A method for controlling ground fracturing in an isolated island facing an empty tunnel in a particularly thick coal seam

Abstract

The present invention discloses a method for controlling ground fracturing in an isolated island facing an empty roadway in a fully-mechanized caving system in an extra-thick coal seam, and relates to the technical field of coal mining. The method comprises: determining the position of the target layer for ground fracturing; calculating the equivalent stiffness of the left and right support bodies below the hard roof and the stress of the target layer for fracturing; determining the position of the horizontal well and the ground fracturing parameters, so as to control the ground fracturing in an isolated island facing an empty roadway in a fully-mechanized caving system in an extra-thick coal seam. The present invention can realize the ground fracturing control in an isolated island facing an empty roadway in a fully-mechanized caving system in an extra-thick coal seam.

Description

Technical Field

[0001] The invention relates to the technical field of coal mining, and more particularly to a ground fracturing control method for an isolated island facing an empty tunnel in a particularly thick coal seam. Background Art

[0002] In recent years, surface fracturing technology has been widely used in the field of coal mine roof control and has gradually become one of the important means to deal with hard roof problems.

[0003] However, despite the ever-expanding application scope of ground fracturing technology, the scientificity and effectiveness of its operation are still in the stage of exploration and improvement.

[0004] At present, how to scientifically determine the position of the target layer to ensure the maximum fracturing effect, how to reasonably design and arrange the location of ground fracturing wells to optimize pressure transfer and stress distribution, and how to accurately determine and regulate the parameters of ground fracturing to achieve the expected control effect, these issues have become key difficulties in technical research and practice.

[0005] Therefore, it is an urgent problem for technical personnel in this field to propose a ground fracturing control method for an isolated island facing an empty tunnel in an extremely thick coal seam to solve the difficulties existing in the prior art. Summary of the invention

[0006] In view of this, the present invention provides a ground fracturing control method for an isolated island facing an empty tunnel in an extremely thick coal seam, which has the advantages of scientific accuracy, precise operation, and effective control of penetration.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A method for controlling ground fracturing in an isolated island facing an empty roadway in a fully mechanized caving area of ​​an extra-thick coal seam comprises the following steps:

[0009] Determine the target layer for ground fracturing;

[0010] Calculate the equivalent stiffness of the left and right support bodies under the hard roof and the stress of the fracturing target layer;

[0011] Determine the horizontal well position and ground fracturing parameters, so as to control the ground fracturing of the empty roadway facing the fully mechanized caving island in the extra-thick coal seam;

[0012] The specific contents of determining the target layer of ground fracturing are as follows:

[0013] Numerical simulation software is used to simulate the energy released by the hard roof in different layers under the same mining height and the same hard roof thickness, and the target layer for ground fracturing is determined by the formula:

[0014] E p =2.1665H3 -1199.1H 2 +183620H-3×10 6 ;

[0015] Among them, E p is the energy released by the destruction of the hard roof at different hard roof levels, and H is the level of the hard roof;

[0016] The specific contents of calculating the equivalent stiffness of the left and right supporting bodies under the rigid top plate are as follows:

[0017] The coal pillar is composed of several springs connected in parallel, with a length of l n The equivalent stiffness K of the supporting bodies on both sides below the rigid top plate is calculated using the following formula 左 , K 右 :

[0018]

[0019] Among them, α and β are the collapse angles on both sides of the equivalent model of the coal pillar equivalent support body, l n is the length of the support, l n-1 is the length of the n-1th layer of support, H n is the thickness of the nth layer of support, K ​​is the equivalent stiffness of the support under the rigid top plate, K i The stiffness of the support body of the i-th layer from the 1st layer to the nth layer, l i is the length of the i-th support layer from the 1st layer to the nth layer;

[0020] The specific contents of calculating the stress of the target layer of fracturing are as follows:

[0021]

