EA040615B1 - SYSTEM AND METHOD FOR EVALUATION OF MECHANICAL PROPERTIES OF ROCKS USING MODELS OF INTERGRAIN CONTACT - Google Patents

Description

Link to related application

This application claims priority under U.S. Provisional Application No. 62/688,912 titled Systems and Methods for Evaluating the Mechanical Properties of Rocks Using Grain Contact Models, filed June 22, 2018, the contents of which are incorporated herein by reference as if it were fully described in this description.

Background of the Invention

In the field of hydrocarbon production, obtaining accurate data on the petrophysical properties of subsurface rocks is of great importance for estimating the volume of hydrocarbons contained in rock formations and for formulating a strategy for extracting hydrocarbons from a rock formation. Rock samples, such as those from core samples or cuttings, are typically subjected to physical laboratory tests to measure their petrophysical properties such as permeability, porosity, reservoir coefficient, elastic moduli, and other properties of this kind. Some of these measurements require long periods of time, and in some cases extend beyond a few months, depending on the nature of the rock itself. The equipment used to make these measurements can also be quite expensive.

Taking into account the cost and time to perform direct measurement of petrophysical properties in order to effectively assess physical properties such as porosity, absolute permeability, relative permeability, reservoir coefficient, elastic moduli and other properties of this kind of rock samples, including rock samples of various types, such as gas-saturated sandstone reservoirs and carbonate rocks, direct numerical modeling can be applied. According to this approach, a three-dimensional tomographic image of a rock sample is formed, for example, by its computed tomography (CT) scanning. The voxels in the 3D tomographic image volume are segmented (eg, by binarization or thresholding of their brightness values, or otherwise) to isolate the rock skeleton from the free pore volume. This is followed by direct numerical simulation of fluid flow or other dynamic physical properties such as elasticity or electrical conductivity, from which porosity, permeability (absolute and/or relative), elastic properties, electrical properties, and other similar properties can be derived. A variety of numerical methods can be used to solve or approximate physical equations that model the corresponding dynamic characteristics. These methods include the Lattice Boltzmann Method, the Finite Element Method, the Finite Difference Method, the Numerical Finite Volume Method, and other similar methods.

Brief summary of the invention

The invention describes embodiments of methods for analyzing a granular rock sample to determine one or more mechanical properties of that rock sample. In one embodiment, this method involves segmenting a digital volume of an image corresponding to an image of a rock sample. In addition, this method involves splitting the digital image volume to map multiple voxels in the digital image volume to multiple grains of a rock sample. In addition, this method involves determining voxels from among a plurality of voxels that are adjacent to each other to identify a plurality of contact pairings between grains. Moreover, this method involves determining the contact area of each of the contact pairings using neighboring voxels on the corresponding interface between the grains. This method also includes determining the number of contact mates that each grain of the plurality of grains has with each neighboring grain. Moreover, this method involves determining one or more mechanical properties of a rock sample based on the number of contact mates of each of the plurality of grains and the contact area of each of the contact mates.

The invention describes embodiments of systems for analyzing a rock sample to determine one or more mechanical properties of a rock sample. In one embodiment, this system includes an imaging device configured to generate a digital volume of an image representing a rock sample. In addition, this system contains a computing device connected to the imaging device. The computing device includes one or more processors and one or more storage devices coupled to one or more processors. One or more memories are configured to store instructions that, when executed by one or more processors, configure one or more processors to perform the following operations: segment the digital image volume corresponding to one or more images of a rock sample, to correlate voxels in the digital image volume with grains of a rock sample; partitioning the digital image volume to map the plurality of voxels in the digital image volume to the plurality of grains of the rock sample; definitions of voxels from among the set of voxels that are adjacent to each other

- 1 040615 to a friend, to identify a plurality of contact interfaces between grains; determining the contact area of each of the contact interfaces using neighboring voxels on the corresponding contact interface; determining the number of contact mates that each grain of the plurality of grains has with each neighboring grain; and determining one or more mechanical properties of the rock sample based on the number of contact mates of each of the plurality of grains and the contact area of each of the contact mates.

This document describes embodiments of a non-volatile computer-readable storage medium. In one embodiment, this non-volatile computer-readable storage medium is encoded with instructions that, when executed, cause one or more processors to perform the following operations: segmenting the digital image volume corresponding to one or more images of a rock sample, to associate voxels in the digital image volume with grains rock sample; partitioning the digital image volume to map the plurality of voxels in the digital image volume to the plurality of grains of the rock sample; determining voxels from among the plurality of voxels that are adjacent to each other to identify a plurality of contact mates between grains; determining the contact area of each of the contact interfaces using neighboring voxels on the corresponding contact interface; determining the number of contact mates that each grain of the plurality of grains has with each neighboring grain; and determining one or more mechanical properties of the rock sample based on the number of contact mates of each of the plurality of grains and the contact area of each of the contact mates.

