CN111597721A - Shale matrix fluid-solid coupling scale upgrading method based on homogenization theory - Google Patents

Shale matrix fluid-solid coupling scale upgrading method based on homogenization theory Download PDF

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CN111597721A
CN111597721A CN202010429057.9A CN202010429057A CN111597721A CN 111597721 A CN111597721 A CN 111597721A CN 202010429057 A CN202010429057 A CN 202010429057A CN 111597721 A CN111597721 A CN 111597721A
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CN111597721B (en
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严侠
姚军
黄朝琴
刘礼军
王子杰
孙海
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China University of Petroleum East China
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Abstract

The invention discloses a shale matrix fluid-solid coupling scale upgrading method based on a homogenization theory, which is established and can effectively represent respective characteristics of organic matters and inorganic matters on a micro scale into a macroscopic simulation. Firstly, a shale matrix is regarded as a heterogeneous porous elastic medium consisting of organic matters and inorganic matters, and a micro-scale fluid-solid coupling model is established by considering different occurrence modes and flow mechanisms of real gas in the two media; secondly, scale upgrading is carried out by adopting a homogenization theory, a macroscopic equivalent fluid-solid coupling model of the shale matrix is obtained through deduction, and definition and calculation modes of relevant equivalent parameters are given; finally, the correctness of the method is verified through numerical calculation, and the influence of the mechanical property, the content and the distribution of the organic matters on the macroscopic fluid-solid coupling numerical simulation of the shale gas reservoir is analyzed.

Description

Shale matrix fluid-solid coupling scale upgrading method based on homogenization theory
Technical Field
The invention relates to the field of numerical reservoir simulation, in particular to a shale matrix fluid-solid coupling scale upgrading method based on a homogenization theory
Background
Shale gas resources are wide in distribution and large in reserve, but the matrix permeability is extremely low, commercial exploitation can be carried out only by hydraulic fracturing, a fractured shale reservoir has the characteristic of multi-scale pore gaps and is under the combined action of a complex ground stress field and a seepage field, and the fluid-solid coupling effect is obvious. The shale matrix is used as a main gas storage space, and the establishment of the fluid-solid coupling model is the basis of the shale gas reservoir macroscopic fluid-solid coupling numerical simulation. Because the shale matrix is generally composed of micro-scale organic matters and inorganic matters, the difference of mechanical properties of the two mediums is large, and the occurrence mode and the flowing mechanism of gas in the two mediums are different, different micro-scale models need to be established aiming at the two mediums for accurately describing the fluid-solid coupling process of the gas in the shale matrix, but due to the problem of computational efficiency, the micro-scale models cannot be directly used for macroscopic simulation. In recent years, scholars at home and abroad respectively adopt a flow equivalent method and a homogenization theory to study the influence of organic matter distribution in a shale matrix on a gas macroscopic seepage rule, but the fluid-solid coupling effect is not considered. Therefore, it is necessary to establish a scale upgrading method to effectively characterize the respective characteristics of organic matters and inorganic matters on a micro scale into the shale gas reservoir macroscopic fluid-solid coupling simulation to solve the problems.
Disclosure of Invention
The invention aims to provide a shale matrix fluid-solid coupling scale upgrading method based on a homogenization theory, which is to establish the shale matrix fluid-solid coupling scale upgrading method considering respective characteristics of organic matters and inorganic matters on a microscale based on the homogenization theory, verify the correctness of the scale upgrading method through numerical example, and analyze the influence of mechanical properties, content and distribution of the organic matters on macroscopic fluid-solid coupling numerical simulation of a shale gas reservoir so as to solve the problems in the prior art.
In order to achieve the purpose, the invention provides the following scheme: the invention provides a shale matrix fluid-solid coupling scale upgrading method based on a homogenization theory, which comprises the following steps:
the shale matrix is regarded as a heterogeneous porous elastic medium consisting of organic matters and inorganic matters, and a micro-scale fluid-solid coupling model is established by considering different occurrence modes and flow mechanisms of real gas in the two media;
scale upgrading is carried out by adopting a homogenization theory to obtain a macroscopic equivalent fluid-solid coupling model of the shale matrix, and definition and calculation modes of relevant equivalent parameters are given;
the accuracy of the shale matrix fluid-solid coupling scale upgrading method based on the homogenization theory is verified, and the influence of the mechanical property, content and distribution of organic matters on the macroscopic fluid-solid coupling numerical simulation of the shale gas reservoir is analyzed.
