CN114048640B - Method for evaluating shale microcosmic fracture development degree based on nanoindentation experiment - Google Patents

Method for evaluating shale microcosmic fracture development degree based on nanoindentation experiment Download PDF

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CN114048640B
CN114048640B CN202210034397.0A CN202210034397A CN114048640B CN 114048640 B CN114048640 B CN 114048640B CN 202210034397 A CN202210034397 A CN 202210034397A CN 114048640 B CN114048640 B CN 114048640B
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杨柳
张子涵
孟思炜
左建平
何剑英
徐红超
夏东岳
王建淇
何满潮
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China University of Mining and Technology Beijing CUMTB
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Abstract

The invention discloses a method for evaluating shale microfracture development degree based on a nanoindentation experiment. Firstly, carrying out a nano indentation experiment, and drawing a fitting curve and a theoretical curve of H/Er and Ue/Ut according to the obtained related data; calculating the vertical distance from the indentation point to the theoretical curve and the average value of the vertical distance; and calculating a first evaluation value; then, calculating a second evaluation value according to the slope of the fitting curve and the slope of the theoretical curve; then calculating the average value of the vertical distances within the threshold range, and calculating a third evaluation value; and finally, calculating a fracture development degree evaluation value according to the three evaluation values, and evaluating the shale micro fracture development degree, wherein the larger the fracture development degree evaluation value is, the better the shale micro fracture development degree is. The method solves the problems that the internal crack observation means is complex, the period is long and the in-situ monitoring is difficult in the existing nano indentation technology, and the internal crack of the sample can be evaluated only by acquiring displacement load data through an in-situ indentation experiment.

Description

Method for evaluating shale microcosmic fracture development degree based on nanoindentation experiment
Technical Field
The invention relates to the technical field of soil layer or rock drilling, in particular to a method for evaluating the development degree of shale microcracks based on a nanoindentation experiment.
Background
Shale oil gas is an important unconventional energy source, and can greatly improve the energy supply structure of the world. The reservoir structure and mechanical properties play a crucial role in the efficient exploitation of shale oil and gas.
At present, the research on shale reservoir structure and mechanical properties is generally completed by taking cores to prepare shale samples to perform indoor experiments and micro-nano indentation mechanical testing technology. However, in actual operation, due to unstable chemical and physical properties of shale and development of natural fractures and fissures, the shale is very easy to break and argillize during coring, and the quality is difficult to ensure, so that laboratory mechanical experiments under conventional scales are difficult to develop, and reservoir structure and mechanical property researches cannot be smoothly completed. In addition, the laboratory scale test belongs to a destructive test, the sample is difficult to be recycled, and the utilization value of the sample is reduced; and the laboratory scale test cycle is long, the price is expensive, and the cost is high.
The micro-nano indentation mechanical testing technology is particularly suitable for testing samples such as rock debris, and parameters such as the elastic modulus, the hardness, the fracture toughness and the strength of the rock can be measured by means of loading and unloading of a pressure head on a micro area. In recent years, micro-nano indentation mechanical testing technology, as a testing method for obtaining material micro-physical mechanical properties, has the advantages of simple operation, low cost, high accuracy, less sample consumption, reusability and the like, and is widely applied to research of micro rock mechanics. However, after the nano indentation technique is used for mechanical experiments, if the fracture development condition of the experimental sample is further known, the fracture development characteristics of the sample are determined by the form of a displacement load curve or a series of microscopic observation means including a field emission Scanning Electron Microscope (SEM), a micro-nano electronic Computed Tomography (CT), and the like for auxiliary identification. However, in most cases, only a small portion of the cracks will cause the loading inrush phenomenon in the image due to fracture, the existence of most of the cracks will not cause the curve to change greatly, and the apparent mechanical properties of low hardness and low elastic modulus are similar to clay, so it is often difficult to directly judge the crack development degree of the sample through the curve form and the mechanical parameters. And the microscopic observation means has high cost and long period in the actual operation process, and is difficult to meet the requirements of completing analysis in a short time and even in-situ real-time monitoring.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides the following technical scheme.
The invention provides a method for evaluating the development degree of shale microcracks based on a nanoindentation experiment, which comprises the following steps of:
performing a nano indentation experiment, drawing a fitting curve and a theoretical curve of H/Er and Ue/Ut according to related data obtained by the nano indentation experiment, and calculating the slope of the fitting curve and the slope of the theoretical curve; wherein Er is elastic modulus, H is contact hardness, Ue is elastic energy, and Ut is total energy;
calculating the vertical distance from the indentation point to the theoretical curve in the nano indentation experiment
Figure 615063DEST_PATH_IMAGE001
And average value thereof
Figure 1045DEST_PATH_IMAGE002
；
The first evaluation value is calculated using the following formula
Figure 515203DEST_PATH_IMAGE003
：
Figure 831784DEST_PATH_IMAGE004
In the formula (I), the compound is shown in the specification,
Figure 957740DEST_PATH_IMAGE005
is a vertical distance in
Figure 514624DEST_PATH_IMAGE006
The number of the indentation points in the interval,
Figure 703028DEST_PATH_IMAGE007
is a vertical distance in
Figure 636349DEST_PATH_IMAGE008
The number of the indentation points in the interval,
Figure 538184DEST_PATH_IMAGE009
the total number of the indentation points is,
Figure 452919DEST_PATH_IMAGE010
is a vertical distance less than
Figure 879352DEST_PATH_IMAGE002
The probability of the occurrence of the indentation point of (c),
Figure 600053DEST_PATH_IMAGE011
、
Figure 264383DEST_PATH_IMAGE012
、
Figure 677916DEST_PATH_IMAGE013
is a constant;
calculating a second evaluation value according to the slope of the fitting curve and the slope of the theoretical curve
Figure 591645DEST_PATH_IMAGE014
；
Calculating an average of vertical distances within a threshold range
Figure 335610DEST_PATH_IMAGE015
；
The third evaluation value is calculated using the following formula
Figure 697190DEST_PATH_IMAGE016
：
Figure 501198DEST_PATH_IMAGE017
In the formula (I), the compound is shown in the specification,
Figure 698962DEST_PATH_IMAGE018
、
Figure 246618DEST_PATH_IMAGE019
is a constant;
calculating a fracture development degree evaluation value according to the first evaluation value, the second evaluation value and the third evaluation value;
and evaluating the shale micro-fracture development degree according to the fracture development degree evaluation value, wherein the larger the fracture development degree evaluation value is, the better the shale micro-fracture development degree is.
