CN107045580A - A kind of shale mechanics parameter quick calculation method based on digital cores - Google Patents
A kind of shale mechanics parameter quick calculation method based on digital cores Download PDFInfo
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- 238000004364 calculation method Methods 0.000 title claims abstract description 29
- 229910052500 inorganic mineral Inorganic materials 0.000 claims abstract description 84
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- 238000006073 displacement reaction Methods 0.000 claims description 15
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- 239000010453 quartz Substances 0.000 claims description 10
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N silicon dioxide Inorganic materials O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 claims description 10
- 229910021532 Calcite Inorganic materials 0.000 claims description 7
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- 238000010276 construction Methods 0.000 claims description 5
- 239000004927 clay Substances 0.000 claims description 4
- 239000011028 pyrite Substances 0.000 claims description 4
- 229910052683 pyrite Inorganic materials 0.000 claims description 4
- NIFIFKQPDTWWGU-UHFFFAOYSA-N pyrite Chemical compound [Fe+2].[S-][S-] NIFIFKQPDTWWGU-UHFFFAOYSA-N 0.000 claims description 4
- 238000002083 X-ray spectrum Methods 0.000 claims description 3
- DLHONNLASJQAHX-UHFFFAOYSA-N aluminum;potassium;oxygen(2-);silicon(4+) Chemical compound [O-2].[O-2].[O-2].[O-2].[O-2].[O-2].[O-2].[O-2].[Al+3].[Si+4].[Si+4].[Si+4].[K+] DLHONNLASJQAHX-UHFFFAOYSA-N 0.000 claims description 3
- XKRFYHLGVUSROY-UHFFFAOYSA-N argon Substances [Ar] XKRFYHLGVUSROY-UHFFFAOYSA-N 0.000 claims description 3
- 229910052786 argon Inorganic materials 0.000 claims description 3
- -1 argon ion Chemical class 0.000 claims description 3
- 230000015572 biosynthetic process Effects 0.000 claims description 3
- 238000002939 conjugate gradient method Methods 0.000 claims description 3
- 238000003384 imaging method Methods 0.000 claims description 3
- 238000001000 micrograph Methods 0.000 claims description 3
- 229910052655 plagioclase feldspar Inorganic materials 0.000 claims description 3
- 238000005498 polishing Methods 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 3
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- 229910052570 clay Inorganic materials 0.000 claims description 2
- 239000000203 mixture Substances 0.000 abstract description 3
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Abstract
The present invention relates to a kind of shale mechanics parameter quick calculation method based on digital cores, including：(1) shale minerals component 3-dimensional digital rock core is built；A, scanning shale structure, obtain shale minerals structure chart, calculate brittle mineral percentage composition；B, structure shale minerals component 3-dimensional digital rock core；(2) it is based on shale minerals component 3-dimensional digital rock core FEM parallel computation；C, Region Decomposition, discretization are carried out successively to 3-dimensional digital rock core, obtain some voxels；D, one macro-strain of application so that the 3-dimensional digital rock core elastic potential energy is minimum, asks for being tried to achieve the rock mechanics parameters of overall shale as mean stress caused by the macro-strain.The present invention considers influence of the shale minerals component to shale mechanics parameter, and result of calculation is more accurate.Region Decomposition is carried out to digital cores, finite element modelling is carried out to 3-dimensional digital rock core based on parallel computation, digital cores information is not lost, rock mechanics parameters are accurately calculated, the calculating time is saved.
Description
Technical field
The present invention relates to a kind of shale mechanics parameter quick calculation method based on digital cores, belong to shale oil-gas reservoir and survey
Visit development technique field.
Background technology
The acquisition of shale mechanics parameter plays an important roll for horizontal well drilling and hydraulic fracture mining, and research shows bullet
Property modulus has certain correlation with shale fragility, therefore Accurate Determining shale modulus of elasticity also has for look for oil and gas dessert
Play an important role.Actual mining site generally determines shale mechanics parameter using Rock Mechanics Test, high yet with shale fragility, right
Shale carries out Rock Mechanics Test difficulty greatly, and has the shortcomings that the costly, time is long.
