Prediction of mechanical properties of sedimentary rocks based on a particle-particle parametric cohesive contact model

Abstract

To provide a method of, a computer system for, and a program for carrying out simulation of physical properties of a porous medium by a computer.SOLUTION: A method according to the present invention includes steps of receiving a micro CT3D image capturing a representative element volume of a porous medium, labelling the micro CT3D image as an individual voxel in accordance with a kind of mineral or fluid, and labelling the mineral voxel as one belonging to a separated and fixed individual particle. The method further includes steps of converting the labelled voxel to non-structuring conformal mesh representation for all particles, and applying the non-structuring conformal mesh representation to a parametric aggregation contact engine. The parametric aggregation contact engine executes a parametric aggregation contact model having critical separation δ0 conditioned in accordance with adjustable parameters and a compaction level.SELECTED DRAWING: Figure 5

Description

[Background technology]

[0001] Multi-component fluid flows through porous regions are a key feature of hydrocarbon reservoir rocks, which are a vital input to the oil and gas industry, as well as other industries.

[0002] Numerical simulation of multi-component fluid flow in porous regions with complex solid structures is of great importance in many industrial applications, e.g., enhanced oil recovery (EOR) and personal protective equipment (PPE). To achieve accurate simulation results, it is crucial to capture relevant data from porous structures at all scales.

[0003] In the oil and gas industry, so-called digital rock simulation has been developed based on X-ray microtomography (microCT) imaging, which allows the capture of pore-scale three-dimensional (3D) images of reservoir rock structures at the micrometer scale. Such images are used to perform computer simulations of simulated fluid (i.e., oil / water) flow under different production conditions.

[0004] However, digital rock simulation of rock mechanical properties has been considered challenging given the inherent limitation of micro-CT images to capture the degree of compaction between particles within rock due to limitations in imaging resolution. Another drawback is that micro-CT images are usually acquired at ambient conditions, which do not capture the actual net confining pressure (NCS) on the pore structure.

[0005] Different levels of compaction, compression, recrystallization, and diagenesis can generally produce a wide range of particle contact behaviors in sedimentary rocks, from loosely consolidated sandpacks to fully fused particles forming a single solid structure. Numerical methods in the literature usually use a single solid frame formed by the mineral particles, which often overestimates the simulated rock stiffness compared to experimental measurements. Some ideas have been discussed to assign different properties to the contact and particle regions. Summary of the Invention

[0006] A commonality among these prior art methods is that they do not allow particle rearrangement, which limits the particle-particle contact behavior of real rocks and large displacement rock fracture.

[0007] According to an aspect, a computer-implemented method for simulating physical properties of a porous medium includes receiving, by a computer, a micro-CT 3D image capturing a representative elemental volume of the porous medium, the porous medium being defined as having mineral and fluid species with individual particles and particle-particle contacts; labeling, by the computer, the micro-CT 3D image as individual voxels according to the mineral and fluid species; labeling, by the computer, the mineral species voxels as belonging to isolated and fixed individual particles; converting, by the computer, the labeled voxels into an unstructured conformal mesh representation for all particles; and applying the unstructured conformal mesh representation to a parametric cohesive contact engine, the parametric cohesive contact engine having adjustable parameters, such as consolidation level, (consolidation level) Critical separation δ conditioned according to 0 and implementing / applying a parametric cohesive contact model having:

[0008] Embodiments of the method can include any one or more of the following features or other features as disclosed herein.

[0009] The second segmentation is performed by watershed analysis. Micro-CT 3D has sufficient resolution to identify individual particles and the associated pore geometry. The particles are modeled as free particle contacts, where only friction exists between particles, and fixed particle contacts, where particles are fully fused. Converting the labeled voxelized 3D image further includes optimizing elements of the same particle for finite element simulation, where elements on either side of the particle contact fit together without gaps or overlaps at the contact boundary.

[0010] The parametric coagulation contact engine is a critical separation δ 0 relates to the level of compaction, defined as C, by the following equation:

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[0011] Δx is estimated from the particle size distribution or particle-particle contact area distribution as extracted from the micro-CT 3D images. The compaction level is a dimensionless value, varying from 0 to 1 with increasing levels of compaction. δ 0 =∞, C=1, δ 0 = 0, where C = 0, and C represents the polarities of fixed and free particle-particle contact. The porous medium is a porous rock sample, and the method further includes applying the parametric cohesive contact engine to a finite element solver with prescribed strain / stress boundary conditions and particle-particle contact according to a parametric cohesive contact model, determining contact behavior at different levels of particle solidification to convert the parametric cohesive contact engine to a net confining pressure model, and performing flow simulations for the net confining pressure model.