Embodiments of the invention disclosed herein have a combination of features and characteristics that serve to overcome various disadvantages associated with certain devices, systems and methods of the prior art. The features and technical characteristics of the disclosed embodiments of the invention have been outlined above only in general terms in order to better understand the detailed description below. The various described and other characteristics and features will become apparent to those skilled in the art upon reading the following detailed description in conjunction with the accompanying drawings. It should be noted that the concept and specific embodiments of the claimed invention disclosed herein can be used without any difficulty as a basis for modification or design of other structures that serve the same purposes as the described embodiments. It should also be understood that such equivalent constructions do not go beyond the essence and scope of the principles of the claimed invention disclosed in this document.

Brief description of the figures

A detailed description of exemplary embodiments of the invention is given in conjunction with the accompanying drawings, which are not necessarily drawn to scale, and where in FIG. 1A is a schematic representation of one embodiment of onshore and offshore sources of rock samples for analysis using embodiments of the test system and methods according to the principles disclosed herein;

in fig. 1B is a schematic representation of one embodiment of a test system for analyzing rock samples according to the principles disclosed herein;

in fig. 1C is a schematic representation of one embodiment of a computing device suitable for use in the test system shown in FIG. 1B;

in fig. 2 shows one embodiment of a method for analyzing a rock sample according to the principles disclosed herein;

in fig. 3A is a segmented two-dimensional (2D) section of a three-dimensional (3D) image of a rock sample;

in fig. 3B is a segmented two-dimensional (2D) slice of the image shown in FIG. 3A after splitting;

in fig. 3C is a segmented and split two-dimensional (2D) slice of the image shown in FIG. 3B, after identification of grain contacts;

in fig. 4 is a graph illustrating the bulk modulus of a rock sample measured in a laboratory and the calculated bulk modulus of a rock sample as determined by the embodiments of the invention described herein (both normalized and plotted against porosity); and in FIG. 5 is a graph illustrating the shear modulus of a rock sample measured in a laboratory and the calculated shear modulus of a rock sample as determined by the embodiments of the claimed invention described herein (both normalized and plotted against porosity).

Terminology and system of representation of numerical values.

In the following description and the appended claims, the terms including and containing are used as non-limiting terms and should therefore be construed as including, but not limited to, .... Any use of any form of the term

- 2 040615 new connects, engages, binds, attaches and other terms of this kind that describe the interaction between elements, does not imply its limitation to direct interaction between elements, and may also include indirect interaction between the described elements. The term software includes any executable program capable of being run by a processor, regardless of the medium used to store the software. Thus, a program stored in memory (eg, non-volatile memory), sometimes referred to as firmware, is included in the definition of software. The phrase on the basis is intended to mean on the basis of, at least in part. Therefore, if the value of X is based on the value of Y, then the value of X can be based on the value of Y and any number of additional factors. In the context of this document, the terms approximately, about, essentially, and other terms of this kind mean the fluctuation of the specified value within 10% (ie, plus or minus 10%). Thus, for example, said angle of about 80° refers to an angle that ranges from 72 to 88°.

Detailed disclosure of the invention

The following description refers to various embodiments of the present invention. However, one skilled in the art will appreciate that the examples disclosed herein are of wide application and that the description of any embodiment of the present invention is for illustrative purposes only and does not imply that the scope of the claimed invention, including its claims, is limited to that embodiment.

Certain terms are used throughout the following description and in the claims to refer to specific features or components. Any person skilled in the art will appreciate that different people may refer to the same feature or component by different names. This document does not distinguish between components or features that differ in name but not in function. The figures are not necessarily drawn to scale. Certain features and components in this document may be exaggerated or represented to some extent in a schematic form, and some details of standard elements may not be shown for simplicity and brevity of presentation.

Unless the context clearly dictates otherwise, all ranges herein are to be construed as including their limit values, and unrestricted ranges are to be construed to include only practically applicable values. Likewise, all lists of values are to be considered as containing intermediate values, inclusive, unless the context indicates otherwise.

In the drawings and in the following description, the same elements are usually designated throughout the text and in the drawings by the same reference numbers. The figures are not necessarily drawn to scale. Certain features of the embodiments of the present invention may be scaled up or represented to some extent in a schematic form, and some details of the standard elements may not be shown for simplicity and brevity of presentation. The present invention is represented by various variants of its implementation. Specific embodiments of the present invention are described in detail and illustrated in the drawings with the understanding that the present disclosure should be considered as an illustrative example of the implementation of the principles of the present invention and is not intended to be limited by the description illustrated and presented herein. It should be clearly understood that the various ideas and components of the embodiments of the present invention described below can be used individually or in any suitable combination to obtain the desired results.