With the development of CT and scanning electron-microscopy, the research to shale microstructure achieves great progress.Pass through
Binary image segmentation method, is converted into digital cores image to characterize the binary map of interstitial space and grain structure, the method pair
In traditional hypertonic sandrock effect preferably, but for fine and close shale, mineral constituent information is complicated, and bianry image can not be accurate
Ground describes shale mechanical characteristics, and being directly used in measure shale elastic parameter has larger error.Therefore, shale minerals component is set up
3-dimensional digital rock core is significant for calculating its rock mechanics parameters.
The content of the invention
In view of the shortcomings of the prior art, quickly calculated the invention provides a kind of shale mechanics parameter based on digital cores
Method；
Shale minerals constitutional diagram can be set up according to x-ray fluorescence analysis (or EDS energy spectrum analysis), digital rock is then based on
Heart construction method, can build the 3-dimensional digital rock core for considering mineral constituent.It is each when carrying out finite element modelling to digital cores
Individual pixel is expressed as a three linear finite elements, in order to calculate the mechanics parameter of shale exactly, it is necessary to take what structure was obtained
The larger overlay area of 3-dimensional digital rock core, but this will cause the finite element free degree rapidly to increase, it is therefore necessary to use area
Domain decomposition method is based on parallel computation and carries out finite element modelling to 3-dimensional digital rock core, finally asks for overall shale rock mechanics ginseng
Number.
Not only calculating speed is fast for the method for the invention, but also spends few.
Term is explained
1st, shale mechanics parameter, refers to the rock mechanics parameters of shale, mainly including Young's modulus, bulk modulus, shearing
The parameters such as modulus, Poisson's ratio, tensile strength and compression strength.
2nd, brittle mineral, refers to be broken or mineralogical composition few or without plastic deformation is shown before destroying, shale is crisp
Property mineral mainly include quartz and carbonate mineral.
3rd, voxel, is volume element (volumepixel) abbreviation, the solid comprising voxel can be rendered by solid or
The polygon contour surface that person extracts given threshold value profile is showed.
4th, shale volume modulus, refers to the ratio of shale mean stress and body strain.
5th, shale modulus of shearing, refers to shale shear stress and the ratio of shear strain.
6th, shale Young's modulus, refers to the ratio between Rock Under Uniaxial Compression stress and uniaxial strain.
7th, shale Poisson's ratio, refers to rock when unidirectional tension or in compression, transverse normal strain is absolute with axial direction normal strain
The ratio of value.
The technical scheme is that：
A kind of shale mechanics parameter quick calculation method based on digital cores, including：
(1) shale minerals component 3-dimensional digital rock core is built
A, scanning shale structure, analysis obtains shale minerals structure chart, and calculates the volumn concentration of brittle mineral；
B, based on shale minerals structure chart, shale minerals component 3-dimensional digital rock is built using digital cores construction method
The heart；Each voxel of shale minerals component 3-dimensional digital rock core is made up of shale minerals component；
(2) FEM parallel computation based on shale minerals component 3-dimensional digital rock core
C, Region Decomposition, discretization are carried out successively to shale minerals component 3-dimensional digital rock core, obtain several three-dimensional images
Element, each voxel is considered as three linear finites of 8 nodes；
D, to step C processing after shale minerals component 3-dimensional digital rock core apply a macro-strain so that the three-dimensional
Digital cores elastic potential energy is minimum, is asked for based on parallel computation using quick conjugate gradient method as average caused by the macro-strain
Stress, tries to achieve the rock mechanics parameters of overall shale, and rock mechanics parameters include shale volume modulus, shale modulus of shearing, page
Rock Young's modulus and shale Poisson's ratio.Basic data is provided for shale pressure break.
According to currently preferred, the step A, shale structure is scanned by CT or FIB-SEM.