[0012] Aspects also include computer systems and computer program products.

[0013] One or more of the above aspects may provide one or more of the following advantages.

[0014] The approach described herein provides a workflow to more accurately model varying particle-particle solidification to accurately simulate mechanical rock properties, while having the ability to recover the correct net confining stress (NCS) pore structure to simulate petrophysical properties under the correct conditions, and enabling particle relocation capabilities, including destructive testing simulations.

[0015] The described approach uses a parameterized cohesive contact model that can capture extreme free and fixed particle contact behavior, as well as intermediate degrees of particle compaction. The approach addresses issues including (1) modeling variable particle-particle solidification to accurately simulate mechanical rock properties, (2) recovering the correct NCS pore structure to simulate petrophysical properties under field conditions, and (3) enabling particle relocation, including destructive testing simulations.

[0016] The proposed method can be used to simulate petrophysical properties in NCS, such as fluid flow in porous rocks, and is applicable to the lattice Boltzmann method as well as other computational fluid dynamics methods, including the finite volume method, the finite element method, etc.

[0017] Other features and advantages of the invention will become apparent from the following description, and from the claims. [Brief explanation of the drawings]

[0018] [Figure 1] FIG. 1 illustrates a system for simulation of micromechanical modeling using a model of a porous structure. [Figure 2A]1 is a diagram showing cohesive contact behavior and a graph showing a typical pull-separation response. [Figure 2B] 1 is a diagram showing cohesive contact behavior and a graph showing a typical pull-separation response. [Figure 3A-C] The tension-separation response curves are shown for fixed particles, intermediate particle contact, and free particle contact, respectively. [Figure 4A] FIG. 1 shows particle meshes with three-grain packing and particle behavior at fixed (C=1), free (C=0), and intermediate cohesive contact levels (C=0.5). [Figure 4B] FIG. 1 shows particle meshes with three-grain packing and particle behavior at fixed (C=1), free (C=0), and intermediate cohesive contact levels (C=0.5). [Figure 5] FIG. 1 is a flow diagram illustrating the Parametric Coagulation Catalytic Engine process. [Figure 6A-C] FIG. 1 shows the image for a binary micro-CT image of sphere packing, the segmented particles shown by gray shading, and the particle mesh for the FE solver. [Figure 7A-C] Figure 1 shows a binary micro-CT image of Grosmont Carbonate, with segmented particles shown by grey shading, and a particle mesh for the FE solver (only the outer edge is shown for better visualization). [Figure 8A-C] FIG. 1 shows the image for a binary micro-CT image of the Fontainebleau model, the segmented particles shown by gray shading, and the particle mesh for the FE solver. [Figure 9A] FIG. 1 shows a graph of stress-strain response for various compaction levels and normalized elastic modulus as a function of compaction level. [Figure 9B] FIG. 1 shows a graph of stress-strain response for various compaction levels and normalized elastic modulus as a function of compaction level. [Figure 10A-C]FIG. 1 shows a binary micro-CT image of Fontainebleau sandstone, segmented particles, and images relative to the particle mesh. [Figure 11A] FIG. 1 shows the stress-strain response for various compaction levels C and the normalized elastic modulus as a function of compaction level. [Figure 11B] FIG. 1 shows the stress-strain response for various compaction levels C and the normalized elastic modulus as a function of compaction level. [Figure 12A-B] FIG. 12A shows a voxelized image of the segmented particles and the particle meshing for FE simulation of the fracture test (FIG. 12B). [Figure 13] FIG. 1 illustrates the evolution of the vertical displacement field as the Fontainebleau model is compressed vertically. [Figure 14] Figure 1 shows normal stress as a function of normal strain for various consolidation levels C. [Figure 15A-C] FIG. 1 shows bulk modulus as a function of porosity for various samples. DETAILED DESCRIPTION OF THE INVENTION

[0019] This application describes a parametric cohesive contact model implemented in a parametric cohesive engine to simulate a wide range of sedimentary rocks, from unconsolidated to well-consolidated, and a benchmark study on sandstone samples, which is compared with laboratory-measured elastic moduli to calibrate the degree of consolidation of the parametric cohesive contact engine. Additionally, numerical uniaxial compression tests are conducted to demonstrate the impact of adequately capturing the degree of consolidation on rock strength and failure patterns.

