WO2017086824A1 - Procédé mis en œuvre par ordinateur et système de détermination de propriétés élastiques efficaces d'un échantillon d'un milieu poreux - Google Patents
Procédé mis en œuvre par ordinateur et système de détermination de propriétés élastiques efficaces d'un échantillon d'un milieu poreux Download PDFInfo
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- WO2017086824A1 WO2017086824A1 PCT/RU2015/000797 RU2015000797W WO2017086824A1 WO 2017086824 A1 WO2017086824 A1 WO 2017086824A1 RU 2015000797 W RU2015000797 W RU 2015000797W WO 2017086824 A1 WO2017086824 A1 WO 2017086824A1
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- Prior art keywords
- elastic properties
- volume element
- effective elastic
- representative volume
- volume
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- 238000000034 method Methods 0.000 title claims abstract description 51
- 239000011435 rock Substances 0.000 claims abstract description 40
- 238000000265 homogenisation Methods 0.000 claims description 24
- 238000012545 processing Methods 0.000 claims description 7
- 239000011148 porous material Substances 0.000 claims description 5
- 238000010884 ion-beam technique Methods 0.000 claims description 3
- 238000010603 microCT Methods 0.000 description 7
- 239000000463 material Substances 0.000 description 6
- 239000002131 composite material Substances 0.000 description 5
- 238000002474 experimental method Methods 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- 230000005483 Hooke's law Effects 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 2
- 238000013459 approach Methods 0.000 description 2
- 239000011365 complex material Substances 0.000 description 2
- 239000000835 fiber Substances 0.000 description 2
- 239000012530 fluid Substances 0.000 description 2
- 238000003384 imaging method Methods 0.000 description 2
- 229910052500 inorganic mineral Inorganic materials 0.000 description 2
- 239000011159 matrix material Substances 0.000 description 2
- 239000011707 mineral Substances 0.000 description 2
- 239000000203 mixture Substances 0.000 description 2
- 230000011218 segmentation Effects 0.000 description 2
- 101100172619 Danio rerio erh gene Proteins 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 238000002591 computed tomography Methods 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 101150076266 e(r) gene Proteins 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000009472 formulation Methods 0.000 description 1
- 239000004973 liquid crystal related substance Substances 0.000 description 1
- 238000000386 microscopy Methods 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000004044 response Effects 0.000 description 1
- 229920006395 saturated elastomer Polymers 0.000 description 1
- 238000004626 scanning electron microscopy Methods 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 238000007619 statistical method Methods 0.000 description 1
- 238000003325 tomography Methods 0.000 description 1
Classifications
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/0058—Kind of property studied
- G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
- G01N2203/0075—Strain-stress relations or elastic constants
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
- G01N2203/02—Details not specific for a particular testing method
- G01N2203/0202—Control of the test
- G01N2203/0212—Theories, calculations
- G01N2203/0216—Finite elements
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
Definitions
- This invention relates to methods for estimating effective elastic properties of core samples using digital models of these samples and numerical modeling.
- micro-CT X-ray micro-Computed Tomography
- a method for determining effective elastic properties of a sample of a porous medium comprises obtaining a sample of a porous medium, selecting at least one sub-volume within a volume of the sample and creating a three dimensional digital representation by scanning the sample using a scanning device to make a three dimensional digital image of the sample of the porous medium, cropping of the image to extract a sub image of the selected sub- volume of the sample and processing the sub image to produce the three dimensional representation of the selected sub- volume of the sample. Then a first representative volume element within the three dimensional digital representation of the selected sub-volume is selected.
- the first selected representative volume element is used for creating a first numerical model for the selected sub- volume of the sample, applying a direct homogenization method and determining effective elastic properties for the selected first representative volume element. Then another representative volume element from the same place within the digital representation of the selected sub- volume is selected, the other selected representative volume element has a volume larger than the volume of the first selected representative volume element so that the first selected representative volume element is a part of the other selected representative volume element.
- the other selected representative volume element is used for creating another numerical model for the selected sub-volume of the sample, applying the direct homogenization method and determining effective elastic properties for the other selected representative volume element. The effective elastic properties determined for the first selected representative volume element and the effective elastic properties determined for the other selected representative volume element are compared.
- a new representative volume element from the same place within the digital representation of the selected sub-volume is selected, the new representative volume element having a volume larger than the volume of the previous representative volume element so that the previous selected representative volume element is a part of the new selected representative volume element.
- the new selected representative volume element is used for creating a new numerical model for the selected sub-volume of the sample, applying the direct homogenization method and determining effective elastic properties for the new selected representative volume element.
- the effective elastic properties determined for the previous selected representative volume element and the effective elastic properties determined for the new selected representative volume element are compared.
