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 PDF

Info

Publication number
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
Authority
WO
WIPO (PCT)
Prior art keywords
elastic properties
volume element
effective elastic
representative volume
volume
Prior art date
Application number
PCT/RU2015/000797
Other languages
English (en)
Inventor
Dmitry Alexandrovich Belov
Alexander Nikolaevich NADEEV
Yamid Pico
Original Assignee
Schlumberger Technology Corporation
Schlumberger Canada Limited
Services Petroliers Schlumberger
Schlumberger Technology B.V.
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Schlumberger Technology Corporation, Schlumberger Canada Limited, Services Petroliers Schlumberger, Schlumberger Technology B.V. filed Critical Schlumberger Technology Corporation
Priority to PCT/RU2015/000797 priority Critical patent/WO2017086824A1/fr
Publication of WO2017086824A1 publication Critical patent/WO2017086824A1/fr

Links

Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058Kind of property studied
    • G01N2203/0069Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0075Strain-stress relations or elastic constants
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02Details not specific for a particular testing method
    • G01N2203/0202Control of the test
    • G01N2203/0212Theories, calculations
    • G01N2203/0216Finite elements
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00Details relating to CAD techniques
    • G06F2111/10Numerical 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.

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Analysing Materials By The Use Of Radiation (AREA)

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.
PCT/RU2015/000797 2015-11-17 2015-11-17 Procédé mis en œuvre par ordinateur et système de détermination de propriétés élastiques efficaces d'un échantillon d'un milieu poreux WO2017086824A1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
PCT/RU2015/000797 WO2017086824A1 (fr) 2015-11-17 2015-11-17 Procédé mis en œuvre par ordinateur et système de détermination de propriétés élastiques efficaces d'un échantillon d'un milieu poreux

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/RU2015/000797 WO2017086824A1 (fr) 2015-11-17 2015-11-17 Procédé mis en œuvre par ordinateur et système de détermination de propriétés élastiques efficaces d'un échantillon d'un milieu poreux

Publications (1)

Publication Number Publication Date
WO2017086824A1 true WO2017086824A1 (fr) 2017-05-26

Family

ID=58719162

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/RU2015/000797 WO2017086824A1 (fr) 2015-11-17 2015-11-17 Procédé mis en œuvre par ordinateur et système de détermination de propriétés élastiques efficaces d'un échantillon d'un milieu poreux

Country Status (1)

Country Link
WO (1) WO2017086824A1 (fr)

Cited By (2)

* Cited by examiner, † Cited by third party
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)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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)

* Cited by examiner, † Cited by third party
Title
"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)

* Cited by examiner, † Cited by third party
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

Similar Documents

Publication Publication Date Title
Sutton et al. Recent advances and perspectives in digital image correlation
Forsberg et al. Full Three‐dimensional strain measurements on wood exposed to three‐point bending: analysis by use of digital volume correlation applied to synchrotron radiation micro‐computed tomography image data
Herrmann et al. Methods for fibre orientation analysis of X-ray tomography images of steel fibre reinforced concrete (SFRC)
JP2021529949A (ja) デジタルイメージングによる岩石構造の幾何学的特性の識別
Ji et al. Characterization of pore structure and strain localization in Majella limestone by X-ray computed tomography and digital image correlation
Bernard et al. Constrained sintering of glass films: Microstructure evolution assessed through synchrotron computed microtomography
Speijer et al. Quantifying foraminiferal growth with high-resolution X-ray computed tomography: New opportunities in foraminiferal ontogeny, phylogeny, and paleoceanographic applications
Stavropoulou et al. Dynamics of water absorption in callovo-oxfordian claystone revealed with multimodal X-ray and neutron tomography
Hu et al. Three-dimensional segmentation of computed tomography data using Drishti Paint: new tools and developments
Proudhon et al. Coupling diffraction contrast tomography with the finite element method
Friese et al. Analysis of tomographic mineralogical data using YaDiV—Overview and practical case study
Escoda et al. Three‐dimensional morphological modelling of concrete using multiscale Poisson polyhedra
Al-Raoush Change in microstructure parameters of porous media over representative elementary volume for porosity
Schilling et al. Reviving the dinosaur: virtual reconstruction and three-dimensional printing of a dinosaur vertebra
Ushizima et al. Materials data science for microstructural characterization of archaeological concrete
Stojanovic et al. Service-oriented semantic enrichment of indoor point clouds using octree-based multiview classification
Stojanovic et al. A service-oriented approach for classifying 3D points clouds by example of office furniture classification
Medina et al. A geometry-based algorithm for cloning real grains 2.0
WO2017086825A1 (fr) Procédé informatique et système de détermination de propriétés élastiques efficaces d'un échantillon d'un milieu poreux
Kim et al. Characterizing partially saturated compacted-sand specimen using 3D Image registration of high-resolution neutron and X-ray tomography
Liu et al. Improved estimates of percolation and anisotropic permeability from 3‐DX‐ray microtomography using stochastic analyses and visualization
Heitor et al. Aluminium alloy foam modelling and prediction of elastic properties using X-ray microcomputed tomography
WO2017086824A1 (fr) Procédé mis en œuvre par ordinateur et système de détermination de propriétés élastiques efficaces d'un échantillon d'un milieu poreux
Tsafnat et al. Micro-finite element modelling of coke blends using X-ray microtomography
Mutiargo et al. Defect detection using trainable segmentation

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 15908886

Country of ref document: EP

Kind code of ref document: A1

NENP Non-entry into the national phase

Ref country code: DE

122 Ep: pct application non-entry in european phase

Ref document number: 15908886

Country of ref document: EP

Kind code of ref document: A1