[0020] Referring to FIG. 1, a system 10 for simulating the physical properties of multiscale porous materials is shown using a cohesive contact model that captures both extremes of contact behavior, i.e., free and fixed particles, as well as intermediate degrees of particle compaction. Finite element (FE) simulations are performed on the results of the parametric contact model to produce a net confining pressure (NCS) model as input to the flow simulation. The flow simulations can be for various purposes, such as simulating "wetability restoration" or "aging" processes representative of subsurface reservoir conditions, i.e., "numerical aging." Other simulations can include effects such as steam flow on the PPE. The flow simulations can use lattice Boltzmann or other computational fluid dynamics techniques.

[0021] Generally, system 10 in this implementation is based on a client-server or cloud-based architecture and includes a network 12, e.g., the Internet or other network, a client system 14 including a mesh provided by a user, and a server system 16 implemented as a massively parallel computing system (standalone or cloud-based) operatively coupled to client system 14. Server system 16 includes memory 18, a bus system 22, interfaces 20 (e.g., user interface / network interface / display or monitor interface, etc.), and a processing device 24.

[0022] The memory 18 contains a parametric cohesive contact engine 32 that operates on a digital representation 32' of a physical rock sample. The digital representation 32' of the physical rock sample represents the pore space, grains, and grain boundaries of the physical rock sample. The parametric cohesive contact engine 32 can be used to simulate bonded interfaces with and without the possibility of bond damage and failure. The parametric cohesive contact engine 32 includes a linear elastic tension-separation model 32a, a damage initiation criteria model 32b, and a damage evolution model 32c, all of which allow for an accurate description of grain contact behavior.

[0023] The contact model can be used in conjunction with the FE analysis engine 33 to provide the NCS model as input to a flow simulation engine 34 to simulate multi-phase flow behavior occurring through reservoir rock, for example, adjacent to a gas or oil well (e.g., drilling rig 37). Determining multi-phase flow behavior can include, for example, wettability changes of a physical rock sample.

[0024] The digital representation of the physical rock sample 32′ can be a third-party application running on the same or a different system as the server 16. The system 10 simply requires the digital representation of the physical rock sample 32′, and the coagulation contacting engine 34 then digitally prepares the digital representation of the physical rock sample 32′.

[0025] One approach to producing a digital representation 32' of a rock sample is to obtain the representation 32' from a 3D image generated, for example, from a micro-CT scan of the rock sample. The micro-CT 3D image is voxelized and used as input to identify the individual grains and associated pore geometry of the rock. A limitation of micro-CT images for adequately capturing micromechanical rock models relates to insufficient contrast for distinguishing different mineral grains and for distinguishing particle-particle contacts between the same mineral grains. Identification of grain mineralogy and contacts can be improved by complementing 3D micro-CT imaging with higher 2D resolution and mineralogy imaging, such as scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS).

[0026] To construct a finite element (FE) micromechanical rock model from micro-CT data, two preprocessing steps are required: (1) particle-particle partitioning and (2) conformal meshing of particle contacts. For a description of these steps, see Z. Sun, R. Salazar-Tio, L. Duranti, B. Crouse, A. Fager, and G. Balasubramanian, Prediction of Rock Elastic Moduli Based on a Micromechanical Finite Element Model, Comput. Geotech. 135, 104149 (2021). A brief description is provided below.

[0027] For particle-particle segmentation, a direct binary thresholding operation is applied to the microCT scan to classify voxels as pores or solids. After this thresholding operation, solid voxels are reclassified using an integer index representing which particle the voxel belongs to. For this purpose, we use a type of watershed method, which is used to separate bordering objects in binary images. For further details, see D. Legland, I. Arganda-Carreras, and P. Andrey, Morpho Lib J: Integrated Library and Plugins for Mathematical Morphology with Image J, Bioinformatics 32, 3532 (2016). The watershed method first calculates the distance transform of the 3D image, where for each solid voxel, the Euclidean distance value to the nearest pore / solid interface is recorded. If this is considered a topographical depth map, the deeper parts of the image are the centers of the objects. Watershed classification considers each solid voxel by its center of gravity when subjected to this inverse distance transform topographical map. In the final particle segmented 3D image, each particle voxel has a corresponding particle index value, while pore voxels are labeled as 0.

