Material properties derived from two-dimensional images

Abstract

This invention discloses a method for analyzing rock samples, the method comprising: performing scanning electron microscopy (SEM) imaging of multiple physical surfaces of the rock sample to generate two-dimensional (2D) SEM images of the physical surfaces; applying a cross-correlation function to a first 2D SEM image and a second 2D SEM image to generate a three-dimensional (3D) digital model volume based on the first and second 2D SEM images; and determining a probability distribution of the aperture of the 3D digital model volume based on the image intensity values ​​of pixels in each of the first and second 2D SEM images.

Description

[0001] Cross-references to related applications

[0002] This application claims the benefit of U.S. Provisional Patent Application No. 63 / 021,885, filed May 8, 2020, entitled “Material Properties from Two-Dimensional Image,” which is incorporated herein in its entirety for all purposes. Background of the Invention

[0004] In hydrocarbon production, obtaining accurate estimates of the rock physical properties of rock formations is crucial for assessing the volume of hydrocarbons contained within the formations and for developing strategies for hydrocarbon extraction. Traditionally, rock samples, such as those from core samples or drill cuttings, are subjected to physical laboratory testing to measure rock physical properties such as permeability, porosity, formation factor, and elastic modulus. Some of these measurements are lengthy, sometimes lasting several months, depending on the properties of the rock itself. The equipment used to perform these measurements is also very expensive.

[0005] Because directly measuring the physical properties of rocks is costly and time-consuming, direct numerical simulation techniques can be used to efficiently estimate the physical properties of rock samples, such as porosity, absolute permeability, relative permeability, formation factor, and elastic modulus, including samples from challenging rock types, such as dense gas-bearing sands or carbonates. According to this method, three-dimensional tomographic images of the rock samples are obtained, for example, via computed tomography (CT) scans. Voxels in the three-dimensional image volume are "segmented" (e.g., by "thresholding" their brightness values, or by another method) to distinguish the rock matrix and pore spaces. Direct numerical simulations of fluid flow or other physical behaviors such as elasticity or electrical conductivity are then performed, from which porosity, permeability (absolute and / or relative), elastic properties, electrical properties, etc., can be derived. Various numerical methods can be applied to solve or approximate the physical equations for appropriate behavior. These methods include lattice-Boltzmann, finite element, finite difference, finite volume numerical methods, etc. Summary of the Invention

[0006] According to at least one example of the present invention, a method for analyzing a rock sample includes: performing scanning electron microscopy (SEM) imaging of multiple physical surfaces of the rock sample to generate two-dimensional (2D) SEM images of the physical surfaces; applying a cross-correlation function to a first 2D SEM image and a second 2D SEM image to generate a three-dimensional (3D) digital model volume based on the first and second 2D SEM images; and determining a probability distribution of the pore size of the 3D digital model volume based on the image intensity values ​​of pixels in each of the first and second 2D SEM images.

[0007] According to another example of the invention, a system for analyzing rock samples includes: a scanning electron microscope (SEM) configured to generate two-dimensional (2D) SEM images of the physical surfaces of the rock sample; and a computing device coupled to the SEM. The computing device includes a processor and a memory coupled to the processor. The memory is configured to store instructions, which, when executed by the processor, configure the computing device to apply a cross-correlation function to a first 2D SEM image and a second 2D SEM image, generate a three-dimensional (3D) digital model volume based on the first and second 2D SEM images, and determine a probability distribution of the aperture of the 3D digital model volume based on the image intensity values ​​of pixels in each of the first and second 2D SEM images.

[0008] According to yet another example of the invention, a non-transitory computer-readable medium is encoded with instructions that, when executed by a processor, cause the processor to: receive two-dimensional (2D) scanning electron microscope (SEM) images of the physical surfaces of a rock sample; apply a cross-correlation function to a first 2D SEM image and a second 2D SEM image to generate a three-dimensional (3D) digital model volume based on the first and second 2D SEM images; and determine a probability distribution of the aperture of the 3D digital model volume based on the image intensity values ​​of pixels in each of the first and second 2D SEM images.

[0009] The embodiments described herein include a combination of features and characteristics designed to address various drawbacks associated with certain existing apparatuses, systems, and methods. The foregoing has provided a fairly broad overview of the features and technical characteristics of the disclosed embodiments to facilitate a better understanding of the following detailed description. Those skilled in the art will readily understand the various features and characteristics described above by reading the following detailed description and referring to the accompanying drawings. It should be understood that the disclosed concepts and specific embodiments can be readily used as the basis for modifying or designing other structures for the same purposes as the disclosed embodiments. It should also be appreciated that these equivalent structures do not depart from the spirit and scope of the principles disclosed herein. Brief description of the attached diagram

[0011] For a detailed description of the exemplary embodiments, reference will now be made to the accompanying drawings, which may not be drawn to scale, in which:

[0012] Figure 1a is a schematic horizontal diagram illustrating an example of a rock sample source for a test system constructed and operated according to the principles disclosed herein;

[0013] Figure 1b shows a block diagram of a testing system for analyzing rock samples based on the principles disclosed herein;

[0014] Figure 1c shows a block diagram of a computing device suitable for a testing system for analyzing rock samples, based on the principles disclosed herein;

[0015] Figure 2 shows a flowchart of a method for analyzing rock samples based on the principles disclosed herein;

[0016] Figures 3a and 3b show two-dimensional (2D) slice images of rock samples suitable for use with the various embodiments disclosed herein;

[0017] Figure 4 Rock samples containing multiple rock textures are shown in preparation for machining according to various embodiments disclosed herein;

[0018] Figures 5a-5c show scanning electron microscope (SEM) images of rock surfaces machined at different scales according to various embodiments disclosed herein;

[0019] Figure 5d shows alternative examples of the methods of Figures 5a-5c according to the various embodiments disclosed herein;

[0020] Figures 6a and 6b illustrate the segmentation operation of SEM images according to various implementation schemes disclosed herein;

[0021] Figures 7a and 7b illustrate the generation of a set of statistically similar 3D models from a set of segmented SEM images according to various implementation schemes disclosed herein;

[0022] Figure 8 Visual representations of numerical simulations of one of the 3D models derived from Figure 7b are shown, based on the various embodiments disclosed herein.

[0023] Figure 9 A flowchart is shown for another method for analyzing rock samples based on the principles disclosed herein;

[0024] Figure 10An example is shown of the fractional bounce parameter (FBP) used in the grayscale lattice Boltzmann (GSLB) model, determined according to the principles disclosed herein;

[0025] Figures 11a-11d show a set of nomograms that correlate the material properties, FBP values, and different grid sizes of rock samples according to the principles disclosed herein.

[0026] Figure 12 An example is shown of segmenting an image volume using the grid size of a column plot selected from the set of column plots in Figure 11;

[0027] Figure 13 A comparison of the original digital images and simulated flow fields based on the principles disclosed herein is shown; and

[0028] Figure 14 A flowchart illustrating another method for analyzing rock samples based on the principles described herein is shown.

[0029] Symbols and nomenclature

[0030] In the following discussion and claims, the terms “comprising” and “including” are used in an open-ended manner and should therefore be interpreted as “including, but not limited to…”. Any use of the terms “connected,” “participating,” “coupled,” “attached,” or any other term describing the interaction between elements does not imply that the interaction is limited to direct interaction between elements, and may also include indirect interaction between the described elements. The term “software” includes any executable code capable of running on a processor, regardless of the medium used to store the software. Thus, code stored in memory (e.g., non-volatile memory) and sometimes referred to as “embedded firmware” is included in the definition of software. The reference “based on” is intended to mean “at least partially based on”. Therefore, if X is based on Y, then X may be based on Y and any number of other factors. Detailed Implementation

[0031] In the following figures and description, similar parts are generally labeled with the same reference numerals throughout the specification and figures. The figures are not necessarily drawn to scale. Certain features of the embodiments may be enlarged to scale or shown in some schematic form, and some details of conventional elements may be omitted for clarity and brevity. The invention is susceptible to various forms of embodiments. Specific embodiments are described in detail and illustrated in the figures; it should be understood that the invention is considered to be illustrative of the principles of the invention and is not intended to limit the invention to what is illustrated and described herein. It should be fully appreciated that the different teachings and components of the embodiments discussed below can be used alone or in any suitable combination to produce the desired results.