Preferably, the relevant data obtained by the nanoindentation experiment include: load and displacement data.
Preferably, the drawing of the fitting curve and the theoretical curve of H/Er and Ue/Ut comprises the following steps:
respectively calculating Ue, Ut, H and Er according to the load and displacement data;
drawing a fitting curve of H/Er and Ue/Ut according to the calculation result;
and drawing a theoretical curve of H/Er and Ue/Ut according to the pressure head type or equivalent angle of the nano indentation experiment.
Preferably, the calculating Ue, Ut, H, Er according to the load and displacement data includes:
h, Er is calculated using the following formula:
Figure 180813DEST_PATH_IMAGE020
Figure 608252DEST_PATH_IMAGE021
Figure 496574DEST_PATH_IMAGE022
Figure 113500DEST_PATH_IMAGE023
Figure 980831DEST_PATH_IMAGE024
wherein S represents contact stiffness, hc is contact depth, h is displacement depth, hmax is maximum depth, p is load, Pmax is maximum load,
Figure 392221DEST_PATH_IMAGE025
is a parameter related to geometry and is constant, Ac is the contact area;
drawing a displacement-load curve according to the load and the displacement data;
and calculating Ue and Ut according to the displacement-load curve.
Preferably, the first and second electrodes are formed of a metal,
Figure 548264DEST_PATH_IMAGE011
the concentration of the carbon dioxide is selected to be 0.0068,
Figure 437723DEST_PATH_IMAGE012
the concentration of the active carbon is selected to be 0.0098,
Figure 845046DEST_PATH_IMAGE013
is chosen as 0.01638.
Preferably, the
Figure 614288DEST_PATH_IMAGE010
The preparation method comprises the following steps:
statistical vertical distance less than
Figure 992048DEST_PATH_IMAGE001
Probability of occurrence of indentation point of
Figure 622881DEST_PATH_IMAGE026
Drawing
Figure 894766DEST_PATH_IMAGE001
And
Figure 647958DEST_PATH_IMAGE026
the relationship curve of (1);
in that
Figure 981857DEST_PATH_IMAGE001
And
Figure 213118DEST_PATH_IMAGE026
in the relationship of (A), according to
Figure 316072DEST_PATH_IMAGE002
To obtain
Figure 974586DEST_PATH_IMAGE010
。
Preferably, the second evaluation value
Figure 343251DEST_PATH_IMAGE027
Calculated according to the following formula:
Figure 689787DEST_PATH_IMAGE028
in the formula (I), the compound is shown in the specification,
Figure 460297DEST_PATH_IMAGE029
in order to fit the slope of the curve,
Figure 555292DEST_PATH_IMAGE030
the slope of the theoretical curve.
Preferably, the calculating averages the vertical distances within a threshold range
Figure 660520DEST_PATH_IMAGE015
The method comprises the following steps:
to be provided with
Figure 702426DEST_PATH_IMAGE031
Is a polar angle variable, the first
Figure 61863DEST_PATH_IMAGE032
Perpendicular distance of indentation point to theoretical curve
Figure 577027DEST_PATH_IMAGE033
Is a variation of the pole diameter
Figure 451442DEST_PATH_IMAGE034
In a polar diagram of (a), wherein,
Figure 93776DEST_PATH_IMAGE009
the total number of the indentation points is,
Figure 573299DEST_PATH_IMAGE035
，
Figure 10096DEST_PATH_IMAGE036
；
in the polar diagram, to
Figure 824337DEST_PATH_IMAGE037
For rounding radii, calculating all points falling within the circle
Figure 739204DEST_PATH_IMAGE033
Average value of (2)
Figure 73233DEST_PATH_IMAGE015
。
Preferably, the first and second electrodes are formed of a metal,
Figure 680932DEST_PATH_IMAGE038
、
Figure 982469DEST_PATH_IMAGE039
the values of (a) are obtained as follows:
selecting indentation points corresponding to the vertical distance within the threshold range to perform a numerical simulation nano indentation experiment, and fitting according to experimental data to obtain:
Figure 701026DEST_PATH_IMAGE040
in the formula, Depth is from the geometric center of a crack to a sample in a numerical simulation nanoindentation experimentThe distance of the upper boundary, displametmax, represents the maximum displacement of the indenter in the numerical simulation nanoindentation experiment,
Figure 951879DEST_PATH_IMAGE041
are coefficients.