According to currently preferred, the step A, shale structure is scanned, analysis obtains shale minerals structure chart, including：
A, shale samples surface is polished successively, argon ion polishing；For reducing sample surfaces roughness, improve into
As quality；
B, shale samples are scanned using CT or FIB-SEM, carry out electronic imaging；
C, collect the X-ray spectrum that produces in scanning shale samples formation Electron Microscope images, and by itself and mineral
Matter characteristic spectrum is compared, and obtains the corresponding mineral matter of each pixel, builds shale minerals structure chart；
D, the volumn concentration for calculating brittle mineral.By counting brittle mineral (quartz and carbonate) voxel number,
Divided by total voxel number, produce the volumn concentration of brittle mineral.
According to currently preferred, the shale minerals component includes quartz, dolomite, calcite, potassium feldspar, plagioclase
Stone, pyrite and clay, the brittle mineral include quartz, dolomite and calcite.
According to currently preferred, the step B, the digital cores construction method includes process simulation method, Ma Er can
The random reconstruction method of husband.
Process simulation method sets up digital rock by the geology diagenetic process (including deposition, compacting and diagenesis) of simulation rock
The heart, not only allows for the particle size distribution of rock, but also by some other rock physicses got by thin section analysis
Matter is incorporated, and can set up anisotropic digital cores；The digital cores that the random reconstruction method of markov is set up have good
The pore communication and modeling speed got well quickly, therefore mainly carry out the structure of digital cores from this two methods.
According to currently preferred, the step C, region point is carried out successively to shale minerals component 3-dimensional digital rock core
Solution, discretization, including：
E, shale minerals component 3-dimensional digital rock core divided equally according to size, obtain many sub-regions, each sub-district
Domain interface meets displacement continuously, shown in the weak form such as formula (I) per sub-regions：
∫Γ(u (l)-v (l)) f (l) dl=0 (I)
In formula (I), l is coordinate variable, and u (l) and v (l) represent the displacement in adjacent subarea domain, and f (l) is finite element shape letter
Number；
F, the every sub-regions obtained to step e carry out discretization, according to pixel cell that digital cores are directly discrete, from
Each voxel obtained after dispersion regards three linear finites of 8 nodes as, and the unit is square, by 8
Individual node composition, finite element shape function represents that X, Y, Z are three directions of digital cores coordinate system respectively using linear function,
Each three linear finite is occupied by a kind of mineral matter, and the modulus of elasticity and Poisson's ratio of various mineral matters are by existing experimental data
Provide.
According to currently preferred, the step D, including step are as follows：
G, 3-dimensional digital rock core elastic potential energy EnExpression formula such as formula (II) shown in：
In formula (II), p, q, rs be digital cores coordinate system x, y, tri- directions of z, d is integral sign, εpqAnd εrsPoint
Not Wei pq directions and rs directions dependent variable, CpqrsFor modulus of elasticity tensor；
Due to symmetry, strain tensor ε includes 6 independent variable (εxx、εyy、εzz、εxy、εxz、εyz), εxx、εyy、εzz、
εxy、εxz、εyzRefer respectively to the dependent variable of all directions, CpqrsIt is expressed as Cαβ, α, β is x, y, tri- directions of z, such as formula (III), formula
(IV) shown in：
In formula (III), formula (IV), upRefer to the displacement in p directions, xpRefer to the coordinate in p directions, uqRefer to the displacement in q directions,
xqRefer to the coordinate in q directions；
CpqrsIt is expressed as Cαβ, εpqIt is expressed as εα, εrsIt is expressed as εβ, the elastic potential energy E of 3-dimensional digital rock corenExpression formula formula
(II) it is converted into formula (V)：
Make 3-dimensional digital rock core elastic potential energy minimum, it is necessary to meet formula (VI)：
In formula (VI), umIt is displacement, m refers to all nodes and all directions；
Formula (VI) is solved using Fast Field method, finite element is carried out to all subregion based on MPI concurrent techniques
Calculate, calculate the stress and strain for obtaining all subregion, the mean stress peace of overall digital rock core is tried to achieve by arithmetic average
Strain；
K, based on 3-dimensional digital rock core mean strain stress, calculating obtains shale volume modulus, shale modulus of shearing, shale
Young's modulus and shale Poisson's ratio：
Shown in the calculation formula of shale volume modulus such as formula (VII)：
In formula (VII), σ0For mean stress, σxx、σyy、σzzThe respectively direct stress in x, y, z direction, K is shale volume mould
Amount, εxx、εyy、εzzThe respectively normal strain in x, y, z direction；
Shown in the calculation formula of shale modulus of shearing such as formula (VIII)：
σij=2 μ εij (Ⅷ)
In formula (VIII), σijRefer to i, the direct stress in j directions, i, j is respectively x, y direction, and μ is shale modulus of shearing, εijFor
Shearing stress；
Shown in the calculation formula of shale Young's modulus such as formula (Ⅸ)：
In formula (Ⅸ), E is shale Young's modulus；
Shown in the calculation formula of shale Poisson's ratio such as formula (Ⅹ)：
In formula (Ⅹ), ν is shale Poisson's ratio.