[0022] Where v is the Poisson's ratio of the target layer, E is the elastic modulus of the target layer, z is the vertical distance from the neutral plane to the calculated stress, ω is the deflection of the target layer, A1, A2, B1, B2, C are coefficients, and the spatial coordinate system is established with the center of the target layer plate. x is the horizontal rightward coordinate, y is the vertical upward coordinate, σ x is the principal stress in the x direction of the target layer for fracturing, σ y is the principal stress in the y direction of the target layer for fracturing, τ xy is the shear stress of the target layer for fracturing;

[0023] The specific contents of determining the location of horizontal wells are:

[0024] The horizontal well position X is determined using the following formula:

[0025]

[0026] Wherein, L is the cantilever length between the supports on both sides of the target layer;

[0027] Then calculate the tensile and compressive stresses generated by the main bending moment on the target fracturing layer:

[0028]

[0029] Compare with Mises stress to determine whether to perform ground fracturing:

[0030]

[0031] Among them, σ z is the principal stress in the direction perpendicular to the xy plane, σ1 is the first principal stress, σ2 is the second principal stress, and σ3 is the third principal stress;

[0032] The specific contents of determining the horizontal well location and ground fracturing parameters are as follows:

[0033] The following formula is used to determine the flow rate V, perforation spacing d, and sand carrying capacity S during ground fracturing to solve the values ​​of various fracturing parameters:

[0034] f=50ln(V+1)+0.02V 1.1 +0.001e (0.01V) ;

[0035]

[0036] f=20ln(S+5)+0.03S 1.2 +0.001 e (0.015S) +0.5S-0.0001S 2 +150;

[0037] Among them, f is the crack extension length, n is the number of horizontal segments, and l is the length of the horizontal segment.

[0038] The above method is optional, 50≤H≤250.

[0039] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method for controlling ground fracturing in an isolated island facing an empty roadway in a particularly thick coal seam, and the beneficial effects thereof are:

[0040] 1. Effectively control the energy released by the top plate

[0041] The use of numerical simulation software to analyze different hard roof layers can more scientifically and accurately identify the areas most prone to energy accumulation and release than traditional empirical judgment methods, and can effectively determine the location where the energy release of the rock layer is the largest, that is, the target layer of ground fracturing. A large amount of strain energy will be released when the roof is destroyed. This method releases the strain energy stored in the roof rock layer by controlling the layer of ground fracturing, so that the destructive energy of the roof can be released without accumulating to a dangerous critical point. If it is not controlled, it will cause serious geological disasters such as mine tremors. Accurately determine the location of the fracturing target layer through the formula, and select the layer with the largest destructive release energy for fracturing, which can greatly reduce the probability of disasters such as mine tremors and roof collapse, thereby improving the safety of the mining process.

[0042] 2. Optimize the stiffness distribution of the support

[0043] The present invention makes the coal pillar support body equivalent to a spring parallel model, calculates the equivalent stiffness of the left and right support bodies under the hard roof, and can measure the stability of the roof support by the stiffness of the support body. By evenly distributing the stiffness, the problem of uneven pressure during the fracturing process is avoided. Traditional fracturing technology is prone to pressure concentration or uneven distribution due to the complexity of the roof structure, and this design optimized by stiffness ensures that the fracturing pressure can be effectively transmitted to the target area, improving the effect of fracturing. The calculation of the equivalent stiffness of the support body can provide a reliable reference basis for the fracturing process, ensure uniform pressure transmission, and optimize the fracturing effect.

[0044] 3. Accurately locate the horizontal well

[0045] The supporting structure of the top plate can be regarded as a cantilever beam. By calculating the length and pressure distribution of the cantilever beam, the present invention can accurately determine the layout position of the horizontal well. Accurate determination of the horizontal well position is a key step to ensure the maximum fracturing effect. Incorrect well position layout may result in inadequate fracturing pressure transmission or stress concentration. According to the calculation results, the horizontal well is offset to the side with weaker rigidity during layout to ensure that the pressure can be evenly transmitted and achieve the ideal fracturing effect.