Preferably, the crack development degree evaluation value is calculated according to the following formula:
Figure 730479DEST_PATH_IMAGE042
in the formula (I), the compound is shown in the specification,
Figure 270045DEST_PATH_IMAGE043
and evaluating the crack development degree.
The invention has the beneficial effects that: the method for evaluating the shale microfracture development degree based on the nanoindentation experiment comprises the steps of firstly, conducting the nanoindentation experiment, obtaining a fitting curve and a theoretical curve by utilizing relevant data of the nanoindentation experiment, calculating the vertical distance between an indentation point and the theoretical curve and the average value of the vertical distance, counting the number and the probability of the indentation point under various development degrees of a fracture, and calculating a first evaluation value and a second evaluation value; then obtaining the relation between the vertical distance and the distance from the geometric center of the crack to the upper boundary of the sample through a numerical simulation nanoindentation experiment, and calculating a third evaluation value; and finally, obtaining a fracture development degree evaluation value by utilizing the three evaluation values, and evaluating the shale microcosmic fracture development degree according to the size of the fracture development degree evaluation value. The method solves the problems that the observation means of the internal crack is complex, the period is long and the in-situ monitoring is difficult in the existing nano indentation technology, and particularly under the condition that the in-situ state can not directly observe and evaluate the inside, the displacement load data can be obtained only through the in-situ indentation experiment, so that the internal crack of the sample can be evaluated, and the development degree of the internal crack of the sample can be obtained.
Drawings
FIG. 1 is a schematic flow chart of a method for evaluating shale microfracture development degree based on a nanoindentation experiment according to the present invention;
FIG. 2 is a schematic diagram of a nanoindentation experiment described herein;
FIG. 3 is a schematic diagram of the dot matrix distribution of the indentation points according to the present invention;
FIG. 4 is a schematic view of a displacement-load curve according to the present invention;
FIG. 5 shows a sample I of the present invention
Figure 41561DEST_PATH_IMAGE001
And
Figure 84603DEST_PATH_IMAGE026
the relationship curve of (1);
FIG. 6 shows a sample No. two of the present invention
Figure 34105DEST_PATH_IMAGE001
And
Figure 795387DEST_PATH_IMAGE026
the relationship curve of (1);
FIG. 7a is a schematic representation of the present invention
Figure 370594DEST_PATH_IMAGE044
A polar coordinate graph of (a);
FIG. 7b is an enlarged view of the annular region of the polar diagram of FIG. 7 a;
FIG. 8 is a schematic diagram of the meaning of Depth in the numerically simulated nanoindentation experiment described herein;
FIG. 9 shows Depth/displayementmax and Depth/displayementmax obtained by the numerical simulation nanoindentation experiment described in the present invention
Figure 533722DEST_PATH_IMAGE001
The relationship curve of (1);
FIG. 10 is a schematic SEM analysis of a sample of the present invention at a different location;
FIG. 11 is a schematic view of SEM analysis images of two different positions of a sample according to the present invention.
Detailed Description
In order to better understand the technical solution, the technical solution will be described in detail with reference to the drawings and the specific embodiments.
The method provided by the invention can be implemented in the following terminal environment, and the terminal can comprise one or more of the following components: a processor, a memory, and a display screen. Wherein the memory has stored therein at least one instruction that is loaded and executed by the processor to implement the methods described in the embodiments described below.
A processor may include one or more processing cores. The processor connects various parts within the overall terminal using various interfaces and lines, performs various functions of the terminal and processes data by executing or executing instructions, programs, code sets, or instruction sets stored in the memory, and calling data stored in the memory.
The Memory may include a Random Access Memory (RAM) or a Read-Only Memory (ROM). The memory may be used to store instructions, programs, code sets, or instructions.
The display screen is used for displaying user interfaces of all the application programs.
In addition, those skilled in the art will appreciate that the above-described terminal configurations are not intended to be limiting, and that the terminal may include more or fewer components, or some components may be combined, or a different arrangement of components. For example, the terminal further includes a radio frequency circuit, an input unit, a sensor, an audio circuit, a power supply, and other components, which are not described herein again.
Example one
As shown in fig. 1, an embodiment of the present invention provides a method for evaluating a shale microfracture development degree based on a nanoindentation experiment, including:
s101, performing an in-situ nano indentation experiment, drawing a fitting curve and a theoretical curve of H/Er and Ue/Ut according to related data obtained by the nano indentation experiment, and calculating the slope of the fitting curve and the slope of the theoretical curve; wherein Er is elastic modulus, H is contact hardness, Ue is elastic energy, and Ut is total energy;
s102, calculating the indentation point to in the nano indentation experimentVertical distance of the theoretical curve
Figure 654125DEST_PATH_IMAGE001
And average value thereof
Figure 168283DEST_PATH_IMAGE002
；
S103, calculating a first evaluation value by using the following formula
Figure 750443DEST_PATH_IMAGE045
：
Figure 768077DEST_PATH_IMAGE004
In the formula (I), the compound is shown in the specification,
Figure 324961DEST_PATH_IMAGE005
is a vertical distance in
Figure 310103DEST_PATH_IMAGE006
The number of the indentation points in the interval,
Figure 977845DEST_PATH_IMAGE007
is a vertical distance in
Figure 646723DEST_PATH_IMAGE008
The number of the indentation points in the interval,
Figure 374508DEST_PATH_IMAGE009
the total number of the indentation points is,
Figure 784630DEST_PATH_IMAGE010
is a vertical distance less than
Figure 990483DEST_PATH_IMAGE002
The probability of the occurrence of the indentation point of (c),
Figure 717131DEST_PATH_IMAGE011
、
Figure 865084DEST_PATH_IMAGE012
、
Figure 309972DEST_PATH_IMAGE013
is a constant;
s104, calculating a second evaluation value according to the slope of the fitting curve and the slope of the theoretical curve
Figure 319516DEST_PATH_IMAGE027
；
S105, calculating the average value of the vertical distance within the threshold value range
Figure 431829DEST_PATH_IMAGE015
；
S106, calculating a third evaluation value by the following formula
Figure 485104DEST_PATH_IMAGE046
：
Figure 479605DEST_PATH_IMAGE017
In the formula (I), the compound is shown in the specification,
Figure 27261DEST_PATH_IMAGE038
、
Figure 994080DEST_PATH_IMAGE039
is a constant;
s107, calculating a fracture development degree evaluation value according to the first evaluation value, the second evaluation value and the third evaluation value;
and S108, evaluating the shale micro-fracture development degree according to the fracture development degree evaluation value, wherein the larger the fracture development degree evaluation value is, the better the shale micro-fracture development degree is.
