of the slurry satisfy the no-slip boundary condition; (4) The diffusion mode of the slurry is complete displacement diffusion, without considering the mixing of water and slurry at the slurry-water interface; (5) The flow of the slurry is laminar flow; The Brinkman equation, used to describe the flow of incompressible fluids in porous media induced by reinforcing materials, is obtained as follows: The motion of viscous incompressible fluids is described using the Navier-Stokes equations; Darcy drag terms are added to the Navier-Stokes equations to simulate the drag of a fluid on a solid skeleton when flowing in a porous medium. Porosity is then introduced to correct the density term, in order to describe fluids that flow only within the pore space of the porous medium. Based on the premise that porous media are isotropic, the viscosity term and pressure gradient term are expressed as divergence forms of the viscous stress tensor and pressure tensor, respectively, and the Brinkman equation is obtained to describe the incompressible fluid flow caused by reinforcing materials in porous media.

2. The method as described in claim 1, characterized in that, The stratigraphic parameters of the well field include: regional division information of the stratigraphic strata in each well field and geological parameter information of the stratigraphic strata in each well field; wherein, the geological parameter information includes: porosity, permeability and thickness; The grouting borehole parameters include: the location and segmentation information of the grouting borehole, and the drill bit diameter of each segment.

3. The method as described in claim 1, characterized in that, The Navier-Stokes equations are expressed as follows: ； In the formula, Indicates fluid density; Indicates fluid velocity; μ represents fluid pressure; μ represents fluid dynamic viscosity. This represents the external force acting on a fluid; This represents the gradient operator.

4. The method as described in claim 3, characterized in that, The Darcy resistance term Represented as: In the formula, -μ / κ·u This represents linear resistance based on Darcy's law; -βρ|u|u This represents the nonlinear resistance introduced due to increased flow velocity, which typically dominates under high flow velocity conditions. β This represents a constant related to fluids and porous media, reflecting the degree of nonlinear resistance.

5. The method as described in claim 4, characterized in that, The following equation describes a fluid flowing only within the pore space of a porous medium: In the formula, Porosity represents the porosity of porous media. Indicates the viscosity term. This represents the pressure gradient term.

6. The method as described in claim 5, characterized in that, The viscosity term and pressure gradient term can be expressed in divergence form as the viscous stress tensor and pressure tensor, respectively, using the following equations: ; In the formula, Represents the velocity gradient; Represents the transpose of the velocity gradient; Represents the pressure tensor, where I It is a unit tensor; the Brinkman equation is expressed as: ; .

7. The method as described in claim 1, characterized in that, The initial grouting parameters for the slurry-driven water discharge model are set as follows: The initial grouting pressure was 9 MPa and the initial grout density was 1200 kg / m³. 3 The initial dynamic viscosity of the grout was 3 mPa∙s, and the permeability of the grouting-modified rock strata was 1.2E-11m. 2 The grouting modification experience showed a porosity of 0.05 and a fault zone permeability of 0.5m. 2 The porosity of the fault zone is 0.

01.

8. The method as described in claim 1, characterized in that, The optimal parameter combination and the corresponding slurry diffusion range are obtained through the following method: Obtain various parameter combinations, and the slurry diffusion range corresponding to various parameter combinations obtained through multiphysics coupling numerical simulation; Based on multiple parameter combinations and their corresponding slurry diffusion ranges, the influence characteristics of single factors on slurry diffusion ranges were analyzed using analysis of variance, and the main and secondary factors were identified. Based on the primary and secondary factors, and the influence characteristics of each factor on the slurry diffusion range, the optimal parameter combination is determined, and the predicted slurry diffusion range is obtained using the Brinkman equation and the slurry water displacement model.

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