[0028] To achieve an initial static solution for the segmented particles, a conformal mesh is prepared at the particle-particle contacts. A conformal mesh indicates that there is no separation or overclosure between any two particles in contact. The labeled voxelized 3D image is converted to an unstructured mesh representation, suitable for finite element (FE) simulation, where elements of the same particle perfectly fit together, without gaps or overlaps at the contact boundary. For a more thorough explanation, see Z. Sun, R. Salazar-Tio, L. Duranti, B. Crouse, A. Fager, and G. Balasubramanian, "Prediction of Rock Elastic Moduli Based on a Micromechanical Finite Element Model," Comput. Geotech. 135, 104149 (2021). A mesh is generated for all of the particles together, preserving the indices that represent the segmented particles, resulting in a conformal mesh at the particle-particle contacts. The mesh can be either two separate surfaces or one combined interface, which corresponds to two case scenarios: free or fixed particle-particle contact.

[0029] The meshed model, along with prescribed strain / stress boundary conditions and particle-particle contact models, is input to the FE solver 33. For a more complete description, see S. Qin, R. McLendon, V. Oancea, and A. M. Beese, Micromechanics of Multiaxial Plasticity of DP600: Experiments and Microstructural Deformation Modeling, Mater. Sci. Eng. A 721, 168 (2018); Abaqus, Abaqus 6.10 Online Documentation, Abaqus User Subroutines Ref. Man. (2010).

[0030] Parametric Cohesive Contact Engine A general parameterization of the basic contact model is used to capture the contact behavior of different levels of particle solidification, including two extreme scenarios: free particles, where only friction between particles is modeled, and fixed particles, where the particles are fully fused together. From the FE simulation perspective, free particle contact introduces replicated nodes and elements that allow particle relocation, while fixed particle contact models the solid framework as a whole.

[0031] After the results of the parameterized cohesive contact model are applied to the FE solver 33, the FE results are subsequently applied to, for example, a fluid simulation 34.

[0032] For details of the fluid simulation process 34, see commonly assigned U.S. patent application Ser. No. 15 / 880,867, entitled "Multi-Phase Flow Visualizations Based On Fluid Occupation Time," filed Jan. 26, 2018. For other exemplary cases, see commonly assigned U.S. patent application Ser. No. 16 / 243,285, entitled "Determining Fluid Flow Characteristics Of Porous Mediums," filed Jan. 9, 2019, or U.S. patent application Ser. No. 16 / 545,387, entitled "Determination Of Oil Removed By Gas Via Miscible Displacement In Reservoir Rock," filed Aug. 20, 2019.

[0033] Memory 18 may store parameters used by engines 32, 33, and 34. Specifically, for one or more of the above-mentioned applications of the subject matter of the present disclosure, the parameters used may include particle surface properties obtained by assigning mineral species to particles to determine surface properties for each of those mineral species, as well as surface texture and roughness characteristics. Memory 18 may also store fluid properties, such as fluid density and viscosity of each expected fluid (e.g., two or more of water, gas, and oil), and parameters such as fluid-fluid interface tension properties. Memory 18 also stores parameters such as fluid chemical composition data and affinity data of fluid components for specific mineral species. Memory 18 also stores dissociation pressures for each mineral species in combination with the fluids used by flow simulation engine 34. In addition, reservoir pressure and temperature data are also stored. The mineral species evaluated may be those found or expected in the actual reservoir field.

[0034] The simulation engine 34 may include modules for setting up a rock sample simulation environment, a module for performing drainage / swelling simulations, and a module for calculating the local curvature of surfaces within the pore space. The simulation engine 34 may also include a module 50 for processing multi-scale porous materials having regions of low resolution.

[0035] The system 10 has access to a data repository 38 that stores 3D meshes, coordinate systems, and libraries that can be used to apply meshes to 3D images generated from micro-CT scans of rock samples and for fluid simulations such as drainage / swelling simulations using any well-known computational technique such as computational fluid dynamics or the so-called lattice Boltzmann method.

[0036] The "bonded-particle" concept is widely adopted in discrete element methods (DEM), which simulate each individual particle as a discrete rigid body, as discussed in M. Obermayr, K. Dressler, C. Vrettos, and P. Eberhard, A Bonded-Particle Model for Cemented Sand, Comput. Geotech. 49, 299 (2013), DO Potyondy and PA Cundall, A Bonded-Particle Model for Rock, Int. J. Rock Mech. Min. Sci. 41, 1329 (2004), or Z. Sun, DN Espinoza, and MT Balhoff, Discrete Element Modeling of Indentation Tests to Investigate Mechanisms of CO2-Related Chemo-Mechanical Rock Alteration, J. Geophys. Res. Solid Earth 121, 7867 (2016).