Preferably, the process of constructing the micro-scale fluid-solid coupling model is as follows:
Figure BDA0002499835650000021
Figure BDA0002499835650000022
Figure BDA0002499835650000023
in the formula, σ and σsRespectively representing total stress tensor and effective stress tensor, p is pore pressure, α is Biot coefficient, I is unit tensor, C is elastic tensor, u is elastic tensorsIs the skeleton displacement, β represents the comprehensive compression coefficient, t represents the time, is the Crohn's symbol, phi is the porosity, mgRepresents an adsorption/desorption term; rhogIs the gas density; v is the gas flow rate; k is a radical ofaApparent permeability of gas; μ is the gas viscosity;
from the assumption of small deformation, the strain tensor e (u)s) The definition is as follows:
Figure BDA0002499835650000031
combined compressibility β and true gas density ρgThe expression of (a) is as follows:
Figure BDA0002499835650000032
in the formula, KsIs matrix skeleton bulk modulus; mgIs the gas molar mass; z represents a gas compression factor; r is a universal gas constant; t represents reservoir temperature;
gas adsorption/desorption term m according to Langmuir isothermal adsorptiongThe expression of (a) is as follows:
Figure BDA0002499835650000033
in the formula, ρrRepresenting the rock density; rhogstdRepresents the gas density under standard conditions; vLAnd PLIndicating the Langmuir volume and Langmuir pressure, respectively, of the organic matter.
The transport mechanisms of gases in inorganic substances are mainly viscous flow and Knudsen diffusion, the apparent permeability k of whichaiComprises the following steps:
Figure BDA0002499835650000034
the transport mechanism of gas in organic matters is mainly viscous flow, Knudsen diffusion and surface diffusion, and the apparent permeability k of the gas isakComprises the following steps:
Figure BDA0002499835650000035
in the formula (I), the compound is shown in the specification,
Figure BDA0002499835650000036
is intrinsic permeability, wherein rhAnd τ is pore radius and tortuosity, respectively; kn＝λ/reffIs the number Knudsen, where λ is the mean free path of the gas molecule, reffIs the effective radius of the pores; b is-1 is a slip coefficient; dsRepresents the surface diffusion coefficient of the adsorbed gas; cmaxAnd θ is the maximum adsorption amount of organic matter and gas coverage, respectively:
Figure BDA0002499835650000037
the heterogeneous coefficient of the shale matrix fluid-solid coupling model is respectively valued in inorganic matters and organic matters as follows:
Figure BDA0002499835650000041
in the formula, subscripts i and k represent inorganic and organic substances, respectively; dmIs the methane molecular diameter.
Preferably, scale upgrading is performed by adopting a homogenization theory to obtain a macroscopic equivalent fluid-solid coupling model of the shale matrix, and the specific process of defining and calculating relevant equivalent parameters is as follows:
considering a shale matrix with the characteristic length L, wherein the shale matrix consists of a large number of periodic micro-scale cells, the characteristic length of each micro-scale cell is L, the ratio of different characteristic lengths is introduced to be L/L, and variables sigma and u in the shale matrix fluid-solid coupling model are variable in the shale matrix fluid-solid coupling modelsV and p are approximated by the following progressive expansion:
Figure BDA0002499835650000042
wherein y is x/and y represents a microscale coordinate; x represents a macro scale coordinate;
Figure BDA0002499835650000043
representing a periodic variable with respect to coordinates x, y and time t;
according to the chaining criterion, we get:
Figure BDA0002499835650000044
substituting the equation (11) into the equations (1) to (3), converting by adopting the equation (12), and comparing coefficients of different orders in the equations;
by comparing in equation (3)-1And in equation (1)-2The coefficients of (a) yield:
Figure BDA0002499835650000045
from this, p is known(0)And us(0)Only on the macro scale x, independent of the micro scale y, i.e.:
p(0)＝p(0)(x,t),us(0)＝us(0)(x,t) (14)
by comparing in equation (2)-1And in equation (3)0The coefficients of (a) yield:
Figure BDA0002499835650000051
are respectively paired with v(0)And p(1)Carrying out separation variable analysis:
Figure BDA0002499835650000052
where ω and π are both periodic variables with respect to y;
substituting equation (16) for equation (15) yields the cell-assist equation:
Figure BDA0002499835650000053
in the formula, eiIs a unit vector of i-direction in a cartesian coordinate system;
for v in equation (16)(0)Carrying out volume averaging on the cells to obtain a macroscopic seepage equation:
Figure BDA0002499835650000054
in the formula, | Ω | is the volume of the whole cell;<a>denotes the volume average, k, of the variable aequTo the equivalent apparent permeability tensor:
Figure BDA0002499835650000055
Figure BDA0002499835650000056
in comparative equation (1)-1The coefficients of (a) yield:
Figure BDA0002499835650000061
from this, u iss(1)Comprises the following steps:
Figure BDA0002499835650000062
in the formula (I), the compound is shown in the specification,
Figure BDA0002499835650000063
representing an arbitrary variable independent of the coordinate y, and a periodic variable ξ associated with the coordinate ypqSatisfies the equation:
Figure BDA0002499835650000064
wherein, the symbol is Crohn's symbol;
in comparative equation (1)0The coefficients of (a) yield:
Figure BDA0002499835650000065
the equation (24) is volume-averaged over the cells, and using the divergence theorem and periodic boundary conditions, we obtain:
Figure BDA0002499835650000066
and (3) according to the volume average theorem and the periodic boundary condition, finishing to obtain a macroscopic stress balance equation:
Figure BDA0002499835650000067
in the formula, equivalent elastic tensor CequAnd equivalent Biot coefficient αequAre respectively defined as follows:
Cequijkl＝<Cijkl+Cijmneymn(ξkl)>, αequ＝<α>(27)
in comparative equation (2)0The coefficients of (a) yield:
Figure BDA0002499835650000068
carrying out volume averaging on the cells by using the equation (28), and obtaining a macroscopic mass conservation equation by adopting a divergence theorem, a volume averaging theorem and a periodic boundary condition:
Figure BDA0002499835650000071
wherein the equivalent integrated compression factor βequAnd equivalent adsorption/desorption term mgequAre respectively defined as follows:
Figure BDA0002499835650000072
Figure BDA0002499835650000073
in the formula, aTOCRepresenting the volume fraction of organic matter in the cells;
finally, the subscript hm is used for representing the subscript (0), and the macroscopic equivalent continuous medium fluid-solid coupling model is written into the following form:
Figure BDA0002499835650000074
Figure BDA0002499835650000075
Figure BDA0002499835650000076
preferably, the cell assist equations (17) and (23) are numerically solved using a finite element method.
The invention discloses the following technical effects: the invention establishes a shale matrix fluid-solid coupling scale upgrading method based on a homogenization theory, and can effectively represent respective characteristics of organic matters and inorganic matters on a microscale into a macroscopic simulation. Firstly, a shale matrix is regarded as a heterogeneous porous elastic medium consisting of organic matters and inorganic matters, and a micro-scale fluid-solid coupling model is established by considering different occurrence modes and flow mechanisms of real gas in the two media; secondly, scale upgrading is carried out by adopting a homogenization theory, a macroscopic equivalent fluid-solid coupling model of the shale matrix is obtained through deduction, and definition and calculation modes of relevant equivalent parameters are given; finally, the correctness of the method is verified through numerical calculation, and the influence of the mechanical property, the content and the distribution of the organic matters on the macroscopic fluid-solid coupling numerical simulation of the shale gas reservoir is analyzed.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a SEM picture of a real shale sample in which the dark portions are organic matter;
fig. 2 is a schematic diagram of an organic matter uniform distribution model and different gridding division result diagrams, wherein fig. 2a) is a schematic diagram of an ideal shale matrix model, fig. 2b is a diagram of a fine gridding division result diagram, and fig. 2c is a diagram of a coarse gridding division result diagram;
FIG. 3 is a graph of the equivalent apparent permeability of coarse grid cells of the present invention as a function of pressure;
fig. 4 is a comparison diagram of the pressure field and the displacement field after 1s simulation of the fine grid and the coarse grid, wherein fig. 4a is a diagram of the pressure field after 1s simulation of the fine grid, fig. 4b is a diagram of the pressure field after 1s simulation of the coarse grid, fig. 4c is a diagram of the y-direction displacement field after 1s simulation of the fine grid, and fig. 4d is a diagram of the y-direction displacement field after 1s simulation of the coarse grid;
FIG. 5 is a pressure and displacement comparison graph calculated by two methods under different organic matter contents, wherein FIG. 5a is a pressure variation comparison graph of an observation point along with time, and FIG. 5b is a displacement variation comparison graph of the observation point along the y direction along with time;
FIG. 6 is a shale gas reservoir model and a matrix characterization unit thereof, wherein FIG. 6a is the shale gas reservoir model, and FIG. 6b is the matrix characterization unit;
FIG. 7 is a graph of equivalent apparent permeability of matrix characterization unit bodies as a function of pressure;
FIG. 8 is a graph comparing cumulative gas production of shale gas reservoirs under different conditions;
FIG. 9 is a schematic diagram of a matrix characterization unit cell for different organic content, wherein FIG. 9a shows 0.03 organic content, FIG. 9b shows 0.086 organic content, and FIG. 9c shows 0.138 organic content;
FIG. 10 is a graph of equivalent apparent permeability of matrix characterization unit bodies of different organic matter contents as a function of pressure;
FIG. 11 is a graph comparing cumulative gas production for shale gas reservoirs with different organic matter content;
fig. 12 is a schematic diagram of matrix characterization unit bodies with different organic matter distributions, where 12a is distribution 1, 12b is distribution 2, and 12c is distribution 3;
FIG. 13 is a graph of equivalent apparent permeability of matrix characterization unit bodies with different organic matter distribution as a function of pressure;
FIG. 14 is a graph comparing cumulative gas production of shale gas reservoirs under different organic matter distributions;
FIG. 15 is a schematic flow chart of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
On a microscopic scale, organic matter is dispersedly embedded in inorganic matter, as shown in fig. 1. Assuming that both organic matters and inorganic matters meet the continuous medium hypothesis, the shale matrix is regarded as a heterogeneous porous elastic medium consisting of the organic matters and the inorganic matters, wherein only free gas exists in the inorganic matters, the migration mechanism of the gas mainly comprises viscous flow and Knudsen diffusion, the adsorption gas and the free gas simultaneously exist in the organic matters, and the migration mechanism of the gas mainly comprises viscous flow, Knudsen diffusion and surface diffusion.