[0046] 4. Precisely control fracturing parameters

[0047] The present invention uses a series of formulas to accurately determine parameters such as flow rate, perforation spacing, and sand carrying capacity involved in the fracturing process. The flow rate determines the injection speed of the fracturing fluid and the propagation speed of the pressure. A reasonable flow value is obtained through formula calculation to ensure that the fracturing fluid can be smoothly propagated to the target layer and form a stable fracture network. If the flow rate is too large, it may cause excessive damage to the target layer; if the flow rate is too small, the cracks cannot be effectively expanded. The perforation spacing determines the point of application of the fracturing pressure, and the sand carrying capacity affects the expansion and stability of the cracks. By optimizing these two parameters, the present invention can ensure that the formation of the fracture network will not excessively damage the coal seam, and can effectively release energy. The precise control of these parameters is the key to ensuring the success of fracturing, as they affect the generation and development of cracks and the final energy release effect.

[0048] 5. Improve mine safety in multiple dimensions

[0049] In addition to the above technical advantages, this method can effectively improve the safety of the mine through scientific design from multiple aspects such as target layer selection, support body optimization, well location layout, fracturing parameters, etc. By optimizing the design of fracturing layers and support bodies, the stress concentration of the roof is effectively alleviated, avoiding the risk of sudden roof collapse during coal mining.

[0050] 6. Flexibility to adapt to different conditions

[0051] The present invention has strong flexibility and can be adjusted according to different coal seam thicknesses, roof structures, support conditions, etc. Under different coal mine conditions, the method of the present invention can ensure the best fracturing effect through corresponding calculations and adjustments. Even for unconventional or complex mine conditions, accurate design solutions can be obtained through simulation and calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0053] Figure 1 A flow chart of a method for controlling ground fracturing in an isolated island facing an empty roadway in a fully mechanized caving caving system in an extra-thick coal seam provided by the present invention;

[0054] Figure 2 A three-dimensional diagram of the ground fracturing control method for an isolated island facing an empty tunnel in a super-thick coal seam fully mechanized caving provided by the present invention;

[0055] Figure 3The numerical simulation diagrams of the collapse of the overburden under different hard roof layers provided by the present invention; wherein, 3a is the numerical simulation diagram of the collapse at a layer of 50m; 3b is the numerical simulation diagram of the collapse at a layer of 100m; 3c is the numerical simulation diagram of the collapse at a layer of 150m; 3d is the numerical simulation diagram of the collapse at a layer of 200m; 3e is the numerical simulation diagram of the collapse at a layer of 250m;

[0056] Figure 4 A graph of energy released by the destruction of a hard roof at different hard roof levels provided by the present invention;

[0057] Figure 5 This is a diagram of the coal pillar equivalent stiffness calculation model provided by the present invention; wherein 5a is the coal pillar size model, and 5b is the coal pillar elastic stiffness equivalent model;

[0058] Among them, 1-the goaf of the isolated island face, 2-the collapsed zone of the mined working face, 3-the fissure zone and the curved subsidence zone of the mined working face, 4-the cantilever structure in the middle of the isolated island face, 5-the collapsed angle on the left side of the coal pillar size model of the isolated island face, 6-the collapsed angle on the right side of the coal pillar size model of the isolated island face, 7-the coal pillar size model on the left side of the isolated island face, and 8-the coal pillar size model on the right side of the isolated island face. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] See also Figure 1 As shown, the present invention discloses a method for controlling ground fracturing in an isolated island facing an empty roadway in a fully mechanized caving of an extra-thick coal seam, comprising the following steps:

[0061] Determine the target layer for ground fracturing;

[0062] Calculate the equivalent stiffness of the left and right support bodies under the hard roof and the stress of the fracturing target layer;

[0063] Determine the horizontal well position and ground fracturing parameters to control the ground fracturing of empty tunnels facing isolated islands in extremely thick coal seams.

[0064] For details, see Figure 2 As shown, the structure of the three-dimensional diagram is: goaf of isolated island face 1, collapsed zone of mined working face 2, fissure zone and curved subsidence zone of mined working face 3, cantilever structure in the middle of isolated island face 4, collapsed angle on the left side of coal pillar size model of isolated island face 5, collapsed angle on the right side of coal pillar size model of isolated island face 6, coal pillar size model on the left side of isolated island face 7, and coal pillar size model on the right side of isolated island face 8.

