CN117875212A - Impact damage deep rock permeability prediction method based on equivalent aperture model - Google Patents
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Abstract
The invention discloses an impact damage deep rock permeability prediction method based on an equivalent aperture model, which constructs a micromechanics seepage model according to a superposition principle; constructing an equivalent aperture model according to the principle of a Carman-Kozeny equivalent capillary; characterizing damage to the model specimen at a microscopic angle in terms of fracture extension length; in experiments, the dissipated energy characterizes the energy expended in the rock sample for fracture propagation, and therefore, at a macroscopic angle to dissipate energy damage to the rock sample. Constructing a damage evolution model through the relation to obtain the relation between the damage and the permeability; and obtaining an equivalent permeability model according to the model and the damage relation, and giving corresponding model parameters according to working conditions, so that permeability evolution rules under different working conditions can be obtained.
Description
Technical Field
The invention belongs to the field of rock mechanics, and particularly relates to an impact damage deep rock permeability prediction method based on an equivalent aperture model.
Background
The deep rock is a rock under the coupling action of confining pressure and osmotic pressure, and simulates the high ground stress and high osmotic pressure state of the rock in the real deep stratum. Rock damage refers to the continued development of micro-cracks that exist within a rock mass under external loading, the process being rock damage, characterized in the art by crack extension length as damage to a model specimen. The rock permeability refers to the capacity of the rock for allowing water to pass through under a certain pressure difference, the rock permeability is a parameter for representing the capacity of the rock for conducting liquid, the equivalent pore diameter refers to equivalent pore diameter treatment of cracks in a micro-mechanical seepage model, so that the crack opening and closing state can represent the change of the equivalent pore diameter, the change of the permeability is represented by the change of the equivalent pore diameter, and the model obtained after the equivalent treatment is an equivalent pore diameter model.
In the existing model for researching permeability evolution, only the permeability evolution law is characterized, and the analysis of an exact numerical value is lacking or the numerical value of the permeability is difficult to calculate, so that the accuracy of the evolution model is reduced, and the permeability evolution law under a specific working condition is not sufficiently described; the other type establishes a related deduction formula of the permeability model, but the model is a three-dimensional model, the calculated amount is extremely large, the assumed conditions are extremely large and cause trouble to the calculated personnel, and some models are only suitable for specific rocks (coal rocks), so that the model applicability is low, and the simulation effect is not obvious when the assumption is not established.
The invention takes the cracks in the rock as a research object, effectively avoids the limitation on the rock category, establishes the seepage model as a micromechanics two-dimensional model, and greatly simplifies the problems by utilizing the force balance and the volume equivalent principle.
Disclosure of Invention
The invention aims to solve the technical problems in the background art and provides an impact damage deep rock permeability prediction method based on an equivalent aperture model, wherein an equivalent aperture model and a damage evolution model are firstly constructed, and on the basis, an equivalent permeability model is finally constructed by utilizing the correlation between macroscopic mechanics and micromechanics and is used for calculating rock permeability of different damage degrees under the action of confining pressure and osmotic pressure.
In order to solve the technical problems, the technical scheme of the invention is as follows:
an impact damage deep rock permeability prediction method based on an equivalent pore diameter model, the method comprising:
based on the superposition principle, constructing a micromechanics seepage model;
based on a micromechanics seepage model, constructing an equivalent aperture model according to the principle of a Carman-Kozeny equivalent capillary;
characterizing damage to the model sample by crack extension length at a microscopic angle, characterizing damage to the rock sample by dissipation energy at a macroscopic angle, and then constructing a damage evolution model to acquire the relation between the damage and the permeability;
and obtaining an equivalent permeability model based on the equivalent aperture model and the damage relation, and giving corresponding model parameters according to working conditions to obtain permeability evolution rules under different working conditions.