Referring to fig. 1 to 15, the invention provides a shale matrix fluid-solid coupling scale upgrading method based on a homogenization theory, which comprises the following steps:
constructing a fluid-solid coupling model:
Figure BDA0002499835650000101
Figure BDA0002499835650000102
Figure BDA0002499835650000103
in the formula, σ and σsRespectively representing total stress tensor and effective stress tensor, p is pore pressure, α is Biot coefficient, I is unit tensionAn amount; c is the elasticity tensor; u. ofsIs the skeleton displacement, β represents the comprehensive compression coefficient, t represents the time, is the Crohn's symbol, phi is the porosity, mgRepresents an adsorption/desorption term; rhogIs the gas density; v is the gas flow rate; k is a radical ofaApparent permeability of gas; μ is the gas viscosity.
From the assumption of small deformation, the strain tensor e (u)s) The definition is as follows:
Figure BDA0002499835650000104
combined compressibility β and true gas density ρgThe expression of (a) is as follows:
Figure BDA0002499835650000105
in the formula, KsIs matrix skeleton bulk modulus; mgIs the gas molar mass; z represents a gas compression factor; r is a universal gas constant; t represents the reservoir temperature.
Gas adsorption/desorption term m according to Langmuir isothermal adsorptiongThe expression of (a) is as follows:
Figure BDA0002499835650000106
in the formula, ρrRepresenting the rock density; rhogstdRepresents the gas density under standard conditions; vLAnd PLIndicating the Langmuir volume and Langmuir pressure, respectively, of the organic matter.
The transport mechanisms of gases in inorganic substances are mainly viscous flow and Knudsen diffusion, the apparent permeability k of whichaiComprises the following steps:
Figure BDA0002499835650000111
the transport mechanism of gas in organic matters is mainly viscous flow, Knudsen diffusion and surface diffusion, and the apparent permeability k of the gas isakComprises the following steps:
Figure BDA0002499835650000112
in the formula (I), the compound is shown in the specification,
Figure BDA0002499835650000113
is intrinsic permeability, wherein rhAnd τ is pore radius and tortuosity, respectively; kn＝λ/reffIs the number Knudsen, where λ is the mean free path of the gas molecule, reffIs the effective radius of the pores; b is-1 is a slip coefficient; dsRepresents the surface diffusion coefficient of the adsorbed gas; cmaxAnd θ is the maximum adsorption amount of organic matter and gas coverage, respectively:
Figure BDA0002499835650000114
the heterogeneous coefficients of the shale matrix fluid-solid coupling model are respectively valued in inorganic matters and organic matters as follows:
Figure BDA0002499835650000115
in the formula, subscripts i and k represent inorganic and organic substances, respectively; dmIs the methane molecular diameter.
In the theory of homogenization, the physical quantity characteristic function depends on two different scales: one is a macro scale, which is used for representing the gradual change of a medium characteristic function on a large scale; the other is the microscopic scale, which is used to characterize the rapid oscillatory changes of the characteristic function on a small scale. The invention realizes the scale upgrading of the shale matrix fluid-solid coupling based on the homogenization theory:
consider a shale matrix of characteristic length L, consisting of a large number of periodic microscale cells of characteristic length L, incorporating the ratio between different characteristic lengths L/L. The variable sigma, u in the shale matrix fluid-solid coupling modelsV and p can be approximated by the following progressive expansion:
Figure BDA0002499835650000121
wherein y is x/and y represents a microscale coordinate; x represents a macro scale coordinate;
Figure BDA0002499835650000124
representing periodic variables with respect to coordinates x, y and time t. Furthermore, according to the chaining criterion, we get:
Figure BDA0002499835650000122
substituting equation (11) into equations (1) - (3), transforming with equation (12), and comparing coefficients of different orders in the equations.