Beneficial effects of the present invention are：
1. the present invention can build shale minerals structure chart exactly using EDS/X ray fluorescence analysis, so as to set up page
Rock mineral constituent 3-dimensional digital rock core, the present invention considers influence of the shale minerals component to shale mechanics parameter, therefore calculates knot
Fruit is more accurate.
2. by carrying out Region Decomposition to digital cores, finite element mould is carried out to 3-dimensional digital rock core based on parallel computation
Intend, due to taking the entirety or large area of 3-dimensional digital rock core, digital cores information is not lost, therefore, it is possible to accurately calculate its rock
Stone mechanics parameter, in addition parallel computation can save many calculating times.
3rd, the present invention has the advantages that speed is fast, expense is low, and the exploration and development for shale gas is significant.
Brief description of the drawings
Fig. 1 is a kind of shale mechanics parameter quick calculation method flow chart based on digital cores of the present invention；
Fig. 2 is embodiment shale core CT scan image schematic diagram；
Fig. 3 is embodiment 3-dimensional digital rock core Region Decomposition schematic diagram；
Fig. 4 is embodiment pixel cell node serial number sequential schematic.
Embodiment
The present invention is further qualified with reference to Figure of description and embodiment, but not limited to this.
Embodiment
A kind of shale mechanics parameter quick calculation method based on digital cores, as shown in figure 1, including：
(1) shale minerals component 3-dimensional digital rock core is built
A, shale structure, obtained wherein piece image scanned as shown in Fig. 2 analysis obtains page by CT or FIB-SEM
Rock mineral structure figure, and calculate the volumn concentration of brittle mineral；Shale minerals component include quartz, dolomite, calcite,
Potassium feldspar, plagioclase, pyrite and clay, brittle mineral include quartz, dolomite and calcite.
B, based on shale minerals structure chart, shale minerals group is built using process simulation method or the random reconstruction method of markov
Divide 3-dimensional digital rock core；Each voxel of shale minerals component 3-dimensional digital rock core is made up of shale minerals component；Process simulation method is led to
Cross the geology diagenetic process (including deposition, compacting and diagenesis) of simulation rock to set up digital cores, not only allow for rock
Particle size distribution, but also some other petrophysical property got by thin section analysis is incorporated, it can set up
Anisotropic digital cores；The digital cores that the random reconstruction method of markov is set up have good pore communication and modeling
Speed quickly, therefore mainly carries out the structure of digital cores from this two methods.
