CN109871507A - Orthotropy cracks in coal seam absolute permeability calculation method - Google Patents
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Abstract
Present invention assumes that the crack in coal seam is three groups of mutually orthogonal joints, by the anisotropy for comprehensively considering fissured structure, four aspect of mechanical parameters of joints, the deformation of matrix of coal adsorption/desorption and crustal stress, orthotropy cracks in coal seam absolute permeability evolutionary model under effective stress variation and gas adsorption/desorption double action is constructed, is shown below
Description
Technical field
The present invention relates to a kind of method for calculating coal seam absolute permeability more particularly to a kind of calculating orthotropy coals
The method of layer crack absolute permeability.
Background technique
Coal seam absolute permeability and effective stress and the quantitative relationship of adsorption/desorption are the research heat in coal-bed gas field
Point, the mathematical model for describing this quantitative relationship is coal seam absolute permeability evolutionary model.Existing model can by boundary condition
To be divided into three classes: the coal seam absolute permeability evolutionary model under uniaxial strain boundary condition, this class model are mainly used for simulating
With the evolved behavior of coal seam absolute permeability in prediction coal bed gas recovery process and coal bed gas extraction；Constant confining pressure boundary condition
Under coal seam absolute permeability evolutionary model, this class model be mainly used for simulate and predict absolute permeability laboratory experiment during
The evolved behavior of coal sample absolute permeability；Coal seam absolute permeability evolutionary model without specific border condition, this class model not office
It is limited to specific boundary condition, but different forms can be launched into according to different boundary conditions, is absolutely seeped with preceding two class
Saturating rate model is compared, and the application range of this class model is wider, but model expression is usually more complicated.
The member in entire coal seam absolute permeability evolutionary model family can satisfy different sides compared with horn of plenty substantially at present
The demand of boundary's condition.But these models are mostly based on the assumption of isotropy, have ignored the anisotropy of coal seam absolute permeability.It removes
Other than absolute permeability, mechanics parameter and the adsorption/desorption deformation of coal also have anisotropic character.In recent years, some scholars
The anisotropic character for recognizing coal seam property establishes coal seam anisotropy absolute permeability evolutionary model.But existing coal
Layer anisotropy absolute permeability evolutionary model only accounts for the anisotropic some effects factor of absolute permeability, still endless
It is kind.
Summary of the invention
It is an object of the invention to accurately calculate the absolute permeability of orthotropy cracks in coal seam.
The purpose of the present invention is what is be achieved through the following technical solutions:
Orthotropy cracks in coal seam absolute permeability calculation method of the invention, mathematic(al) representation are as follows:
As seen from the above technical solution provided by the invention, the orthotropy coal that embodiment of the present invention provides
Layer absolute permeability calculation method, due to considering the anisotropic properties of cracks in coal seam and directly being calculated absolutely by parameters of fissure
To permeability, the precision of coal seam absolute permeability prediction is improved.
Detailed description of the invention
Fig. 1 is orthotropy cracks in coal seam schematic diagram in specific embodiment.
Specific embodiment
Cracks in coal seam structure
Crack-pore media that matrix of coal of the coal by crack and full of micro-pore forms.Due to hole in matrix of coal
Size be much smaller than crack, coal seam absolute permeability typically refers to the absolute permeability in crack.According in connectivity and direction
Difference, crack can be divided into close to mutually orthogonal face joint, end segment reason and bed plane (as shown in Figure 1).Face joint and end segment
Reason is the main thoroughfare of Gas Flow in coal seam: the development length at face joint is big, and connectivity is good, surfacing, and each other
Close in parallel；End segment manages surfacing but connectivity is poor compared with face joint, therefore the absolute permeability of end segment reason is usually less than face section
Reason；Bed plane is typically well below face joint and end segment reason by its absolute permeability of the compression of vertical direction crustal stress.
Fig. 1 cracks in coal seam structural schematic diagram
Assuming that face joint, end segment manage and spacing mutually orthogonal with bed plane it is equal.When osmotic pressure gradient and joint plane just
It hands over, permeability tensor is represented by
In formula, kx、kyAnd kzRespectively indicate x, the absolute permeability of y and z-axis parallel direction.