By comparing in equation (3)-1And in equation (1)-2The coefficients of (a) can be given as:
Figure BDA0002499835650000123
from this, p is known(0)And us(0)Only on the macro scale x, independent of the micro scale y, i.e.:
p(0)＝p(0)(x,t),us(0)＝us(0)(x,t) (14)
by comparing in equation (2)-1And in equation (3)0The coefficients of (a) can be given as:
Figure BDA0002499835650000131
are respectively paired with v(0)And p(1)Carrying out separation variable analysis:
Figure BDA0002499835650000132
where ω and π are both periodic variables with respect to y. By substituting equation (16) for equation (15), the following cellular assist equation can be obtained:
Figure BDA0002499835650000133
in the formula, eiIs the unit vector of the i-direction in a cartesian coordinate system.
For v in equation (16)(0)Performing volume averaging on the cells can obtain a macroscopic seepage equation:
Figure BDA0002499835650000134
in the formula, | Ω | is the volume of the whole cell;<a>denotes the volume average, k, of the variable aequTo the equivalent apparent permeability tensor:
Figure BDA0002499835650000135
Figure BDA0002499835650000136
in comparative equation (1)-1The coefficients of (a) can be given as:
Figure BDA0002499835650000137
from this, u iss(1)The following can be written:
Figure BDA0002499835650000138
in the formula (I), the compound is shown in the specification,
Figure BDA0002499835650000141
representing an arbitrary variable independent of the coordinate y, and a periodic variable ξ associated with the coordinate ypqThe following equation is satisfied:
Figure BDA0002499835650000142
wherein, the symbol is Crohn's symbol.
In comparative equation (1)0The coefficients of (a) can be given as:
Figure BDA0002499835650000143
the equation (24) is volume-averaged over the cells, and using the divergence theorem and periodic boundary conditions, we obtain:
Figure BDA0002499835650000144
the equations are arranged according to the volume average theorem and the periodic boundary condition, so that a macroscopic stress balance equation can be obtained:
Figure BDA0002499835650000145
in the formula, equivalent elastic tensor CequAnd equivalent Biot coefficient αequAre respectively defined as follows:
Cequijkl＝<Cijkl+Cijmneymn(ξkl)>,αequ＝<α>(27)
in comparative equation (2)0The coefficients of (a) can be given as:
Figure BDA0002499835650000146
the macroscopic conservation of mass equation can be obtained by averaging the volume of equation (28) over the cells and using the divergence theorem, the volume averaging theorem, and the periodic boundary conditions:
Figure BDA0002499835650000147
wherein the equivalent integrated compression factor βequAnd equivalent adsorption/desorption term mgequAre respectively defined as follows:
Figure BDA0002499835650000151
Figure BDA0002499835650000152
in the formula, aTOCRepresenting the volume fraction of organic matter within the cell. Finally, we use subscript hm to denote subscript (0), and write the macroscopically equivalent continuous medium fluid-solid coupling model as follows:
Figure BDA0002499835650000153
Figure BDA0002499835650000154
Figure BDA0002499835650000155
it can be seen that the form of the above macroscopically equivalent continuous medium fluid-solid coupling model is consistent with equations (1) to (3), but the coefficient of the model changes due to the consideration of the existence of organic matters and inorganic matters. The cell auxiliary equations (17) and (23) are difficult to solve analytically, and the finite element method is adopted to carry out numerical solution.
The model is simulated by a finite element method based on a fine grid and a coarse grid respectively, grid division results are shown in FIGS. 2(b) and 2(c), wherein the fine grid finely describes the organic matter, the simulation result is taken as a reference solution, equivalent parameters of each coarse grid element are calculated by a scale upgrading method provided herein, and equation (23) is solved by the finite element method in combination with equation (27)The equivalent elastic tensor can be obtained as
Figure BDA0002499835650000156
The curve of the equivalent apparent permeability versus pressure for GPa is shown in FIG. 3. Fig. 4 shows the comparison of the pressure field and the y-direction displacement field after the two fields are simulated for 1s, and it can be seen that the two results are basically consistent.
