CN109871507B - Method for calculating absolute permeability of fracture of orthotropic coal seam - Google Patents
Method for calculating absolute permeability of fracture of orthotropic coal seam Download PDFInfo
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Abstract
The invention assumes that the cracks in the coal seam are three groups of mutually orthogonal joints, and constructs an evolution model of the absolute permeability of the cracks of the orthogonal anisotropic coal seam under the dual actions of effective stress change and gas adsorption/desorption by comprehensively considering the four anisotropies of crack structure, joint mechanical parameters, coal matrix adsorption/desorption deformation and ground stress, wherein the model is shown in the following formula
Compared with the traditional absolute permeability model of the coal bed, the method is closer to the structural characteristics of the real coal bed fracture, so that the evolution rule of the absolute permeability in the coal bed gas exploitation and coal bed gas extraction processes can be predicted more accurately.
Description
Technical Field
The invention relates to a method for calculating absolute permeability of a coal seam, in particular to a method for calculating absolute permeability of an orthotropic coal seam fracture.
Background
The quantitative relation between the absolute permeability of the coal bed and the effective stress and adsorption/desorption is a research hot spot in the field of coal bed gas, and the mathematical model describing the quantitative relation is a model of evolution of the absolute permeability of the coal bed. Existing models can be divided into three classes according to boundary conditions: the model is mainly used for simulating and predicting the evolution behavior of the absolute permeability of the coal bed in the coal bed gas exploitation process and the coal bed gas extraction; the model is mainly used for simulating and predicting the evolution behavior of the absolute permeability of the coal sample in the indoor experimental process of the absolute permeability; the absolute permeability evolution model of the coal seam without specific boundary conditions is not limited to the specific boundary conditions, but can be developed into different forms according to different boundary conditions, and compared with the absolute permeability models of the first two types, the absolute permeability evolution model of the coal seam has wider application range, but model expressions are generally more complex. At present, members in the whole coal bed absolute permeability evolution model family are relatively rich, and the requirements of different boundary conditions can be basically met. But these models are mostly based on isotropic assumptions, ignoring the anisotropy of the absolute permeability of the coal seam. In addition to absolute permeability, the mechanical parameters and adsorption/desorption deformation of coal also have anisotropic characteristics. In recent years, partial scholars are aware of the anisotropic characteristics of coal seam properties, and establish a model of evolution of coal seam anisotropic absolute permeability. However, the existing coal seam anisotropy absolute permeability evolution model only considers partial influence factors of absolute permeability anisotropy, and is still imperfect.
Disclosure of Invention
The invention aims to accurately calculate the absolute permeability of an orthotropic coal seam fracture.
The invention aims at realizing the following technical scheme:
the invention relates to a method for calculating absolute permeability of an orthotropic coal seam fracture, which comprises the following mathematical expression:
according to the technical scheme provided by the invention, the method for calculating the absolute permeability of the orthotropic coal seam, which is provided by the embodiment of the invention, has the advantages that the anisotropic property of the coal seam fracture is considered, the absolute permeability is directly calculated through fracture parameters, and the accuracy of the prediction of the absolute permeability of the coal seam is improved.
Drawings
FIG. 1 is a schematic diagram of an orthotropic coal seam fracture in an embodiment.
Detailed Description
The coal seam fracture structure coal is a fracture-pore medium consisting of fractures and coal matrix filled with micro pores. Because the size of the pores in the coal matrix is much smaller than the fissures, the absolute permeability of the coal seam is generally referred to as the absolute permeability of the fissures. According to the differences in connectivity and orientation, the fracture may be divided into near-mutually orthogonal face, end and layer joints (as shown in fig. 1). The face joints and the end joints are main channels for gas flow in the coal seam: the extension length of the surface joint is large, the connectivity is good, the surface is flat, and the surface joints are nearly parallel to each other; the end joints are flat in surface but poor in connectivity compared with the surface joints, so that the absolute permeability of the end joints is generally lower than that of the surface joints; the absolute permeability of the layer interface under compression of vertical stress is typically much lower than the interface and end joints.