In step S101, an in-situ nanoindentation experiment is first performed. Specifically, in a preferred embodiment, the nanoindentation experiment is conducted using a method in which h isfResidual depth (as can be seen in fig. 2): in rock samplesAnd selecting a square lattice (as shown in figure 3) on the surface of the product, and performing a nano indentation experiment. The load initially increased linearly at a loading rate of 200 μ N/s, and after reaching a maximum load of 998 μ N, the load was held for 2s, at which time the penetration depth reached a maximum. After that, the indenter starts to unload at a rate of 200 μ N/s, and after leaving the surface, the surface deformation will recover to a certain extent due to the simultaneous existence of elasticity and plasticity of the rock, and finally an indentation smaller than the maximum indentation depth is formed. In the process, the sensor records real-time data of the displacement and the load in the process in real time.
In another preferred embodiment, before placing the rock sample in the nanoindentation testing apparatus for testing, the method may further include: the shale samples were first processed by cutting the samples into appropriate pieces (about 10 mm x 3 mm), selecting the section to be polished, and sanding them with coarse to fine sandpaper. And then fixing the sample on a polishing instrument, and polishing by using a high-energy argon ion beam to polish the roughness of the loading surface to a micron level.
After the nanoindentation experiment is performed to obtain real-time data of displacement and load, H, Er can be calculated by using the following formula:
Figure 968989DEST_PATH_IMAGE020
Figure 903316DEST_PATH_IMAGE021
Figure 254663DEST_PATH_IMAGE022
Figure 810409DEST_PATH_IMAGE023
Figure 221799DEST_PATH_IMAGE024
wherein S represents contact stiffness, hc is contact depth, h is displacement depth, hmax is maximum depth, p is load, Pmax is maximum load, ε is a parameter related to geometry and is a constant, and Ac is contact area;
the displacement-load curve (as shown in FIG. 4) is plotted from the load and displacement data, such as in one embodiment, two 200X 200 μm samples on the surface2The area (2) is provided with a 5 x 5 lattice, and respective P-h curves of 50 effective points are obtained.
In the displacement-load curve shown in fig. 4, the area of the curved trapezoid abcd is Up, the area of cde is Ue, the area of the curved trapezoid abce is Ut, and Ut = Ue + Up.
After Ue, Ut, H and Er are obtained through calculation according to the method, fitting curves of H/Er and Ue/Ut are drawn, and a direct proportion function is fitted according to the curves
Figure 377843DEST_PATH_IMAGE047
Wherein, in the step (A),
Figure 267301DEST_PATH_IMAGE048
the slope (scaling factor) of the fitted curve.
Drawing a theoretical curve of H/Er and Ue/Ut according to the indenter type or the equivalent angle of the nanoindentation experiment, wherein the slope (proportionality coefficient) u of the theoretical curve2Is composed of
Figure 208713DEST_PATH_IMAGE049
(wherein,
Figure 322162DEST_PATH_IMAGE050
in order to obtain the head poisson ratio,
Figure 716234DEST_PATH_IMAGE045
indenter angle for nanoindentation experiments).
Step S102 is executed, firstly, a perpendicular line is drawn from the indentation point in the nano indentation experiment to the theoretical curve, and the length of the perpendicular line segment is calculated to obtain the indentationPerpendicular distance of the trace point from the theoretical curve
Figure 658651DEST_PATH_IMAGE001
. The average of the perpendicular distances of all indentation points to the theoretical curve is then calculated
Figure 454569DEST_PATH_IMAGE002
。
Step S103 is executed, and the total number of the indentation points is counted
Figure 942182DEST_PATH_IMAGE009
At a vertical distance of
Figure 823551DEST_PATH_IMAGE051
Number of impression points within interval
Figure 304079DEST_PATH_IMAGE005
And a vertical distance is
Figure 954503DEST_PATH_IMAGE008
Number of impression points within interval
Figure 878597DEST_PATH_IMAGE007
Wherein, in the step (A),
Figure 247262DEST_PATH_IMAGE011
、
Figure 531481DEST_PATH_IMAGE052
is constant and can be obtained empirically.