(2) FEM parallel computation based on shale minerals component 3-dimensional digital rock core
C, Region Decomposition, discretization are carried out successively to shale minerals component 3-dimensional digital rock core, obtain several three-dimensional images
Element, each voxel is considered as three linear finites of 8 nodes；
D, to step C processing after shale minerals component 3-dimensional digital rock core apply a macro-strain so that the three-dimensional
Digital cores elastic potential energy is minimum, is asked for based on parallel computation using quick conjugate gradient method as average caused by the macro-strain
Stress, tries to achieve the rock mechanics parameters of overall shale, and rock mechanics parameters include shale volume modulus, shale modulus of shearing, page
Rock Young's modulus and shale Poisson's ratio.Basic data is provided for shale pressure break.
Step A, scans shale structure, and analysis obtains shale minerals structure chart, including：
A, shale samples surface is polished successively, argon ion polishing；For reducing sample surfaces roughness, improve into
As quality；
B, shale samples are scanned using CT or FIB-SEM, carry out electronic imaging；
C, collect the EDS/X ray spectrums that produce in scanning shale samples formation Electron Microscope images, and by its with
Mineral matter characteristic spectrum is compared, and obtains the corresponding mineral matter of each pixel, builds shale minerals structure chart；
D, the volumn concentration for calculating brittle mineral.By counting brittle mineral (quartz and carbonate) voxel number,
Divided by total voxel number, produce the volumn concentration of brittle mineral.
Step C, Region Decomposition, discretization are carried out to shale minerals component 3-dimensional digital rock core successively, including：
E, shale minerals component 3-dimensional digital rock core divided equally according to size, many sub-regions are obtained, such as Fig. 3 institutes
Show, each sub-region interface meets displacement continuously, shown in the weak form such as formula (I) per sub-regions：
∫Γ(u (l)-v (l)) f (l) dl=0 (I)
In formula (I), l is coordinate variable, and u (l) and v (l) represent the displacement in adjacent subarea domain, and f (l) is finite element shape letter
Number；
F, the every sub-regions obtained to step e carry out discretization, according to pixel cell that digital cores are directly discrete, from
Each voxel obtained after dispersion regards three linear finites of 8 nodes as, and pixel cell node serial number is suitable
Sequence figure is as shown in figure 4, for any pixel unit of digital cores, according to being from bottom to top counterclockwise numbered, the list
Member is square, is made up of 8 nodes, finite element shape function is represented using linear function, X, Y, Z are digital cores coordinate respectively
Three directions of system, each three linear finite occupies by a kind of mineral matter, the modulus of elasticity and Poisson's ratio of various mineral matters by
Existing experimental data is provided.
Step D, including step are as follows：
G, 3-dimensional digital rock core elastic potential energy EnExpression formula such as formula (II) shown in：
In formula (II), p, q, rs be digital cores coordinate system x, y, tri- directions of z, d is integral sign, εpqAnd εrsPoint
Not Wei pq directions and rs directions dependent variable, CpqrsFor modulus of elasticity tensor；
Due to symmetry, strain tensor ε includes 6 independent variable (εxx、εyy、εzz、εxy、εxz、εyz), εxx、εyy、εzz、
εxy、εxz、εyzRefer respectively to the dependent variable of all directions, CpqrsIt is expressed as Cαβ, α, β is x, y, tri- directions of z, such as formula (III), formula
(IV) shown in：
In formula (III), formula (IV), upRefer to the displacement in p directions, xpRefer to the coordinate in p directions, uqRefer to the displacement in q directions,
xqRefer to the coordinate in q directions；
CpqrsIt is expressed as Cαβ, εpqIt is expressed as εα, εrsIt is expressed as εβ, the elastic potential energy E of 3-dimensional digital rock corenExpression formula formula
(II) it is converted into formula (V)：
Make 3-dimensional digital rock core elastic potential energy minimum, it is necessary to meet formula (VI)：
In formula (VI), umIt is displacement, m refers to all nodes and all directions；
Formula (VI) is solved using Fast Field method, finite element is carried out to all subregion based on MPI concurrent techniques
Calculate, calculate the stress and strain for obtaining all subregion, the mean stress peace of overall digital rock core is tried to achieve by arithmetic average
Strain；
K, based on 3-dimensional digital rock core mean strain stress, calculating obtains shale volume modulus, shale modulus of shearing, shale
Young's modulus and shale Poisson's ratio：
Shown in the calculation formula of shale volume modulus such as formula (VII)：
In formula (VII), σ0For mean stress, σxx、σyy、σzzThe respectively direct stress in x, y, z direction, K is shale volume mould
Amount, εxx、εyy、εzzThe respectively normal strain in x, y, z direction；
Shown in the calculation formula of shale modulus of shearing such as formula (VIII)：
σij=2 μ εij(Ⅷ)
In formula (VIII), σijRefer to i, the direct stress in j directions, i, j is respectively x, y direction, and μ is shale modulus of shearing, εijFor
Shearing stress；
Shown in the calculation formula of shale Young's modulus such as formula (Ⅸ)：
In formula (Ⅸ), E is shale Young's modulus；
Shown in the calculation formula of shale Poisson's ratio such as formula (Ⅹ)：
In formula (Ⅹ), ν is shale Poisson's ratio.