- the reselection of representative volume elements with further creation of numerical models for the selected sub- volume of the sample, application of the direct homogenization method, determination of effective elastic properties for the reselected representative volume element and comparison of the determined effective elastic properties are repeated until differences between the effective elastic properties determined for the previous representative volume element and the effective elastic properties determined for the reselected representative volume element are not more than the specified value.
- the volume of the selected representative volume element for which the differences between the effective elastic properties determined for the previous selected representative volume element and the effective elastic properties determined for the selected representative volume element is not more than the specified value is used for selection of all representative volume elements from the digital representation of the selected sub-volume of the sample of the porous medium.
- the selected representative volume elements are used for creating numerical models for the selected sub-volume of the sample, applying the direct homogenization method and determining effective elastic properties for the selected sub-volume of the sample.
- Fig.l shows a flow chart of an example process for determining effective elastic properties of a rock sample.
- Fig.2 shows selection of sub- volumes for a cylindrical core plug.
- Fig. 3 shows a typical cubical shape of considered RVE for definition of effective properties for core samples.
- Fig.4 shows selection of RVE from the digital model of sub- volume of rock core.
- Fig.5 shows selection of RVEs from the digital model of cylindrical sub- volume of rock core. The cross-section of such sub-volume is presented on this picture.
- Fig.6 shows a computing system in accordance with one or more embodiments.
- a method of an example of the present invention is shown.
- step 1 a physical sample from a porous medium, such as rock, is obtained and at least one sub-volume within a volume of a rock sample is selected. If more sub-volumes are selected, these sub- volumes have to be uniformly distributed in the volume of the rock sample and such selected set of the sub- volumes must be representative for the full volume of the rock sample. The number of such sub- volumes is depended on the size of the rock sample. For example, five cylindrical sub-volumes can be selected for a cylindrical core plug. These cylindrical sub-volumes with the height h are uniformly distributed in the volume of the rock sample (Fig. 2). The distances L between such sub-volumes are the same.
- three-dimensional digital rock representation of the selected sub- volume is created by scanning the sample using a device capable of producing a three-dimensional representation of the porous structure of the sample, for example, an X-ray micro-computed tomographic (micro-CT) scanner.
- the representation is created by following these steps: rock sample imaging using X-ray micro-computed tomography (micro-CT), cropping of the obtained 3D rock image to extract sub image of the selected sub- volume of the sample, image processing and regularization applied to the 3D image (or to stack of 2D images), image binarization or segmentation to pore/mineral matrix, and mesh model construction ("Direct hydrodynamic simulation of multiphase flow in porous rock". 2014, Petrophysics, V. 55, Iss. 3, 294-303.
- rock imaging techniques can be used to extend micro-CT (micrometer) scale and construct 3D rock models by capturing rock features with millimeter and nanometer scale: X-ray whole core CT and FIB- SEM (Focused Ion Beam Scanning Electron Microscopy).
- a first representative volume element (RVE) within the created three-dimensional digital representation of the selected sub-volume of the rock sample is selected.
- This RVE must contain at least 10-15 pores or other features (cracks, inclusions, etc.) inside its volume.
- the first selected representative volume element is used for creating a first numerical model for the selected sub- volume of the rock sample, for example a finite-element model.
- a finite-element model for example a finite-element model.
- any other numerical methods can be used which allow to receive the stress-strain distribution for such digital rock models. For example, it can be spectral-element method (SEM) of finite-different method (FDM).
- step 5 the Direct Homogenization method is applied for definition of effective elastic properties (constants) for the first selected RVE and effective elastic properties for the selected first representative volume element are determined.
- Effective elastic constants are the components of effective stiffness tensor (fourth rank tensor C*). This effective stiffness tensor has 21 independent components in case of general anisotropy.
- the Direct Homogenization method allows to replace the heterogeneous microstructure with the effective homogeneous media and, that most important, to receive the effective anisotropic properties of this effective homogeneous media.
- the Direct Homogenization method initially was developed for homogenization of composite materials. There is an assumption, that any representative volume element of rock sample can be considered as a type of composite material. Hence, a consideration of the special boundary conditions on the outer boundary of the representative volume element (RVE) V gives the opportunity to determine the microscopic field of the displacements U(r), strains e(r) and stresses o(r).
- the equation (1) is the Hooke's law for heterogeneous media, where ⁇ and ⁇ are accordingly the second rank stress and strain tensors. Each of them is symmetric and has six independent components. Correspondingly, macroscopic strain and stress tensors ⁇ ⁇ > and ⁇ ⁇ > are:
- the fourth rank tensor C* is called the effective stiffness tensor and has 21 independent components (see M. Kumar et al., Micro-Petrophysical Experiments Via Tomography and Simulation, In K. A. Alshibli (Ed.), Advances in computed tomography of geomaterials / GeoX 2010, New La: John Wiley & Sons, Inc., 2010. (pp. 238-253) and S.G. Lekhnitskii "Theory of elasticity of an anisotropic body", Moscow: Nauka, 1977).