[0032] Unconventional shale reservoirs are inherently heterogeneous, leading to complexities when attempting to simulate their behavior. A better understanding of how nanoscale and microscale fabrication governs fluid flow in shale reservoirs will benefit the optimization or improvement of hydrocarbon production. Achieving this understanding is challenging. Imaging rock samples derived from shale reservoirs to characterize their nanoscale and microscale fabrication requires high resolution in terms of its impact on the overall hydrocarbon volume and fluid flow. Currently, focused ion beam scanning electron microscopy (FIB-SEM) can provide 3D information at this resolution. However, FIB-SEM imaging of rock samples is extremely time-consuming and resource-intensive, making it uneconomical and inefficient at the scale required to characterize the nanoscale and microscale fabrication of rock samples. Furthermore, existing attempts to simulate shale reservoir behavior using FIB-SEM imaging do not account for the uncertainties in the determined material properties, which are important when profiling risks for well production planning. For example, FIB-SEM imaging is insufficient in this regard because the field of view of a given FIB-SEM image is limited. Furthermore, physically sampling the numerous representations within a textural family is extremely time-consuming. Moreover, even if a specific region of a 2D SEM image is intended to yield statistically representative 3D FIB-SEM samples, the initially available 2D surface information does not accurately indicate the information that can be obtained from the underlying 3D volume.

[0033] Figure 1a illustrates at a high level the collection and analysis of rock samples according to the principles disclosed herein. Embodiments of the invention may be particularly advantageous in analyzing rock samples derived from subsurface formations important for oil and gas production. Thus, Figure 1a illustrates an environment 100 according to various embodiments from which rock samples 104 to be analyzed using testing system 102 can be obtained. In these illustrated examples, rock samples 104 can be obtained from a land drilling system 106 or from an offshore (ocean, sea, lake, etc.) drilling system 108, either of which can be used to extract resources such as hydrocarbons (oil, natural gas, etc.), water, etc. As is fundamental in the art, optimizing oil and gas production operations is largely influenced by the structure and material properties of the rock formations being drilled or previously drilled by the land drilling system 106 or the offshore drilling system 108.

[0034] The methods of obtaining rock samples 104 and the physical forms of these samples can vary widely. Examples of rock samples 104 used in conjunction with the embodiments disclosed herein include whole core samples, sidewall core samples, outcrop samples, drill cuttings, and laboratory-generated synthetic rock samples such as sand fillers and cemented fillers.

[0035] As illustrated in Figure 1a, environment 100 includes a testing system 102 configured to analyze images 128 (Figure 1b) of rock sample 104 to determine the material properties of the corresponding subsurface rock, including the physical properties of the rock in the context of oil and gas exploration and production.

[0036] Figure 1b illustrates, in a general manner, the components of the test system 102 for analyzing image 128. In a general sense, the test system 102 includes an imaging device 122 for obtaining 2D or 3D images and other representations of the rock sample 104, including details of the internal structure of the rock sample 104. An example of the imaging device 122 is an X-ray computed tomography (CT) scanner, which, as is known in the art, emits X-ray radiation 124 that interacts with an object and measures the attenuation of the X-ray radiation 124 by the object, thereby generating an image of its internal structure and composition. Specific types, constructions, or other properties of the CT scanner 122 can correspond to any type of X-ray device, such as a miniature CT scanner, capable of producing images representative of the internal structure of the rock sample 104. The imaging device 122 generates one or more images 128 of the rock sample 104 and forwards these images 128 to a computing device 120.

[0037] The image 128 generated by the imaging device 122 can be in the form of a three-dimensional (3D) digital image volume (i.e., a digital rock) composed of or generated from multiple two-dimensional (2D) portions of the rock sample 104. In this case, the individual image volumes are divided into 3D regular elements called volume elements, or more commonly, "voxels." Typically, each voxel is a parallelepiped and may have different dimensions in the x, y, and z directions. In some examples, voxels may also be cubes with sides of equal length in the x, y, and z directions. On the other hand, the digital image volume 128 itself may contain different numbers of voxels in the x, y, and z directions. Each voxel within the digital volume has an associated numerical value or amplitude representing the relative material properties of the imaged sample at that location in the medium represented by the digital volume. The range of these values, often referred to as the grayscale range, depends on the type of digital volume, the granularity of the values ​​(e.g., 8-bit or 16-bit values), etc. For example, 16-bit data values ​​allow the voxels of an X-ray tomographic image volume to have a range from 0 to 65,536 at a granularity of 1.

[0038] The testing system 102 may also include a scanning electron microscope (SEM) 123 for obtaining 2D SEM images of the rock sample 104. The SEM 123 is also coupled to a computing device 120, whereby the 2D SEM images generated by the SEM 123 can be used by (e.g., received by) the computing device 120, which processes such 2D SEM images as further described below.

[0039] As described above, imaging device 122 forwards image 128 to computing device 120, which, in the example of FIG. 1b, can be any type of computing device, such as a desktop computer or workstation, laptop computer, server computer, tablet computer, etc. SEM 123 also forwards 2D SEM images to computing device 120. Therefore, computing device 120 will contain hardware and software components typically found in conventional computing devices. As shown in FIG. 1b, these hardware and software components of computing device 120 include testing tool 130, which is configured to analyze image 128 to determine the rock physical properties of rock sample 104 under one or more simulated fluid saturation conditions, including fluid saturation conditions that underground rock formations may encounter. In this respect, testing tool 130 can be implemented as software, hardware, or a combination of both, including the necessary and useful logic, instructions, routines, and algorithms for performing the functions and processes described further in detail herein. In a general sense, the testing tool 130 is configured to analyze the image volume 128 of the rock sample 104 to perform direct numerical simulations of the rock physical properties under fluid saturation conditions that represent the subsurface conditions of the rock strata, including the degree of saturation variation of various fluids.

[0040] Figure 1c generally illustrates the architecture of a computing device 120 in a test system 102 according to various embodiments. In this example architecture, the computing device 120 includes one or more processors 152, which may have different core configurations and clock frequencies available in the industry. Memory resources of the computing device 120 for storing data and / or program instructions for execution by the one or more processors 152 include: one or more memory devices 154 that serve as main memory during operation of the computing device 120; and one or more storage devices 160, such as one or more non-volatile solid-state memories, disk or optical disk drives, or random access memory. One or more peripheral interfaces 156 are provided for coupling to corresponding peripheral devices such as a display, keyboard, mouse, touchpad, touchscreen, printer, etc. A network interface 158, which may take the form of an Ethernet adapter, wireless transceiver, serial network component, etc., is provided to facilitate communication between computing devices 120 via one or more networks such as Ethernet, Wireless Ethernet, Global System for Mobile Communications (GSM), Enhanced Data Rate GSM Evolution (EDGE), Universal Mobile Telecommunications System (UMTS), Global Microwave Access Interoperability (WiMAX), Long Term Evolution (LTE), etc. In this example architecture, processor 152 is shown coupled to components 154, 156, 158, and 160 via a single bus; of course, different interconnect architectures, such as multiple dedicated buses, may be incorporated into computing device 120.

[0041] Although illustrated as a single computing device, computing device 120 can contain several computing devices that work together to provide the functionality of a computing device. Similarly, although illustrated as a physical device, computing device 120 can also represent abstract computing devices such as virtual machines and "cloud" computing devices.

[0042] As shown in the example embodiment of FIG1c, the computing device 120 includes a software program 162, which includes one or more operating systems, one or more application programs, etc. According to an embodiment, the software program 162 includes program instructions (FIG. 1b) corresponding to the test tool 130, and is implemented as a standalone application, a program module as part of another application or program, a suitable plug-in or other software component for accessing the test tool software on a remote computer networked with the computing device 120 via a network interface 158, or other forms or combinations thereof.