Instance calculation and influence factor analysis
(1) Analysis of influence of mechanical properties of organic matter on gas production
Fig. 6(a) shows a shale gas reservoir model with a size of 100m × 100m, and it is assumed that the characterization unit volume size of the matrix is 1mm × 1mm, the organic matter content is 0.138, and the internal organic matter distribution is shown in fig. 6 (b). The gas reservoir model satisfies the plane strain assumption, the mechanical boundary conditions are shown in fig. 6(a), the flowing boundary is a closed boundary, the initial formation pressure is 20MPa, the production well is positioned at the lower left corner of the gas reservoir model, the bottom hole flowing pressure is 5MPa, and the rest model parameters are shown in table 1.
TABLE 1 shale matrix fluid-solid coupling model parameters
Table 1 The HM model parameters of shale matrix
Figure BDA0002499835650000161
In order to investigate the effect of organic mechanical properties on gas production, the present example set the organic young's modulus to 1GPa, 10GPa, and 40GPa, respectively. The equivalent parameters of the characterization unit bodies are calculated by adopting the scale upgrading method provided by the invention: the equivalent apparent permeability is shown in fig. 7; the equivalent elastic tensor is respectively
Figure BDA0002499835650000162
GPa、
Figure BDA0002499835650000163
GPa and
Figure BDA0002499835650000171
GPa. It can be seen that the substrate characterization sheet shown in FIG. 6(b) is usedThe element body and the organic matter cause weak anisotropy of the equivalent apparent permeability of the matrix, and the value of the non-principal diagonal in the equivalent apparent permeability tensor is far smaller than the value of the principal diagonal. In addition, it can be seen that the organic matter Young modulus has a great influence on the equivalent elasticity tensor of the matrix characterization unit body.
Performing macroscopic fluid-solid coupling numerical simulation on the shale gas reservoir in the figure 6(a) by adopting a finite element method according to the equivalent parameters of the characterization unit bodies obtained by calculation, and taking the influence of rock deformation on permeability into consideration by adopting the following dynamic permeability model in the simulation process
Figure BDA0002499835650000172
Wherein 0 represents an initial state, ΔvAnd Δ p represent the volume strain and the amount of change in gas pressure, respectively.
The comparison of the accumulated gas production rates calculated when the organic matter Young's modulus is measured in different values is given in FIG. 8, and it can be seen that the smaller the organic matter Young's modulus, the higher the accumulated gas production rate is, because the organic matter Young's modulus is reduced, the compressibility of the shale matrix is enhanced, and in the elastic mining process, the more the matrix porosity is reduced due to the same pressure drop, the higher the accumulated gas production rate is. In addition, it can be seen from the figure that the stress sensitivity of the shale matrix is weak, that is, the effect of the reduction of the permeability and the reduction of the accumulative gas production caused by rock deformation is not obvious, which is another reason of the increase of the accumulative gas production caused by the reduction of the Young modulus of the organic matter.
(2) Analysis of influence of organic matter content on gas production
FIG. 9 is a schematic diagram of 3 substrate characterization unit bodies with different organic matter contents, each having a size of 1mm × 1mm, organic matter contents of 0.03, 0.086 and 0.138, respectively, and the remaining model parameters shown in Table 1. the scale-up method proposed herein is used to calculate the equivalent parameters of each characterization unit body, wherein the equivalent apparent permeability in the x-direction is shown in FIG. 10, and the equivalent elastic tensors are respectively shown in FIG. 10
Figure BDA0002499835650000181
GPa、
Figure BDA0002499835650000182
GPa and
Figure BDA0002499835650000183
GPa. It can be seen that the higher the organic matter content is, the smaller the equivalent apparent permeability and equivalent elasticity tensor of the characterized unit cell are.
And (3) according to the equivalent parameters of each characterization unit body obtained by calculation, considering the influence of rock deformation on permeability, and performing macroscopic fluid-solid coupling numerical simulation on the shale gas reservoir in the figure 6 (a). The cumulative gas production calculated for different organic content is compared in fig. 11. It can be seen that the higher the organic content is, the lower the early cumulative gas production is, and the higher the later cumulative gas production is, because the increased organic content increases the gas reserve in the reservoir, but also leads to a decrease in the equivalent apparent permeability of the matrix, and the stress sensitivity of the matrix increases, because the early cumulative gas production is more affected by the apparent permeability, the higher the early cumulative gas production is, the lower the early cumulative gas production is, and the later cumulative gas production is mainly affected by the gas reserve, so the higher the organic content is, the higher the later cumulative gas production is.
(3) Analysis of influence of organic matter distribution on gas production
FIG. 12 shows schematic diagrams of 3 matrix characterization unit bodies with different organic matter distributions, wherein the sizes of the units are all 1mm × 1mm, the organic matter content is 0.138, and the model parameters are shown in Table 1
Figure BDA0002499835650000184
GPa、
Figure BDA0002499835650000185
GPa and
Figure BDA0002499835650000186
the GPa, equivalent apparent permeability is shown in fig. 13. It can be seen that the organic matter distribution is right basicThe equivalent apparent permeability and the equivalent elasticity tensor of the texture characterization unit body have great influence, and are important factors for causing the shale matrix seepage and the anisotropy of mechanical properties.