Joint porosity, face porosity and body porosity
The porosity at single group joint is defined as joint porosity；Every two groups of joints are orthogonal and common vertical is in one
Coordinate plane, therefore the porosity at two groups of joints is defined as face porosity, face porosity has symmetry；The hole at three groups of joints
Rate is defined as body porosity.The relationship of joint porosity, face porosity and body porosity can be expressed from the next.By the formula it is found that
Body porosity is equal to the sum of joint porosity, equal to the half of the sum of face porosity.
In formula, subscript c indicates joint；φiIndicate the joint porosity vertical with i axis；φijIt indicates vertical with Oij plane
Two groups of joints porosity, i.e. face porosity；φtIndicate the overall porosity at three groups of joints, i.e. body porosity.
Coal body, matrix of coal and joint deformation
For closer true coal bed texture, matrix of coal is not completely separable in the characterization volume elements of Fig. 1, but passes through rock bridge
Connection.The presence of rock bridge makes joint also have some strength, therefore the mechanics parameter of rock bridge can be equal to the mechanics at joint
Parameter.Gas pressure variation causes effective stress variation and gas adsorption/desorption, and then coal body, matrix of coal and joint is caused to become
Shape is shown below
In formula, subscript M indicates medium, and when M=b indicates coal body, and when M=c indicates joint, and when M=m indicates matrix of coal；Δ
Indicate variable quantity；ε indicates medium overall strain；εeIndicate that effective stress changes caused medium strain；εsIndicate gas adsorption/solution
The strain of medium caused by inhaling
Assuming that coal body, joint and matrix of coal are elastic fluid, thenIt can be expressed from the next
In formula, E indicates Young's modulus；ν indicates Poisson's ratio；σeIt indicates effective stress, can be expressed from the next
σe=-σt+p(5)
In formula, σeIndicate total stress；P indicates gas pressure；'-', indicates that compression is negative, and tensile stress is positive.
Gas adsorption/desorption will cause matrix of coal expansion/contraction distortion, generate pressure/tensile stress is compressed/and stretch rock bridge, make
Joint closure/opening.When the stress that rock bridge internal stress and the deformation of matrix of coal adsorption/desorption generate reaches balance, rock bridge deformation
Stop, joint width also no longer changes, and remaining matrix of coal adsorption/desorption deformation is converted into the deformation of entire coal body.Therefore, coal base
Matter adsorption/desorption total deformation is represented by the sum of two parts, i.e.,
In formula, b indicates joint spacing, i.e. matrix of coal width；Indicate the total deformation of matrix of coal adsorption/desorption；It indicates
The part for causing joint to deform in the deformation of matrix of coal adsorption/desorption, deformation referred to as in matrix of coal adsorption/desorption；Indicate coal base
The part for leading to coal deformation in the deformation of matter adsorption/desorption, referred to as deforms outside matrix of coal adsorption/desorption.
Assuming that the ratio between deformation and the total deformation of matrix of coal adsorption/desorption are constants in matrix of coal adsorption/desorption, i.e.,
In formula, FIReferred to as deformation coefficient in matrix of coal adsorption/desorption.
Formula (7) substitution formula (6), which can be obtained the expression formula deformed outside matrix of coal adsorption/desorption, is
The strain of coal body caused by matrix of coal adsorption/desorption is represented by
In formula, a indicates joint width；It indicates the overall strain of matrix of coal adsorption/desorption, can be expressed from the next
In formula,WithIt is matrix of coal adsorption/desorption deformation constant, whereinPhysical significance be gas pressure infinity
When matrix of coal the limit adsorb strain；Physical significance be to work asWhen corresponding gas pressure.
The strain of joint caused by matrix of coal adsorption/desorption is represented by
Negative sign in above formula indicates that matrix of coal expansion is closed joint, and Coal matrix shrinkage opens joint.