[0043] The program memory for the executable instructions of the software program 162 corresponding to the functionality of the storage and testing tool 130 may physically reside within the computing device 120 or at other computing resources accessible to the computing device 120, i.e., within the local memory resources of memory devices 154 and 160, or within server or other network-accessible memory resources, or distributed across multiple locations. In any case, the program memory constitutes a non-transitory computer-readable medium storing executable computer program instructions, according to which the operations described herein are performed by the computing device 120 or by a server or other computer coupled to the computing device 120 via network interface 158 (e.g., in the form of an interactive application when transferring input data from the computing device 120, for display or output by a peripheral device coupled to the computing device 120). The computer-executable software instructions corresponding to the software program 162 associated with the test tool 130 may have been initially stored on a removable or other non-volatile computer-readable storage medium (e.g., DVD, flash memory, etc.), or downloaded as coded information about an electromagnetic carrier signal in the form of a software package, which is then installed via the computing device 120 in a conventional manner for software installation. It is anticipated that those skilled in the art will be able to readily implement the storage and retrieval of applicable data, program instructions, and other useful information related to this implementation in a manner suitable for various specific applications, without extensive experimentation.

[0044] The specific computer instructions constituting the software program 162 associated with the test tool 130 may be in the form of one or more executable programs, or in the form of source code or higher-level code from which one or more executable programs are derived, assembled, interpreted, or compiled. Any number of computer languages ​​or protocols may be used depending on the desired operation to be performed. For example, these computer instructions for creating a model according to the implementation scheme may be written in a traditional high-level language such as PYTHON, JAVA, FORTRAN, or C++, or arranged as a traditional linear computer program or in an object-oriented manner. These instructions may also be embedded in higher-level applications. In any case, it is expected that those skilled in the art, with reference to this specification, will be able to readily implement the implementation scheme in a manner suitable for the desired installation without excessive experimentation.

[0045] The specific functions of the testing tool 130 for analyzing rock samples under various saturation conditions according to the embodiment will now be described with reference to Figures 2 and 1a-1c, including those functions implemented by software program 162.

[0046] Figure 2A and Figure 2BA flowchart of a method 200 for analyzing rock samples under various saturation conditions according to the principles disclosed herein is shown. Although depicted sequentially for convenience, at least some of the actions shown can be performed in a different order and / or in parallel. Furthermore, some embodiments may perform only a portion of the actions shown. In some embodiments, at least a portion of the operations of method 200, as well as other operations described herein, can be implemented as instructions stored in a computer-readable medium and executed by one or more processors 152.

[0047] In box 202, test system 102 acquires rock sample 104 to be analyzed, such as from subsurface rock formations obtained by land drilling system 106 or offshore drilling system 108, or from other sources. Specific rock sample 104 can be prepared from a larger volume of subsurface rock formations, for example, by drilling or cutting out a portion of a larger volume of rock formation of interest to have dimensions, specifications, and structure that can be imaged by imaging device 122 (e.g., a CT scanner).

[0048] In block 204, imaging device 122, together with computing device 120 of test system 102, generates a digital image volume 128 representing rock sample 104, including its internal structure. For example, if imaging device 122 is a CT scanner, X-ray imaging of rock sample 104 is performed (i.e., radiation directed at rock sample 104 is emitted and attenuation is measured) to generate an image volume 128 of a 2D slice image or from said 2D slice image. Specific conventional techniques for acquiring and processing the 3D digital image volume 128 of rock sample 104 in block 204 include, but are not limited to, X-ray tomography, X-ray microtomography, X-ray nanotomography, focused ion beam scanning electron microscopy, and magnetic resonance imaging. In some embodiments, digital image volume 128 can be generated computationally rather than by scanning a physical sample. In embodiments where digital image volume 128 is generated by scanning a rock sample, the rock sample can be naturally occurring rock or an artificial porous material (e.g., synthetic rock).

[0049] Figure 3a shows an example of a 2D slice image 300 of a 3D image of a rock sample, illustrating a cross-sectional slice of the structural details of the rock sample, including features of solid material 302, pore or void spaces 304, and partial solid / pore spaces 306. The image data at this time can be in the form of grayscale values ​​representing the attenuation of X-ray radiation by the composition of the rock sample 104. Although Figure 3a shows a 2D slice image 300, the 3D digital image volume 128 of the rock sample 104 is typically composed of multiple 2D slice images (e.g., a "pile" of multiple 2D slice images) located at stepped positions along an axis of the rock sample 104, together forming a 3D image of the rock sample 104. Depending on the specific architecture of the testing system 102, incorporating the 2D slice images into the 3D digital image volume 128 can be done using the computing resources within the imaging device 122 itself, or by using the computing device 120 to process a series of 2D slice images 128 generated by the imaging device 122.

[0050] In block 206, the testing system 102 segments or uses other image enhancement techniques on the digital image volume 128 of the rock sample 104 to distinguish and label different components or phases of the image volume 128 from the grayscale values ​​of the image. More specifically, the computing device 120 performs this segmentation to identify components such as pore spaces and mineral components (e.g., clay and quartz). In some embodiments, the testing tool 130 is configured to segment the image volume 128 into more than two significant phases, representing material components such as pore spaces, clay proportions, quartz proportions, various other mineral types, organic matter, or composite materials.

[0051] The computing device 120 is capable of utilizing any of a variety of segmentation algorithms. One segmentation method involves applying a “thresholding” approach to the image volume 128, where the computing device 120 selects a threshold within a voxel amplitude range. Voxels with amplitudes below the threshold are assigned a specific value representing pore space, while voxels with amplitudes above the threshold are assigned another value representing matrix space (i.e., solid material). In another example, multiple thresholds are defined for multiple different voxel amplitude ranges. In this method, thresholding converts the grayscale image volume into a segmented volume of voxels with one of two (or more) possible values, typically chosen as 0 and 1. Figure 3b illustrates an example of segmentation of a 2D slice image 310 (e.g., a portion of a 3D digital image volume 128) using thresholding with more than two possible values. As illustrated, the segmentation allows for the differentiation of structural details in a rock sample, where in this example, solid material 302 is shown as white, pore or void spaces 304 are shown as black, and partial solid / pore spaces 306 are shown as light and dark gray. Further segmentation can be applied once or multiple times to differentiate various features in the grayscale image. If simple thresholding is used, it is possible to distinguish multiple thresholds among different materials such as clay, quartz, and feldspar that exhibit different X-ray attenuation characteristics.

[0052] The computing device 120 may alternatively utilize other segmentation algorithms. An example of such an alternative algorithm is known in the art as the Otsu method, where a histogram-based thresholding technique selects a threshold to minimize the combined variance (i.e., "intra-class variance") of the lobes of the bimodal distribution of grayscale values. The Otsu method can be easily automated and can also be extended to repeatedly threshold the image multiple times to distinguish other material components such as quartz, clay, and feldspar. The computing device 120 may alternatively or additionally use other examples of automated segmentation algorithms with varying complexities to distinguish different features of image volumes, including indicator kriging, converging active contours, watershed slicing, etc.

[0053] The computing device 120 can also utilize other image enhancement techniques to enhance or improve the structures defined in the image volume 128, thereby further distinguishing structures, reducing the effects of noise, etc. Similarly, although the computing device 120 is capable of segmentation or other image enhancement techniques, it is anticipated that other components of the testing system 102, such as the imaging device 122 itself, can alternatively perform all or part of the image enhancement.

[0054] Thus, segmentation associates voxels in the digital image volume 128 with specific materials (or pore spaces, as appropriate) at corresponding physical locations within the rock sample 104. Each voxel is labeled with a unique material identifier corresponding to a specific component assigned to a given X-ray attenuation amplitude. This component includes pore space, matrix material, mixed pore-clay ratio, individual grains, grain contact, mineral type, etc.

[0055] Figure 4 The representation 400 of a digital image volume 128 of rock sample 104 is shown. As described above, the digital image volume 128 can be constructed from a series of 2D slice images 300 (or segmented 2D slice images 310). The representation 400 includes different rock textures, such as those corresponding to rock textures identified from the 2D slice images 300. In some examples, a texture refers to a pattern shared by “regions” or portions of an image. For example, regions can be grouped together as textures based on shared underlying properties such as porosity, constituent phases and their proportions, image entropy, etc. Specific examples of rock textures include pore space and various types of solids. For example, different types of solid materials can correspond to different rock textures. Therefore, a texture can be viewed as a quantification of a spatial pattern of a particular domain or pixel values ​​(e.g., pixel intensity) within an image.