Further, the method takes the cracks in the rock as a research object, and builds a micromechanics seepage model according to the superposition principle, and specifically comprises the following steps:
for any cross section fracture water pressure P in the model w (x) The relation with the overall osmotic pressure delta P of the model is shown in a formula (1):
wherein P is w (x) The fracture water pressure of any cross section in the model; x is the number of cross sections, x=1, 2, 3 … … n; Δp is the difference in water pressure across the model, i.e., osmotic pressure;
using superposition principle to make confining pressure sigma 0 Confining pressure sigma 3 Water pressure P w The induced type I stress intensity factors are summed together to give the total type I stress intensity factor (equation (2)):
wherein,is sigma (sigma) 0 Stress intensity factor of type I induced to the tip of the slit, < +.>Is sigma (sigma) 3 Stress intensity factor of type I induced to the tip of the slit, < +.>Is P w For the I-type stress intensity factor and K caused by crack tip I To superimpose the stress intensity factor of type I induced by the tip of the fracture, the initial length of the fracture is 2a 0 ；
The I-type stress intensity factor of the crack tip is K I When the vertical displacement of the fracture surface at different positions from the fracture tip is v, as shown in formula (3):
wherein r is the distance from the datum point to the tip of the crack; θ is the angle between the reference line and the x-axis, where θ=180°; g=e/(2+2 v); kappa = 3-4 v; e is the elastic modulus of the sample; v is the poisson's ratio of the sample.
Further, the construction of the equivalent pore diameter model specifically comprises the following steps:
the limit length of the crack is the total length of the crack after the crack is expanded to the limit length, and the limit expansion length l of one end of the crack lim As shown in formula (4):
wherein L is the total length of the sample;
according to the equivalent aperture principle, the fracture volume is consistent with the equivalent hole volume, and the equivalent hole is a hole with uniform aperture and the length of the equivalent hole is distributed on the limit length of the fracture, as shown in the formula (5):
the left side of the equation is the fracture volume, the right side of the equation is the equivalent hole volume, wherein the equivalent hole length is the fracture limit length, and the equivalent aperture is d (x);
equation (6) is derived from equation (5):
and the formulas (1) - (4) are carried into (6) to obtain the microcosmic equivalent aperture diameter d (x), the crack expansion length l and the macroscopic confining pressure sigma in the equivalent aperture model 3 Relationship between osmotic pressure Δp, equation (7):
further, the constructing the damage evolution model specifically includes:
characterizing the damage D of the model sample by a crack extension length l, wherein when l=0, the damage of the model sample is zero; when l is extended to the limit length l lim When the damage reaches a maximum, i.e., d=1, as shown in formula (8):
in order to relate the damage evolution process of the model to the experimental process, the damage of the rock sample in the experiment needs to be characterized, and in the experiment, the energy consumed by crack expansion in the rock sample can be characterized by dissipation energy, so the damage of the rock sample can be characterized by dissipation energy, and the definition formula is shown as the formula (9):
wherein the method comprises the steps ofFor the dissipation energy consumed by the rock sample on the Nth impact, W d The related data of the two dissipation energies can be directly measured through experiments for the dissipation energy required when the complete rock sample is completely destroyed;
finally, the relation between the crack expansion length l in the model sample and the dissipation energy of the rock sample in the experiment can be obtained by using formulas (8) and (9), and the formula deduced from the damage evolution model is formula (10):
further, the equivalent permeability model specifically includes:
based on an equivalent aperture model, the osmotic pressure delta P of a model sample is obtained by using Darcy's law, and the osmotic pressure delta P is shown as a formula (11):
wherein q is the seepage flow obtained by the whole model; μ is the dynamic viscosity coefficient of the fluid; k is the equivalent permeability of the model sample; a is that e Equivalent aperture of the model sample; equivalent pore diameter A of model sample e The derived formula is as follows:
based on an equivalent pore diameter model, the osmotic pressure delta P obtained by sequentially superposing the osmotic pressures of equivalent holes along the length direction of a model sample is shown as a formula (15):
wherein q (x) is the fluid flow in the equivalent pore and k (x) is the permeability of the equivalent pore; the permeability k (x) of the equivalent pore and the equivalent pore diameter d (x) have a relation, and the relation is deduced as follows:
according to the research conclusion of David and Louis, the laminar flow of the fluid in the smooth flat plate channel accords with the cubic law of the width between the flat plates, namely the fluid flow is in direct proportion to the cubic formula of the width between the flat plates, and the method can be used for obtaining:
according to Darcy's law of seepage, can get the seepage flow calculation formula of the equivalent hole:
combining equation (16) with equation (17) yields the final k (x) and d (x) relationship, as shown in equation (18):
equation (19) is obtained by combining equation (11) with equation (15):
finally, the formula (14) and the formula (18) are brought into the formula (19), and the equivalent permeability of the final model can be deduced:
the formula (20) is an expression of d (x), an equivalent pore diameter model formula (7) and a damage evolution model formula (10) are required to be brought into the formula (20) when specific values are calculated, reasonable model parameters are selected, and rock permeability under different confining pressure, osmotic pressure and damage conditions is predicted based on an equivalent permeability calculation method.