FIG. 1 is a schematic diagram of a fracture structure of a coal seam
The surface joints, end joints and layer joints are assumed to be orthogonal to each other and equally spaced. When the osmotic pressure gradient is orthogonal to the joint plane, the permeability tensor can be expressed as
Wherein k is x 、k y And k z Absolute permeabilities in the x, y and z axes parallel are shown, respectively.
Joint porosity, face porosity and bulk porosity
Defining the porosity of the single set of joints as joint porosity; every two groups of joints are mutually perpendicular and are mutually perpendicular to a coordinate plane, so that the porosity of the two groups of joints is defined as the surface porosity, and the surface porosity has symmetry; the porosity of the three sets of joints is defined as the bulk porosity. The relationship of the joint porosity, the face porosity, and the bulk porosity can be expressed by the following formula. From this formula, the bulk porosity is equal to the sum of the joint porosities, which is equal to one half of the sum of the face porosities.
Wherein, the superscript c represents a joint; phi (phi) i Represents the joint porosity perpendicular to the i-axis; phi (phi) ij Representing the porosity of two sets of joints perpendicular to the Oij plane, i.e., face porosity; phi (phi) t The total porosity, i.e. bulk porosity, of the three sets of joints is indicated.
Coal body, coal matrix and joint deformation
To more closely approximate the true coal seam structure, the coal matrices in the token of fig. 1 are not completely separated, but are connected by a rock bridge. The existence of the rock bridge enables the joint to have certain strength, so that the mechanical parameters of the rock bridge can be equivalent to those of the joint. The change of the gas pressure causes effective stress change and gas adsorption/desorption, thereby causing deformation of coal bodies, coal matrixes and joints, and the effective stress change is shown as the following formula
Wherein, the superscript M represents a medium, m=b represents a coal body, m=c represents an joint, and m=m represents a coal matrix; delta represents the amount of change; epsilon represents the total strain of the medium; epsilon e Representing the strain of the medium caused by the effective stress variation; epsilon s Indicating gas adsorption/desorption induced medium strain
Assuming that the coal body, the joints and the coal matrix are all elastic media, then
Can be represented by the following formula
Wherein E represents Young's modulus; v represents poisson's ratio; sigma (sigma) e The effective stress is represented by the following formula
σ e ＝-σ t +p (5)
In sigma e Representing the total stress; p represents the gas pressure; ' indicates that the compressive stress is negative and the tensile stress is positive.
The gas adsorption/desorption will cause the coal matrix to expand/shrink and deform, creating compressive/tensile stress compression/stretching of the rock bridge, closing/opening the joints. When the internal stress of the rock bridge and the stress generated by the adsorption/desorption deformation of the coal matrix reach balance, the deformation of the rock bridge is stopped, the joint width is not changed any more, and the adsorption/desorption deformation of the residual coal matrix is converted into the deformation of the whole coal body. Thus, the total deformation of the coal matrix adsorption/desorption can be expressed as the sum of the two parts, i.e
Wherein b represents the joint distance, i.e., the coal matrix width;
indicating the total deformation of coal matrix adsorption/desorption; />
The portion of the coal matrix adsorption/desorption deformation that causes joint deformation is referred to as the coal matrix adsorption/desorption internal deformation; />
The portion of the coal matrix adsorption/desorption deformation that causes deformation of the coal matrix is referred to as the coal matrix adsorption/desorption outer deformation.
Assuming that the ratio of the internal deformation of the adsorption/desorption of the coal matrix to the total deformation of the adsorption/desorption of the coal matrix is constant, i.e
Wherein F is I Known as the internal deformation coefficient of adsorption/desorption of the coal matrix.