[0065] Furthermore, the specific contents of determining the target layer of ground fracturing are as follows:

[0066] Numerical simulation software is used to simulate the energy released by the hard roof in different layers under the same mining height and the same hard roof thickness, and the target layer for ground fracturing is determined by the formula:

[0067] E p =2.1665H 3 -1199.1H 2 +183620H-3×10 6 ;

[0068] Among them, E p is the energy released by the destruction of the hard roof at different hard roof levels, and H is the level of the hard roof.

[0069] Furthermore, 50≤H≤250.

[0070] For details, see Figure 3 As shown in the figure, these are the numerical simulation diagrams of the collapse of the overburden under different hard roof layers, among which 3a is the numerical simulation diagram of the collapse at the layer of 50m; 3b is the numerical simulation diagram of the collapse at the layer of 100m; 3c is the numerical simulation diagram of the collapse at the layer of 150m; 3d is the numerical simulation diagram of the collapse at the layer of 200m; 3e is the numerical simulation diagram of the collapse at the layer of 250m.

[0071] See also Figure 4 As shown, this is a curve diagram of the energy released by the destruction of hard roof at different hard roof levels.

[0072] Specifically, the hard rock strata with the largest fracture release energy and the strongest mine pressure will have an important impact on the fully-mechanized caving island face mining of extra-thick coal seams.

[0073] Furthermore, the specific contents of calculating the equivalent stiffness of the left and right supporting bodies under the rigid top plate are as follows:

[0074] The coal pillar is composed of several springs connected in parallel, with a length of l n The equivalent stiffness K of the supporting bodies on both sides below the rigid top plate is calculated using the following formula 左 , K 右 :

[0075]

[0076]

[0077] Among them, α and β are the collapse angles on both sides of the equivalent model of the coal pillar equivalent support body, l n is the length of the support, l n-1 is the length of the n-1th layer of support, Hn is the thickness of the nth layer of support, K ​​is the equivalent stiffness of the support under the rigid top plate, K i The stiffness of the support body of the i-th layer from the 1st layer to the nth layer, l i is the length of the i-th support layer from the 1st layer to the nth layer.

[0078] Furthermore, the specific content of calculating the stress of the target layer of fracturing is:

[0079]

[0080] Where v is the Poisson's ratio of the target layer, E is the elastic modulus of the target layer, z is the vertical distance from the neutral plane to the calculated stress, ω is the deflection of the target layer, A1, A2, B1, B2, C are coefficients, and the spatial coordinate system is established with the center of the target layer plate. x is the horizontal rightward coordinate, y is the vertical upward coordinate, σ x is the principal stress in the x direction of the target layer for fracturing, σ y is the principal stress in the y direction of the target layer for fracturing, τ xy is the shear stress of the target layer for fracturing.

[0081] Specifically, the calculation method of A1, A2, B1, B2, and C is:

[0082] A1=-(98371448175qa 14 ) / (8D(2063736675a 20 +36243146940a 18 b 2 +713239540090a 16 b 4 +3717181093724a 14 b 6 +18112906423493a 12 b 8 +15913861356536a 10 b 10 +18112906423493a 8 b 12 +3717181093724a 6 b 14 +713239540090a 4 b 16 +36243146940a 2 b 18 +2063736675b 20 ))+(214543444115qa 12 b 2<h2 style=";text-align:left;direction:ltr">) / (2D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 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style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12+3717181093724a 6 b 14 +713239540090a 4 b 16 +36243146940a 2 b 18 +2063736675b 20 ))-(1788571785qb 12 ) / (4D(2063736675a 20 +36243146940a 18 b 2 +713239540090a 16 b 4 +3717181093724a 14 b 6 +18112906423493a 12 b 8 +15913861356536a 10 b 10 +18112906423493a 8 b 12 +3717181093724a 6 b 14 +713239540090a 4 b 16 +36243146940a 2 b 18 +2063736675b 20 ));