Be respectively adopted the method for the present embodiment with Experimental Method in Laboratory in the prior art, do not consider the meter of shale minerals component
Calculation method, the calculating of rock mechanics parameters is carried out to certain shale core, and the shale component information of shale core as shown in table 1, is counted
Calculate result as shown in table 2.
Table 1
| Sequence number | Component | Percent by volume | E(GPa) | v |
| 1 | Hole (oil/gas) | 4 | 0 | 0.5 |
| 2 | Clay | 33 | 27 | 0.35 |
| 3 | Calcite | 20 | 55 | 0.3 |
| 4 | Quartz | 40 | 47 | 0.12 |
| 5 | Pyrite | 3 | 85 | 0.17 |
Table 2
Can be obtained by table 1, table 2, the present embodiment methods described computational solution precision is high, the error with test value within 5%,
Without considering that the error calculated of shale minerals component is larger.Do not consider that the computational methods of shale minerals component refer to numeral
Rock core is regarded as to be only made up of hole and skeleton, and the rock mechanics parameters of skeleton are provided by the arithmetic mean of instantaneous value of mineral constituent.
In addition, compared for the calculating time of the present embodiment method and conventional method, sub-district for different pixels number of unit
Domain number and parallel computation check figure are all 8, as shown in table 3, and research finds using Region Decomposition and uses parallel computation can
Save many calculating times.Table 3
| Pixel cell | Conventional method/h | The present embodiment method/h |
| 60*60*60 | 0.35 | 0.06 |
| 80*80*80 | 4.4 | 0.72 |
| 100*100*100 | 8.22 | 1.55 |
Claims (7)
1. a kind of shale mechanics parameter quick calculation method based on digital cores, it is characterised in that including：
(1) shale minerals component 3-dimensional digital rock core is built
A, scanning shale structure, analysis obtains shale minerals structure chart, and calculates the volumn concentration of brittle mineral；
B, based on shale minerals structure chart, shale minerals component 3-dimensional digital rock core is built using digital cores construction method；
(2) FEM parallel computation based on shale minerals component 3-dimensional digital rock core
C, Region Decomposition, discretization are carried out successively to shale minerals component 3-dimensional digital rock core, obtain several voxels, often
Individual voxel is considered as three linear finites of 8 nodes；
D, to step C processing after shale minerals component 3-dimensional digital rock core apply a macro-strain so that the 3-dimensional digital
Rock core elastic potential energy is minimum, is asked for based on parallel computation using quick conjugate gradient method as averagely should caused by the macro-strain
Power, tries to achieve the rock mechanics parameters of overall shale, and rock mechanics parameters include shale volume modulus, shale modulus of shearing, shale
Young's modulus and shale Poisson's ratio.
2. a kind of shale mechanics parameter quick calculation method based on digital cores according to claim 1, its feature exists
In the step A scans shale structure by CT or FIB-SEM.