- the Palmov & Borovkov's notation can be used:
- step 6 another representative volume element from the same place within the digital representation of the selected sub- volume is selected.
- the other selected representative volume element should have a volume larger than the volume of the first selected representative volume element so that the first selected representative volume element is a part of the other selected representative volume element.
- the increasing of size must be -50 % for every edge of cubical volume.
- step 7 the other selected RVE is also used for creation of another numerical model and further application of the Direct Homogenization method with definition of effective elastic properties (in step 8).
- step 9 the determined effective elastic properties are compared for two cases and the relative differences between them are calculated.
- the obtained values of relative differences are compared with an initially specified permissible relative difference (can be, for example, 5%). If the values of obtained relative differences are less than defined permissible relative difference, step 10 directly follows step 9 and the size (volume) of the initially selected first RVE is taken as the size for all RVE for the selected sub-volume.
- step 11 the set of RVEs with such size is selected from this sub-volume with further creation of numerical models and application of the Direct Homogenization method with definition of effective elastic properties for each selected RVE.
- the bigger volume of cubic RVE must be re-selected from the digital representation of the selected sub- volume of rock core.
- the volume of the other RVE, selected on step 6, must be inside of a volume of a new re-selected RVE (Fig. 4).
- This new third RVE is used for creation of a new numerical model and further application of the Direct Homogenization method with definition of effective elastic properties. Then the values of effective elastic properties for this new RVE and the previous RVE are compared with further calculation of relative differences between them.
- the size (volume) of the other selected RVE on the previous step of this process is taken as the size for all RVE for the considered sub-volume.
- the set of RVEs with such size is selected from this sub-volume with further creation of numerical models and application of the Direct Homogenization method with definition of effective elastic properties for each selected RVE.
- the process may be repeated n times (some iterations) until (n-1) and (n) RVEs are meeting the requirements about values of relative difference.
- the finally defined size of (n-1) RVE is used for selection of all other RVEs from the considered digital representation of the selected sub- volume of the rock sample.
- this procedure can be fulfilled only once for one selected sub-volume and defined size of RVE may be used for all sub- volumes.
- the size of RVEs is the same for all sub-volumes of rock sample.
- RVE's set selection from one digital representation of a cylindrical sub-volume of a rock sample is presented in Fig. 5.
- one RVE must be selected for one of the sectors (marked as RVE on the picture) and the described above procedure must be fulfilled for it that allows to define the size of the RVE for the current sub-volume.
- the RVEs with such size must be selected for all other sectors of this sub-volume and these RVEs are used for creation of finite-element numerical models and further application of the Direct Homogenization method for definition of effective elastic properties.
- Eight different sets of effective elastic properties will be defined for this sub-volume. There are 5 sub-volumes for the rock sample in Fig. 4, so such procedure must be completed for all five sub- volumes. In this case there will be finally 40 different sets of effective elastic properties for rock sample.
- a system which can be used for performing the presented method.
- a scanning device 12 is used for obtaining a digital image of the sample of the porous medium.
- a computer tomographic (CT) scanner, or a Focused Ion Beam Scanning Electron Microscope (FIB-SEM) or similar device capable of producing a three dimensional image of the sample of the porous medium can be used as the scanning device 12.
- CT computer tomographic
- FIB-SEM Focused Ion Beam Scanning Electron Microscope
- the 3D image output of the scanning device 12 is transferred to a computing system 13 having program instructions for further cropping of the image to extract a sub image of the selected sub-volume of the sample and processing the sub image to produce the three dimensional representation of the selected sub- volume of the sample.
- a computing system may be one or more mobile devices, desktop computer, server or any other type of computing device or devices that includes at least the minimum processing power, memory, and input and output devices to perform one or more embodiments.
- the computing system may include one or more computer processor(s) 14 which is adapted to run the programs, an associated memory 15 (e.g., random access memory (RAM), cache memory, flash memory, etc.), one or more storage device(s) 16 (e.g., a hard disk, an optical drive such as a compact disk (CD) drive or digital versatile disk (DVD) drive, a flash memory stick, etc.), and numerous other elements and functionalities.
- the computer processor(s) 14 may be an integrated circuit for processing instructions.
- the computer processor(s) may be one or more cores, or micro-cores of a processor.
- the computing system may also include one or more input device(s), such as a touchscreen, keyboard, mouse, microphone, touchpad, electronic pen, or any other type of input device.