In general, the bulk modulus of a substance (e.g., rock) is a measure of that substance's ability to resist compression (e.g., loads applied perpendicular to the outer surfaces of the substance), while the shear modulus of a substance (e.g., rock) describes the ability of that substance to resist shear forces (for example, loads applied parallel to the outer surfaces of the substance). The bulk modulus and the shear modulus of the rock in the reservoir serve as input to various types of calculations and numerical simulations used to derive various static elastic mechanical properties of the rock, including the modulus of elasticity, the transverse strain coefficient, the P _wave modulus, the Lamé constant, and - along with material density - also P _wave speed and S _wave speed. The bulk modulus and shear modulus of rocks are often measured in geomechanical laboratory tests. Without laboratory test data, the bulk modulus and shear modulus can be estimated using various models/approaches to study the petrophysical properties of the formation, such as the Hertz-Mindlin model. These approaches require data such as the average number of contacts between individual rock grains and the size (area) of these contacts to be used as input to calculate the effective bulk and shear moduli of the rocks. The number and size of contacts are estimated based on simplified rock geometry, such as spherical grains, and ideal or random grain arrangements. However, these simplifications

- 3 040615 lead to a decrease in the accuracy of the results of measurements of the properties of the rock.

The embodiments of the invention described herein relate to systems and methods for determining the number and size of contacts between individual rock grains, which are used in subsequent calculations to determine the bulk and shear moduli of the rock, which in turn can be used to derive other elastic mechanical properties of rock. In particular, embodiments of the claimed invention described herein provide for obtaining a three-dimensional (3D) digital volume of an image of a rock (i.e., digital rock), segmenting a 3D digital image into component grains and pore space, splitting a segmented 3D digital image for identification of contacts between grains of rock components and subsequent determination of the number and size (area) of each of the contacts between grains of components from a divided segmented digital 3D image. The number and size of each of the contacts between the grains of the components can then be used to calculate the bulk modulus and shear of the rock.

In FIG. 1A illustrates - at a high level - the acquisition of rock samples and the analysis of rock samples in accordance with the principles described herein. Embodiments of the claimed invention can be particularly effective in the analysis of rock samples from buried formations that play an important role in the field of oil and gas production. In this regard, in FIG. 1A shows an environment 100 from which rock samples 104 may be extracted for analysis with a test system 102 in various embodiments. In these illustrated examples, rock samples 104 may be obtained using a land drilling system 106 or an offshore drilling system 108 (ocean, sea, lake, etc.), each of which is used to extract resources such as hydrocarbons ( oil, natural gas, etc.), water and other similar resources. The optimization of oil and gas production operations, one of the fundamental factors in the art, depends to a large extent on the structure and physical properties of rock formations that are drilled or have been drilled in the past using land drilling system 106 or offshore drilling system 108.

Methods for obtaining rock samples 104 and the physical form of these samples can vary over a wide range. Examples 104 of rocks suitable for use in the context of the embodiments of the claimed invention described herein include full size core samples; core samples taken from the borehole wall; rock samples from outcrops; and laboratory-created synthetic rock samples such as sand and cement plugs.

As shown in FIG. 1A, environment 100 includes a test system 102 configured to analyze images 128 (see FIG. 1B) of rock samples 104 to determine the physical properties of the corresponding subsurface rock, which properties include petrophysical properties in the context of oil and gas exploration and oil and gas production.

In FIG. 1B shows in general terms the constituent elements of a test system 102 that analyzes images 128. Broadly, test system 102 includes an imaging device 122 for obtaining two-dimensional (2D) or three-dimensional (3D) images, as well as other forms of representation of rock samples 104. rocks, and such images and representations include details of the internal structure of the samples 104 rocks. One example of an implementation of the imaging device 122 is an X-ray computed tomography (CT) scanner, which - as is known in the art - emits X-rays 124 interacting with an object and measures the X-ray attenuation 124 of the object to generate an image of its internal structure. and structural elements. The particular type, design, or other features of the CT scanner 122 may correspond to those of any type of X-ray device, such as a micro-CT scanner capable of generating an image that displays the internal structure of the rock sample 104. The imaging device 122 generates one or more images 128 of the rock sample 104 and transmits these images 128 to the computing device 120.

The images 128 generated by the imaging device 122 may be represented as a three-dimensional (3D) digital volume of an image (ie, a digital image) consisting of or generated from a plurality of two-dimensional (2D) segments of the rock sample 104. In this case, the volume of the image is broken down into regularly repeating 3D elements, called volume elements, or more commonly voxels. In general, each voxel is a cube with sides of the same length in the X, Y, and Z directions. On the other hand, the digital image volume 128 itself may contain a different number of voxels in the X, Y, and Z directions. Each voxel within the digital volume is characterized by an associated a numerical value or an amplitude that represents the corresponding material properties of the depicted sample at that point in the medium that is displayed by the digital volume. The range of these numerical values, better known as the gray scale, depends on the type of digital volume, the granularity of the values (for example, 8-bit or 16-bit values), and other parameters of this kind. For example, 16-bit data values allow voxels in the volume of an X-ray tomographic image to have an amplitude that varies within

0-65.536 with granularity 1.