Compared with the prior art, the invention has the advantages that:
according to the invention, by establishing a micromechanics model, the seepage property of the rock is closely related to the crack state in the rock, and the relation between the equivalent aperture and the crack expansion length is deduced; the damage led out by the crack extension length is equivalent to the damage led out by the dissipation energy, so that the relation between the crack extension length and the dissipation energy is deduced; finally, the relation between the permeability and the equivalent pore diameter and the relation between the permeability and the dissipation energy (the dissipation energy can be measured by an impact test) are deduced by utilizing the principles of Darcy's law, macro-micro mechanics principle, equivalent pore diameter principle and the like.
The invention determines that the seepage property of the rock is closely related to the state of cracks in the rock, and takes the cracks in the rock as a research object to construct a micromechanics seepage model; the method is used for researching the relation between seepage and cracks, so that the problem of limitation of model application is skillfully solved; the invention is deduced based on a two-dimensional model, has less calculation amount and less assumption conditions, greatly simplifies the calculation difficult problem and reduces errors caused by the fact that the assumption is not true or is not suitable for a specific working condition.
Drawings
FIG. 1, a micromechanics seepage model and an equivalent aperture model derivation diagram;
FIG. 2, micro-mechanical seepage model (upper), equivalent pore size model (lower);
FIG. 3, a damage evolution model derivation diagram;
FIG. 4, equivalent permeability model derivation;
fig. 5, a graph of comparative analysis of model data and experimental data.
Detailed Description
The following describes specific embodiments of the present invention with reference to examples:
it should be noted that the structures, proportions, sizes and the like illustrated in the present specification are used for being understood and read by those skilled in the art in combination with the disclosure of the present invention, and are not intended to limit the applicable limitations of the present invention, and any structural modifications, proportional changes or size adjustments should still fall within the scope of the disclosure of the present invention without affecting the efficacy and achievement of the present invention.
Also, the terms such as "upper," "lower," "left," "right," "middle," and "a" and the like recited in the present specification are merely for descriptive purposes and are not intended to limit the scope of the invention, but are intended to provide relative positional changes or modifications without materially altering the technical context in which the invention may be practiced.
Example 1:
the invention firstly builds an equivalent aperture model and a damage evolution model, and finally builds an equivalent permeability model by utilizing the correlation between macroscopic mechanics and microscopic mechanics on the basis.
The model is derived as follows:
as shown in fig. 1, a micro-mechanical seepage model is constructed by taking a crack in rock as a research object:
wherein P is w (x) Is water pressure, K I σ0 Is sigma (sigma) 0 For the I-type stress intensity factor and K caused by crack tip I σ3 Is sigma (sigma) 3 For the I-type stress intensity factor and K caused by crack tip I Pw Is P w For the I-type stress intensity factor and K caused by crack tip I The stress intensity factor of the type I caused by the tip of the crack after superposition is given, and v is the vertical displacement of the crack surface at different positions from the tip of the crack; g=e/(2+2 v); kappa = 3-4 v; e is the elastic modulus of the sample; v is the poisson's ratio of the sample.
Sigma is added by using superposition principle 0 、σ 3 、P w The induced type I stress intensity factors are added together to give a total type I stress intensity factor (equation (2));
then combining the equivalent aperture model to obtain the vertical displacement v (formula (3)) and the crack limit extension length l lim (equation (4)); as shown in fig. 2, the upper graph is a micromechanical percolation model, and the lower graph is an equivalent pore size model.
Then, the fissure volume is equal to the equivalent hole volume to obtain a formula (5), a basic expression (formula (6)) of the equivalent pore diameter is further obtained, and then (1) - (4) are brought into the formula (6), so that a final expression (7) of the equivalent pore diameter is obtained;
from here on the equivalent aperture d (x) and the confining pressure sigma are represented by the expression of formula (7) 3 Relationship between osmotic pressure Δp and fracture expansion length/.