Orthotropy cracks in coal seam absolute permeability exponential type model expression
The ratio between the derivative of face gap and face porosity can export following formula
At elastic deformation stage joint, the variation of porosity is usually smaller, andWithWithChange direction it is identical (i.e. same
Shi Zeng great reduces simultaneously), it may therefore be assumed that
Formula (13) are substituted into formula (12) to obtain
For the joint vertical with j axis, the relationship of porosity, strain and coal body strain can be expressed from the next[6]
Formula (15) are substituted into formula (14) to obtain
It quadratures to formula (16)
Formula (3), formula (4), formula (9) and formula (11) are substituted into formula (17) and arranged
Deformation coefficient (F in matrix of coal adsorption/desorptionI) the order of magnitude be 10-1, and the order of magnitude of porosity is usually 10-3
~10-2, therefore FI/φc> > (1-FI).In addition, coal mass strength is much higher than joint, it is therefore assumed that coal body can not compared with joint
Compression, i.e. Eb> > Ec.To sum up, formula (18) is degenerated to
In formula
There are cubic relationships with face porosity for anisotropy absolute permeability, i.e.,
Formula (20) are substituted into formula (21) to obtain
Formula (22) is that effective stress variation and coal seam orthotropy crack in gas adsorption/desorption process are absolutely exhausted
To the exponential type expression formula of permeability evolution model, which has comprehensively considered fissured structure (initial absolute permeability and initial apertures
Gap rate), mechanical parameters of joints (elasticity modulus and Poisson's ratio), the deformation of matrix of coal adsorption/desorption and the aspect of crustal stress four it is each to
It is anisotropic.
Claims (2)
1. orthotropy cracks in coal seam absolute permeability calculation method of the invention, mathematic(al) representation are
2. orthotropy cracks in coal seam absolute permeability calculation method described in claim 1 has comprehensively considered coal seam and has split
The anisotropy of gap structure, four aspect of mechanical parameters of joints, the deformation of matrix of coal adsorption/desorption and crustal stress.
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| CN110500069A (en) * | 2019-08-02 | 2019-11-26 | 中国矿业大学(北京) | Anisotropy heterogeneous reservoir coal-bed gas exploitation completion technique selection method |
| CN111221039A (en) * | 2020-01-21 | 2020-06-02 | 中国石油大学(北京) | Method, device and equipment for determining elastic wave velocity of natural gas hydrate |
| CN111460601A (en) * | 2019-12-06 | 2020-07-28 | 西南石油大学 | Orthotropic formation ground stress prediction method based on rock physics modeling |
| CN112727534A (en) * | 2021-01-15 | 2021-04-30 | 重庆大学 | Gas drilling hole arrangement method based on true three-dimensional stress and permeability dynamic change |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110500069A (en) * | 2019-08-02 | 2019-11-26 | 中国矿业大学(北京) | Anisotropy heterogeneous reservoir coal-bed gas exploitation completion technique selection method |
| CN110500069B (en) * | 2019-08-02 | 2022-05-17 | 中国矿业大学(北京) | Selection method of anisotropic heterogeneous reservoir coalbed methane exploitation well completion technology |
| CN111460601A (en) * | 2019-12-06 | 2020-07-28 | 西南石油大学 | Orthotropic formation ground stress prediction method based on rock physics modeling |
| US11106843B2 (en) | 2019-12-06 | 2021-08-31 | Southwest Petroleum University | Systems and methods for determining in-situ stresses based on orthotropic rock physics model |
| CN111221039A (en) * | 2020-01-21 | 2020-06-02 | 中国石油大学(北京) | Method, device and equipment for determining elastic wave velocity of natural gas hydrate |
| CN111221039B (en) * | 2020-01-21 | 2021-01-12 | 中国石油大学(北京) | Method, device and equipment for determining elastic wave velocity of natural gas hydrate |
| CN112727534A (en) * | 2021-01-15 | 2021-04-30 | 重庆大学 | Gas drilling hole arrangement method based on true three-dimensional stress and permeability dynamic change |
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