[0056] exist Figure 4 In the example, representation 400 includes a first rock texture 402, a second rock texture 404, and a third rock texture 406, as well as a main or sedimentary dominant sedimentary rock texture 408, which constitutes the bulk of the rock sample between rock textures 402, 404, and 406. At least a portion of the voxels comprising representation 400 are associated with or mapped to the physical coordinate space associated with the rock sample 104. This allows the imaged rock textures 402, 404, and 406 to be mapped to specific physical locations within the rock sample 104.

[0057] Embodiments of the present invention utilize the positions of the imaged rock formations 402, 404, 406 within the representation 400 of the digital image volume 128 to identify one or more digital planes intersecting the rock formations 402, 404, 406 across the digital image volume 128, as shown in box 208 of FIG. 2. In some examples, the segmentation described above, performed in box 206 of FIG. 2, provides spatial identification of these formations 402, 404, 406. After segmentation, and depending on the complexity and arrangement of the rock formations 402, 404, 406 within the digital image volume 128, multiple digital planes may be required to adequately intersect all the different rock formations 402, 404, 406. Furthermore, in some examples, digital planes are identified to reduce or minimize the number of planes required to adequately intersect all the different rock formations 402, 404, 406.

[0058] For example, to intersect rock formations 402, 404, and 406, the first set of digital planes includes digital plane 410 intersecting rock formations 402 and 406 and digital plane 412 intersecting rock formation 404. However, if possible, reducing the number of digital planes, thereby reducing subsequent machining and SEM imaging requirements, may be advantageous. Therefore, in at least one embodiment, digital plane 414 intersecting rock formations 402, 404, and 406 is selected, thereby reducing the required machining and imaging to adequately image all rock formations 402, 404, and 406.

[0059] After recognizing digital plane 414 (e.g., according to...) Figure 2A In box 208), method 200 continues in box 210, wherein the physical rock sample 104 is machined (or otherwise mechanically prepared) to expose physical surfaces corresponding to the set of identified digital planes (e.g., digital plane 414). As described above, because the digital image volume 128 (e.g., its complex voxels) is mapped to the physical coordinate space associated with the rock sample 104, the identified digital plane 414 corresponds to a plane in that physical coordinate space, making it relatively simple to machine the corresponding physical surfaces.

[0060] Once the physical rock sample 104 has been machined or otherwise mechanically prepared to expose one or more physical surfaces corresponding to the identified set of digital planes, method 200 continues in block 212 to obtain a series of SEM images of the physical surfaces. In various embodiments, SEM imaging of the physical surfaces of the rock sample 104 is performed at various scales (e.g., sequentially as the magnification of the physical surfaces of the rock sample 104 increases). Figures 5a-5c illustrate example SEM images captured at different (e.g., sequentially magnified) scales, which helps define one or more rock fabrics (e.g., rock surfaces) within digital plane 414. Figure 4 The spatial characteristics of the components 402, 404, and 406.

[0061] In one example, the magnified region can vary depending on the environment of the ongoing imaging. In one example where organic porosity is particularly important for a given project, the focus is on acquiring magnified images of regions that appear to contain that type of texture. Continuing with this example, regions that do not appear to contain textures exhibiting organic porosity are sampled less frequently (i.e., smaller magnified images are acquired for regions that do not appear to contain texture volumes including at least a threshold amount of organic porosity, and the scaling level can also be lower for those regions that do not contain textures exhibiting at least a threshold amount of organic porosity). In another example, overall pore connectivity is particularly important for a given project. In this example, all regions can be sampled equally to avoid ignoring image data relevant to determining pore connectivity. An example of equal sampling involves acquiring magnified images along a rectangular grid path with regular spacing in the dimensions of the image.

[0062] Figure 5a shows a SEM image 500 approximately 100 micrometers wide. A first zoomed portion 502 of the SEM image 500 contains multiple rock textures, including a first texture 504 and a second texture 506. For example, the first texture 504 corresponds to an inorganic, porosity-rich texture, while the second texture 506 corresponds to an organic, porosity-rich texture. The zoomed portion 502 can be identified as a result of containing a particular texture of interest with finer details that are not easily discernible at lower resolution. For example, the zoomed portion 502 can be selected from the SEM image 500 because it indicates the presence of organic, rich porosity. The zoomed portion 502 provides greater visual clarity of the organic pore structure compared to what can be discerned from the SEM image 500. Furthermore, magnification can sometimes be used to discern sufficient structural detail in various regions of interest.

[0063] Figure 5b shows the first scaled portion 502 in more detail. For example, the more detailed information in Figure 5b was obtained by performing SEM imaging of the first scaled portion 502 at a higher scaling level, thus the first scaled portion 502 is equivalent to the scaled SEM image 502. Specifically, as shown in Figure 5b, the scaled SEM image 502 is approximately 50 micrometers wide. In Figure 5b, the first and second structures 504, 506 appear larger and more detailed. Furthermore, the second scaled portion 510 was identified in a similar manner to how the first scaled portion 502 was identified in Figure 5a. For example, the second scaled portion 510 can be selected from the scaled SEM image 502 because the second scaled portion 510 has a higher diversity of the represented rock structures than other portions of the scaled SEM image 502.

[0064] Figure 5c shows the second scaled portion 510 in more detail. For example, the more detailed information in Figure 5c was obtained by SEM imaging the second scaled portion 510 at a higher scaling level; therefore, the second scaled portion 510 is equivalent to a second scaled SEM image 510. Specifically, as shown in Figure 5c, the second scaled SEM image 510 is approximately 10 micrometers wide. The first structure 504 is not present in the second scaled SEM image 510 because it is not included in the second scaled portion 510 in Figure 5b. However, the second structure 506 appears larger and more detailed. In the example of Figure 5c, the second structure 506 identified in the central region of the second scaled SEM image 510 illustrates an organic-rich pore structure that may influence or contribute to the description of the flow, transport, and storage of the larger rock sample 104.

[0065] Although the examples of Figures 5a-5c include first and second scaled images 502, 510, other examples of the invention can be extended to additional or fewer scaling iterations as needed to capture a sufficient level of diversity in the represented rock textures. Furthermore, the process can be repeated on the physical surface of a larger rock sample 104 or multiple scaled SEM images can be captured. For example, a set of SEM images scaled to the level shown in Figure 5c can be obtained over the area represented by SEM image 500 of Figure 5a. Thus, a set of scaled SEM images spanning multiple scales (e.g., “multi-scale”) is produced, capturing finer details of the physical surface of the larger rock sample 104. The set of multi-scale SEM images can contain at least a threshold number of rock textures among the multiple rock textures contained in the aforementioned digital image volume 128. In this case, a higher threshold will result in a set of multi-scale SEM images that capture or represent a larger percentage of textures in the digital image volume 128 (e.g., in some cases, about 70%, 80%, 90%, or 100%). In this context, a lower threshold results in a collection of multi-scale SEM images that capture or represent a relatively low percentage (e.g., less than about 70%) of the composition within the digital image volume 128, for example, to reduce the computational or processing resources required for subsequent steps of the method. Furthermore, as will be further explained below, the second scaled SEM image can be segmented to extract feature quantities (such as pore space, organic solid material, and solid inorganic material), which can be used for further numerical prediction or judgment in relation to the larger rock sample 104.

[0066] Figure 5d provides an alternative example of the methods shown in Figures 5a-5c and described above. Specifically, in step 3 of Figure 5d, a probability map is generated based on the segmented, lower-resolution image obtained in step 2 of Figure 5d (e.g., using an unsupervised learning algorithm). The probability map of step 3 probabilistically groups similar textures. For example, a type 1 probability map shows the probability that a region is a non-porous, organic-rich texture, while a type 2 probability map shows the probability that a region is a porous, organic-rich texture. In some cases, grouping similar textures indicates or identifies regions of interest (ROIs) in rock sample 104 for higher-resolution imaging. In the example of Figure 5d, the identified ROI corresponds to the boxed area at the bottom of type 2 material, indicating that the area is likely to be a similar rock texture. In one example, the identified ROI or a first region in the SEM image contains a first number of pixels associated with the primary texture type (e.g., a porous, organic-rich texture in the case of the type 2 probability map) and a second number of pixels associated with textures other than the primary texture type. Therefore, regions of interest can be identified based on the ratio of a first quantity above a threshold to a second quantity, indicating a specific percentage (or more) of the main structural types in that region. Once the region of interest is identified, additional SEM imaging can be performed at a higher (e.g., finer) resolution, as shown in step 4 of Figure 5d.