Similarly, according to the equivalent parameters of the three characterization unit bodies obtained by calculation, the influence of rock deformation on permeability is considered, and the shale gas reservoir in fig. 6(a) is subjected to macroscopic fluid-solid coupling numerical simulation. The comparison of the cumulative gas production rates calculated under different organic matter distribution conditions is given in fig. 14, and by combining the inorganic matter connectivity conditions under the three distribution conditions, it can be seen that the worse the inorganic matter connectivity, the lower the cumulative gas production rate.
The invention provides a shale matrix fluid-solid coupling scale upgrading method based on a homogenization theory, which can effectively represent respective characteristics of organic matters and inorganic matters on a microscale into macroscopic fluid-solid coupling simulation, verify the correctness of the scale upgrading method through numerical example, and analyze the influence of mechanical properties, content and distribution of the organic matters on the macroscopic fluid-solid coupling numerical simulation of a shale gas reservoir on the basis of the method.
The above-described embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solutions of the present invention can be made by those skilled in the art without departing from the spirit of the present invention, and the technical solutions of the present invention are within the scope of the present invention defined by the claims.

Claims (4)

1. A shale matrix fluid-solid coupling scale upgrading method based on a homogenization theory is characterized by comprising the following steps: the method comprises the following steps:
the shale matrix is regarded as a heterogeneous porous elastic medium consisting of organic matters and inorganic matters, and a micro-scale fluid-solid coupling model is established by considering different occurrence modes and flow mechanisms of real gas in the two media;
scale upgrading is carried out by adopting a homogenization theory to obtain a macroscopic equivalent fluid-solid coupling model of the shale matrix, and definition and calculation modes of relevant equivalent parameters are given;
the accuracy of the shale matrix fluid-solid coupling scale upgrading method based on the homogenization theory is verified, and the influence of the mechanical property, content and distribution of organic matters on the macroscopic fluid-solid coupling numerical simulation of the shale gas reservoir is analyzed.
2. The shale matrix fluid-solid coupling scale upgrading method based on the homogenization theory as claimed in claim 1, wherein: the process of constructing the micro-scale fluid-solid coupling model comprises the following steps:
Figure FDA0002499835640000011
Figure FDA0002499835640000012
Figure FDA0002499835640000013
in the formula, σ and σsRespectively representing total stress tensor and effective stress tensor, p is pore pressure, α is Biot coefficient, I is unit tensor, C is elastic tensor, u is elastic tensorsIs the skeleton displacement, β represents the comprehensive compression coefficient, t represents the time, is the Crohn's symbol, phi is the porosity, mgRepresents an adsorption/desorption term; rhogIs the gas density; v is the gas flow rate; k is a radical ofaApparent permeability of gas; μ is the gas viscosity;
from the assumption of small deformation, the strain tensor e (u)s) The definition is as follows:
Figure FDA0002499835640000014
combined compressibility β and true gas density ρgThe expression of (a) is as follows:
Figure FDA0002499835640000021
in the formula, KsIs matrix skeleton bulk modulus; mgIs the gas molar mass; z represents a gas compression factor; r is a universal gas constant; t represents reservoir temperature;
gas adsorption/desorption term m according to Langmuir isothermal adsorptiongThe expression of (a) is as follows:
Figure FDA0002499835640000022
in the formula, ρrRepresenting the rock density; rhogstdRepresents the gas density under standard conditions; vLAnd PLIndicating the Langmuir volume and Langmuir pressure, respectively, of the organic matter.
The transport mechanisms of gases in inorganic substances are mainly viscous flow and Knudsen diffusion, the apparent permeability k of whichaiComprises the following steps:
Figure FDA0002499835640000023
the transport mechanism of gas in organic matters is mainly viscous flow, Knudsen diffusion and surface diffusion, and the apparent permeability k of the gas isakComprises the following steps:
Figure FDA0002499835640000024
in the formula (I), the compound is shown in the specification,
Figure FDA0002499835640000025
is intrinsic permeability, wherein rhAnd τ is pore radius and tortuosity, respectively; kn＝λreffIs the number Knudsen, where λ is the mean free path of the gas molecule, reffIs the effective radius of the pores; b is-1 is a slip coefficient; dsRepresents the surface diffusion coefficient of the adsorbed gas; cmaxAnd θ is the maximum adsorption amount of organic matter and gas coverage, respectively:
Figure FDA0002499835640000026
the heterogeneous coefficient of the shale matrix fluid-solid coupling model is respectively valued in inorganic matters and organic matters as follows:
Figure FDA0002499835640000031
in the formula, subscripts i and k represent inorganic and organic substances, respectively; dmIs the methane molecular diameter.
