Method for judging and controlling instability of coal mass around cavity under water jet impact load

Abstract

The application discloses a kind of water jet impact load under the judgment and control method of instability of coal body around cavity, and the instability model of coal body around cavity under water jet impact based on energy principle established in the judgment method simultaneously considers the synergistic effect of triaxial dynamic effective stress field and gas pressure field around cavity on the stability of cavity, can directly reflect the strength of outburst and the energy field of unit volume inside coal body, with high reliability, can provide theoretical basis and data support for maintaining the stability of coal body around cavity in the process of water creating cavity and gas extraction operation, in the application of water creating cavity engineering, the way of "ladder pressure boost" can effectively control the instability of cavity, when initial gas pressure or ground stress is higher, gas pressure inside coal seam can be lowered in advance before water creating cavity, and then safe and efficient operation of water creating cavity and gas extraction can be realized.

Description

Technical Field

[0001] This invention relates to a method for judging coal body instability, specifically a method for judging and controlling the instability of coal body around a cavity under the impact load of water jet during hydraulic cavity creation and permeability enhancement gas extraction operations, belonging to the field of coal mine safety technology. Background Technology

[0002] During coal mining, gas can cause disasters such as outbursts, combustion, or explosions, posing a significant threat to safe coal mine production. Pre-mining gas drainage is an effective method for controlling gas disasters. In recent years, with the increasing depletion of shallow coal resources, coal mining has had to extend deeper underground. These deep coal seams generally have characteristics such as low permeability, high gas pressure, and high ground stress, significantly increasing the difficulty of mining and the intensity of gas disasters. Conventional gas drainage methods can no longer meet the needs of deep mining. Hydraulic cavity-making technology uses high-pressure water jets to break up the coal body around the borehole, creating several large-sized cavities within the coal seam to promote the development and interconnection of fracture structures within the coal seam. This increases the permeability of the coal seam, thereby significantly improving gas drainage efficiency. It is a highly effective "permeability-flow enhancement" method for high-gas, low-permeability coal seams. However, when using hydraulic cavity drilling to control outburst-prone coal seams, the high-pressure water jet enlargement can cause a strong disturbance to the coal seam, leading to the instantaneous instability of the gas-bearing coal body around the cavity. This gas mixture is then ejected in large quantities from the borehole within a short period, causing borehole blowouts, especially common in boreholes with outburst risks. This can easily lead to excessive gas levels in the working area and may even cause gas explosions or coal and gas outbursts. Therefore, maintaining the stability of the coal body around the cavity under water jet impact loads is crucial.

[0003] Since borehole excavation is similar to small-scale tunnel excavation, current industry research on borehole (or cavitation) blowouts is often based on the coal and gas outburst mechanism of the tunnel, and it is believed that the instability process is jointly affected by stress, gas and coal properties. For example, Zhao et al. used a self-developed dynamic monitoring device to study the deformation of boreholes under static loads and found that the reduction of borehole circumferential strain is an important indicator leading to borehole instability; Karatela and Taheri simulated borehole construction under overequilibrium conditions and found that rock strength is the controlling factor of surrounding rock stability; Asaka and Holt studied borehole stability under anisotropic surrounding rock conditions and found that induced pore pressure has a significant impact on borehole instability, and this value depends on the anisotropy of the Skempton parameter, the in-situ stress state, and the wellbore orientation; Qu et al. combined field production data to analyze the impact of pore pressure changes on coal and rock stability and found that the coal powder content in drainage increases with the decrease of pore pressure; Zhao et al. studied the impact of mud intrusion and weakened fracture strength on the borehole stability of fractured rocks and found that mud intrusion reduces the shear strength of the fracture surface, thus leading to the deterioration of borehole stability.

[0004] Based on this, since the transformation from the gestation state to the activation state of borehole (or cavity) instability is often instantaneous, the details of the changes in various physical quantities during this process are difficult to capture. Industry scholars often use energy changes before and after instability to explain the activation mechanism of instability, and believe that the elastic energy of the coal body and the gas expansion energy are the key energies that trigger the blowout. Regarding the elastic energy of the coal body, for example, Anand Cheng used the elastic energy calculation formula under triaxial hydrostatic stress conditions to analyze the outburst risk from the perspective of stress conditions, finding that increased tectonic stress leads to a larger proportion of elastic energy, making instability more likely to occur; Lu et al. constructed a method for coal body elastic energy and an instability energy criterion based on the hydrostatic pressure assumption, and studied the instability mechanism under various coal seam combinations (primary coal seams and tectonic coal seams), showing that when tectonic coal seams are interbedded in the total coal seam, the total outburst energy will increase significantly; Tu et al. studied the stress conditions for the destruction, breakage, and pulverization of intact coal based on energy theory, and proposed that the breaking work is the energy limiting factor for the outburst of intact coal seams. Regarding gas expansion energy, for example, Peng et al. used a coal and gas outburst simulation test device combined with a seepage control system to study the influence mechanism of gas seepage on coal and gas outbursts, and found that gas seepage weakens the mechanical properties of coal, making coal and gas outbursts more likely to occur; Luo et al. established a force-energy criterion for coal and gas outbursts in dynamic geological systems that considers the influence of desorbed gas, and believed that gas-bearing coal is the material basis for outbursts, and mining disturbances provide the initiation force and spatial conditions for outbursts; Fan et al. proposed a multi-field coupling model that considers elastic damage and the spatiotemporal evolution of permeability, and found that the internal energy density of the gas dominates the change of the released energy density, the gas pressure generates tensile stress in the coal body, crushes the coal into small fragments, accelerates the process of coal damage and destruction, and finally the high-pressure gas ejects the coal body into the roadway.

[0005] While numerous studies have investigated the influencing factors and mechanisms of borehole (or cavity) instability, these researches typically consider borehole (or cavity) formation as the termination state of instability and construct instability models and energy criteria based on hydrostatic pressure and the average gas pressure within the working area (or directly using the initial gas pressure). However, in actual hydraulic cavity creation operations, the gas extraction pipeline is connected to the borehole opening at the start of drilling, resulting in a significant gas pressure gradient around the borehole before jet reaming begins. Furthermore, because the pressure exerted by the high-pressure water jet on the coal body (reaching over 30 MPa) is far greater than the geostress, the effective stress field of the coal body around the borehole changes under strong external disturbances, making dynamic disasters more likely to occur during reaming rather than after cavity formation. These characteristics mean that existing research conclusions cannot directly explain the mechanism of cavity instability during hydraulic cavity creation. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a method for judging and controlling the instability of coal body around a cavity under water jet impact load. This method can achieve safe and efficient operation of hydraulic cavity creation for gas extraction and can provide theoretical basis and data support for maintaining the stability of coal body around a cavity during hydraulic cavity creation for gas extraction.

[0007] To achieve the above objectives, the method for determining the instability of coal seam around a cavity under water jet impact load specifically includes the following steps:

[0008] Step 1, Calculation of the elastic energy of the coal body: The formula for calculating the elastic energy W1 of the coal body is as follows:

[0009]

[0010] In the formula: U e ν is the elastic energy per unit volume of coal; l is the length of the coal section exposed to hydraulically created cavities, in meters; ν is the Poisson's ratio of the coal; E is the Young's modulus of the coal, in gigabytes of Pa. and are the radii of the plastic zone surrounding the cavity before and after the jet impact load is applied; r is the distance of the particle from the center of the cavity, in meters; P 0e The effective radial stress is at r→∞, in MPa; C is the integration constant.