[0084] B1=596190595qa 14 / (D(2063736675a 20 +36243146940a 18 b 2 +713239540090a 16 b 4 +3717181093724a 14 b 6 +18112906423493a 12 b 8 +15913861356536a 10 b 10 +18112906423493a 8 b 12 +3717181093724a 6 b 14 +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+(128249113993qa<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> ) / (8D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+(741110627257qa<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> ) / (2D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2<h2 style=";text-align:left;direction:ltr">b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+(9841907858783qa<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> ) / (4D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+(24031149427285qa<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> ) / (2D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20<h2 style=";text-align:left;direction:ltr">))+(29161963866035qa<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> ) / (4D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))-(98371448175qb<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> ) / (8D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ));<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0085] <h2 style=";text-align:left;direction:ltr"> B2=-(1788571785qa<h2 style=";text-align:left;direction:ltr"> 12<h2 style=";text-align:left;direction:ltr">) / (4D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))-4475079609qa<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> / (D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))-(104261099943qa<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> ) / (2D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18<h2 style=";text-align:left;direction:ltr">b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+151297449303qa<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> / (D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+(2529767725485qa<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> ) / (2D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4+3717181093724a 14 b 6 +18112906423493a 12 b 8 +15913861356536a 10 b 10 +18112906423493a 8 b 12 +3717181093724a 6 b 14 +713239540090a 4 b 16 +36243146940a 2 b 18 +2063736675b 20 ))+3201287984895qa 2 b 10 / (D(2063736675a 20 +36243146940a 18 b 2 +713239540090a 16 b 4 +3717181093724a 14 b 6 +18112906423493a 12 b 8 +15913861356536a 10 b 10 +18112906423493a 8 b 12 +3717181093724a 6 b 14 +713239540090a 4 b 16 +36243146940a 2 b 18 +2063736675b 20 ))+(1672314618975qb 12 ) / (4D(2063736675a 20 +36243146940a 18 b 2 +713239540090a 16 b 4 +3717181093724a 14 b 6 +18112906423493a12 b 8 +15913861356536a 10 b 10 +18112906423493a 8 b 12 +3717181093724a 6 b 14 +713239540090a 4 b 16 +36243146940a 2 b 18 +2063736675b 20 ));

[0086] C=(98371448175qa 16 ) / (64D(2063736675a 20 +36243146940a 18 b 2 +713239540090a 16 b 4 +3717181093724a 14 b 6 +18112906423493a 12 b 8 +15913861356536a 10 b 10 +18112906423493a 8 b 12 +3717181093724a 6 b 14 +713239540090a 4 b 16 +36243146940a 2 b 18 +2063736675b 20 ))+(394081983295qa 14 b 2 ) / (16D(2063736675a 20 +36243146940a 18 b 2 +713239540090a 16 b 4 +3717181093724a 14 b 6 +18112906423493a 12 b 8<h2 style=";text-align:left;direction:ltr">+15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+(28365438278177qa<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> ) / (64D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+(21409089448747qa<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> ) / (8D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10<h2 style=";text-align:left;direction:ltr">+18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+(215495164733849qa<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> ) / (16D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> +15913861356536a<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> +18112906423493a<h2 style=";text-align:left;direction:ltr"> 8 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+(21409089448747qa<h2 style=";text-align:left;direction:ltr"> 6 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 10 <h2 style=";text-align:left;direction:ltr"> ) / (8D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> +3717181093724a<h2 style=";text-align:left;direction:ltr"> 14 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style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 16 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> +2063736675b<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> ))+(28365438278177qa<h2 style=";text-align:left;direction:ltr"> 4 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 12 <h2 style=";text-align:left;direction:ltr"> ) / (64D(2063736675a<h2 style=";text-align:left;direction:ltr"> 20 <h2 style=";text-align:left;direction:ltr"> +36243146940a<h2 style=";text-align:left;direction:ltr"> 18 <h2 style=";text-align:left;direction:ltr"> b<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +713239540090a<h2 style=";text-align:left;direction:ltr"> 16 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[0087] Among them, a is the length of the working surface, b is the width of the working surface, q is the distributed load on the target layer, and D is the basic top bending stiffness.