3. The shale matrix fluid-solid coupling scale upgrading method based on the homogenization theory as claimed in claim 1, wherein: adopting a homogenization theory to carry out scale upgrading to obtain a macroscopic equivalent fluid-solid coupling model of the shale matrix, and giving out the definition and calculation mode of relevant equivalent parameters as follows:
considering a shale matrix with the characteristic length L, wherein the shale matrix consists of a large number of periodic micro-scale cells, the characteristic length of each micro-scale cell is L, the ratio of different characteristic lengths is introduced to be L/L, and variables sigma and u in the shale matrix fluid-solid coupling model are variable in the shale matrix fluid-solid coupling modelsV and p are approximated by the following progressive expansion:
Figure FDA0002499835640000032
wherein y is x/and y represents a microscale coordinate; x represents a macro scale coordinate;
Figure FDA0002499835640000033
representing a periodic variable with respect to coordinates x, y and time t;
according to the chaining criterion, we get:
Figure FDA0002499835640000034
substituting the equation (11) into the equations (1) to (3), converting by adopting the equation (12), and comparing coefficients of different orders in the equations;
by comparing in equation (3)-1By a factor ofAnd in equation (1)-2The coefficients of (a) yield:
Figure FDA0002499835640000035
from this, p is known(0)And us(0)Only on the macro scale x, independent of the micro scale y, i.e.:
p(0)＝p(0)(x,t),us(0)＝us(0)(x,t) (14)
by comparing in equation (2)-1And in equation (3)0The coefficients of (a) yield:
Figure FDA0002499835640000041
are respectively paired with v(0)And p(1)Carrying out separation variable analysis:
Figure FDA0002499835640000042
where ω and π are both periodic variables with respect to y;
substituting equation (16) for equation (15) yields the cell-assist equation:
Figure FDA0002499835640000043
in the formula, eiIs a unit vector of i-direction in a cartesian coordinate system;
for v in equation (16)(0)Carrying out volume averaging on the cells to obtain a macroscopic seepage equation:
Figure FDA0002499835640000044
in the formula, | Ω | is the volume of the whole cell;<a>denotes the volume average, k, of the variable aequTo the equivalent apparent permeability tensor:
Figure FDA0002499835640000045
Figure FDA0002499835640000046
in comparative equation (1)-1The coefficients of (a) yield:
Figure FDA0002499835640000047
from this, u iss(1)Comprises the following steps:
Figure FDA0002499835640000051
in the formula (I), the compound is shown in the specification,
Figure FDA0002499835640000052
representing an arbitrary variable independent of the coordinate y, and a periodic variable ξ associated with the coordinate ypqSatisfies the equation:
Figure FDA0002499835640000053
wherein, the symbol is Crohn's symbol;
in comparative equation (1)0The coefficients of (a) yield:
Figure FDA0002499835640000054
the equation (24) is volume-averaged over the cells, and using the divergence theorem and periodic boundary conditions, we obtain:
Figure FDA0002499835640000055
and (3) according to the volume average theorem and the periodic boundary condition, finishing to obtain a macroscopic stress balance equation:
Figure FDA0002499835640000056
in the formula, equivalent elastic tensor CequAnd equivalent Biot coefficient αequAre respectively defined as follows:
Cequijkl＝<Cijkl+Cijmneymn(ξkl)>,αequ＝<α>(27)
in comparative equation (2)0The coefficients of (a) yield:
Figure FDA0002499835640000057
carrying out volume averaging on the cells by using the equation (28), and obtaining a macroscopic mass conservation equation by adopting a divergence theorem, a volume averaging theorem and a periodic boundary condition:
Figure FDA0002499835640000058
wherein the equivalent integrated compression factor βequAnd equivalent adsorption/desorption term mgequAre respectively defined as follows:
Figure FDA0002499835640000061
Figure FDA0002499835640000062
in the formula, aTOCRepresenting the volume fraction of organic matter in the cells;
finally, the subscript hm is used for representing the subscript (0), and the macroscopic equivalent continuous medium fluid-solid coupling model is written into the following form:
Figure FDA0002499835640000063
Figure FDA0002499835640000064
Figure FDA0002499835640000065
。
4. the shale matrix fluid-solid coupling scale upgrading method based on the homogenization theory as claimed in claim 1, wherein: the cell assist equations (17) and (23) are numerically solved using a finite element method.
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