As shown in fig. 3, a model of the evolution of the damage is next constructed. The invention introduces parameters(the dissipated energy consumed by the rock sample at the Nth impact), W d (the dissipated energy required when a complete rock sample is fully destroyed), the data relating to both of these dissipated energies can be measured directly by experimentation; and defining the damage degree as D, wherein the damage degree is the ratio of crack extension length or the dissipation energy consumed by the rock sample in the N-th impact is compared with the dissipation energy required by the complete rock sample when the complete rock sample is completely damaged (formulas (8) and (9)), and finally, obtaining an expression of crack extension length l by using the equality of formulas (8) and (9), wherein a formula derived from the damage evolution model is formula (10).
As shown in fig. 4, the equivalent permeability model is finally derived. The invention is based on an equivalent aperture model, which is obtained by sequentially superposing osmotic pressures of equivalent holes along the length direction of a model sampleThe osmotic pressure is equal to the osmotic pressure Δp of the model sample obtained by darcy's law (i.e., formula (11) =formula (15)), and the basic expression of k is obtained (formula (19)); due to A in the expression e With k (x) not known, the invention uses the equivalent hole volume of the model sample and the equivalent hole volume of each cross section to lead out the formula (12), and the equations (12) (13) are combined to obtain A e In order to solve the expression of k (x), the invention refers to the research conclusion of David and Louis on the equivalent hole seepage flow (formula (16)), solves the equivalent hole seepage flow calculation formula (17)) by using Darcy's law, and combines the formula (16) and the formula (17) to obtain the expression of k (x) (formula (18)). Will A e The expression of k (x) is taken into equation (19), and finally an equivalent permeability model (equation (20)) can be derived.
Note that: equation (20) is an expression for d (x), and the equivalent pore diameter model (equation (7)) and the damage evolution model (equation (10)) need to be brought into equation (20) when calculating a specific value.
Example 2:
reasonable model data were selected as shown in table 1:
TABLE 1 model parameters
The above model parameters are taken into a seepage model, corresponding working condition parameters such as confining pressure, osmotic pressure and damage are given, so that permeability evolution rules under different working conditions are obtained, permeability data deduced by the model are listed in table 2, the units of the permeability data in the table are md, and the model data and experimental data are subjected to comparative analysis, and the permeability evolution rules deduced by the model are well matched with the rules measured by the experiment, as shown in the following figure 5.
While the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the above embodiments, and various changes may be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Many other changes and modifications may be made without departing from the spirit and scope of the invention. It is to be understood that the invention is not to be limited to the specific embodiments, but only by the scope of the appended claims.
Claims (5)
1. An impact damage deep rock permeability prediction method based on an equivalent aperture model, which is characterized by comprising the following steps:
based on the superposition principle, constructing a micromechanics seepage model;
based on a micromechanics seepage model, constructing an equivalent aperture model according to the principle of a Carman-Kozeny equivalent capillary;
characterizing damage to the model sample by crack extension length at a microscopic angle, characterizing damage to the rock sample by dissipation energy at a macroscopic angle, and then constructing a damage evolution model to acquire the relation between the damage and the permeability;
and obtaining an equivalent permeability model based on the equivalent aperture model and the damage relation, and giving corresponding model parameters according to working conditions to obtain permeability evolution rules under different working conditions.
2. The method for predicting the permeability of the impact damage deep rock based on the equivalent aperture model according to claim 1, which is characterized by taking cracks in the rock as a research object and constructing a micromechanics seepage model according to a superposition principle, and specifically comprises the following steps:
for any cross section fracture water pressure P in the model w (x) The relation with the overall osmotic pressure delta P of the model is shown in a formula (1):
wherein P is w (x) The fracture water pressure of any cross section in the model; x is the number of cross sections, x=1, 2, 3 … … n; Δp is the difference in water pressure across the model, i.e., osmotic pressure;
by utilizing the principle of superposition,will enclose the pressure sigma 0 Confining pressure sigma 3 Water pressure P w The induced type I stress intensity factors are summed together to give the total type I stress intensity factor (equation (2)):
wherein,is sigma (sigma) 0 Stress intensity factor of type I induced to the tip of the slit, < +.>Is sigma (sigma) 3 Stress intensity factor of type I induced to the tip of the slit, < +.>Is P w For the I-type stress intensity factor and K caused by crack tip I To superimpose the stress intensity factor of type I induced by the tip of the fracture, the initial length of the fracture is 2a 0 ；
The I-type stress intensity factor of the crack tip is K I When the vertical displacement of the fracture surface at different positions from the fracture tip is v, as shown in formula (3):
wherein r is the distance from the datum point to the tip of the crack; θ is the angle between the reference line and the x-axis, where θ=180°; g=e/(2+2 v); kappa = 3-4 v; e is the elastic modulus of the sample; v is the poisson's ratio of the sample.