As noted above, imaging device 122 transmits images 128 to computing device 120, which may be, as in the example shown in FIG. 1B, any type of computing device, such as a desktop or workstation, laptop, server, tablet, or the like. Accordingly, computing device 120 will include hardware and software components typically found in a standard type computing device. As shown in FIG. 1B, these hardware and software components of computing device 120 include a testing tool 130 that is configured to analyze images 128 to determine the petrophysical properties of a rock sample 104 under one or more simulated fluid conditions, including fluid conditions that may be encountered. rock layers in the near-surface zone. In this regard, test tool 130 may be implemented in software, hardware, or a combination of hardware and software, including all necessary and useful logic, instructions, routines, and algorithms to perform the functions and processes described in more detail below. In a general sense, testing tool 130 is configured to analyze image volume 128 of rock sample 104 to perform direct numerical modeling of petrophysical properties under fluid saturation conditions representing the state of rock formations in the subsurface zone, including varying degrees of saturation with multiple fluids.

In FIG. 1C schematically shows the architecture of computing device 120 as part of test system 102 in accordance with various embodiments of the present invention. In this exemplary architecture, computing device 120 includes one or more processors 902, which may be of various processor core configurations and clock speeds used in the art. Memory resources of computing device 120 for storing data and/or program instructions executed by one or more processors 902 include one or more memory devices 904 serving as main memory during operation of computing device 120 and one or more storage devices 910, for example, implemented as one or more non-volatile solid state drives, magnetic or optical disk drives, or random access memory. One or more peripheral interfaces 906 are provided to connect appropriate peripherals such as displays, keyboards, mice, touch pads, touch screens, printers, and the like. Network interfaces 908, which may be in the form of Ethernet adapters, wireless transceivers, serial network components, and other devices, are designed to facilitate interaction between computing device 120 and one or more networks such as Ethernet, wireless Ethernet, global system for mobile communications ( GSM), EDGE (Enhanced Data Rate GSM Evolution), Universal Mobile Telecommunications System (UMTS), Global Interoperability Communications System for Microwave Access (WiMAX), Long Term Network Evolution (LTE) standard system, and the like. In this architecture example, processors 902 are shown to communicate with components 904, 906, 908, and 910 via a single bus; but, of course, a different communication architecture can be implemented in the computing device 120, for example, in the form of a plurality of specialized buses, etc.

Although the computing device 120 is represented as a separate computing device, it may include multiple computing devices that interact with each other to implement the functionality of the computing device. Similarly, although computing device 120 is represented as a physical device, computing device 120 may also be an abstract computing device such as a virtual machine and a cloud computing device.

As shown in the embodiment illustrated in FIG. 1C, computing device 120 includes software products 912 containing one or more operating systems, one or more application programs, and the like. According to embodiments of the present invention, software products 912 comprise software instructions corresponding to a test tool 130 (see FIG. 1B) implemented as a stand-alone application; as a software module that is part of another application or program; in the form of appropriate plug-ins or other software components for accessing the software of the testing tool on a remote computer connected via a network to the computing device 120 through the network interfaces 908; or in other forms and combinations thereof.

Program memory that stores executable instructions for software products 912 corresponding to the functions of test tool 130 may be physically located on computing device 120 or other computing resources available to computing device 120, i. in the local memory resources of devices 904 and drives 910; or it may be located on a server or other memory resources accessible through the network; or it may be dispersed over many locations. In any event, this program memory constitutes a non-volatile, computer-readable storage medium that stores executable computer program instructions that cause the operations described herein to be performed by computing device 120 or by a server or other computing device connected to computing device 120 via network interfaces. 908 (eg, as an interactive application for input from computing device 120 to be displayed or provided by peripheral devices connected to computing device 120). The computer-executable program instructions corresponding to the software products 912 that are associated with the test tool 130 may initially be stored on a removable or other non-volatile machine-readable storage medium (e.g., a DVD, flash memory, or similar device) or loaded into in the form of encoded information on an electromagnetic carrier signal in the form of a software package from which computer-executable program instructions are installed by the computing device 120 in the usual way that is used to install software. It is expected that those skilled in the art will be able to easily store and retrieve the necessary data, program instructions, and other information useful in connection with this embodiment of the present invention in a manner suitable for each particular application without resorting to undue experimentation.