- the computing system may include one or more output device(s), such as a screen (e.g., a liquid crystal display (LCD), a plasma display, touchscreen, cathode ray tube (CRT) monitor, projector, or other display device), a printer, external storage, or any other output device.
- a screen e.g., a liquid crystal display (LCD), a plasma display, touchscreen, cathode ray tube (CRT) monitor, projector, or other display device
- a printer external storage, or any other output device.
- One or more of the output device(s) may be the same or different from the input device(s).
- Software instructions in the form of computer readable program code to perform embodiments may be stored, in whole or in part, temporarily or permanently, on a non-transitory computer readable medium such as a CD, DVD, storage device, a diskette, a tape, flash memory, physical memory, or any other computer readable storage medium.
- the software instructions may correspond to computer readable program code that when executed by a processor(s), is configured to perform embodiments.
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Abstract
La présente invention concerne un procédé mis en œuvre par informatique permettant de déterminer des propriétés élastiques efficaces d'un échantillon d'un milieu poreux comprenant la sélection d'au moins un sous-volume dans le volume d'un échantillon. L'échantillon est balayé et l'image numérique tridimensionnelle obtenue de l'échantillon est utilisée pour créer des représentations numériques tridimensionnelles des sous-volumes sélectionnés. Les volumes élémentaires représentatifs (RVE) initiaux sont sélectionnées à partir de la représentation numérique créée de n'importe quel sous-volume. Ce RVE est utilisé pour la création d'un modèle numérique et la définition ultérieure de propriétés élastiques efficaces. Ensuite, le second RVE supérieur est choisi à partir du même endroit du sous-volume. Le second RVE est également utilisé pour la création d'un modèle numérique et la définition ultérieure de propriétés élastiques efficaces. Ensuite, les valeurs de propriétés élastiques efficaces sont comparées pour deux boîtiers et les différences relatives entre ceux-ci est calculée. Si les valeurs des différences relatives obtenues sont inférieures à une différence relative initialement définie autorisée, le volume du RVE sélectionné initialement est considéré comme la taille de tous les RVE pour le sous-volume en question. Si la valeur des différences relatives obtenues sont plus grandes que la différence relative définie autorisée, le volume plus important de RVE doit être resélectionné à partir de la représentation numérique de sous-volume de l'échantillon. Le procédé peut être répété n fois jusqu'à ce les RVE (n-1) et (n) répondent aux exigences concernant les valeurs de la différence relative. La taille finalement définie du RVE (n-1) est utilisée pour la sélection de tous les autres RVE à partir du modèle numérique considéré de sous-volume de carotte de roche. Ces RVE sont utilisés pour créer des modèles numériques à éléments finis et définir ultérieurement des propriétés élastiques efficaces.
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Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US11009497B2 (en) | 2018-06-22 | 2021-05-18 | Bp Corporation North America Inc. | Systems and methods for estimating mechanical properties of rocks using grain contact models |
CN115410668A (zh) * | 2022-08-31 | 2022-11-29 | 中南大学 | 一种纤维复合材料弹性性能的预测方法 |
Citations (1)
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WO2013148632A1 (fr) * | 2012-03-29 | 2013-10-03 | Ingrain, Inc. | Procédé et système pour estimer des propriétés de milieux poreux, tels que des roches denses ou à pores fins |
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WO2013148632A1 (fr) * | 2012-03-29 | 2013-10-03 | Ingrain, Inc. | Procédé et système pour estimer des propriétés de milieux poreux, tels que des roches denses ou à pores fins |
Non-Patent Citations (3)
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"BELOV Dmitry Aleksanrovich. Gomogenizatsiya i geterogenizatsiya odnonapravlennykh uprugikh voloknistykh kompozitov.", AVTOREFERAT DISSERTATSII NA SOISKANIE UCHENOI STEPENI KANDIDATA TEKHNICHESKIKH NAUK., 2009, Sankt-Peterburg, pages 1 - 16 * |
CARPINTERI ALBERTO ET AL.: "Anisotropic linear elastic properties of fractal-like composites.", PHYSICAL REVIEW E, vol. 82, 2010, pages 1 - 7, XP055383678 * |
MEILLE S ET AL.: "Linear elastic properties of 2D and 3D models of porous materials made from elongated objects.", MODELLING SIMUL. MATER. SCI. ENG., vol. 9, 2001, pages 371 - 390, XP020072659 * |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US11009497B2 (en) | 2018-06-22 | 2021-05-18 | Bp Corporation North America Inc. | Systems and methods for estimating mechanical properties of rocks using grain contact models |
CN115410668A (zh) * | 2022-08-31 | 2022-11-29 | 中南大学 | 一种纤维复合材料弹性性能的预测方法 |
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