[0011] Step 2, Calculation of the gas expansion energy involved in the outburst: The formula for calculating the gas expansion energy W2 involved in the outburst is as follows:

[0012]

[0013] In the formula: The expansion energy of free gas is expressed in J. The unit is the expansion energy of adsorbed gas, expressed in J. The expansion energy of free gas per unit volume, in J / m³ 3 ; The expansion energy of adsorbed gas per unit volume, in J / m³. 3 ;

[0014] Step 3, Calculation of coal crushing work: The formula for calculating coal crushing work A1 is as follows:

[0015] A1 = s b w b ρ c V

[0016] In the formula: s b Specific surface area generated by coal crushing, in cm² 2 / g;w b The specific work of coal crushing, in J / cm³. 2;ρ c The apparent density of the coal, in kg / m³ 3 V represents the volume of the energy release zone, in meters. 3 ;

[0017] Step 4, Calculation of coal powder handling work: The formula for calculating the coal powder handling work A2 is as follows:

[0018]

[0019] In the formula: v is the velocity of the pulverized coal when it is thrown out of the orifice, in m / s; g is the acceleration due to gravity, in m / s². 2 ;l c The distance of pulverized coal ejected from the nozzle during jet impact-induced ejection is expressed in meters (m) or hours (h). c The distance between the borehole and the tunnel floor, in meters;

[0020] Step 5: Construct the energy balance equation for the coal body surrounding the cavity under water jet impact load, as shown below:

[0021] W = W1 + W2

[0022] A = A1 + A2

[0023] W1 + W2 = A1 + A2

[0024] In the formula: W is the instability initiation energy, in J; A is the dissipated energy, in J;

[0025] Under water jet impact load, when the instability initiation energy W of the coal body around the cavity is greater than the dissipated energy A, the coal body around the cavity is in an unstable state.

[0026] Based on the judgment method of coal body instability around cavity under water jet impact load, the control method of coal body instability around cavity under water jet impact load is to ensure the stability of coal body around cavity by setting a reasonable pressure gradient in the hole expansion stage of hydraulic cavity making when the initial gas pressure p0 and ground stress P0 of coal seam are determined, so as to gradually increase the jet pressure.

[0027] Compared with existing technologies, the method for judging the instability of coal around cavities under water jet impact loads, based on the energy principle, establishes an instability model of coal around cavities under water jet impact. This model simultaneously considers the synergistic influence of the triaxial dynamic effective stress field and the gas pressure field on the stability of the cavities. It can intuitively reflect the outburst intensity and the unit volume energy field inside the coal body. Verification through engineering applications shows that the numerical solution agrees well with the field data, indicating high reliability. This model can be used to maintain the stability of coal around cavities during hydraulic cavity creation and permeability enhancement gas extraction operations. The stability provides theoretical basis and data support; based on the instability model of coal body around cavities under water jet impact, the control method for coal body instability around cavities under water jet impact load is proposed. In the application of hydraulic cavity creation engineering, the jet pressure is gradually increased in a "step-by-step pressurization" manner to effectively control cavity instability. When the initial gas pressure or ground stress is high, the gas pressure inside the coal seam can be reduced in advance before hydraulic cavity creation to ensure that cavity instability is effectively controlled by the hydraulic cavity creation method of "step-by-step pressurization", thereby realizing the safe and efficient operation of hydraulic cavity creation for permeability enhancement and gas extraction. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the elastoplastic mechanical model of coal under water jet impact load;

[0029] Figure 2 This is a schematic diagram of a hydraulic cavity-building model;

[0030] Figure 3 This is a schematic diagram of the numerical model and boundary conditions;

[0031] Figure 4 This is a comparative diagram of numerical simulation results and field hydraulic cavity-induced outburst test results. (a) is a comparison diagram of instability initiation energy and instability dissipation energy under different test parameters, and (b) is a comparison diagram of field results and numerical simulation results of outburst intensity under different test parameters.

[0032] Figure 5 This is a schematic diagram of the effective stress distribution of the coal body around the cavity under different jet pressures.

[0033] Figure 6 These are global distribution diagrams of the effective stress plastic or elastic solutions under different jet pressures, where (a) is the global distribution diagram of the tangential effective stress plastic and elastic solutions under different jet pressures, (b) is the global distribution diagram of the radial effective stress plastic and elastic solutions under different jet pressures, and (c) is the dimensionless unit volume elastic energy distribution diagram under different jet pressures.

[0034] Figure 7These are elastic energy distribution diagrams under different geostresses, where (a) is the global distribution diagram of the plastic and elastic solutions of the tangential effective stress under different geostresses, (b) is the global distribution diagram of the plastic and elastic solutions of the radial effective stress under different geostresses, and (c) is the dimensionless elastic energy distribution diagram per unit volume under different geostresses.

[0035] Figure 8 These are energy distribution diagrams per unit volume under different initial gas pressures, where (a) is the elastic energy distribution diagram and (b) is the gas expansion energy distribution diagram.

[0036] Figure 9 It is different gas pressure ratios (p) f / p m A graph showing the relationship between the unit volume gas expansion energy and pore gas pressure under the given conditions.

[0037] Figure 10 These are graphs showing the relationship between the cavity-forming radius and the energy ratio under different jet pressures and different ground stresses. (a) shows the relationship between the cavity-forming radius and the energy ratio under different jet pressures, and (b) shows the relationship between the cavity-forming radius and the energy ratio under different ground stresses.

[0038] Figure 11 The diagrams show the optimal pressurization gradient (target pressure 40 MPa) to ensure the stability of the coal body around the cavity under different initial gas pressures p0 and ground stresses p0. (a) shows the optimal jet pressurization gradient and its energy relationship (P0 = 8.3 MPa) under different initial gas pressures, and (b) shows the optimal jet pressurization gradient and its energy relationship (p0 = 0.8 MPa) under different ground stresses.

[0039] Figure 12 The figure shows the effect of gas extraction time on the optimal pressurization gradient under different ground stress P0 conditions (target pressure is 40 MPa, initial gas pressure p0 is 1.0 MPa), where (a) is when ground stress P0 is 8.3 MPa and (b) is when ground stress P0 is 10.0 MPa. Detailed Implementation

[0040] The invention will now be further described with reference to the accompanying drawings.

[0041] I. Construction of a model for coal body instability around cavities under water jet impact

[0042] (I) Basic Assumptions

[0043] To reduce the difficulty of constructing a model for the instability of coal around cavities under water jet impact, the following simplifications are made based on actual working conditions:

[0044] (1) The thickness of the coal seam and the length of the cavity are much greater than the diameter of the cavity. The process of water jet impacting the coal body around the cavity can be regarded as the expansion process of an infinitely long cylindrical hole in an infinite medium.

[0045] (2) Ignoring the influence of coal gravity, the coal body is considered to be an isotropic, homogeneous dual-pore medium, including matrix pores and fractures;

[0046] (3) The migration of gas in the coal body is regarded as a two-step series process, first from the matrix pores to the fractures, and then from the fractures to the cavities or roadways, only considering the change in permeability in the fractures;

[0047] (4) The migration of gas in coal is regarded as an isothermal process. The adsorption process of gas in coal satisfies the adsorption isotherm equation (Langmuir equation), and the migration of free gas satisfies the ideal gas law.

[0048] (5) The seepage of gas in the fractures satisfies Darcy's law, and the diffusion of gas in the matrix pores satisfies Fick's law.

[0049] (6) The process of the drill rod rotating and driving the jet to impact the cavity wall is regarded as applying a uniformly distributed load on the coal surface, and the gas pressure distribution during the jet cavity creation process does not change.

[0050] (II) Calculation of Coal Body Elasticity

[0051] 1. Calculation of disturbance stress field

[0052] The expansion process of an infinitely long cylindrical hole in an infinitely large medium conforms to a plane strain problem, and the theoretical model is as follows: Figure 1 As shown. Since the elastoplastic mechanical model is centrally symmetric along the direction of cavity extension, the stress and strain components in the coal body are only related to the radial coordinate. Therefore, polar coordinates are used for elastoplastic analysis, and compressive stress is defined as positive.