3. a kind of shale mechanics parameter quick calculation method based on digital cores according to claim 1, its feature exists
In, the step A scans shale structure, and analysis obtains shale minerals structure chart, including：
A, shale samples surface is polished successively, argon ion polishing；
B, shale samples are scanned using CT or FIB-SEM, carry out electronic imaging；
The X-ray spectrum that c, collection are produced in scanning shale samples formation Electron Microscope images, and itself and mineral matter is special
Levy spectrum to be compared, obtain the corresponding mineral matter of each pixel, build shale minerals structure chart；
D, the volumn concentration for calculating brittle mineral.
4. a kind of shale mechanics parameter quick calculation method based on digital cores according to claim 1, its feature exists
In the shale minerals component includes quartz, dolomite, calcite, potassium feldspar, plagioclase, pyrite and clay, the fragility
Mineral include quartz, dolomite and calcite.
5. a kind of shale mechanics parameter quick calculation method based on digital cores according to claim 1, its feature exists
In the step B, the digital cores construction method includes process simulation method, the random reconstruction method of markov.
6. a kind of shale mechanics parameter quick calculation method based on digital cores according to claim 1, its feature exists
In, the step C carries out Region Decomposition, discretization successively to shale minerals component 3-dimensional digital rock core, including：
E, shale minerals component 3-dimensional digital rock core divided equally according to size, many sub-regions are obtained, per sub-regions circle
Face meets displacement continuously, shown in the weak form such as formula (I) per sub-regions：
∫Γ(u (l)-v (l)) f (l) dl=0 (I)
In formula (I), l is coordinate variable, and u (l) and v (l) represent the displacement in adjacent subarea domain, and f (l) is finite element shape function；
Each voxel that f, the every sub-regions obtained to step e obtained after discretization, discretization is regarded as
Three linear finites of one 8 node, each three linear finite is occupied by a kind of mineral matter, the modulus of elasticity of various mineral matters
Provided with Poisson's ratio by existing experimental data.
7. according to a kind of any described shale mechanics parameter quick calculation methods based on digital cores of claim 1-6, its
It is characterised by, the step D, including step are as follows：
G, 3-dimensional digital rock core elastic potential energy EnExpression formula such as formula (II) shown in：
<mrow>
<msub>
<mi>E</mi>
<mi>n</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>&Integral;</mo>
<msup>
<mi>d</mi>
<mn>3</mn>
</msup>
<msub>
<mi>l&epsiv;</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<msub>
<mi>C</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
<mi>r</mi>
<mi>s</mi>
</mrow>
</msub>
<msub>
<mi>&epsiv;</mi>
<mrow>
<mi>r</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mi>I</mi>
<mi>I</mi>
<mo>)</mo>
</mrow>
</mrow>
In formula (II), p, q, rs be digital cores coordinate system x, y, tri- directions of z, d is integral sign, εpqAnd εrsRespectively pq
Direction and the dependent variable in rs directions, CpqrsFor modulus of elasticity tensor；
Due to symmetry, strain tensor ε includes 6 independent variable (εxx、εyy、εzz、εxy、εxz、εyz), εxx、εyy、εzz、εxy、εxz、
εyzRefer respectively to the dependent variable of all directions, CpqrsIt is expressed as Cαβ, α, β is x, y, tri- directions of z, such as formula (III), formula (IV) institute
Show：
<mrow>
<msub>
<mi>&epsiv;</mi>
<mrow>
<mi>p</mi>
<mi>p</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mi>p</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>x</mi>
<mi>p</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mi>I</mi>
<mi>I</mi>
<mi>I</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>&epsiv;</mi>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mi>p</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>x</mi>
<mi>q</mi>
</msub>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mi>q</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>x</mi>