[0037] Similarly, FE simulations can simulate bonded particle interfaces based on cohesive contact models with or without the possibility of bond damage and fracture (Figure 2A). The parametric cohesive contact engine 32 includes a linear elastic tension-separation model 32a, a damage initiation criterion 32b, and a damage evolution 32c, which allow for an accurate description of contact behavior. Discussed below is an overview of the contact model. Further details on the contact model can be found in the FE solver documentation (see Abaqus 6.10 Online Documentation, Abaqus User Subroutines Ref. Man. (2010); H. Harkness, G. Ang, P. Vijalapura, and D. Cojocaru, Contact Stress Accuracy with Robust and Broadly Applicable Implicit Contact Algorithm, in NWC (Nafems World Congress) (2011)).

[0038] The parametric cohesive contact engine 32 assumes tension-separation behavior that is initially elastic followed by damage initiation and evolution. The elasticity matrix K relates normal and shear stresses to normal and shear separation.

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[0039] Referring now to Figure 2A, an overview of the cohesive contact behavior is shown, and Figure 2B shows a typical tension-separation response plot for the parametric cohesive contact engine 32. The parameters of the parametric cohesive contact engine 32 are stiffness K in normal and shear directions for elastic behavior, RR and K. SS , critical separation δ R 0 and δ S 0, and the effective separation δ at complete fracture for damage behavior m f The parametric cohesive contact engine 32 includes stiffness normal and shear direction K to reduce the number of parameters. RR =K SS , δ R 0 =δ S 0 =δ 0 , and δ m f =2.5×δ m 0 The stiffness in the normal and shear directions is assumed to be K RR and K. SS is predetermined to replicate the mechanical behavior of a fixed particle-particle contact when no damage occurs. That is, K is determined to ensure that the results are consistent with a fixed particle-particle contact. RR and K. SS It is possible to determine the value of

[0040] Therefore, the parametric coagulation contact engine 32 is 0 The parametric coagulation contact engine 32 has only one adjustable parameter, δ, which is conditioned by the compaction level "C". 0 is related to the compaction level C as follows:

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[0041] 3A-3C, typical tension-separation response curves are shown for various compaction levels.

[0042] Figure 3A shows the tension-separation response curve for a fixed particle contact, where the curves are C = 1 and δ 0 =∞. Figure 3B shows the tension-separation response curve for intermediate particle contact, where C∈(0,1). Figure 3C shows the tension-separation response curve for free particle contact, where C=0. These tension-separation curves for various consolidation levels are quantified by the parameter C. Figures 3A-3C represent the parametric cohesive contact engine 32, showing a general parameterization that captures contact behavior at different levels of particle solidification. This parametric cohesive contact engine 32 allows for particle repositioning capabilities instead of modeling the particle space as a single solid, overall framework of particles.

[0043] The cohesive contact model 32 is capable of simulating linear elastic moduli comparable to experimental values ​​and simulating significant compaction found in in situ conditions that are difficult to capture using micro-CT imaging at ambient conditions. The parametric cohesive contact engine 32 is capable of simulating a wide range of sedimentary rocks, from unconsolidated to well-consolidated rocks.

[0044] 4A and 4B, a particle mesh with a three-particle packing is shown (FIG. 4A), where the particles are distinguished by different shades of gray. FIG. 4B shows that the parametric cohesive contact engine 32 can reproduce the behavior of fixed particle contacts 42 and free particle contacts 44 by varying the compaction level C.

[0045] To validate this proposed simplification, we first test the parametric cohesive contact engine through a simple scenario of a three-particle packing. The particles are extracted from micro-CT images of a Fontainebleau sandstone model (see F.D.E. Latief, B. Biswal, U. Fauzi, and R. Hilfer, Continuum Reconstruction of the Pore Scale Microstructure for Fontainebleau Sandstone, Phys. A Stat. Mech. Its Appl. 389, 1607 (2010)). The bottom of the packing is fixed, and a tensile stress is applied acting on the top of the packing.