3. The method for predicting the permeability of the impact damage deep rock based on the equivalent pore size model as set forth in claim 1, wherein the constructing the equivalent pore size model specifically includes:
the limit length of the crack is the total length of the crack after the crack is expanded to the limit length, and the limit expansion length l of one end of the crack lim As shown in formula (4):
wherein L is the total length of the sample;
according to the equivalent aperture principle, the fracture volume is consistent with the equivalent hole volume, and the equivalent hole is a hole with uniform aperture and the length of the equivalent hole is distributed on the limit length of the fracture, as shown in the formula (5):
the left side of the equation is the fracture volume, the right side of the equation is the equivalent hole volume, wherein the equivalent hole length is the fracture limit length, and the equivalent aperture is d (x);
equation (6) is derived from equation (5):
and the formulas (1) - (4) are carried into (6) to obtain the microcosmic equivalent aperture diameter d (x), the crack expansion length l and the macroscopic confining pressure sigma in the equivalent aperture model 3 Relationship between osmotic pressure Δp, equation (7):
4. the method for predicting the permeability of the impact damage deep rock based on the equivalent aperture model according to claim 1, wherein the constructing the damage evolution model specifically comprises:
characterizing the damage D of the model sample by a crack extension length l, wherein when l=0, the damage of the model sample is zero; when l is extended to the limit length l lim When the damage reaches a maximum, i.e., d=1, as shown in formula (8):
characterization of damage to a rock sample in an experiment, the dissipation energy characterizes the energy consumed by fracture expansion in the rock sample, and therefore, the damage to the rock sample is characterized by the dissipation energy, and the definition formula is shown in formula (9):
wherein the method comprises the steps ofFor the dissipation energy consumed by the rock sample on the Nth impact, W d The dissipated energy required when a complete rock sample is completely destroyed;
finally, the relation between the crack expansion length l in the model sample and the dissipation energy of the rock sample in the experiment can be obtained by using formulas (8) and (9), and the formula deduced from the damage evolution model is formula (10):
5. the method for predicting the permeability of impact damage deep rock based on the equivalent pore diameter model as claimed in claim 1, wherein the equivalent permeability model specifically comprises the following steps:
based on an equivalent aperture model, the osmotic pressure delta P of a model sample is obtained by using Darcy's law, and the osmotic pressure delta P is shown as a formula (11):
wherein q is the seepage flow obtained by the whole model; μ is the dynamic viscosity coefficient of the fluid; k is the equivalent permeability of the model sample; a is that e Equivalent aperture of the model sample; equivalent pore diameter A of model sample e The derived formula is as follows:
based on an equivalent pore diameter model, the osmotic pressure delta P obtained by sequentially superposing the osmotic pressures of equivalent holes along the length direction of a model sample is shown as a formula (15):
wherein q (x) is the fluid flow in the equivalent pore and k (x) is the permeability of the equivalent pore; the permeability k (x) of the equivalent pore and the equivalent pore diameter d (x) have a relation, and the relation is deduced as follows:
according to the research conclusion of David and Louis, the laminar flow of the fluid in the smooth flat plate channel accords with the cubic law of the width between the flat plates, namely the fluid flow is in direct proportion to the cubic formula of the width between the flat plates, and the method can be used for obtaining:
according to Darcy's law of seepage, can get the seepage flow calculation formula of the equivalent hole:
combining equation (16) with equation (17) yields the final k (x) and d (x) relationship, as shown in equation (18):
equation (19) is obtained by combining equation (11) with equation (15):
finally, the formula (14) and the formula (18) are brought into the formula (19), and the equivalent permeability of the final model can be deduced:
the formula (20) is an expression of d (x), an equivalent pore diameter model formula (7) and a damage evolution model formula (10) are required to be brought into the formula (20) when specific values are calculated, reasonable model parameters are selected, and rock permeability under different confining pressure, osmotic pressure and damage conditions is predicted based on an equivalent permeability calculation method.
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