[0067] Referring generally to Figures 5a-5d, some examples in this specification utilize one or more machine learning algorithms to determine various aspects of the scaling and capture methods described above. For example, the number of rock features to be sampled (e.g., the total number of features identified in a digital image volume of 128) can be determined in response to the application of a machine learning algorithm. Similarly, the resolution for capturing a particular rock feature (e.g., how much magnification is appropriate for a given rock feature) can be determined in response to the application of a machine learning algorithm. In one example, these values ​​or levels are determined iteratively to generate a set of data that can be processed within a reasonable timeframe (e.g., avoiding brute-force sampling of all possible combinations of the number of features to be captured and the resolution for capturing those features), while still providing useful data for a given number of features. For example, this avoids situations such as underscaling the first feature, thus missing important details of that feature; or overscaling the second feature, thus wasting valuable time and processing resources (during the capture and / or subsequent processing of overly detailed images).

[0068] Returning to method 200 with reference to Figure 2, once a set of SEM images has been obtained at approximately 2 to 4 times the resolution, method 200 continues in box 214, optionally applying segmentation to the 2D SEM images for the smallest pore size to be analyzed for a given application or other material features of interest. For example, if characterizing the microporosity of a sample (e.g., pore sizes less than 5 nm), the required resolution might be approximately 2 nm. As another example, if characterizing pyrite pores larger than 15 nm, the required resolution might be approximately 5 nm, thus the required scaling level might be relatively more lenient. Segmenting the 2D SEM image is similar to the segmentation described above with respect to box 206 and Figures 3a and 3b regarding the segmentation of the 2D slice image 300. Figure 6a shows an exemplary simple two-component (e.g., pore space and organic matter) SEM image 600, the scale of which can be similar to the second scaled SEM image 510 described above with respect to Figure 5c. In this example, where the SEM image 600 is relatively simple, segmentation can be performed using a single threshold to distinguish between the pore space and the organic matter. Figure 6b shows the resulting segmented SEM image 610, where pore spaces are shown in black and organic matrix material is shown in white. By segmenting the SEM image obtained in box 212 into two phases (e.g., pore spaces and organic matter), the pore spaces of the larger rock sample 104 are captured in two dimensions at a fine-grained level, which can then be used to create a 3D digital model volume representing the rock sample 104, but with a finer resolution (e.g., a greater level of detail) than the originally captured digital image volume. In particular, the segmented 2D SEM image 610 in Figure 6b can be used as a training image for 2D-to-3D volume transformation, which will be explained in more detail below. In other examples, the SEM image obtained in box 212 can be segmented into any number of phases to represent various rock textures.

[0069] Figure 7a illustrates a group 700 of segmented 2D SEM images, similar to the segmented SEM image 610 explained above. The group 700 of 2D SEM images is extracted from multiple SEM images containing different representations of specific textures (e.g., 402, 404, 406). Returning to reference method 200, in block 216, the group 700 of segmented 2D SEM images is used to generate a set of statistically similar 3D digital model volumes for specific rock textures. In a particular example, one or more random algorithms (e.g., cross-correlation functions) are applied to a group of 2D SEM images 700 to generate statistically similar realizations or statistically equivalent 3D pore-organic matrix volumes. In the example of the cross-correlation function, the method uses structural information (e.g., data indicating the correlation between different parts of the image) from 2D training images (e.g., 2D SEM image 610 above) to first decompose the image into smaller component regions, and then randomly recombine these regions to synthesize versions of the original 2D training images that are statistically similar but not identical. Subsequently, the original 2D training images and their statistically similar versions are projected onto one or more imaginary planes (e.g., in 3D). These 3D projections, or “digital model volumes,” can be used to statistically adjust subsequent iterations that generate synthetic, statistically similar images. In one example, this adjustment process can be used to iteratively generate synthetic images that may be positioned above or below previously generated synthetic images in a manner that appears to more accurately reflect the natural appearance and / or structural continuity of real-world rock samples.

[0070] Figure 7b illustrates an exemplary group 710 of 3D pore-organic matrix model volumes that are statistically similar to each other. For example, a first digital model volume is statistically similar to a second digital model volume when the algorithms for the pore phases of a first model volume and a second model volume have the same properties or are within a threshold amount (e.g., based on engineering tolerances). In some cases, statistical equivalence is controlled by assumptions about ergodicity in randomized algorithms. Because the group 710 of 3D digital model volumes of a given configuration type is calculated from 2D images obtained from a single physical surface or a small number of physical surfaces of rock sample 104, the group 710 can be generated more easily and at a relatively lower cost compared to, for example, FIB-SEM in which a portion of the rock material is continuously machined and imaged layer by layer. In some examples, the voxel values ​​in the 3D digital model volumes of group 710 are determined based on the spatial distribution of pixel values ​​in the individual 2DSEM images used to generate the 3D digital model volumes. In a specific but non-limiting example, circular particles in a 2D SEM image (e.g., 100 white pixels in an approximate circle surrounded by black pixels) result in spherical particles (e.g., 1000 white voxels in an approximate sphere surrounded by black voxels) being generated in the volume of a 3D digital model.

[0071] Furthermore, since group 710 of a 3D digital model volume of a given configuration type can be calculated and generated from 2D images taken from multiple physical surfaces of rock sample 104, such 2D images can have different axial orientations of rock sample 104. In a specific but non-limiting example, a first 2D SEM image of the physical surface of rock sample 104 is taken along a first axis relative to the position of rock sample 104, while a second 2D SEM image of the physical surface of rock sample 104 is taken along a second axis relative to the position of rock sample 104. This allows the generated 3D digital model volume to take into account features whose axial symmetry may differ. For example, a feature that is circular along one axis may typically appear spherical in the generated 3D digital model volume. However, if the same feature is rectangular along another axis, the feature may appear oval in the generated 3D digital model volume.

[0072] Furthermore, the process of generating a group 710 of 3D digital model volumes for a given fabric type can be repeated for multiple fabric types, resulting in each of the multiple (e.g., M) fabric types being realized multiple times (e.g., N times). The N realizations of the 3D digital model volume for a given fabric type represent multiple possibilities of how a 3D version of that fabric type would look in nature. This provides a way to compute or determine rock physical properties at the fabric level, thereby generating probability distributions of various rock physical properties for that particular fabric type. In some cases, the estimates of rock physical properties determined from the 3D digital model volume are more accurate than those of the same properties derived from a 2D model. As a result, the generation of 3D digital model volumes described in this paper improves the accuracy of rock physical property estimation relative to, for example, 2D SEM images.

[0073] Compared to the original digital image volume 128, the 3D digital model volumes in group 710 have a higher (e.g., finer) resolution due to being generated based on 2D SEM images. Furthermore, each 3D digital model volume is specific to one of the various common configuration types present in the digital image volume 128.

[0074] Once a set of statistically similar 3D models 710 has been generated, method 200 continues in box 218 to perform numerical simulations on the 3D digital model volumes 710 to determine one or more material or rock physical properties associated with each 3D digital model volume 710. In one example, the 3D digital model volume 710 is used as a modeling mesh for a type of rock fabric (e.g., N-fold realization of a fabric type) to determine one or more desired material properties for that fabric type. In various examples, material properties may include porosity, pore size distribution, permeability, capillary pressure, resistivity, and elastic modulus.

[0075] The exemplary Table 1 below illustrates representative porosity and permeability values ​​derived from a set of 3D pore-organic matrix volumes 710 shown in Figure 7b. In this example, the 3D pore-organic matrix volumes 710 are used to calculate porosity and / or permeability using one or more image analysis algorithms such as segmentation (e.g., for porosity) and lattice-Boltzmann simulation (e.g., for permeability). In one example, the set of calculated values ​​generated by applying these algorithms represents all possible porosities and permeabilities that might be encountered in a real-world rock sample containing this fabrication. Thus, the algorithms create or provide probability distributions for various porosities and permeabilities of a particular fabric type (e.g., porous organic material in this example). Generating additional implementation or digital model volumes results in the ability to determine rock physical properties based on a larger number of models, thereby producing a correspondingly larger set of probability distribution data. This leads to a more accurate and / or precise determination of the probability distributions of those rock physical properties.

[0076]

[0077] Table 1.