[0053] exist Figure 1 In this context, P0 represents the uniform load on the outer boundary, which is assumed to be equal to the original in-situ stress of the coal seam, in MPa; P represents the uniform load on the inner boundary, which is assumed to be equal to the jet pressure, in MPa; p f and p m p0 is the initial gas pressure in the coal seam, which depends only on the distance r from the particle to the center of the cavity, in MPa; a is the radius of the cavity, in mm; R is the gas pressure in the fractures and pores. P R is the radius of the plastic zone, in mm. ∞ Let be the outer radius, which is taken as infinity here.

[0054] Based on the effective stress principle of porous media, the effective stress of coal can be expressed as:

[0055]

[0056] In the formula: σ er σ is the effective radial stress of the coal mass, in MPa. eθ β represents the effective tangential stress of the coal mass, in MPa; f and β m This is the effective stress coefficient.

[0057] β f and β m Satisfy β f =1-K / K m And β m =K(1 / K) m -1 / K s ), where K is the bulk modulus of the coal, in GPa; K m Bulk modulus of coal matrix, in GPa; K s This represents the bulk modulus of the coal skeleton, expressed in GPa.

[0058] K and K m The calculation formula is as follows:

[0059] K = E / [3(1-2ν)]

[0060] K m =E m / [3(1-2ν)]

[0061]

[0062] In the formula: E is the Young's modulus of the coal, in GPa; ν is the Poisson's ratio of the coal; E m Young's modulus of coal matrix, in GPa; Porosity of the coal matrix, in percentage.

[0063] Throughout the process, the coal body surrounding the cavity satisfies the equilibrium equation:

[0064]

[0065] In the formula: σ r σ represents the radial stress of the coal mass, in MPa. θ denoted as tangential stress in the coal mass, in MPa; r is the distance from the particle to the center of the cavity, in meters.

[0066] The yield condition during sculpted hole expansion satisfies the Mohr-Coulomb criterion σ. er =ασ eθ+Y, the opposite of the bore shrinkage process, at which point the tangential stress component is the minimum principal stress, and the radial stress component is the maximum principal stress. Among these, denoted as the internal friction angle of the coal body, in rad, and c as the cohesion of the coal body, in MPa.

[0067] Combining formula ② with the Mohr-Coulomb criterion, and assuming that the coal in the plastic zone is in a critical yield state, and incorporating the boundary condition σ... r | r＝a Solving the differential equation for P, we can obtain the general solution for the stress in the plastic region:

[0068]

[0069] In the formula: k is a constant, satisfying r is the distance from the particle to the center of the hole, in meters; P e This represents the effective radial stress at r = a, in MPa.

[0070] The radial and tangential strains of the coal body in the elastic region are ε0 and ε1, respectively. r =du / dr, ε θ =u / r; the stress-strain relationship satisfies ε r =(1-ν 2 )[σ r -νσ θ / (1-ν)] / E,ε θ =(1-ν 2 )[σ θ -νσ r / (1-ν)] / E.

[0071] Differentiate the geometric equation and constitutive equation for tangential strain respectively, solve equation ① simultaneously, and combine with the boundary condition σ r | r→∞ =P0, the general solution for the stress in the elastic region is:

[0072]

[0073] In the formula: P 0e The effective radial stress is at r→∞, in MPa; C is the integration constant.

[0074] Using σ er The continuity of the elastic-plastic interface determines the integral constant C:

[0075]

[0076] In the formula: R P The radius of the plastic zone.

[0077] Using σeθ The radius of the plastic zone is determined by the continuity of the elastic-plastic interface:

[0078]

[0079] 2. Determination of energy release zone and calculation of elastic energy

[0080] The basis for determining the energy release zone is as follows: Figure 2 The hydraulic cavity-forming model is shown. After the jet impact load is applied, the radius of the plastic zone around the cavity changes from R... P0 Expand to The range of values ​​for the energy release zone is:

[0081]

[0082] L∈(0,l)

[0083] In the formula: l is the length of the coal-bearing section of the hydraulically created cavity, in meters; L is the length of the coal-bearing section of the borehole, in meters.

[0084] The volume of the infinitesimal element in the energy release region can then be expressed as:

[0085] The effective stresses of the coal body within the energy release zone are σ er σ eθ σ ez , where σ ez The effective stress component is σ in the direction of the bore's extension. Since the expansion process satisfies the plane strain problem, σ is assumed to be... eθ =σ ez The elastic energy per unit volume of coal can be expressed as: Combining this with the stress components of the elastic region, we can obtain the specific form of the elastic energy per unit volume of coal:

[0086]

[0087] The elastic energy W1 of the coal body can be obtained by integrating the elastic energy per unit volume of coal body within the energy release region:

[0088]

[0089] (II) Calculation of Gas Expansion Energy

[0090] 1. Calculation of gas diffusion and seepage

[0091] Gas diffusion is driven by the gas pressure difference between the pores and fractures of the coal matrix. Both adsorbed and free gas exist within the pores of the coal matrix; the sum of their masses constitutes the total gas content in the coal matrix. Based on the law of conservation of mass, the diffusion process satisfies the following:

[0092]

[0093] In the formula: τ is the adsorption time in days, and for a coal matrix conforming to the cubic model, τ = L0 is satisfied. 2 / 3π 2 D, where L0 is the coal seam cleavage spacing in meters, and D is the gas diffusion coefficient in meters. -2 R is the universal gas constant, in J / (mol·K); T is the coal temperature, in K; V g The molar volume of methane under standard conditions, in m³. 3 / mol;V L Langmuir volume, in meters (m). 3 / kg; P L Langmuir pressure, in MPa; The porosity of the coal matrix is ​​expressed as %; ρ c The apparent density of the coal, in kg / m³ 3 .

[0094] For a unit volume of coal, the change in the mass of free gas in the fractures over time is equal to the sum of the mass of gas flowing out of the fractures per unit time and the mass of gas diffusing into the fractures from the coal matrix. This process satisfies:

[0095]

[0096] In the formula: μ is the dynamic viscosity of methane, in Pa·s; The porosity of the fracture is expressed as a percentage (%); k e Permeability, in meters (m) 2 .

[0097] For a coal matrix conforming to a cubic model, there is a cubic relationship between fracture porosity and permeability. Therefore, the governing equation for coal permeability (under constant external stress conditions) can be expressed as:

[0098]

[0099] In the formula: k0 is the initial fracture permeability, in meters. 2 ; Initial fracture ratio, in %; ε L K represents the maximum adsorption-induced volumetric strain constant of the coal body. f The bulk modulus of the fracture is expressed in GPa.

[0100] 2. Participate in the calculation of prominent gas volume and expansion energy.

[0101] The prominent gas involved includes free gas and adsorbed gas that desorbs within a short period of time, which can be represented as:

[0102]

[0103] In the formula: W2 is the gas expansion energy, in J; The expansion energy of free gas is expressed in J. The unit is the expansion energy of adsorbed gas, expressed in J. The expansion energy of free gas per unit volume, in J / m³ 3 ; The expansion energy of adsorbed gas per unit volume, in J / m³. 3 .

[0104] Free gas in pores and fractures participates in the instability process of coal. The expansion energy of free gas per unit volume of coal can be expressed as:

[0105]

[0106] In the formula: p atm The pressure in the roadway after the coal body becomes unstable is expressed in MPa; n is the process index, which is taken as 1.25 here because the coal body instability process is a variable process.

[0107] The expansion energy of free gas can then be expressed as:

[0108]

[0109] The instability occurs in a very short time (a few seconds to tens of seconds), and the amount of gas desorption is sufficient. Q ∞ The amount of desorbable gas in coal, in cubic meters. 3 / kg, t is the time of outburst occurrence in seconds; d is the average particle size of gas desorption in the coal body in meters.