[0088] Furthermore, the specific contents of determining the horizontal well position are:

[0089] The horizontal well position X is determined using the following formula:

[0090]

[0091] Wherein, L is the cantilever length between the supports on both sides of the target layer;

[0092] Specifically, since the widths of the coal pillars left on both sides of the isolated working face are different, the ground fracturing position needs to be offset to one side when arranging it.

[0093] Then calculate the tensile and compressive stresses generated by the main bending moment on the target fracturing layer:

[0094]

[0095] Compare with Mises stress to determine whether to perform ground fracturing:

[0096]

[0097] Among them, σ z is the principal stress in the direction perpendicular to the xy plane, σ1 is the first principal stress, σ2 is the second principal stress, and σ3 is the third principal stress.

[0098] Furthermore, the specific contents of determining the horizontal well position and ground fracturing parameters are as follows:

[0099] The following formula is used to determine the flow rate V, perforation spacing d, and sand carrying capacity S during ground fracturing to solve the values ​​of various fracturing parameters:

[0100] f=50ln(V+1)+0.02V 1.1 +0.001e (0.01V) ;

[0101]

[0102] f=20ln(S+5)+0.03S 1.2 +0.001 e (0.015S) +0.5S-0.0001S 2 +150;

[0103] Among them, f is the crack extension length, n is the number of horizontal segments, and l is the length of the horizontal segment.

[0104] In a specific embodiment, a sandstone layer with a thickness of 18m and a burial depth of 400m is overlying a certain isolated island surface of Tashan Coal Mine of Jinneng Holding Group. The uniaxial compressive strength σ of the sandstone layer is 90MPa. The inclined length of the isolated island surface is 200m, the strike length is 1000m, the width of the coal pillar left in the upper section on the left is l1=42m, and the width of the coal pillar left in the lower section on the right is 8m. The specific fracturing process is as follows:

[0105] Numerical simulation software is used to simulate the energy released by the hard roof at different levels when destroying the rock strata under the conditions of the same mining height and the same hard roof thickness. Figure 3 From Figures 3a-3e, we can see that the peak value of the energy released by the hard roof is roughly between 100m and 150m of the hard roof layer, indicating that the violent release of energy by the hard roof between 100m and 150m will have an important impact on the mine pressure of the working face. The formula can be used to determine that the distance between the fracturing target layer and the coal seam is 115m, and the length of the cantilever L is 128m.

[0106] like Figure 5 The support shown is composed of 6 layers, among which, Figure 5 a is the coal pillar size model, Figure 5b is the equivalent model of elastic stiffness of coal pillar, Figure 5 The various parameters in represent: n is the number of equivalent support layers, l n is the length of each layer, H n is the thickness of each layer, K n is the stiffness coefficient of each layer, and α and β are the collapse angles on both sides of the coal pillar size model.

[0107] After on-site measurement, the support body collapse angles below the target layer are α = 55°, β = 45°, and the thickness of each layer is H1 = 15m, H2 = 7.2m, H3 = 11.4m, H4 = 12.1m, H5 = 8.6m, H6 = 12.8m. The calculation results show that each layer l2 = 54.2m, l3 = 73.6m, l4 = 83.1m, l5 = 97.7m, l6 = 119.4m, and the equivalent support body K on the left can be obtained. 左 =6.5×10 5 N / m, and K can be obtained by the same logic 右 =0.7×10 4 N / m;

[0108] Since the widths of the coal pillars left on both sides of the isolated working face are different, the ground fracturing position needs to be offset to one side. 左 , K 右 With the cantilever length L in the middle, determine the reasonable horizontal well layout position at a distance of X = 50m from the left equivalent support body;

[0109] Calculate the stress σ of the target layer x =5Mpa,σ y =80Mpa, τ xy =36Mpa, from which the tensile and compressive stress σ generated by the main bending moment on the target fracturing layer is obtained to be 98.2Mpa, which is greater than the Mises stress σ von mises =95Mpa, at which time the target layer of fracturing yields. Therefore, ground fracturing should be adopted. Therefore, the ground fracturing control method of the isolated island facing the empty roadway in the extra-thick coal seam should be adopted to control the coal mine geological disasters such as mine earthquake caused by the hard roof from the source.