<mi>p</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mi>I</mi>
<mi>V</mi>
<mo>)</mo>
</mrow>
</mrow>
In formula (III), formula (IV), upRefer to the displacement in p directions, xpRefer to the coordinate in p directions, uqRefer to the displacement in q directions, xqIt is
Refer to the coordinate in q directions；
CpqrsIt is expressed as Cαβ, εpqIt is expressed as εα, εrsIt is expressed as εβ, the elastic potential energy E of 3-dimensional digital rock corenExpression formula formula (II)
It is converted into formula (V)：
<mrow>
<msub>
<mi>E</mi>
<mi>n</mi>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>&Integral;</mo>
<msup>
<mi>d</mi>
<mn>3</mn>
</msup>
<msub>
<mi>r&epsiv;</mi>
<mi>&alpha;</mi>
</msub>
<msub>
<mi>C</mi>
<mrow>
<mi>&alpha;</mi>
<mi>&beta;</mi>
</mrow>
</msub>
<msub>
<mi>&epsiv;</mi>
<mi>&beta;</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mi>V</mi>
<mo>)</mo>
</mrow>
</mrow>
Make 3-dimensional digital rock core elastic potential energy minimum, it is necessary to meet formula (VI)：
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>E</mi>
<mi>n</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>u</mi>
<mi>m</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mi>V</mi>
<mi>I</mi>
<mo>)</mo>
</mrow>
</mrow>
In formula (VI), umIt is displacement, m refers to all nodes and all directions；
Formula (VI) is solved using Fast Field method, FEM calculation is carried out to all subregion based on MPI concurrent techniques,
The stress and strain for obtaining all subregion is calculated, the mean stress peace for trying to achieve overall digital rock core by arithmetic average all should
Become；
K, based on 3-dimensional digital rock core mean strain stress, calculating obtains shale volume modulus, shale modulus of shearing, shale Young
Modulus and shale Poisson's ratio：
Shown in the calculation formula of shale volume modulus such as formula (VII)：
<mrow>
<msub>
<mi>&sigma;</mi>
<mn>0</mn>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>x</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>y</mi>
<mi>y</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>z</mi>
<mi>z</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>K</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&epsiv;</mi>
<mrow>
<mi>x</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&epsiv;</mi>
<mrow>
<mi>y</mi>
<mi>y</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&epsiv;</mi>
<mrow>
<mi>z</mi>
<mi>z</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mi>V</mi>
<mi>I</mi>
<mi>I</mi>
<mo>)</mo>
</mrow>
</mrow>
In formula (VII), σ0For mean stress, σxx、σyy、σzzThe respectively direct stress in x, y, z direction, K is shale volume modulus,
εxx、εyy、εzzThe respectively normal strain in x, y, z direction；
Shown in the calculation formula of shale modulus of shearing such as formula (VIII)：
σij=2 μ εij (Ⅷ)
In formula (VIII), σijRefer to i, the direct stress in j directions, i, j is respectively x, y direction, and μ is shale modulus of shearing, εijShould to cut
Power；
Shown in the calculation formula of shale Young's modulus such as formula (Ⅸ)：
<mrow>
<mi>E</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>9</mn>
<mi>K</mi>
<mi>&mu;</mi>
</mrow>
<mrow>
<mn>3</mn>
<mi>K</mi>
<mo>+</mo>
<mi>&mu;</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mi>I</mi>
<mi>X</mi>
<mo>)</mo>
</mrow>
</mrow>
In formula (Ⅸ), E is shale Young's modulus；
Shown in the calculation formula of shale Poisson's ratio such as formula (Ⅹ)：
<mrow>
<mi>&nu;</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>3</mn>
<mi>K</mi>
<mo>-</mo>
<mn>2</mn>
<mi>&mu;</mi>
</mrow>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mi>K</mi>
<mo>+</mo>
<mi>&mu;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mi>X</mi>
<mo>)</mo>
</mrow>
</mrow>
In formula (Ⅹ), ν is shale Poisson's ratio.
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| CN111680440B (en) * | 2020-06-03 | 2024-03-19 | 中国地质大学（北京） | Method for analyzing acoustic characteristics of digital rock core at different temperatures |
| CN111767650A (en) * | 2020-06-28 | 2020-10-13 | 中国石油大学(华东) | Method and device for estimating equivalent elastic parameters of digital rock core |
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