[0110] When considering the moisture and ash content in the coal body, the amount of desorbable gas in the coal body satisfies:

[0111]

[0112] In the formula: w ad Moisture content in coal, expressed as a percentage; A ad Ash content in coal, expressed as a percentage.

[0113] The gas expansion energy per unit volume of coal can be expressed as:

[0114]

[0115] The expansion energy of adsorbed gas can be expressed as:

[0116]

[0117] (III) Instability Judgment

[0118] 1. Calculation of dissipated energy

[0119] The energy consumed during coal crushing is mainly used to increase the surface area. The specific work of coal crushing is directly proportional to the surface area, and the crushing work of coal can be expressed as:

[0120]

[0121] In the formula: s b Specific surface area generated by coal crushing, in cm² 2 / g; V is the volume of the energy release zone, in m³. 3 ;w b The specific work of coal crushing, in J / cm³. 2 .

[0122] w b The value is linearly related to the robustness coefficient f, satisfying w b =1.043×10 -2 f, while the firmness coefficient f is related to the friction angle within the coal body. And cohesion c satisfies

[0123] The process of the broken coal powder being ejected from the cavity within the energy release zone can be considered as projectile motion. Ignoring the kinetic energy loss caused by the coal powder during its movement through the borehole, the work done in transporting the coal powder can be expressed as:

[0124]

[0125] In the formula: v is the velocity of the pulverized coal when it is thrown out of the orifice, in m / s; g is the acceleration due to gravity, in m / s². 2 h c The characteristic height of pulverized coal, in meters (m), here refers to the distance between the borehole and the tunnel floor; l c The characteristic distance of the pulverized coal is in meters. Here, it is the distance at which the pulverized coal is ejected when the jet impact induces the nozzle. Based on engineering experience, it is taken as 0.5m.

[0126] 2. Construct the energy balance equation

[0127] The instability of the coal body surrounding the cavity under water jet impact load is a process of energy consumption of the coal body. (Formulas 8 and 9 are used in conjunction.) formula and formula The energy balance equation for the coal body surrounding the cavity under water jet impact load is obtained as follows:

[0128]

[0129] Under water jet impact load, when the instability initiation energy W (the sum of the elastic energy W1 of the coal body and the gas expansion energy W2, in J) of the coal body around the cavity is greater than the dissipated energy A (the sum of the crushing work A1 of the coal body and the transport work A2 of the coal powder, in J), the coal body around the cavity is in an unstable state.

[0130] II. Model Validation

[0131] To verify the stability and accuracy of the instability model of this invention, numerical simulation was conducted based on the actual mining conditions of a coal seam in a certain coal mine, and the numerical simulation results were compared with the actual results of the on-site hydraulic cavity-induced outburst test.

[0132] The main coal seam (Seam No. 21) of this coal mine is a single coal seam with a high risk of outburst. The coal body is soft (firmness coefficient less than 0.3) and has low permeability (air permeability coefficient less than 0.1m). 2 / MPa 2 •d) Gas control is quite difficult. Currently, Chaohua Coal Mine mainly uses in-seam and cross-seam hydraulic cavity drilling technology to prevent coal and gas outbursts. However, due to the significant heterogeneity of gas occurrence in coal seams and the fact that the coal body structure is mainly composed of fragmented coal, dynamic phenomena such as blowouts are very likely to occur during the implementation of hydraulic cavity drilling.

[0133] (I) On-site hydraulic cavity induction protrusion test:

[0134] A hydraulic cavity-induced outburst test was conducted in the mine using a remotely controlled drilling rig (maximum jet pressure approximately 15 MPa). The gas content of the coal seam at the test site (21121, located in the gas drainage roadway at the bottom) ranged from 7.96 to 12.41 m³. 3 / t, coal seam burial depth 473~493m, coal seam thickness 4.0~5.9m, the angle between the drilling hole and the coal seam is 65~90°. The key parameters of the hydraulic drilling-induced outburst test are shown in Table 1 below.

[0135] Table 1. Statistics of parameters from hydraulic cavity-inducing outburst test.

[0136]

[0137] During the on-site hydraulic cavity-induced outburst test, a φ113mm ordinary cross-layer borehole was first drilled from the 21121 bottom plate drainage roadway towards the target coal seam. The drilling continued until it reached 1m through the top plate of the coal seam and then stopped. The drill rod was then removed and the drill bit was replaced with a high-pressure water jet reaming device. The high-pressure water jet reaming device was pushed along the borehole to the bottom plate of the hole, and high-pressure water was introduced to perform a "reverse reaming" operation.

[0138] Because the borehole opening was always connected to the gas negative pressure extraction pipeline during the experiment, gas in the coal seam surrounding the borehole continued to desorb and migrate during the normal drilling phase. Based on engineering experience, the drilling speed for drilling in coal seams is 0.004 m / s. Considering factors such as coal seam thickness, the average dip angle between the borehole and the coal seam, and the time required to dismantle the drill rod, it is assumed that the gas in the coal seam surrounding the borehole has undergone 1 hour of desorption and migration when the "retreat-type" reaming operation begins.

[0139] (II) Numerical Simulation

[0140] Numerical simulations were performed using a combination of COMSOL Multiphysics and Python. The core packages used in Python were numpy, pandas, math, scipy.interpolate, and matplotlib.pyplot.

[0141] First, a multiphysics coupled model incorporating the gas seepage field and gas diffusion field was constructed using the Darcy seepage module and general partial differential equation module of COMSOL software. The gas pressure distribution after conventional borehole drilling was solved, and the solution was exported in the form of a regular array. The COMSOL model references a hydraulic cavity-induced outburst test case, with the following geometric structure: Figure 3 As shown. The model's geometric dimensions are 40m × 40m × 26m, with a coal seam thickness of 6m, and roof and floor thicknesses of 10m each. The diameter of the ordinary borehole is 113mm. The borehole starts at the center of the bottom surface of the floor strata and extends along a direction with an angle of 25° to the coal seam until it penetrates 1m through the top surface of the coal seam. In the solid module, the model's sides and bottom are set as roller supports and fixed constraints, respectively, and the stress of the overlying strata is set to 7.8MPa based on the burial depth. In the fluid module, the initial values ​​of pore and fracture gas pressure are set with reference to the original gas pressure data in Table 1. The borehole inner wall is set with a Dirichlet boundary condition of 25kPa, and a horizontal observation plane is set within the coal seam, with the observation plane 3m away from both the roof and floor of the coal seam.

[0142] Then the pore pressure p m and fracture pressure p f The data was imported into Python, and thresholds were set based on pressure gradients to segment the data. Lagrange interpolation was used to supplement the insufficient data segments, and nonlinear fitting was used to obtain the gas pressure function p. m (r) and p f (r); By transforming the integral into a series form, the gas pressure integral in the plastic stress distribution equation system is solved separately. and ) and the integral of the unit gas expansion energy within the energy release zone ( and Based on this, the effective stress distribution, elastic energy, and gas expansion energy of the coal body under jet impact load are obtained, and the dissipation energy of coal body instability is calculated. Finally, the stability of the coal body around the cavity is determined. The main parameters of the numerical simulation are shown in Table 2 below.