[0110] The horizontal well is divided into 5 sections by staged fracturing, each 200m long. It is expected that the cracks produced by fracturing will penetrate the entire target layer and fully release the energy stored in the hard roof. Therefore, the crack extension length f = 78m is determined, and the fracturing parameter flow rate V = 5m can be determined by the formula. 3 / min, perforation spacing d = 40m, sand carrying capacity S = 96.9m 3 .

[0111] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0112] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for controlling ground fracturing in an isolated island facing an empty roadway in a particularly thick coal seam, characterized in that: The following steps are involved: Determine the target layer for ground fracturing; Calculate the equivalent stiffness of the left and right support bodies under the hard roof and the stress of the fracturing target layer; Determine the horizontal well position and ground fracturing parameters, so as to control the ground fracturing of the empty roadway facing the fully mechanized caving island in the extra-thick coal seam; The specific contents of determining the target layer of ground fracturing are as follows: Numerical simulation software is used to simulate the energy released by the hard roof in different layers under the same mining height and the same hard roof thickness, and the target layer for ground fracturing is determined by the formula: E p =2.1665H 3 -1199.1H 2 +183620H-3×10 6 ; Among them, E p is the energy released by the destruction of the hard roof at different hard roof levels, and H is the level of the hard roof; The specific contents of calculating the equivalent stiffness of the left and right supporting bodies under the rigid top plate are as follows: The coal pillar is composed of several springs connected in parallel, with a length of l n The equivalent stiffness K of the supporting bodies on both sides below the rigid top plate is calculated using the following formula 左 , K 右 : Among them, α and β are the collapse angles on both sides of the equivalent model of the coal pillar equivalent support body, l n is the length of the support, l n-1 is the length of the n-1th layer of support, H n is the thickness of the nth layer of support, K ​​is the equivalent stiffness of the support under the rigid top plate, K i The stiffness of the support body of the i-th layer from the 1st layer to the nth layer, l i is the length of the i-th support layer from the 1st layer to the nth layer; The specific contents of calculating the stress of the target layer of fracturing are as follows: Where v is the Poisson's ratio of the target layer, E is the elastic modulus of the target layer, z is the vertical distance from the neutral plane to the calculated stress, ω is the deflection of the target layer, A1, A2, B1, B2, C are coefficients, and the spatial coordinate system is established with the center of the target layer plate. x is the horizontal rightward coordinate, y is the vertical upward coordinate, σ x is the principal stress in the x direction of the target layer for fracturing, σ y is the principal stress in the y direction of the fracturing target layer, τ xy is the shear stress of the target layer for fracturing, a is the length of the working surface, and b is the width of the working surface; The specific contents of determining the location of horizontal wells are: The horizontal well position X is determined using the following formula: Wherein, L is the cantilever length between the supports on both sides of the target layer; Then calculate the tensile and compressive stresses generated by the main bending moment on the target fracturing layer: Compare with Mises stress to determine whether to perform ground fracturing: Among them, σ z is the principal stress in the direction perpendicular to the xy plane, σ1 is the first principal stress, σ2 is the second principal stress, and σ3 is the third principal stress; The specific contents of determining the horizontal well location and ground fracturing parameters are as follows: The following formula is used to determine the flow rate V, perforation spacing d, and sand carrying capacity S during ground fracturing to solve the values ​​of various fracturing parameters: f=50ln(V+1)+0.02V 1.1 +0.001e (0.01V) ; f=20ln(S+5)+0.03S 1.2 +0.001·e (0.015S) +0.5S-0.0001S 2 +150; Among them, f is the crack extension length, n is the number of horizontal segments, and l is the length of the horizontal segment.

2. The method for controlling ground fracturing in an isolated island facing an empty roadway in a super-thick coal seam fully mechanized caving according to claim 1 is characterized in that: 50≤H≤250。

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