The specific machine instructions that make up the software products 912 associated with the test tool 130 may be implemented as one or more executable programs, or as source code or higher level code from which one or more is derived, assembled, interpreted, or compiled. executable programs. In this case, any of a variety of machine languages or protocols can be used, depending on how the required operations are to be performed. For example, these machine instructions for creating a model according to embodiments of the present invention may be written in a standard high-level language such as PYTHON, JAVA, FORTRAN, or C++, or as a conventional linear programming computer program, or for execution in an object-oriented manner. These commands can also be embedded in a higher level application. In any case, it is expected that those skilled in the art, upon reading the present description, will be able to readily implement the various embodiments in any manner suitable for installation without resorting to undue experimentation.

The specific functions of the testing tool 130, including those implemented by the software products 912, for analyzing rock samples under various saturation conditions according to the embodiments of the present invention, which are disclosed in connection with FIG. 2 in combination with FIG. α-IC.

Let us now turn to FIG. 2, which shows one embodiment of a method 200 for analyzing rock samples to determine the number and size of contacts between component grains in rock samples. Although the steps are shown sequentially for convenience, at least some of the illustrated steps may be performed in a different order and/or performed in parallel. In addition, in some embodiments of the present invention, only a portion of the steps shown are performed. In some embodiments of the present invention, at least some of the operations within method 200, as well as other operations described herein, may be implemented as instructions stored in a computer-readable medium and executed by one or more processors 902.

In step 202, the testing system 102 obtains a rock sample 104 to be analyzed, for example, from subsurface rock using a land drilling system 106 or an offshore drilling system 108, or from other sources. A particular rock sample 104 may be obtained from subsurface rock of a larger volume, for example, by drilling or cutting a portion of a large volume from the rock of interest, and the dimensions, size, and configuration of the sample should be such that they can be visualized using an imaging device 122 (eg, a CT scanner).

In step 204, the imaging device 122, in cooperation with the computing device 120 of the test system 102, generates a digital image volume 128 representing the rock sample 104, including its internal structure. For example, if the imaging device 122 is a CT scanner, then an X-ray image of the rock sample 104 (i.e., emitting radiation onto the rock sample 104 and measuring the attenuation of that radiation) is generated to generate image volumes 128 from or from 2D slice images. images of 2D slices. Specific standard techniques for obtaining and processing 3D digital volumes 128 of an image of a rock sample 104 in step 204 include, but are not limited to, X-ray tomography, X-ray microtomography, X-ray nanotomography, focused ion beam scanning electron microscopy, and nuclear magnetic resonance. In some embodiments of the present invention, the digital image volume 128 may be computed rather than by scanning a physical sample. In embodiments where the digital image volume 128 is created by scanning a rock sample, the rock sample may be a naturally occurring rock or an artificial porous material (eg, synthetic rock).

The image data at this stage can be expressed as gray values representing the X-ray attenuation of the rock sample 104 components. As will be described in the next paragraph, FIG. 3A illustrates a single 2D slice image 300 through the digital image volume 128, it being understood that the 3D digital image volume 128 of the rock sample 104 consists of multiple 2D slice images at discrete positions along one axis of the rock sample 104 that collectively form 3D image of rock sample 104. In general, the merging of 2D slice images into a 3D digital image volume 128 may be performed by the computing resources of the imaging device 122 itself, or by the computing device 120 over a number of 2D slice images acquired by the imaging device 122, depending on the particular architecture of the test system 102.

Let us now turn to FIG. 3A, which shows one example of an image 300 of one segmented 2D slice of the digital image volume 128 of the rock sample 104. A segmented 2D slice image 300 illustrates a cross-sectional view of the structural elements of a rock sample 104, including solid material features 302 such as individual rock grains (highlighted in white in FIG. 3A) and pore space or pore volume 304 (highlighted in black in FIG. 3A). ). In step 206, the test system 102 performs segmentation or other image enhancement technique on the digital image volume 128 of the rock sample 104 to distinguish and mark different components or phases of the image volume 128 by gray values in the image. The segmented digital image volume 128 may comprise a two-dimensional (2D) slice image 300 displaying a rock sample 104 . In particular, computing device 120 performs this segmentation to identify components such as pore space and minerals (eg, clays and quartz). In some embodiments of the present invention, the testing tool 130 is configured to segment the image volume 128 into more than two significant phases representing structural material constituents such as pore space, clay fraction, quartz fraction, and various other mineral types.

Computing device 120 may use any type of segmentation algorithms. One approach to segmentation is to apply a binarization process to the image volume 128 in which the computing device 120 selects a threshold value within a range of voxel amplitudes. In this case, those voxels whose amplitude is below the threshold value are assigned one specific numerical value that represents the pore space, while other voxels whose amplitude is above the threshold value are assigned a different numerical value that represents the matrix space (i.e., continuous material) . In this approach, binarization converts the volume of a grayscale image into a segmented volume of voxels having one of two possible numerical values, typically chosen between 0 and 1. FIG. 4A shows one example of segmentation performed on the image 300 of a two-dimensional slice of the digital image volume 128 by the binarization method. As can be seen, the segmentation allows the structural elements of the rock sample to be distinguished, with the solid material 302 in this example colored in different colors (different shades of gray in the grayscale image shown in FIG. 3A) representing the different materials in the volume 128 and the pores or pore volume 304 is painted black. Subsequently, the segmentation may be applied one or more times to different features in the image. If simple binarization is used, then multiple thresholds can distinguish between different materials exhibiting different X-ray attenuation characteristics, such as clay, quartz, feldspar, etc.