Figure 833150DEST_PATH_IMAGE005
The number of indentation points where the crack is small can be represented,
Figure 928145DEST_PATH_IMAGE007
the number of points of indentation where the crack is large can be indicated. In the embodiment of the present invention, it is,
Figure 784105DEST_PATH_IMAGE011
preferably, the concentration of the compound is 0.0068,
Figure 357169DEST_PATH_IMAGE052
preferably 0.0098. Namely counting the number of the indentation points with the vertical distance within the interval (0.0068, 0.0098) (d is more than 0.0068 and less than 0.0098)
Figure 231453DEST_PATH_IMAGE005
And the number of impression points with vertical distance in the interval (0.0098, ∞) (0.0098 < d)
Figure 231770DEST_PATH_IMAGE007
。
Statistical vertical distance less than
Figure 575027DEST_PATH_IMAGE001
Probability of occurrence of indentation point of
Figure 951781DEST_PATH_IMAGE026
And drawing
Figure 680572DEST_PATH_IMAGE001
And
Figure 117369DEST_PATH_IMAGE026
the relationship curve of (1);
in that
Figure 682343DEST_PATH_IMAGE001
And
Figure 597209DEST_PATH_IMAGE026
in the relationship of (A), according to
Figure 993555DEST_PATH_IMAGE002
To obtain
Figure 850522DEST_PATH_IMAGE010
。
For example, in the embodiment of the present invention, obtained
Figure 902792DEST_PATH_IMAGE001
And
Figure 621349DEST_PATH_IMAGE026
as shown in FIGS. 5 and 6, and then according to the relationship
Figure 447702DEST_PATH_IMAGE002
To obtain
Figure 475570DEST_PATH_IMAGE010
. Specifically, FIG. 5 is of rock sample one
Figure 15136DEST_PATH_IMAGE001
And
Figure 537384DEST_PATH_IMAGE026
according to the curve and the relation of sample one
Figure 846005DEST_PATH_IMAGE002
: 0.01995 to obtain
Figure 44774DEST_PATH_IMAGE010
0.63636; FIG. 6 shows a sample II of rock
Figure 602795DEST_PATH_IMAGE001
And
Figure 928734DEST_PATH_IMAGE026
according to the relation between the curve and the sample two
Figure 91862DEST_PATH_IMAGE002
: 0.011755 to obtain
Figure 212265DEST_PATH_IMAGE010
Is 0.67347.
After obtaining the values of the parameters, the first evaluation value can be calculated by the following formula
Figure 975690DEST_PATH_IMAGE053
：
Figure 839741DEST_PATH_IMAGE004
Wherein the content of the first and second substances,
Figure 526550DEST_PATH_IMAGE054
is a constant. In the embodiment of the present invention, the first and second substrates,
Figure 83433DEST_PATH_IMAGE054
preferably 0.01638.
As can be seen from the above calculation formula of the first evaluation value,
Figure 553729DEST_PATH_IMAGE053
the larger the value of (A), the better the crack development.
In step S104, the second evaluation value may be calculated according to the following formula
Figure 205159DEST_PATH_IMAGE027
：
Figure 546141DEST_PATH_IMAGE028
In the formula (I), the compound is shown in the specification,
Figure 273926DEST_PATH_IMAGE029
in order to fit the slope of the curve,
Figure 316723DEST_PATH_IMAGE030
the slope of the theoretical curve.
According to the formula, it can be known that,
Figure 53735DEST_PATH_IMAGE027
the larger the value, the better the crack development.
In step S105, a threshold range is set, the vertical distances within the threshold range are counted, and the average value of the vertical distances within the threshold range is calculated
Figure 45961DEST_PATH_IMAGE015
. The method can be specifically implemented as follows:
to be provided with
Figure 131598DEST_PATH_IMAGE031
Is a polar angle variable, the first
Figure 842065DEST_PATH_IMAGE032
Perpendicular distance of indentation point to theoretical curve
Figure 117188DEST_PATH_IMAGE033
Is a variation of the pole diameter
Figure 416452DEST_PATH_IMAGE055
In a polar diagram of (a), wherein,
Figure 486039DEST_PATH_IMAGE009
the total number of the indentation points is,
Figure 418223DEST_PATH_IMAGE035
，
Figure 231458DEST_PATH_IMAGE036
；
in the polar diagram, to
Figure 447545DEST_PATH_IMAGE037
For rounding radii, calculating all points falling within the circle
Figure 422454DEST_PATH_IMAGE033
Average value of (2)
Figure 904251DEST_PATH_IMAGE015
。
Wherein a radius of a circle in the polar diagram
Figure 255598DEST_PATH_IMAGE037
Namely is providedA set threshold range. The vertical distance within the threshold is that corresponding to all points falling within the circle
Figure 76923DEST_PATH_IMAGE033
. In one embodiment of the present invention, the polar diagram and the circular ring therein can be as shown in fig. 7a and 7 b.
In the step S106,
Figure 472001DEST_PATH_IMAGE015
it can be obtained from the step S105 that,
Figure 113198DEST_PATH_IMAGE038
、
Figure 268236DEST_PATH_IMAGE056
is constant according to the following formula
Figure 944068DEST_PATH_IMAGE017
That is, the third evaluation value can be calculated
Figure 775627DEST_PATH_IMAGE046
。
Wherein the content of the first and second substances,
Figure 966436DEST_PATH_IMAGE038
、
Figure 659586DEST_PATH_IMAGE056
the value of (b) can be obtained as follows:
and selecting indentation points corresponding to the vertical distance within the threshold range determined in the step S105 to perform a numerical simulation nano indentation experiment. In one embodiment of the present invention, for example, the numerical simulation nanoindentation experiment may be performed as follows:
the numerical simulation nanoindentation experiment was performed using abaqus software.