[0078] The various implementations in Table 1 correspond to one of the 3D models in 3D model example group 710. The statistical similarity of the various models is reflected by the relatively close grouping of permeability and porosity values ​​for the various implementations in Table 1. In some examples, the numerical simulations utilize proprietary algorithms derived from exemplary direct numerical simulation techniques. For instance, two-phase lattice Boltzmann simulations can be used to estimate numerical permeability based on the volume of a 3D digital model of a given fabric type, while object partitioning and point counting algorithms can be used to estimate numerical pore size distribution based on the volume of a 3D digital model of a given fabric type.

[0079] In some examples, one or more specific material properties of a given rock fabric are associated with voxels in a 3D digital model volume corresponding to that given rock fabric. Furthermore, locations within the digital model volume can be mapped to a physical coordinate space associated with rock sample 104. Therefore, one or more specific material properties can be associated with the physical coordinate space associated with rock sample 104. As described above, the material properties mapped to specific voxels in the digital model volume can be sampled from the property distribution measured for a given rock fabric, resulting in the digital model volume becoming a composite volumetric mesh of these material properties.

[0080] Figure 8An exemplary 3D model (e.g., one of example groups 710 of 3D models) is shown, in which a flow field (e.g., a defined material property) as a grayscale heatmap is superimposed on the 3D model. Typically, the flow field comprises the velocity values ​​of multiple voxels (e.g., individual voxels) within the volume of the 3D digital model. The permeability tensor simplifies the 3D flow field to representative values ​​(e.g., a single value in some cases), which can then be calculated in response to a defined flow field for a given volume of the 3D digital model. Although... Figure 8 The porosity of the 3D model appears discontinuous, but the flow field indicates the existence of flow paths through the 3D volume. The grayscale heatmap represents the flow velocity, with darker shades representing higher velocities and lighter shades representing lower velocities. Figure 8 The arrows in the diagram represent the overall direction of flow modeled in 3D volume.

[0081] Figure 9 A flowchart of a method 950 for analyzing rock samples based on the principles disclosed herein is shown. Figure 9 Including the above regarding Figure 2A and Figure 2B Similar specific steps. Although depicted sequentially for convenience, at least some of the actions shown can be performed in a different order and / or in parallel. Furthermore, some embodiments may perform only a portion of the actions shown. In some embodiments, at least a portion of the operations of method 950, as well as other operations described herein, can be implemented as instructions stored in a computer-readable medium and executed by one or more processors 152.

[0082] Boxes 952, 954, and 956 are similar to boxes 202, 204, and 206, respectively, and for the sake of brevity, the descriptions of these boxes will not be repeated here.

[0083] In box 958, the material properties of various rock textures associated in box 956 (and box 206) are estimated. In the example below, the material property is permeability; however, in other examples, different material properties of the rock textures can be estimated as described above. As described above with respect to box 218, a numerical simulation of the 3D model 710 can be performed to determine such material properties (e.g., permeability) and then associated with various rock textures (or voxels representing those textures) in the digital image volume. In various examples, material properties may also include porosity, pore size distribution, permeability, capillary pressure, resistivity, and elastic modulus. As described above, voxels of the digital image volume (and thus associated, determined one or more material properties) can be mapped to the physical coordinate space associated with rock sample 104, thereby improving the understanding of the physical rock sample 104 and the strata from which it was sampled.

[0084] Method 950 continues in box 960 by selecting a nodal plot from a set of fractional bounce parameter (FBP) nodal plots, which have an associated or valid grid size that correlates the material property values ​​determined in box 956 with FBP values ​​within a given range. For example, the permeability values ​​determined in box 956 span a permeability range. Each nodal plot in the set correlates the permeability values ​​with FBP values ​​for a given grid size. In some examples, the selected nodal plot is one that correlates the permeability range with FBP values ​​between a lower and upper FBP threshold.

[0085] Figure 10 An example of FBP determination used in a grayscale lattice Boltzmann (GSLB) model or algorithm, based on the principles disclosed herein, is shown. Figure 10 In the diagram, voxel grids are shown both before (e.g., grid 1000) and after (e.g., grid 1020). A streaming step is a step (e.g., an intermediate step) in the GSLB algorithm. "Before streaming" refers to the GSLB state output before the mathematical application of the streaming function / operation. "After streaming" refers to the GSLB state output after the application of the streaming function / operation. A streaming function / operation is a step in the GSLB algorithm that utilizes FBP information provided in the primary inputs (e.g., derived from raw digital images / 3D digital volume inputs). These primary inputs are represented by grid points (e.g., from...). Figure 10 The circles in the diagram represent the points and the specific FBP values ​​associated with each grid point. Figure 10 In the diagram, the FBP values ​​are represented by gray shading at grid points 1002 and 1004. In some examples, individual grid points have associated FBP values. Figure 10 In the example, for simplicity, the grid point coloring is limited to 1002 and 1004.

[0086] The GSLB algorithm is an iterative algorithm, and its output, as described above, can be iteratively modified multiple times through various functions / operations. Streaming is a type of intermediate operation in the GSLB algorithm that performs this iterative modification. These iterative operations can be performed until a desired criterion is met, at which point the iteration stops (e.g., no further iterations of the algorithm). During the iteration of the GSLB algorithm, the output of each step also serves as the input for the next iteration. One variable of this output is a set of fractional streaming values ​​in different directions. For simplicity, in Figure 10 The diagram only shows two directions: f1 and f2. It is a fractional streaming from source grid point 1002 to target grid point 1004 before applying the streaming function / operation. This is a fractional streaming process from target grid point 1004 to the next grid point (e.g., to the right of target grid point 1004) for use in the next iteration (e.g., after applying streaming). It is a fractional streaming process that returns from the target grid point 1004 to the source grid point 1002 after the application of streaming. and It is calculated by streaming functions / operations and is part of the input for subsequent iterations. α S and α T These are the decimal forms of the FBP at grid points 1002 (source) and 1004 (target), respectively.

[0087] The mesh of voxels 1000 and 1020 includes source voxel 1002 and target voxel 1004. In this example, the fluid flow behavior from source voxel 1002 to target voxel 1004 is determined. For example, it was previously determined (e.g., during a previous computational iteration) that source voxel 1002... The target voxel 1004 provides flow in the direction that can be rewritten as a component (1–α). S ) and α S The sum of, where α S It equals FBP divided by 100.

[0088] As shown in the voxel mesh after streaming 1020. Corresponding to component 1–α S It is reflected back to source voxel 1002 by target voxel 1004; Corresponding to component α S It passes through the target voxel 1004 and is transmitted to another adjacent voxel.

[0089] In the example where the target voxel 1004 is a complete pore space, all fluid flow supplied to the target voxel 1004 (e.g.) All of them are transmitted through the target voxel 1004, thus α S =1 and the reflection component (1–α) S Therefore, it is 0. In this example, the FBP associated with the target voxel 1004 is 100.

[0090] In the example where the target voxel 1004 is a completely solid space, all fluid flows supplied to the target voxel 1004 (e.g., All of them are reflected back to the source voxel 1002 through the target voxel 1004, thus α S =0 and the reflection component (1–α) S Therefore, it is 1. In this example, the FBP associated with the target voxel 1004 is 0.

[0091] In other examples where the target voxel 1004 is a partially solid / pore space, the FBP serves as the fluid provided by the target voxel 1004, either reflected back or transmitted through it. The FBP varies as a function of the quantity. As further described below, the FBP of a given voxel can be determined based on its permeability or by another material property as determined above.

[0092] Figure 11a shows a nomogram set 1100 that correlates permeability values ​​with FBP values ​​for various grid sizes. In this case, grid size refers to or is related to voxel size / segmentation volume size. For example, a grid size of one micrometer means that each grid point (e.g., regarding...) Figure 10 The described points are specified to have a spacing of one micrometer relative to other grid points. In this example, the set of nodal plots 1100 includes a first nodal plot 1102 for an exemplary grid size of 1 micrometer, a second nodal plot 1104 for an exemplary grid size of 0.1 micrometer, a third nodal plot 1106 for an exemplary grid size of 0.01 micrometer, and a fourth nodal plot 1108 for an exemplary grid size of 0.001 micrometer. Although not depicted in Figure 11, in some examples, one or more extrapolated nodal plots are also included, which are not necessarily part of the original set of nodal plots 1100, but are derived from nodal plots 1102, 1104, 1106, and 1108, which are part of the set of nodal plots 1100. The generation of the set of nodal plots 1100 is further described below with reference to Figure 11b.