Alternatively, computing device 120 may use other sharding algorithms. One example of such an alternative algorithm is known in the art as the Otsu method, in which a histogram-based binarization method selects a threshold to minimize the cumulative variance of bimodal gray value distribution patterns (i.e., intra-class variance). The Otsu method can be easily automated, and can also be extended to rebinarize an image multiple times to distinguish between additional material components such as quartz, clay, and feldspar. Other examples of automated segmentation algorithms of varying degrees of sophistication may alternatively or additionally be used by computing device 120 to distinguish between different features in an image volume, such algorithms including indicator kriging, active edge convergence, watershed, and others of a similar nature.

Computing device 120 may also use other image enhancement techniques to improve or enhance the quality of structure detected in image volume 128 to further differentiate structure, reduce the effects of noise, and the like. Similarly, it is contemplated that although segmentation or other image quality enhancement techniques may be performed by computing device 120, other components of test system 102, such as imager 122 itself, may alternatively enhance image quality in whole or in part.

Segmentation relates voxels in the digital image volume to a specific material (or pore space, as the case may be) at a corresponding location in the rock sample 104 . Each voxel of some or all of the voxels is associated with one or more material properties corresponding to the particular structural component of the material assigned to that voxel. Such structural constituents include pore space, matrix material, clay fraction, individual grains, grain contacts, mineral types, and the like.

In step 208, computing device 120 decomposes the identified phases of the segmented digital image volume 128 to identify individual contacts or contact interfaces between component grains. The stakeout in step 208 may be performed using third party imaging software such as Avizo™ software from ThermoFisher Scientific™, Hillsborough, Oregon, USA. During stakeout, the grain of each component can be identified by voxels (eg, voxels 303, 305, and 307 shown in FIG. 3B) in the 2D slice image 300. In other words, each voxel or group of voxels defines or displays a single grain, and the voxels of each grain can be displayed with a different color (or color patterns, shades of gray) voxel or group of voxels, as shown in Fig. 3B. In FIG. 3B illustrates one example of a split image 300 of a 2D slice of a 3D image (eg, digital image volume 128) of a rock sample, showing a cross section of the structural elements of that rock sample. The dimensions (eg, area, volume, radius (R), etc.) of each grain may be determined using imaging software. After staked out in step 208, grain-to-grain contacts (eg, mates 309 and 311 shown in FIG. 3C) are identified as the region where the voxel associated with grain X (eg, voxel 303) is adjacent to the voxel associated with grain Y (eg. , voxel 305).

In step 210 following the staking step, computing device 120 identifies contact mates between grains (eg, mates 309 and 311 shown in FIG. 3C) and then determines (eg, calculates) the contact area (also referred to simply as area). Contact mates are identified by voxels of neighboring grains. For example, a contact interface between two grains can be defined by a group or cluster of adjacent voxels between two adjacent grains. Thus, by identifying groups of voxels between adjacent grains, contact mates between grains can be identified. Once the contact interfaces between grains are identified, the boundaries of these contact interfaces become known and they can be used to determine (eg, calculate) the contact area of each contact interface. The area of contact between two voxels is the area of one of the sides of the voxel at the interface (for example, a voxel is a cube). For example, if grain X and grain Y contain 100 voxels adjacent to each other, and the area of one of the sides of the voxel is 4 µm ² , then the total contact area is 400 µm ² .

At step 210, the contact area of each contact mate is used to determine (eg, calculate) the radius a of the contact surface of each contact mate. In particular, it should be appreciated that each grain may have a unique and/or geometrically irregular three-dimensional configuration, whereby the geometry or shape of the contact interface between each pair of contacting grains may also be unique and/or irregular (e.g., non-circular). To simplify calculations and numerical simulations (for example, so that Equations 1-4 below can be used), the irregular shape of each contact mate is converted to a circle with the same contact area, after which the radius a of each such circle is determined. Thus, the shape and contact area of each contact interface is effectively converted to a circle of the same area with a radius a (also referred to as the contact area radius).

After determining the radius a of the contact surface of each contact interface, the shear contact stiffness and the normal contact stiffness of each contact interface are calculated. One of the ways to calculate these stiffnesses is implemented in equations 1 and 2 of wine

St--—

-G

Equation (1) , where the value of St denotes the contact shear stiffness for the case of infinite contact friction; the value of μ denotes the shear modulus of the granular material; the value of υ denotes the coefficient of transverse deformation of the granular material; and the value a denotes the radius of the contact surface. The shear contact stiffness, denoted by St, is zero in the case of zero contact friction.