Firstly, model parameters for numerically simulating a nanoindentation experiment are set. Specifically, the fracture can be simplified to an ellipse, the ratio of the transverse axis to the longitudinal axis is set to a/b =6, a =3 μm, b =0.5 μm, the material boundary is more than ten times the maximum displacement, the experiment is set to the displacement loading mode, and the maximum displacement is set to 1000 nm.
Then, the numerical simulation nanoindentation experiment was performed while changing the value of Depth. Wherein Depth is the distance from the geometric center of the crack to the upper boundary of the sample in the numerical simulation nanoindentation experiment, and the definition thereof can be specifically shown in fig. 8.
Finally, load displacement data of each experiment is obtained, and parameter values of Er, H, Ue and Ut of each experiment and vertical distance in each experiment are calculated and obtained by the same method as the actual nano indentation experiment
Figure 455504DEST_PATH_IMAGE001
. Fitting the experimental results to obtain Depth and
Figure 208696DEST_PATH_IMAGE001
the relationship of (1):
Figure 808173DEST_PATH_IMAGE057
wherein Depth is the distance from the geometric center of the crack to the upper boundary of the sample in the numerical simulation nanoindentation experiment, DisplacementmaxThe maximum displacement of the indenter in the numerically simulated nanoindentation experiment is shown.
In a preferred embodiment of the invention, Depth/displaymaxThe relationship between d and d can be seen in FIG. 9. Depth/displaymaxAnd d is related to:
Figure 305014DEST_PATH_IMAGE058
in the embodiment of the present invention, the first and second substrates,
Figure 955438DEST_PATH_IMAGE059
preferably at least one of 0.03031, preferably,
Figure 879532DEST_PATH_IMAGE019
preferably at least one of 0.00551, preferably,
Figure 44934DEST_PATH_IMAGE060
preferably-3.25764.
According to the above-mentioned method, it can be known that,
Figure 329154DEST_PATH_IMAGE046
the larger the value, the worse the fissure developed.
In step S107, the fracture development degree evaluation value FG may be calculated as follows:
Figure 834084DEST_PATH_IMAGE042
as can be seen,
Figure 397921DEST_PATH_IMAGE043
the larger the value of (A), the better the crack development degree.
Step S108 is executed, and the crack development degree evaluation value is obtained through calculation
Figure 237570DEST_PATH_IMAGE043
And evaluating the shale microscopic fracture development degree according to the fracture development degree evaluation value.
Figure 810633DEST_PATH_IMAGE043
The larger the value of (A) the better the crack development degree,
Figure 435650DEST_PATH_IMAGE043
the smaller the value of (A), the worse the development degree of the crack.
The first embodiment is as follows:
in the embodiment, a sample I is adopted to carry out a nano indentation experiment, a relation image of H/Er and Ue/Ut is drawn according to relevant data obtained by the experiment, and a direct proportion function is fitted
Figure 701546DEST_PATH_IMAGE047
To obtainTo
Figure 575961DEST_PATH_IMAGE048
Is 0.250. Making a theoretical direct proportional curve according to the type or equivalent angle of the experimental pressure head, and making a proportional coefficient of the theoretical curve
Figure 201983DEST_PATH_IMAGE061
Is composed of
Figure 681506DEST_PATH_IMAGE049
=0.231。
Drawing a perpendicular line from the indentation point to the theoretical curve, calculating the value of the perpendicular line segment and recording the value as the value
Figure 118304DEST_PATH_IMAGE001
. Drawing
Figure 417698DEST_PATH_IMAGE001
And
Figure 847411DEST_PATH_IMAGE026
is calculated by
Figure 447020DEST_PATH_IMAGE002
0.01995, then
Figure 851457DEST_PATH_IMAGE010
Is 0.63636.
Is counted to obtain
Figure 638147DEST_PATH_IMAGE005
Is a number of 16, and is,
Figure 622283DEST_PATH_IMAGE062
at a value of 78 f, and is,
Figure 325666DEST_PATH_IMAGE009
to 121, a first evaluation value is calculated according to a formula
Figure 838687DEST_PATH_IMAGE053
The value was 0.69.
According to
Figure 112674DEST_PATH_IMAGE048
And
Figure 634922DEST_PATH_IMAGE061
calculating to obtain a second evaluation value
Figure 740281DEST_PATH_IMAGE027
Is 0.019.
To be provided with
Figure 939050DEST_PATH_IMAGE063
Is spaced out
Figure 965912DEST_PATH_IMAGE001
Polar coordinate diagram of
Figure 26272DEST_PATH_IMAGE064
Obtaining a circle for the radius, selecting points falling in the circle, and averaging to obtain the average value
Figure 454979DEST_PATH_IMAGE065
. Obtaining a third evaluation value according to a calculation formula
Figure 559070DEST_PATH_IMAGE066
。
Calculated according to a formula of a crack development degree evaluation value,
Figure 807649DEST_PATH_IMAGE067
。
the second embodiment is as follows:
in the embodiment, a sample I is adopted to carry out a nano indentation experiment, a relation image of H/Er and Ue/Ut is drawn according to relevant data obtained by the experiment, and a direct proportion function is fitted
Figure 671700DEST_PATH_IMAGE047
To obtain
Figure 954914DEST_PATH_IMAGE048
Is 0.226. Making a theoretical direct proportional curve according to the type or equivalent angle of the experimental pressure head, and making a proportional coefficient of the theoretical curve
Figure 42955DEST_PATH_IMAGE061
Is composed of
Figure 28098DEST_PATH_IMAGE049
=0.231。
Drawing a perpendicular line from the indentation point to the theoretical curve, calculating the value of the perpendicular line segment and recording the value as the value
Figure 695839DEST_PATH_IMAGE001
. Drawing
Figure 833560DEST_PATH_IMAGE001
And
Figure 295765DEST_PATH_IMAGE026
is calculated by
Figure 768204DEST_PATH_IMAGE002
0.011755, then
Figure 974057DEST_PATH_IMAGE010
Is 0.67347.