[0143] Table 2 Main parameters of the numerical model

[0144]

[0145]

[0146]

[0147] (III) Comparative Verification

[0148] Comparison of numerical simulation results with in-situ hydraulic cavity-induced outburst test results Figure 4 As shown. Figure 4 (a) shows a comparison of the initiation energy and dissipation energy of instability under different experimental parameters. Solving the instability model of the coal body around the cavity under water jet impact reveals that, among the initiation energy of instability, the expansion energy of adsorbed gas accounts for the highest proportion (average 53.1%), followed by the expansion energy of free gas (average 33.2%), and the elastic energy accounts for the lowest proportion (average 13.7%). With increasing initial coal seam gas pressure and larger hydraulic cavity radius, the proportion of free gas expansion energy increases, while the proportions of adsorbed gas expansion energy and elastic energy decrease. The greater the difference between the initiation energy and the dissipation energy of instability, the higher the outburst risk. Furthermore, the instability model indicates that the coal body around the cavity will instability under all six working conditions given in Table 1. When the coal body instability occurs, the coal in both the original plastic zone and the energy release zone will disintegrate and be ejected from the borehole opening along the annulus. Therefore, the outburst intensity can be represented by the sum of the masses of the coal in the two zones. Figure 4 (b) This paper presents a comparison between the field results and numerical simulation results of the instability strength under different experimental parameters. The average relative error between the field and simulation results is 9.1%, with maximum relative errors of +23.3% and -9.3%, respectively, both within acceptable error ranges. The above analysis verifies the stability and accuracy of the instability model of this invention.

[0149] III. Analysis of Coal Body Instability Around Voids under Water Jet Impact

[0150] (I) The Influence of Operating Condition Parameters on Instability-Initiated Energy

[0151] 1. Jet pressure

[0152] The initial moment of hydraulic cavity creation is chosen as the research object, and the radius of the cavity at this moment is the borehole radius. Figure 5The study demonstrates the effective stress distribution of the coal body surrounding the cavity when the borehole diameter is 130 mm, the initial gas pressure is 1.0 MPa, the coal seam burial depth is 500 m, and the jet pressures are 15 MPa, 20 MPa, 30 MPa, and 40 MPa.

[0153] Depend on Figure 5 It can be seen that under different jet pressures, the effective stress of the coal body around the cavity has similar distribution characteristics. Analyzing from the perspective of increasing and decreasing trends, as the distance between the internal mass points of the coal body and the cavity boundary increases, the tangential effective stress first decreases in the plastic zone and then increases in the elastic zone, while the radial effective stress decreases throughout the entire region. Analyzing from the perspective of extreme point locations, both the tangential and radial effective stresses reach their maximum values ​​at the cavity boundary. The difference is that the tangential effective stress reaches its maximum value at the plastic zone boundary (R...). P The effective radial stress reaches its minimum value at infinity (ground stress); from a stress numerical perspective, the effective stress exhibits compressive stress throughout the entire region, and the greater the jet pressure, the greater the stress at the same location. Furthermore, when the jet pressure increases from 15 MPa to 40 MPa, the stress at the boundary R of the plastic zone increases. p The energy release zone volume V increased from 0.04 m³ to 0.34 m³. 3 Increased to 2.16m 3 And the jet pressure and R P The two sides approximately satisfy a linear relationship.

[0154] Since elastic energy is released when the coal body transforms from the elastic zone to the plastic zone, the global distribution of the effective stress plastic or elastic solution under different jet pressures can be analyzed to determine the effect of jet pressure on the boundary R of the plastic zone. P Furthermore, by considering the influence of the original elastic solution within the plastic region, the mechanism by which it affects elastic energy can be further derived. The global distribution diagrams of the effective stress plastic or elastic solutions under different jet pressures are shown below. Figure 6 As shown, Figure 6 (a) and Figure 6 (b) shows the global distribution of effective stress plastic and elastic solutions under different jet pressures, where solid lines indicate that the plastic or elastic solution falls within the corresponding domain, and dashed lines indicate that the solution falls outside the domain.

[0155] Under the same jet pressure, such as Figure 6 As shown in (a), the elastic solution of the tangential effective stress monotonically increases throughout the entire domain, and the tangential effective stress changes from tensile stress to compressive stress; as Figure 6 As shown in (b), the elastic solution of the radial effective stress monotonically decreases throughout the entire domain, and the effective stress is always the compressive stress. In the global distribution, the boundary R of the plastic zone... PThe point is the intersection of the effective stress elastic and plastic solutions. As the jet pressure increases, the initial values ​​and variation ranges of both the original elastic solution (red dashed line) and the plastic solution of the effective stress within the plastic region increase, and the boundary of the plastic region shifts away from the cavity boundary. It is worth noting that R... P The effective stress value at this point is independent of the jet pressure. The effective stress at this point can be obtained by simultaneously applying formulas ③ and ⑥. When the coal body parameters are determined, this value is only related to the in-situ stress.

[0156]

[0157] Since the effective stress at the boundary of the plastic zone is independent of the jet pressure, therefore R P The elastic energy per unit volume w1 at a given location is constant. This can be determined by solving... w1 can be transformed into a dimensionless form. Figure 6 (c) shows the dimensionless elastic energy distribution per unit volume under different jet pressures. As the jet pressure increases, w1 near the cavity boundary increases rapidly and then decays to... The required distance is longer, and the average elastic energy per unit volume is higher. It grows exponentially. Therefore, increasing the jet pressure has two effects on the elastic energy W1: firstly, it increases the initial value of the original elastic solution of the effective stress in the plastic region, thereby increasing the magnitude of w1 in the integral region as a whole; secondly, it extends the boundary R of the plastic region. P The corresponding distance, in turn, expands the range of the integration region (energy release zone).

[0158] Furthermore, since the initiation process of coal body instability is completed instantaneously, it can be assumed that the gas pressure does not change. Therefore, the change in gas expansion energy W2 caused by the increase in jet pressure is mainly due to the increase in total amount caused by the expansion of the integral region.

[0159] 2. Ground stress

[0160] Global distribution diagrams of effective stress plastic or elastic solutions under different geostress conditions are shown below. Figure 7 As shown, Figure 7 (a) and Figure 7 (b) shows the global distribution of effective stress plastic or elastic solutions when the cavity diameter is 130 mm, the initial gas pressure is 1.0 MPa, the jet pressure is 20 MPa, and the coal seam burial depth is 350 m, 400 m, 500 m, and 600 m (with ground stresses of 5.8 MPa, 6.7 MPa, 8.3 MPa, and 10.0 MPa, respectively).

[0161] According to the equivalent gravity theorem, the in-situ stress is directly proportional to the burial depth, and the proportionality coefficient is determined by the average density of the overlying strata. In this section, the in-situ stress increases by 1.67 MPa for every 100 m increase in burial depth. Combining this with formula ③, it can be seen that the plastic solution of the effective stress is only related to the jet pressure. Therefore, when the jet pressure is given, the boundary R of the plastic zone... P It is only related to the development trend of the effective stress elastic solution. As the in-situ stress on the coal increases, the value of the effective stress elastic solution at the cavity boundary gradually decreases. This is because high in-situ stress enhances the coal's resistance to deformation and failure, thereby increasing the threshold pressure for jet coal breaking. In addition, combined with the boundary condition σ r | r→∞ =P0, the elastic solution of the effective stress at infinity continuously increases. The development trend of these elastic solutions indicates that high ground stress corresponds to a smaller plastic zone boundary, and since the plastic solution of the effective stress monotonically decreases throughout the entire domain, high ground stress also increases at R. P This corresponds to a larger effective stress.

[0162] Figure 7 (c) shows the distribution of elastic energy per unit volume under different geostress conditions. Under high geostress conditions, w1 is lower at the cavity boundary and R is lower at the plastic zone boundary. P The corresponding distance is shorter, R P At the point where w1 is higher, the decay rate of w1 is smaller. The average elastic energy per unit volume first decreases and then increases with increasing ground stress. This is because as the ground stress and jet pressure gradually approach each other, the decay rate of w1 at the cavity boundary decreases, while R... P The increased growth rate of w1 at that point, caused by the shrinking integration region. The growth gradually exceeds the effect caused by the flattening of the integrand and the decrease in the function value. loss.