ψα

Sn=---

-ν

Equation (2) where the value of Sn denotes the normal contact stiffness; the value of μ denotes the shear modulus of the granular material; the value of υ denotes the coefficient of transverse deformation of the granular material; and the value a denotes the radius of the contact surface.

After calculating the shear contact stiffness St and the normal contact stiffness Sn of each contact mate, using equations 1 and 2, the average shear contact stiffness and the average normal contact stiffness per grain and the average number of contacts per grain are calculated. After that, the effective moduli of bulk elasticity and shear are calculated using equations 3 and 4

C(1 - 0)

Equation (3) where Keff is the effective bulk modulus; the C value denotes the number of contact mates per grain (also referred to as the coordination number per grain); the value 0 denotes porosity; the R value denotes the grain radius; and the value of Sn denotes the normal contact stiffness. . .

^Ue ^ ⁼ 2 _O ER(Sn^l.5SF

Equation (4) where μeff is the effective shear modulus; value C denotes the number of contact interfaces per grain; the value 0 denotes porosity; the R value denotes the grain radius; the value of Sn denotes the normal contact stiffness; and the value of St denotes the contact shear stiffness.

Bulk and shear moduli established using the methods and equations described above can be used to derive a variety of mechanical properties of grains and rock, such as modulus of elasticity, Lame constant, transverse strain coefficient, P _wave modulus, P _wave velocity, and speed S _wave using methods known in the art. It should be noted that the distributions, maxima, minima, and averages of the properties defined above (e.g., number of contact interfaces per grain, contact area of each contact interface, shear contact stiffness, normal contact stiffness, bulk modulus, shear modulus etc.) for all grains can be established and used in subsequent calculations to determine the properties of all grains, reflecting the properties of the rock as a whole. Compared to simplified models for determining rock properties, the embodiments of the claimed invention described herein provide the potential to improve the accuracy of calculations of such properties in relation to granular materials. The embodiments disclosed herein have the potential to increase output speed while providing generally acceptable accuracy. For example, in FIG. 4 shows the bulk modulus of a rock sample measured in the laboratory (Laboratory Measurements) compared to the bulk modulus (K _effective ) of the same rock sample determined using the embodiments of the methods described herein (Calculation). Both the bulk modulus measured in the laboratory and the calculated bulk modulus are normalized by the mineral modulus (Kmineral), which is known in the art as the bulk modulus of a particulate material such as quartz, and which is shown in FIG. 4 as a function of porosity. As another example, in FIG. 5 shows the shear modulus (μ _{e ffective} ) of a rock sample measured in the laboratory (Laboratory Measurements) compared to the shear modulus of the same rock sample determined using the embodiments of the methods described here (Calculations), for the case zero friction (Calculations μ=0) and infinite friction (Calculations μ=”). The shear modulus measured in the laboratory and the calculated shear moduli are normalized by the shear modulus of the particulate material (mineral), which is known in the art as the shear modulus of the particulate material, and which is shown in FIG. 5 as a function of porosity. As shown in FIG. 5, the shear moduli measured in the laboratory usually lie between the calculated shear moduli for the cases of zero and infinite friction.

While preferred embodiments of the claimed invention have been described and illustrated herein, various modifications may be made by one skilled in the art without departing from the scope or spirit of the present invention. Disclosed Options

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Claims (15)