Is counted to obtain
Figure 966284DEST_PATH_IMAGE005
Is the number of the lead-acid storage battery to be 18,
Figure 599390DEST_PATH_IMAGE062
is a group of the chemical formula (42),
Figure 106595DEST_PATH_IMAGE009
to 98, a first evaluation value is calculated according to a formula
Figure 365407DEST_PATH_IMAGE003
The value was 0.49.
According to
Figure 212140DEST_PATH_IMAGE029
And
Figure 484990DEST_PATH_IMAGE030
calculating to obtain a second evaluation value
Figure 213911DEST_PATH_IMAGE027
Is 0.005.
To be provided with
Figure 276414DEST_PATH_IMAGE068
Is spaced out
Figure 977654DEST_PATH_IMAGE001
Polar coordinate diagram of
Figure 218142DEST_PATH_IMAGE069
Obtaining a circle for the radius, selecting points falling in the circle, and averaging to obtain the average value
Figure 372043DEST_PATH_IMAGE070
. Obtaining a third evaluation value according to a calculation formula
Figure 972658DEST_PATH_IMAGE071
。
Calculated according to a formula of a crack development degree evaluation value,
Figure 793983DEST_PATH_IMAGE043
=0.000483。
according to the method provided by the invention, the first sample can be known
Figure 2111DEST_PATH_IMAGE043
Greater than sample two
Figure 908887DEST_PATH_IMAGE043
The crack development degree of the sample one is better than that of the sample two.
In order to confirm that the method provided by the invention can effectively and reliably evaluate the development degree of the shale microcracks, in the invention, the porosity of the shale surface at a plurality of positions is analyzed by using a field emission Scanning Electron Microscope (SEM), the average value of the porosity at each position is calculated, and the surface porosity of the sample is represented by using the average value (see the attached figures 10 and 11). Fig. 10 shows the porosity and the average value of the porosity at a plurality of positions on the first surface of the sample obtained by SEM analysis, and fig. 11 shows the porosity and the average value of the porosity at a plurality of positions on the second surface of the sample obtained by SEM analysis. As can be seen in fig. 10, the surface porosity of sample one is 14.9083%, and as can be seen in fig. 11, the surface porosity of sample two is 8.563%. The larger the porosity of the shale surface is, the better the fracture development degree is. Therefore, the SEM analysis method is adopted to confirm that the crack development degree of the sample I is better than that of the sample II.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention. It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (10)

1. A method for evaluating the development degree of shale microfractures based on a nanoindentation experiment is characterized by comprising the following steps:
performing a nano indentation experiment, drawing a fitting curve and a theoretical curve of H/Er and Ue/Ut according to related data obtained by the nano indentation experiment, and calculating the slope of the fitting curve and the slope of the theoretical curve; wherein Er is elastic modulus, H is contact hardness, Ue is elastic energy, and Ut is total energy;
calculating the vertical distance from the indentation point to the theoretical curve in the nano indentation experiment
Figure 816601DEST_PATH_IMAGE001
And average value thereof
Figure 530479DEST_PATH_IMAGE002
；
The first evaluation value is calculated using the following formula
Figure 575795DEST_PATH_IMAGE003
：
Figure 936718DEST_PATH_IMAGE004
In the formula (I), the compound is shown in the specification,
Figure 78987DEST_PATH_IMAGE006
is a vertical distance in
Figure 839132DEST_PATH_IMAGE007
The number of the indentation points in the interval,
Figure 637324DEST_PATH_IMAGE008
is a vertical distance in
Figure 307995DEST_PATH_IMAGE010
The number of the indentation points in the interval,
Figure 462027DEST_PATH_IMAGE011
the total number of the indentation points is,
Figure 48866DEST_PATH_IMAGE012
is a vertical distance less than
Figure 68775DEST_PATH_IMAGE002
The probability of the occurrence of the indentation point of (c),
Figure 9049DEST_PATH_IMAGE013
、
Figure 424112DEST_PATH_IMAGE014
、
Figure 57219DEST_PATH_IMAGE015
is a constant;
calculating a second evaluation value according to the slope of the fitting curve and the slope of the theoretical curve
Figure 485795DEST_PATH_IMAGE016
；
Calculating an average of vertical distances within a threshold range
Figure 26498DEST_PATH_IMAGE017
；
The third evaluation value is calculated using the following formula
Figure 873231DEST_PATH_IMAGE018
：
Figure 365655DEST_PATH_IMAGE019
In the formula (I), the compound is shown in the specification,
Figure 32259DEST_PATH_IMAGE020
、
Figure 642232DEST_PATH_IMAGE021
is a constant;
calculating a fracture development degree evaluation value according to the first evaluation value, the second evaluation value and the third evaluation value;
and evaluating the shale micro-fracture development degree according to the fracture development degree evaluation value, wherein the larger the fracture development degree evaluation value is, the better the shale micro-fracture development degree is.