[0093] Figure 11b shows an example set of synthetic samples 1120 used to generate the set of nomograms 1100 described above. Multiple synthetic samples are created for each grid size, each with a different assigned FBP. The permeability (or other material property) value is calculated for a grid square of a particular synthetic sample, and a nomogram is generated based on the resulting relationship between the grid size of the synthetic sample, the FBP of that synthetic sample, and the permeability calculated for a grid square of that synthetic sample.

[0094] For example, synthetic sample 1122 was created for a grid size of 1 unit (e.g., micrometer) and with an FBP of approximately 10 (for an FBP scale of 0 to 100). The permeability value of one grid square of synthetic sample 1122 was calculated to be approximately 100 millidarcy (md), which was plotted as a point in nomogram 1102 in Figure 11a, as shown. Similarly, synthetic samples with different FBPs were created for a grid size of 1 unit, and permeability (or other material property) values ​​were calculated for the grid squares of those synthetic samples. When these samples were plotted, nomogram 1102 in Figure 11a was obtained. By creating synthetic samples with multiple grid sizes in a series of FBPs and calculating the permeability (or other material property) values ​​associated with the grid squares of each synthetic sample, a set of nomograms 1100 described above was obtained.

[0095] In these examples, the set of individual nomograms 1100 correlates permeability values ​​(e.g., as determined above) with corresponding FBP values. For illustrative purposes, it can be assumed that... Figure 9 The preceding box in Figure 11c identifies four rock textures with different permeability values. Figure 11c shows the set of nomograms 1100 as a set of nomograms 1150, where the x and y axes are inverted, such that permeability is the independent variable in the set of nomograms 1150. The four rock textures correspond to permeability values, as shown at 1152. In some examples, FBP values ​​within a specific range at the ends of the FBP scale (e.g., <10 and >90 for an FBP scale of 0 to 100) can lead to numerical instability during subsequent modeling, such as using the GSLB algorithm described further below. In Figure 11c, nomogram 1102 is chosen corresponding to a grid size of 1 unit (e.g., micrometer), which results in FBP values ​​greater than 90, corresponding to the permeability value 1152 for the four rock textures. Therefore, if the nodal plot 1102 is selected to generate the input of the GSLB engine 1154, the result or output of the GSLB engine 1154 may be unavailable because numerical instability can occur when the FBP value is in a range that is prone to instability.

[0096] However, as shown in Figure 11c, the permeability values ​​for the four rock textures may intersect with more than one nomogram. As mentioned above, it may be advantageous to avoid nomograms in which the permeability values ​​of the rock textures are correlated with FBP values ​​in ranges that could lead to numerical instability.

[0097] Therefore, in the example of this specification, a nonograph is selected that associates various material properties (e.g., permeability in this example) of the four rock fabrics with FBP values ​​within a given range (e.g., greater than a lower FBP threshold (e.g., 10 for a scale of 0 to 100) and less than an upper FBP threshold (e.g., 90 for a scale of 0 to 100)). Although not shown in the set of nonographs 1100, 1150, in some cases, the set of nonographs 1100 initially does not include nonographs satisfying the FBP range constraints, thereby constructing extrapolated nonographs based on other nonographs in the set of nonographs 1100. In any case, Figure 11d shows the set of nonographs 1150, where nonograph 1104 corresponding to a grid size of 0.1 units (e.g., micrometers) is selected. Thus, the permeability values ​​1152 of the four rock fabrics result in FBP values ​​between 10 and 90, as shown in the figure. As a result, the nomogram 1104 is selected as the input to the GSLB engine 1154 for the permeability value 1152, enabling the GSLB engine 1154 to provide a stable output such as the simulated flow field 1156, which can then be mapped to the recovered aggregated permeability 1158 (e.g., permeability tensor) associated with the initial rock sample.

[0098] Return to reference Figure 9 Method 950 continues in block 962, associating each voxel in the digital image volume (e.g., each defined configuration type) with a corresponding FBP value indicated by a selected column plot (or extrapolated column plot), such as column plot 1104 in the example of FIG11d described above.

[0099] Method 950 then continues in box 964, creating a 3D FBP volume with a size similar to that of the digital image volume. For example, Figure 12 Example digital image volumes showing flow field coverage derived by applying conventional LB to a full-resolution digital image are shown in 1202, and example flow fields derived from 3D FBP volumes by applying GSLB to the corresponding coarsened digital images are shown in 1204. The voxel FBP values ​​of the 3D FBP volumes correspond to the grid size of the selected (or extrapolated) nomograms described above. For example, using nomogram 1104 to determine the FBP values ​​for the permeability value 1152 of four rock fabrics results in a grid size of 0.1 micrometers. Figure 12 As shown, the resolution of the 3D FBP volume 1204 is coarser than that of the digital image volume 1202; however, the specific grid size and FBP value input to the GSLB engine correspond to the selected column line plot 1104 (0.1 micrometers).

[0100] Method 950 then continues in box 966, applying the GSLB algorithm to the 3D FBP volume 1204 created in box 964. The GSLB algorithm receives the FBP values ​​determined in boxes 960 and 962 and described above with reference to Figures 11a-11d as input. Subsequently, GSLB-specific mathematical operations, such as iterative streaming, collision, and fractional bounce operations, are performed on the voxel locations in the 3D FBP volume 1204 until a stable flow velocity is calculated for those voxel locations. These flow velocities, collectively referred to as the “flow field,” can be used to calculate the permeability tensor estimate of the digital image volume.

[0101] Figure 13 A comparison is shown between a raw tomographic image (e.g., a captured digital image) 1302 and a simulated flow field 1304, which is generated, for example, by applying the GSLB algorithm to a 3D FBP volume 1204.

[0102] Figure 14 This is an illustrated flowchart of a method 1400 for analyzing rock samples such as rock sample 104 described above. At 1402, SEM imaging is performed on one or more physical surfaces of rock sample 104 as described above, which produces multiple 2D SEM images of rock sample 104 (in some cases, from axial orientations different from those described above). The 2D SEM images at 1402 can be similar to SEM images 500, 502, and 510 described above with respect to Figures 5a-5c.

[0103] Method 1400 continues at 1404, where the SEM image derived from 1402 is optionally segmented, as described above with reference to Figures 6a and 6b. By segmenting the SEM image obtained at 1402, the fabrication of a larger rock sample 104 is captured in two dimensions at a fine-grained level, which can then be used to create a 3D digital model volume representing the rock sample 104. In particular, the segmented 2D SEM image at 1404 can be used as training images for the 2D-to-3D volume transformation. The 2D SEM image derived from 1402 and the segmented training image derived from 1404 can be derived from multiple adjacent and / or non-adjacent views of the rock sample 104.

[0104] Method 1400 continues at 1406, wherein a cross-correlation function is applied to at least first and second 2D SEM images derived from 1402 to generate 3D digital model volumes. For example, one or more randomized algorithms (e.g., the cross-correlation function) are applied to the 2D SEM image derived from 1402 (or a segmented version derived from 1404) to generate one of multiple implementations of statistically similar or statistically equivalent 3D pore-organic matrix volumes. In the example of the cross-correlation function, the method uses structural information (e.g., data indicating correlations between different parts of the image) in the 2D training images (e.g., the 2D SEM image of 1402 or the segmented version of 1404) to first decompose the image into smaller component regions, which are then randomly recombinated to synthesize versions of the original 2D training images that are statistically similar but not identical. Subsequently, the original 2D training images and their statistically similar versions are projected onto one or more imaginary planes (e.g., in 3D form). These 3D projections, or “digital model volumes,” can be used to statistically adjust subsequent iterations that generate synthetic, statistically similar images. In one example, this adjustment process can be used to iteratively generate synthetic images that can be placed on top of or below previously generated synthetic images in a manner that appears to more accurately reflect the natural appearance and / or structural continuity of real-world rock samples.

[0105] Method 1400 continues at 1408, determining from 1406 a probability distribution (e.g., aperture distribution) of the aperture of a 3D digital model volume. In the example, the aperture distribution is determined based on the image intensity values ​​of pixels in a 2D SEM image derived from 1402, which are used to generate the 3D digital model volume to determine the aperture distribution at 1408.