[0163] As can be seen from the above analysis, the influence of in-situ stress on W1 is also achieved by changing the initial value of the original elastic solution of the effective stress and extending the boundary R of the plastic zone. P The corresponding distance. The difference is that the smaller the ground stress, the greater the distance R. P The lower the w1 at a given location, the longer the R is extended. P The weaker the effect of increasing W1, the more significant the impact of changes in external loads on the elastic properties of the coal body. Similarly, the change in W2 caused by changes in in-situ stress is also mainly due to changes in the integration region.

[0164] 3. Initial gas pressure

[0165] Figure 8The distribution of elastic energy per unit volume and gas expansion energy per unit volume is shown when the cavity diameter is 130 mm, the coal seam burial depth is 500 m, the jet pressure is 20 MPa, and the initial gas pressures are 0.5 MPa, 1.0 MPa, 1.5 MPa, and 2.5 MPa.

[0166] like Figure 8 As shown in (a), regarding elastic properties, the change in gas pressure affects w1 and the boundary of the plastic zone R. P The location has a relatively small impact because, in actual engineering, the range of variation in the gas pressure in coal seams is limited, making the effect of changes in gas pressure on the original additional stress insignificant.

[0167] Regarding gas expansion energy, the average gas expansion energy per unit volume, w2, is positively correlated with the initial gas pressure, p0, and its growth rate increases with increasing p0. It is worth noting that, compared to free gas, adsorbed gas requires a diffusion process to migrate from the coal seam to the cavity. Therefore, the pressure of free gas at the same location is generally lower than that of adsorbed gas, resulting in a pressure difference that is more significant closer to the cavity boundary. Combined with... Figure 8 (b) It can be seen that under the same gas pressure, as the distance from the cavity boundary increases (gas pressure difference decreases), the expansion energy per unit volume of free gas increases. The expansion energy of adsorbed gas per unit volume gradually approaches (p0 = 0.5 MPa, 1.0 MPa, 1.5 MPa) or exceeds (p0 = 2.5 MPa) the expansion energy of adsorbed gas per unit volume. When p0 increases The rate of change with distance increases greater than It approaches or exceeds The speed is faster. The above analysis shows that the dominant energy of w2 is different under different initial gas pressures and gas pressure differences.

[0168] From the formula and formula It can be seen that, Due to pore gas pressure p m and fissure gas pressure p f Joint decision, Only by p m Decision. Therefore, when p m and gas pressure ratio p f / p m Given, and The relationship between them is definite. Figure 9 The relationship between the gas expansion energy per unit volume and the pore gas pressure under different gas pressure ratios is shown. As p m Increase, The growth rate slowed down The increase in the growth rate indicates that for different p... f / p m When p m After increasing to a certain level, w2 will always be... Dominant (Stage I) transforms into The dominant stage (Stage II), and the smaller the gas pressure difference, the lower the p during the transition from Stage I to Stage II. m The smaller.

[0169] Because the gas drainage time is relatively short, p can be approximated. m Equal to p0. Once p0 is determined, increasing the distance r from the cavity boundary will only increase the gas pressure ratio, making... Moving vertically upwards along the y-axis, the initial gas pressure can be divided into three stages based on whether the dominant energy of w2 changes during the process: (1) Approximation stage, when p0 is less than p f / p m =100% curve and The critical gas pressure p at the intersection of the curves c At that time, w2 is always Dominant; (2) Conversion stage, when p0 is less than the gas pressure ratio corresponding to the cavity boundary. curve and The critical gas pressure p at the intersection of the curves e At that time, as r increases, w2 will change from Dominant Dominant transformation; (3) Exceedance stage, when p0 is greater than p e At that time, w2 is always leading.

[0170] The above analysis shows that changing only the initial gas pressure p0 has a relatively small impact on W1, and because the initial gas pressure p0 affects the boundary R of the plastic zone... p The location of the gas has a relatively small impact; it mainly affects W2 by changing the gas expansion energy per unit volume w2. Furthermore, as the initial gas pressure increases, the increase in W2 gradually decreases from... Dominance transforms into leading.

[0171] (II) The dominant energy source for coal body instability around the cavity during hydraulic cavity creation.

[0172] At different stages of hydraulic cavity creation, the cavity radius 'a' affects the proportion of elastic energy or gas expansion energy in the instability initiation energy of the coal body, thus leading to changes in the dominant energy. Figure 10The study demonstrates the ratio of elastic energy to instability initiation energy (W1 / W) and the ratio of free gas expansion energy to adsorbed gas expansion energy as the cavity radius expands from 0.105m to 0.505m under different jet pressures (15MPa, 20MPa, 30MPa, 40MPa) and different ground stresses (5.8MPa, 6.7MPa, 8.3MPa, 10.0MPa).

[0173] Depend on Figure 10 (a) It can be seen that under different jet pressures, W1 / W exhibits the same trend with the increase of the cavity radius a, and the proportion of elastic energy in the instability initiation energy decreases slightly (approximately 3%). This is because, due to the limited influence of gas pressure on stress distribution, the ratio R of the plastic zone boundary to the cavity radius... p / a is only related to the geostress (Equation ⑥). Therefore, when the geostress is constant, increasing a will make R... p The flow rate increases linearly; and as the flow rate moves further away from the cavity boundary, the disturbance effect of the jet decreases, and the initial pressure relief effect of the borehole weakens, resulting in R... p The increase in elastic energy due to increased jet pressure is weaker than that of gas expansion energy. Throughout the hydraulic cavity-forming process, jet pressure determines the dominant energy for coal body instability. Specifically, as jet pressure increases, W1 / W increases linearly, and the proportion of elastic energy successively exceeds that of free gas expansion energy. and the expansion energy of adsorbed gas Ultimately, it surpasses the gas expansion energy (W1 / W = 50%) to become the dominant energy for instability initiation, and the smaller a is, the faster this process occurs. Based on the preceding analysis, p0 = 1 MPa belongs to the Approximation stage, and w2 is constantly... Dominance, manifested as Always less than 1. When hour, Approximately linear growth, while when Approximately logarithmic growth, therefore it can be based on Approaching The velocity divides the region into two parts: Approximate logarithm and Approximate linearization. Furthermore, the lower the jet pressure (or the smaller the cavity radius), the larger the proportion of the linear growth portion. Therefore, it can be considered that... The relationship between jet pressure and cavity radius approximately satisfies a "dome-shaped" structure, meaning that the greater the jet pressure and cavity radius, the better. Approaching The slower the speed.

[0174] Depend on Figure 10(b) It can be seen that under different geostress conditions, the increase in the cavity radius *a* has a relatively small effect on W1 / W (a decrease of approximately 2%), which is consistent with the effect of the cavity radius *a* on the jet pressure. The difference is that when the jet pressure is constant, the effective stress distribution within the plastic zone remains unchanged, and the change in geostress ΔP... 0e R at the boundary of the plastic region p Effective stress variation They are directly proportional (formula) This means that as the ground stress increases, the corresponding R value for the same increase in ground stress will decrease. p The reduction gradually decreases, and the decay rates of w1 and w2 gradually converge, indicating that the proportion of W1 in the instability initiation energy tends to level off. Furthermore, compared with... Figure 10 (a) Similarly, the smaller the geostress (or the smaller the cavity radius), The larger its proportion in the instability initiation energy, and the more pronounced the conditions of high ground stress and small cavity radius, Approximating the ground stress The speed is faster than the cavitation radius, making The contour lines exhibit a radial distribution originating from "low ground stress - small cavity radius". The smaller the cavity radius, the denser the contour lines, and the higher the sensitivity to ground stress.

[0175] Furthermore, under the same ground stress and jet pressure conditions, but with only the initial gas pressure changed, the effective stress and the plastic zone boundary R will be affected. p The impact is limited, with W1 changing very little under different initial gas pressure conditions; however, when neither the jet pressure nor the ground stress changes, the increase in the cavitation radius leads to R... p linearly increasing, due to p f The rate of increase with distance is slower than p m This allows W2 to increase while and As the difference between them decreases, W1 / W decreases accordingly.