2. The method for evaluating the development degree of shale microfractures based on a nanoindentation experiment as claimed in claim 1, wherein the related data obtained by the nanoindentation experiment comprises: load and displacement data.
3. The method for evaluating the development degree of shale microfractures based on a nanoindentation experiment as claimed in claim 2, wherein the drawing of the fitting curve and the theoretical curve of H/Er and Ue/Ut comprises:
respectively calculating Ue, Ut, H and Er according to the load and displacement data;
drawing a fitting curve of H/Er and Ue/Ut according to the calculation result;
and drawing a theoretical curve of H/Er and Ue/Ut according to the pressure head type or equivalent angle of the nano indentation experiment.
4. The method for evaluating the development degree of shale microfractures based on a nanoindentation experiment as claimed in claim 3, wherein the calculating Ue, Ut, H, Er from the load and displacement data respectively comprises:
h, Er is calculated using the following formula:
Figure 530423DEST_PATH_IMAGE022
Figure 833228DEST_PATH_IMAGE023
Figure 987129DEST_PATH_IMAGE024
Figure 15172DEST_PATH_IMAGE025
Figure 633236DEST_PATH_IMAGE026
wherein S represents contact stiffness, hc is contact depth, h is displacement depth, hmax is maximum depth, p is load, Pmax is maximum load, ε is a parameter related to geometry and is a constant, and Ac is contact area;
drawing a displacement-load curve according to the load and the displacement data;
and calculating Ue and Ut according to the displacement-load curve.
5. The method for evaluating the development degree of shale microfractures based on nanoindentation experiment as claimed in claim 1,
Figure 982309DEST_PATH_IMAGE013
the concentration of the carbon dioxide is selected to be 0.0068,
Figure 872773DEST_PATH_IMAGE014
the concentration of the active carbon is selected to be 0.0098,
Figure 558969DEST_PATH_IMAGE015
is chosen as 0.01638.
6. The method for evaluating the development degree of shale microfractures based on nanoindentation experiment as claimed in claim 1, wherein the nanoindentation experiment is performed on the shale microfractures
Figure 438064DEST_PATH_IMAGE012
The preparation method comprises the following steps:
statistical vertical distance less than
Figure 505508DEST_PATH_IMAGE001
Probability of occurrence of indentation point of
Figure 961897DEST_PATH_IMAGE027
Drawing
Figure 327150DEST_PATH_IMAGE001
And
Figure 841177DEST_PATH_IMAGE027
the relationship curve of (1);
in that
Figure 656686DEST_PATH_IMAGE001
And
Figure 210159DEST_PATH_IMAGE027
in the relationship of (A), according to
Figure 769316DEST_PATH_IMAGE002
To obtain
Figure 904893DEST_PATH_IMAGE012
。
7. The method for evaluating the development degree of shale microfractures based on nanoindentation experiment as claimed in claim 1, wherein the second evaluation value is
Figure 235512DEST_PATH_IMAGE016
Calculated according to the following formula:
Figure 666493DEST_PATH_IMAGE028
in the formula (I), the compound is shown in the specification,
Figure 685133DEST_PATH_IMAGE029
in order to fit the slope of the curve,
Figure 81742DEST_PATH_IMAGE030
the slope of the theoretical curve.
8. The method for evaluating the developmental extent of shale microfractures based on nanoindentation experiments of claim 1, wherein the calculating of the average of the vertical distances within a threshold range
Figure 707895DEST_PATH_IMAGE017
The method comprises the following steps:
to be provided with
Figure 298277DEST_PATH_IMAGE031
Is a polar angle variable, the first
Figure 323870DEST_PATH_IMAGE032
Perpendicular distance of indentation point to theoretical curve
Figure 480045DEST_PATH_IMAGE033
Is a variation of the pole diameter
Figure 683625DEST_PATH_IMAGE034
In a polar diagram of (a), wherein,
Figure 246455DEST_PATH_IMAGE011
the total number of the indentation points is,
Figure 685527DEST_PATH_IMAGE036
，
Figure 102733DEST_PATH_IMAGE037
；
in the polar diagram, to
Figure 680476DEST_PATH_IMAGE038
For rounding radii, calculating all points falling within the circle
Figure 901242DEST_PATH_IMAGE033
Average value of (2)
Figure 550529DEST_PATH_IMAGE017
。
9. The method of claim 1The method for evaluating the development degree of the shale microfracture based on the nanoindentation experiment is characterized in that,
Figure 245078DEST_PATH_IMAGE040
、
Figure 836465DEST_PATH_IMAGE021
the values of (a) are obtained as follows:
selecting indentation points corresponding to the vertical distance within the threshold range to perform a numerical simulation nano indentation experiment, and fitting according to experimental data to obtain:
Figure DEST_PATH_IMAGE041
wherein Depth is the distance from the geometric center of the crack to the upper boundary of the sample in the numerical simulation nanoindentation experiment, DisplacementmaxRepresents the maximum displacement of the pressure head in the numerical simulation nano indentation experiment,
Figure DEST_PATH_IMAGE042
are coefficients.
10. The method for evaluating the shale microfracture development degree based on the nanoindentation experiment as claimed in claim 1, wherein the fracture development degree evaluation value is calculated according to the following formula:
Figure DEST_PATH_IMAGE043
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE044
and evaluating the crack development degree.
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