[0106] In some examples, determining the pore size distribution involves numerical simulation using algorithms derived from exemplary direct numerical simulation techniques. For instance, two-phase lattice Boltzmann simulations can be used to estimate numerical permeability based on the volume of a 3D digital model for a given fabric type, while object partitioning and point counting algorithms can be used to estimate the numerical pore size distribution based on the volume of a 3D digital model for a given fabric type.

[0107] In method 1400, information from multiple 2D SEM images (originating from 1402) or optionally segmented training images (originating from 1404) is aggregated, resulting in the 3D digital model volume at 1406 more closely representing the features of the original rock sample 104. Additionally, in some examples, at 1408, multiple 3D model volumes are used to determine corresponding multiple pore size distributions. For example, the 3D digital model volume is used as a modeling mesh for a type of rock texture (e.g., N realizations of a texture type) to determine one or more desired material properties for that texture type. Because the 3D model volume represents N realizations of a texture type, the multiple pore size distributions obtained at 1408 can also be aggregated, resulting in improved accuracy of the final aggregated pore size distribution for that texture type (e.g., compared to a pore size distribution derived from only one 3D model volume realization).

[0108] In another example, because the 3D model volume represents N realizations of a fabric type, 2D SEM images (originating from 1402) and / or segmentation training images (originating from 1404) can be generated from different rock samples 104, including those originating from different geographic regions, provided that the different rock samples 104 include the same fabric type represented by the 3D model volume. For example, a first 2D SEM image has a first rock sample originating from a first geographic region, while another 2D SEM image has a second rock sample originating from a second geographic region. It should be understood that the geographic regions do not need to be far apart, but can simply refer to different locations near the exploration well site. However, the geographic regions may also be far apart, provided that the various different rock samples 104 include the rock fabric type represented by the 3D digital model volume generated at 1406.

[0109] The foregoing discussion is intended to illustrate various principles and embodiments of the invention. Although specific embodiments have been shown and described, those skilled in the art can modify them without departing from the spirit and teachings of the invention. The embodiments described herein are merely exemplary and not restrictive. Therefore, the scope of protection is not limited by the foregoing description, but only by the appended claims, which include all equivalents of the subject matter of the claims.

Claims

1. A method for analyzing rock samples, comprising: Perform scanning electron microscopy (SEM) imaging of multiple physical surfaces of a rock sample to generate two-dimensional 2DSEM images of the physical surfaces; A cross-correlation function is applied to at least a first 2D SEM image and a second 2D SEM image to generate a three-dimensional 3D digital model volume based on the at least first 2D SEM image and the second 2D SEM image; and The probability distribution of the aperture of the 3D digital model volume is determined based on the image intensity values ​​of pixels in each of the at least first 2D SEM image and the second 2D SEM image.

2. The method according to claim 1, wherein, The resolution of the 3D digital model volume is finer than that of the digital image volume.

3. The method according to claim 1, wherein, The axial orientation of the first 2D SEM image is different from that of the second 2D SEM image.

4. The method according to claim 1, wherein, The rock sample is a first rock sample originating from a first geographic region, and the method further includes: Perform SEM imaging of multiple physical surfaces of a second rock sample originating from a second geographic region; The cross-correlation function is applied to the first 2D SEM image and the third 2D SEM image to generate a second 3D digital model volume, wherein the third 2D SEM image is of the second rock sample; The type of rock texture represented by the volume of the 3D digital model exists in each of the first 2D SEM image and the third 2D SEM image.

5. The method according to claim 1, further comprising: The cross-correlation function is applied to multiple 2D SEM images to generate multiple 3D digital model volumes for each of the multiple rock textures; as well as Direct numerical simulations are performed using the plurality of 3D digital model volumes as modeling meshes for one of the rock fabrics to determine the probability distribution of the pore size for the one of the rock fabrics.

6. The method according to claim 5, further comprising: The multiple 3D digital model volumes are aggregated for one of the rock textures to produce an aggregated result; as well as In response to the result of the aggregation, the probability distribution of the updated pore size in the rock fabric is determined.

7. A system for analyzing rock samples, comprising: Scanning electron microscope (SEM), which is configured to generate two-dimensional 2D SEM images of the physical surfaces of a rock sample; and A computing device, coupled to the SEM and comprising: processor; and A memory coupled to the processor and configured to store instructions, which, when executed by the processor, configure the computing device to: A cross-correlation function is applied to at least a first 2D SEM image and a second 2D SEM image to generate a three-dimensional 3D digital model volume based on the at least first 2D SEM image and the second 2D SEM image; and The probability distribution of the aperture of the 3D digital model volume is determined based on the image intensity values ​​of pixels in each of the at least first 2D SEM image and the second 2D SEM image.

8. The system according to claim 7, wherein, The resolution of the 3D digital model volume is finer than that of the digital image volume.

9. The system according to claim 7, wherein, The axial orientation of the first 2D SEM image is different from that of the second 2D SEM image.

10. The system according to claim 7, wherein, The rock sample is a first rock sample originating from a first geographical region, and the instructions, when executed by the processor, configure the computing device to: Receive SEM images of multiple physical surfaces of a second rock sample originating from a second geographic region; The cross-correlation function is applied to the first 2D SEM image and the third 2D SEM image to generate a second 3D digital model volume, wherein the third 2D SEM image is of the second rock sample; The type of rock texture represented by the volume of the 3D digital model exists in each of the first 2D SEM image and the third 2D SEM image.

11. The system according to claim 7, wherein, When the instructions are executed by the processor, the computing device is configured to: The cross-correlation function is applied to multiple 2D SEM images to generate multiple 3D digital model volumes for each of the multiple rock textures; as well as Direct numerical simulations are performed using the plurality of 3D digital model volumes as modeling meshes for one of the rock fabrics to determine the probability distribution of the pore size for the one of the rock fabrics.

12. The system according to claim 11, wherein, When the instructions are executed by the processor, the computing device is configured to: The multiple 3D digital model volumes are aggregated for one of the rock textures to produce an aggregated result; as well as In response to the result of the aggregation, the probability distribution of the updated pore size in the rock fabric is determined.

13. A non-transitory computer-readable medium for storing instructions, which, when executed by a processor, cause the processor to: Two-dimensional 2D scanning electron microscope (SEM) images of the physical surfaces of a received rock sample; A cross-correlation function is applied to at least a first 2D SEM image and a second 2D SEM image to generate a three-dimensional 3D digital model volume based on the at least first 2D SEM image and the second 2D SEM image; and The probability distribution of the aperture of the 3D digital model volume is determined based on the image intensity values ​​of pixels in each of the at least first 2D SEM image and the second 2D SEM image.

14. The non-transitory computer-readable medium according to claim 13, wherein, The resolution of the 3D digital model volume is finer than that of the digital image volume.

15. The non-transitory computer-readable medium according to claim 13, wherein, The axial orientation of the first 2D SEM image is different from that of the second 2D SEM image.

16. The non-transitory computer-readable medium according to claim 13, wherein, The rock sample is a first rock sample originating from a first geographic region, and the instructions therein, when executed by the processor, cause the processor to: Receive SEM images of multiple physical surfaces of a second rock sample originating from a second geographic region; The cross-correlation function is applied to the first 2D SEM image and the third 2D SEM image to generate a second 3D digital model volume, wherein the third 2D SEM image is of the second rock sample; The type of rock texture represented by the volume of the 3D digital model exists in each of the first 2D SEM image and the third 2D SEM image.

17. The non-transitory computer-readable medium according to claim 13, wherein, When the instruction is executed by the processor, the processor: The cross-correlation function is applied to multiple 2D SEM images to generate multiple 3D digital model volumes for each of the multiple rock textures; and Direct numerical simulations are performed using the plurality of 3D digital model volumes as modeling meshes for one of the rock fabrics to determine the probability distribution of the pore size for the one of the rock fabrics.

18. The non-transitory computer-readable medium according to claim 17, wherein, When the instruction is executed by the processor, the processor: The multiple 3D digital model volumes are aggregated for one of the rock textures to produce an aggregated result; as well as In response to the results of the aggregation, the probability distribution for updating the pore size in the rock fabric is determined.

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