[0176] IV. Control of Coal Body Instability Around Voids under Water Jet Impact

[0177] Based on the aforementioned analysis, during the hydraulic cavity-forming process, increasing the cavity radius *a* reduces the proportion of elastic energy in the instability initiation energy within the coal seam and increases the proportion of free gas expansion energy in the gas expansion energy. However, the change in the proportion of each energy is insufficient to alter the dominant energy for coal instability. The jet pressure determines the dominant energy for coal instability. When the coal seam conditions (initial gas pressure *p0*, ground stress *P0*) are fixed, increasing the jet pressure linearly increases the proportion of elastic energy in the instability initiation energy, transforming the coal instability from being dominated by gas expansion energy to being dominated by elastic energy.

[0178] The calculation of the instability initiation energy W is based on the instantaneous pressure increase of the jet (i.e., the jet pressure increases directly from 0 MPa to the target pressure). When the target pressure is high, the instantaneous pressure increase not only generates a large energy release zone, but may even cause the dominant energy for coal body instability to change from gas expansion energy to elastic energy. Therefore, in practical engineering applications, the principle of "step-by-step pressurization" should be followed, and a reasonable pressurization gradient should be set during the cavity enlargement stage of hydraulic cavity creation to ensure the stability of the coal body around the cavity. Figure 11 The optimal pressurization gradient (target pressure 40 MPa) for ensuring coal stability around cavities under different initial gas pressures p0 and geostress p0 is demonstrated. For the same pressurization gradient, a larger cavity radius corresponds to a larger energy release zone, and changes in jet pressure have a more significant impact on cavity stability. Figure 11 The figure shown is based on a hole diameter of 0.5m.

[0179] like Figure 11 As shown in (a), when the initial gas pressure increases from 0.6 MPa to 0.8 MPa, the maximum pressure gradient of the jet decreases from 17 MPa to 4 MPa. Figure 11 As shown in (b), when the local stress increases from 6.7 MPa to 10 MPa, the maximum jet pressure gradient decreases from 10 MPa to 1 MPa. This indicates that the greater the initial gas pressure or ground stress, the smaller the jet pressure gradient. Figure 11 Under the several coal seam conditions shown, only when the initial gas pressure was 0.8 MPa did the jet gradient passively attenuate during the pressurization cycle. Furthermore, when the jet gradient decreased, all the energy within the coal body decreased. This is because the decrease in the jet gradient caused the energy release zone to attenuate, which in turn led to a decrease in the energy of the coal body.

[0180] Initial pressure represents the maximum instantaneous pressure increase that the coal body can withstand under conditions that ensure cavity stability. Higher initial gas pressure or lower ground stress corresponds to lower initial pressure. This is because the initial pressure is mainly affected by the stress distribution of the coal body near the cavity wall, and under conditions of high gas pressure and low ground stress, the same jet pressure has a more significant impact on the stress distribution inside the coal body (especially the coal body near the cavity wall). Furthermore, when the initial gas pressure or ground stress is high, the jet pressure cannot reach the target pressure in a "step-by-step" manner while ensuring cavity stability. This is because when the jet pressure increases from a large value, the energy release zone is farther from the cavity, and the distribution of gas pressure and coal stress is close to an undisturbed state, making the impact of high initial gas pressure or ground stress on cavity stability greater.

[0181] The premise for analyzing cavitation stability is that the jet impact causes a plastic damage zone within the coal body. According to... Figure 11An extreme case can be deduced: when the initial gas pressure increases to a certain critical value, even if an adjustable minimum pressurization gradient is used at the engineering site, as long as the jet impacts the coal body and forms a plastic damage zone, the energy consumed by instability in the energy release zone will be greater than the instability initiation energy (i.e., the initial pressure equals the termination pressure), and cavitation instability will occur. And if... Figure 11 As shown in (b), the threshold for this phenomenon is lower under conditions of high ground stress. Therefore, under conditions of high gas pressure and high ground stress, optimizing the jet pressurization gradient must be combined with other technical measures to reduce the gas pressure inside the coal seam in advance.

[0182] Figure 12 The effect of gas extraction time on the optimal pressurization gradient under different ground stress conditions is demonstrated (target pressure is 40 MPa, initial gas pressure is 1.0 MPa). Under this initial gas pressure, when the adjustable minimum pressurization gradient is 1 MPa, the cavity formation process conforms to the aforementioned extreme case.

[0183] like Figure 12 As shown, with the gas drainage time increasing from 1 day to 7 days, the optimal jet pressure gradient significantly increases, and the initial pressure, termination pressure, and the difference between them (pressure range) gradually increase. Furthermore, as the gas drainage time increases, the ratio of elastic energy to instability initiation energy (W1 / W) increases, especially when the gas drainage time is sufficiently long (e.g., ...). Figure 12 In the case of t=7d), the elastic energy will exceed the gas expansion energy and become the largest instability initiation energy. The main reason for this phenomenon is that gas drainage reduces the gas expansion energy in two ways: firstly, when the gas drainage time is short (e.g., when t=7d), the elastic energy will exceed the gas expansion energy and become the largest instability initiation energy. Figure 12 In the context of t=1d), the pore gas pressure p m The attenuation is not significant; the reduction in gas expansion energy mainly depends on the gas pressure ratio (p). f / p m The reduction in ) is specifically reflected in the ratio of the expansion energy of free gas in the early stage of jet pressurization to the instability initiation energy (W2) f / W) is significantly greater than in the later stage of jet pressurization; on the other hand, when the gas extraction time is long (such as Figure 12 In the cases of t=3d and t=7d, the reduction in gas expansion energy mainly depends on the pore gas pressure p. m The attenuation is specifically manifested in the fact that W1 / W in the early stage of jet pressurization is significantly greater than that in the later stage of jet pressurization. Under the same gas drainage time, the higher the in-situ stress on the coal seam, the larger the jet pressurization range, the higher the proportion of elastic energy in the instability initiation energy, and the more significant the optimization effect of gas pre-drainage on the jet pressure gradient.

[0184] As described above, in hydraulic cavity creation engineering, gradually increasing the jet pressure using a "step-by-step pressurization" method can effectively control cavity instability. Under the premise of ensuring cavity stability, a lower initial jet pressure corresponds to a higher initial gas pressure or lower ground stress; conversely, when the initial gas pressure or ground stress is high, the jet pressure cannot reach the target jet pressure through "step-by-step pressurization." To address these situations, further gas pre-drainage is necessary to optimize the jet pressurization gradient. As the gas drainage time increases, the reduction in gas expansion energy initially depends on a decrease in the ratio of fracture gas pressure to pore gas pressure, and then shifts to a decrease in pore gas pressure. The higher the ground stress on the coal seam, the more significant the optimization effect of gas drainage on the jet pressure gradient.