implementation of the claimed invention are purely illustrative and not restrictive. Many changes and modifications may be made to the systems, devices, and processes described herein, all within the scope of the claimed invention. For example, the relative dimensions of the various parts, the materials from which the various parts are made, and other parameters can be changed. Accordingly, the scope of legal protection is not limited to the embodiments of the claimed invention described herein, but is limited only by the following claims, the scope of which should include all equivalents of the subject matter of the claims. Unless expressly stated otherwise, the steps in the method claims may be performed in any order. The listing of identifiers such as (a), (b), (c) or (1), (2), (3) before describing the steps in the method claims does not imply or indicate a specific order in which these steps are performed, but is used only to simplify the subsequent reference to such stages. CLAIM 1. A method of analyzing a rock sample to determine one or more mechanical properties of a rock sample, the method comprising: (a) segmenting the digital image volume corresponding to the rock sample image to identify the solid phase of the digital image volume and associating a plurality of voxels in the digital image volume with the solid phase; (b) splitting the digital image volume to identify a plurality of grains of the solid phase and correlating the specified set of voxels in the digital image volume with the specified set of grains; (c) determining voxels from among the plurality of voxels that correspond to different grains and are adjacent to each other to identify a plurality of contact pairings between each pair of adjacent grains from among said plurality of grains; (d) determining the contact area of each of the contact interfaces using neighboring voxels on the corresponding contact interface; (e) determining for each contact interface the radius of a circle whose area is equal to the contact area of the corresponding contact interface; (f) determining the number of contact mates that each grain of the plurality of grains has with each neighboring grain; and (g) determining one or more mechanical properties of the rock sample based on the number of contact mates of each of the plurality of grains and the radius of a circle corresponding to each of the contact mates. 2. The method of claim 1, wherein at least some of the plurality of contact interfaces are non-circular contact interfaces, and wherein step (d) comprises determining the contact area of each of the non-circular contact interfaces using adjacent voxels at the location of the corresponding non-circular contact interface. 3. The method of claim 1, wherein step (f) comprises determining the bulk modulus and shear modulus of the rock sample. 4. The method of claim 1, wherein step (f) comprises determining one or more of the following mechanical properties of the rock sample: bulk modulus, shear modulus, modulus of elasticity, transverse strain coefficient, P _wave modulus, P _wave velocity, and S _wave speed. 5. The method of claim 1, further comprising calculating the shear contact stiffness of the rock sample using the radius of the circle corresponding to each contact interface. 6. The method of claim 1, further comprising calculating the normal contact stiffness of the rock sample using the radius of the circle corresponding to each contact mate. 7. A rock sample analysis system for determining one or more mechanical properties of a rock sample, the system including: an imaging device configured to generate a digital image volume representing the rock sample; and a computing device connected to the imaging device and including one or more processors; and one or more memory devices connected to one or more processors and configured to store instructions that, when executed by one or more processors, configure one or more processors to perform the following operations: segmenting the digital image volume corresponding to one or more images of the rock sample to identify the solid phase of the digital image volume and associating a plurality of voxels in the digital image volume with the solid phase; splitting the digital image volume to identify a plurality of grains of the solid phase and correlating the specified set of voxels in the digital image volume with the specified set of grains; determining voxels from among the plurality of voxels that correspond to different grains and are adjacent to each other to identify a plurality of contact mates between each pair of adjacent grains from among said plurality of grains; determining the contact area of each of the contact interfaces using neighboring voxels on the corresponding contact interface; determining for each contact mate the radius of a circle whose area is equal to the contact area of the corresponding contact mate; determining the number of contact mates that each grain of the plurality of grains has with each neighboring grain; and determining one or more mechanical properties of the rock sample based on the number of contact mates of each of the plurality of grains and the radius of a circle corresponding to each of the contact mates. 8. The system of claim 7, wherein at least some of the plurality of contact interfaces are non-circular contact interfaces, and wherein the instructions further configure one or more processors to perform the following operation: determining the contact area of each of the non-circular contact interfaces using neighboring voxels in the place of the corresponding contact interface of a non-circular shape. 9. The system of claim 8, wherein the one or more mechanical properties include a bulk modulus, a shear modulus, a modulus of elasticity, a shear modulus, a modulus Pwave, a velocity P _w ave, or a velocity S _w ave. 10. The system of claim 8, wherein the instructions further configure one or more processors to calculate the shear contact stiffness of the rock sample using the radius of a circle corresponding to each contact interface. 11. The system of claim 8, wherein the instructions further configure one or more processors to calculate the normal contact stiffness of the rock sample using the radius of a circle corresponding to each contact mate. 12. A non-volatile computer-readable storage medium in which instructions are encoded, which, when executed, initiate the execution by one or more processors of the following stages: segmenting the digital image volume corresponding to one or more images of the rock sample to identify the solid phase of the digital image volume and correlating a plurality of voxels in the digital image volume to the solid phase; partitioning the digital image volume to identify a plurality of grains of the solid phase and correlating said plurality of voxels in the digital image volume with said plurality of grains; determining voxels from among the plurality of voxels that correspond to different grains and are adjacent to each other to identify a plurality of contact mates between each pair of adjacent grains from said plurality of grains; determining the contact area of each of the contact interfaces using neighboring voxels on the corresponding contact interface; determining the number of contact mates that each grain of the plurality of grains has with each neighboring grain; and determining for each contact interface the radius of a circle whose area is equal to the contact area of the corresponding contact interface; determining one or more mechanical properties of the rock sample based on the number of contact mates of each of the plurality of grains and the radius of the circle corresponding to each of the contact mates. 13. The computer-readable storage medium of claim 12, wherein at least some of the plurality of contact interfaces are non-circular contact interfaces, and wherein the instructions further configure one or more processors to perform the following operation: determining the contact area of each of the contact interfaces non-circular shape using adjacent voxels at the corresponding non-circular contact interface. 14. The computer-readable storage medium of claim 13, wherein one or more of the mechanical properties includes a bulk modulus, a shear modulus, a modulus of elasticity, a transverse strain coefficient, a modulus Pwave, a velocity Pwave, or a velocity Swave. 15. The computer-readable storage medium of claim 13, wherein the instructions further configure one or more processors to calculate shear contact stiffness of the rock sample. -