Substituting formula (7) into formula (6) can obtain the expression of coal matrix adsorption/desorption external deformation as
The strain of coal caused by adsorption/desorption of the coal matrix can be expressed as
Wherein a represents the joint width;
represents the total adsorption/desorption strain of the coal matrix and can be represented by the following formula
In the method, in the process of the invention,
and->
Is the coal matrix adsorption/desorption deformation constant, wherein +.>
The physical meaning of (2) is the ultimate adsorption strain of the coal matrix at infinite gas pressure; />
Is the physical meaning of->
Corresponding gas pressure.
The joint strain caused by adsorption/desorption of the coal matrix can be expressed as
The negative sign in the above formula indicates that the coal matrix expands to close the joint and the coal matrix contracts to open the joint.
Orthotropic coal seam fracture absolute permeability index type model expression
The ratio of the derivative of the face porosity to the face porosity can be derived as follows
The change in joint porosity during the elastic deformation phase is generally small, and
and->
And->
The direction of change of (i.e. increase simultaneously or decrease simultaneously) is the same, so it can be assumed that
Substituting formula (13) into formula (12)
For joints perpendicular to the j-axis, the relationship between porosity, strain and coal strain can be represented by the following formula
Substituting formula (15) into formula (14)
Integrating (16) to obtain
Substituting the formula (3), the formula (4), the formula (9) and the formula (11) into the formula (17) and finishing the obtained product
Internal deformation coefficient of adsorption/desorption of coal matrix (F) I ) Is of the order of 10 -1 While the order of porosity is generallyIs 10 -3 ～10 -2 Thus F I /φ c ＞＞(1-F I ). In addition, the coal body strength is much higher than the joint, so it is assumed that the coal body is incompressible compared to the joint, i.e. E b ＞＞E c 。
In conclusion, the formula (18) is degraded into
In the middle of
The anisotropic absolute permeability has a cubic relationship with the in-plane porosity, i.e
Substituting formula (20) into formula (21)
The formula (22) is an exponential expression of an evolution model of absolute permeability of an orthogonal anisotropy fracture of the coal seam in the effective stress change and gas adsorption/desorption processes, and comprehensively considers the anisotropism of fracture structure (initial absolute permeability and initial porosity), joint mechanical parameters (elastic modulus and poisson ratio), coal matrix adsorption/desorption deformation and ground stress.
Claims (2)
1. The method for calculating the absolute permeability of the fracture of the orthotropic coal seam is characterized by comprising the following steps of:
wherein k is i Represents the permeability in the i-axis direction; k (k) i0 Is k i Is set to an initial value of (1);
represents the joint porosity perpendicular to the j-axis; />
Represents the joint porosity perpendicular to the k-axis; />
An initial value representing joint porosity perpendicular to the j-axis; />
An initial value representing the joint porosity perpendicular to the k-axis; />
Representing the porosity of two sets of joints perpendicular to the Ojk plane, i.e., face porosity; e (E) i 、E j 、E k Young's moduli in the i, j, k axis directions are respectively represented; Δσ ei 、Δσ ej 、Δσ ek Effective stress variation in the i, j, k axis directions are respectively represented; v (v) ij 、ν jk 、ν ik Respectively representing poisson's ratio on Oij, ojk, oik plane; f (F) Ij And F Ik The coal matrix adsorption/desorption internal deformation coefficients in the j and k axis directions are respectively represented; epsilon Lj And epsilon Lk The ultimate adsorption strain constants of the coal matrix in the j and k axis directions are respectively shown; p is p Lj And p Lk Coal matrix adsorption pressure constants in j-axis and k-axis directions are represented; p represents the gas pressure; p is p 0 An initial value representing the gas pressure; superscript c denotes a joint; the superscript m represents a coal matrix.
2. The method for calculating the absolute permeability of the orthogonal anisotropy coal seam fracture according to claim 1, wherein the method comprises anisotropy of a coal seam fracture structure, anisotropy of a coal seam joint mechanical parameter, anisotropy of adsorption/desorption deformation of a coal matrix and anisotropy of ground stress.
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| CN111460601B (en) * | 2019-12-06 | 2020-11-17 | 西南石油大学 | Orthotropic formation ground stress prediction method based on rock physics modeling |
| 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 |
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