Claims

1. A method for determining the instability of coal body around a cavity under water jet impact load, characterized in that, Specifically, the following steps are included: Step 1, Calculation of the elastic energy of the coal body: The formula for calculating the elastic energy W1 of the coal body is as follows: In the formula: U e ν is the elastic energy per unit volume of coal; l is the length of the coal section exposed to hydraulically created cavities, in meters; ν is the Poisson's ratio of the coal; E is the Young's modulus of the coal, in gigabytes of Pa. and are the radii of the plastic zone surrounding the cavity before and after the jet impact load is applied; r is the distance of the particle from the center of the cavity, in meters; P 0e The effective radial stress is at r→∞, in MPa; C is the integration constant. Step 2, Calculation of the gas expansion energy involved in the outburst: The formula for calculating the gas expansion energy W2 involved in the outburst is as follows: In the formula: The expansion energy of free gas is expressed in J. The unit is the expansion energy of adsorbed gas, expressed in J. The expansion energy of free gas per unit volume, in J / m³ 3 ; The expansion energy of adsorbed gas per unit volume, in J / m³. 3 ; Step 3, Calculation of coal crushing work: The formula for calculating coal crushing work A1 is as follows: A1=s b w b ρ c V In the formula: s b Specific surface area generated by coal crushing, in cm² 2 / g;w b The specific work of coal crushing, in J / cm³. 2 ; ρ c The apparent density of the coal, in kg / m³ 3 V represents the volume of the energy release zone, in meters. 3 ; Step 4, Calculation of coal powder handling work: The formula for calculating the coal powder handling work A2 is as follows: In the formula: v is the velocity of the pulverized coal when it is thrown out of the orifice, in m / s; g is the acceleration due to gravity, in m / s². 2 ;l c The distance of pulverized coal ejected from the nozzle during jet impact-induced ejection, in meters; h c The distance between the borehole and the tunnel floor, in meters; Step 5: Construct the energy balance equation for the coal body surrounding the cavity under water jet impact load, as shown below: W = W1 + W2 A = A1 + A2 W1 + W2 = A1 + A2 In the formula: W is the instability initiation energy, in J; A is the dissipated energy, in J; Under water jet impact load, when the instability initiation energy W of the coal body around the cavity is greater than the dissipated energy A, the coal body around the cavity is in an unstable state.

2. The method for determining the instability of coal body around a cavity under water jet impact load according to claim 1, characterized in that, Step 1 is as follows: Step 1-1 Calculation of Disturbance Stress Field: The effective stress of the coal body is expressed as: Where: σ er σ is the effective radial stress of the coal mass, in MPa. eθ The effective tangential stress of the coal body is expressed in MPa. β f and β m The effective stress coefficient; β f and β m Satisfy β f =1-K / K m And β m =K(1 / K) m -1 / K s ), where K is the bulk modulus of the coal, in GPa; K m Bulk modulus of coal matrix, in GPa; K s Bulk modulus of coal skeleton, in GPa; K and K m The calculation formula is as follows: K = E / [3(1-2ν)] K m =E m / [3(1-2n)] In the formula: E is the Young's modulus of the coal, in GPa; ν is the Poisson's ratio of the coal; E m Young's modulus of coal matrix, in GPa; Porosity of the coal matrix, in %; The coal seam surrounding the cavity satisfies the equilibrium equation: Where: σ r σ is the radial stress of the coal mass, in MPa. θ denoted as tangential stress in the coal mass, in MPa; r is the distance from the particle to the center of the cavity, in meters. Combining formula ② with the Mohr-Coulomb criterion, and assuming that the coal in the plastic zone is in a critical yield state, and incorporating the boundary condition σ... r | r＝a Solving the differential equation for P, the general solution for the stress in the plastic region is: In the formula: denoted as ωc, where ω is the internal friction angle of the coal body, in rad; c is the cohesion of the coal body, in MPa; and k is a constant satisfying ωc. r is the distance from the particle to the center of the hole, in meters; P e The effective radial stress at r = a is expressed in MPa. The radial and tangential strains of the coal body in the elastic region are ε0 and ε1, respectively. r =du / dr, ε θ =u / r; the stress-strain relationship satisfies ε r =(1-ν 2 )[σ r -νσ θ / (1-ν)] / E,ε θ =(1-ν 2 )[σ θ -νσ r / (1-ν)] / E; Differentiate the geometric equation and constitutive equation for tangential strain respectively, solve equation ① simultaneously, and combine with the boundary condition σ r | r→∞ =P0, the general solution for the stress in the elastic region is: In the formula: P 0e The effective radial stress is at r→∞, in MPa; C is the integration constant. Using σ er The continuity of the elastic-plastic interface determines the integral constant C: In the formula: R P The radius of the plastic zone; Using σ eθ The radius of the plastic zone is determined by the continuity of the elastic-plastic interface: Step 1-2: Determination of Energy Release Zone and Calculation of Elastic Performance After the jet impact load is applied, the radius of the plastic zone around the cavity is changed from... Expand to The range of values ​​for the energy release zone is: L∈(0,l) In the formula: l is the length of the coal-bearing section of the hydraulically created cavity, in meters; L is the length of the coal-bearing section of the borehole, in meters. The volume of the infinitesimal element in the energy release region is then expressed as: The elastic energy per unit volume of coal is expressed as Combining this with the stress components of the elastic region, we can obtain the specific form of the elastic energy per unit volume of coal: The elastic energy W1 of the coal body is obtained by integrating the elastic energy per unit volume of coal body within the energy release zone.

3. The method for determining the instability of coal body around a cavity under water jet impact load according to claim 1, characterized in that, Step 2 is as follows: Step 2-1 Calculation of gas diffusion and seepage: The gas diffusion process satisfies: In the formula: τ is the adsorption time in days, and the coal matrix satisfies τ = L0 2 / 3π 2 D, where L0 is the coal seam cleavage spacing in meters, and D is the gas diffusion coefficient in meters. -2 R is the universal gas constant, in J / (mol·K); T is the coal temperature, in K; V g The molar volume of methane under standard conditions, in m³. 3 / mol;V L Langmuir volume, in meters (m). 3 / kg; P L Langmuir pressure, in MPa; The porosity of the coal matrix is ​​expressed as %; ρ c The apparent density of the coal, in kg / m³ 3 ; The change in the mass of free gas in the fractures of a unit volume of coal satisfies: In the formula: μ is the dynamic viscosity of methane, in Pa·s; The porosity of the fracture is expressed as a percentage (%); k e Permeability, in meters (m) 2 ; The governing equation for coal permeability is then expressed as: In the formula: k0 is the initial fracture permeability, in meters. 2 ; Initial fracture ratio, in %; ε L K represents the maximum adsorption-induced volumetric strain constant of the coal body. f The bulk modulus of the fracture is expressed in GPa. Step 2-2 involves the calculation of prominent gas volume and expansion energy: Free gas expansion energy per unit volume of coal The calculation formula is as follows: In the formula: p atm The pressure in the roadway after coal instability is expressed in MPa; n is the process index, with a value of 1.

25. The expansion energy of free gas The calculation formula is as follows: When the coal body becomes unstable, the amount of gas desorption meets the following requirements. Q ∞ The amount of desorbable gas in coal, in cubic meters. 3 / kg, t is the time of outburst occurrence in seconds, and d is the average particle size of gas desorption in the coal body in meters; The amount of desorbable gas in the coal body, Q ∞ satisfy: In the formula: w ad Moisture content in coal, expressed as a percentage; A ad Ash content in coal, expressed as a percentage. The gas expansion energy per unit volume of coal is then adsorbed. The calculation formula is as follows: Adsorbed gas expansion energy The calculation formula is as follows:

4. The method for determining the instability of coal body around a cavity under water jet impact load according to claim 1, characterized in that, In Step 3, w b The value is linearly related to the robustness coefficient f, satisfying w b =1.043×10 -2 f, while the firmness coefficient f is related to the friction angle within the coal body. And cohesion c satisfies 5. A method for controlling the instability of coal body around a cavity under a water jet impact load, based on the judgment method for instability of coal body around a cavity under a water jet impact load as described in claim 1, characterized in that, When the initial gas pressure p0 and ground stress P0 of the coal seam are determined, the stability of the coal body around the cavity can be ensured by setting a reasonable pressure gradient during the cavity expansion stage of hydraulic cavity making, so as to gradually increase the jet pressure.

6. The method for controlling coal body instability around a cavity under water jet impact load according to claim 5, characterized in that, When the initial gas pressure p0 or ground stress P0 of the coal seam is high, the gas pressure inside the coal seam needs to be reduced in advance before hydraulic cavity creation.

Images