[0046] Figures 4A and 4B show that the parametric cohesive contact engine 32 can reproduce fixed and free particle contact behavior when C = 1 and C = 0, respectively. Figure 4A shows the particle mesh used in the FE simulation. Figure 4B shows three simulation results for the cohesive contact model with different compaction levels C, as well as two simulation results for fixed and free particle contact (no cohesive contact applied). When C = 0, the particles become easily separated by tensile stress. External work increases as a result of particle displacement due to applied force. When C = 1, the three particles behave as a solid framework with no particle separation, and external work accounts for tension and overall displacement. When C = 0.5, the results show a transition from fixed to free particle contact due to bond damage and fracture. The transition is not very smooth due to the fact that there are only two bonded surfaces within the packing.

[0047] Referring to Figure 5, a process 50 is shown for accurately modeling variable particle-particle solidification to accurately simulate mechanical rock properties. Process 50, followed by process 33, restores the correct NCS pore geometry to simulate petrophysical (oil containing rock sample) properties under the correct conditions. Process 50 also enables particle relocation capabilities, including destructive testing simulations.

[0048] The process 50 receives as input at 52 a micro-CT 3D image that is voxelized at 54, meaning that it is fitted with a computer-generated mesh to yield a 3D voxelized image. The voxelized image captures a representative elemental volume of the rock with sufficient resolution to identify individual grain and pore geometries within the rock.

[0049] Process 50 labels a first segmentation of the micro-CT image, labeling individual voxels as belonging to different mineral and fluid species at 56. Process 50 labels a second segmentation of mineral species voxels as belonging to different individual particles at 58. Such a process may be performed by so-called watershed and derivative methods (see discussion above).

[0050] The labeled voxelized 3D image is then converted 60 into an unstructured mesh representation, e.g., a particle meshed model, where elements of the same particle are optimized for FE simulation, and elements on each side of the contact between particles fit together without gaps or overlaps at the contact boundary (see discussion above). The particle meshed model is input into the Abacus simulation engine 33, and strain / stress boundary conditions are set using a micromechanics plugin (see Qin et al., 2018, above).

[0051] A general parameterization of the parametric cohesive contact engine 32 is used in 62 to capture the contact behavior of different levels of particle solidification, including two extreme scenarios: free particles, where only friction between particles is modeled (see Figure 3C), and fixed particles, where particles are fully fused (see Figure 3A). Free particle contact introduces replicated nodes and elements that allow particle relocation, while fixed particle contact models the solid framework as a whole. Strain / stress boundary conditions from the micromechanics plugin inform the parameterization of the parametric cohesive contact engine 32. A general parameterization of the parametric cohesive contact engine 32 is used to capture the contact behavior of different levels of particle solidification between these extremes (see Figure 3B).

[0052] Discussed below are test results performed on sandstone samples that are compared with laboratory-measured elastic moduli to calibrate their degree of consolidation. Conventional simulations that do not include particle contact modeling tend to overestimate the elastic moduli. The parametric cohesive contact engine 32 discussed herein accurately captures particle contact behavior through the parameter C.

[0053] Test Case Results Referring now to Figures 6A-6C, simulation test results are shown for a rock sample containing sphere packing. Monodisperse sphere packing is a very good example of free particle-particle contact behavior. Numerical simulations based directly on image voxels and allowing only fixed particle-particle contact tend to overestimate the elastic moduli and stiffness. Micromechanical finite element models allow for particle relocation, resulting in elastic moduli that are very close to "laboratory" data (solutions from fine-grained dynamic simulations).

[0054] Figure 6A shows a binary micro-CT image of the original sphere packing, Figure 6B shows the segmented particles indicated by gray shading, and Figure 6C shows the particle mesh for the FE solver. Using this sphere packing model, we demonstrate that a parametric cohesive contact engine can mimic free particle contact. The material properties of quartz for the sphere packing are a density of 2.65 g / cm, according to Z. Sun, R. Salazar-Tio, L. Duranti, B. Crouse, A. Fager, and G. Balasubramanian, "Prediction of Rock Elastic Moduli Based on a Micromechanical Finite Element Model," Comput. Geotech. 135, 104149 (2021). 3 , bulk modulus 37.0 GPa, and shear modulus 44.0 GPa. Table 1 summarizes the specifications for the sphere-packing model. Table 1. Sphere packing specifications

[0055] [Table 1]

[0056] The parametric cohesive contact engine has two parameters: the compaction level C and the stiffness K. The compaction level C is equal to 0 for free particle contacts. The stiffness K is predetermined to reproduce the mechanical behavior of fixed particle contacts.

[0057] Hydrostatic compression tests can be performed to measure bulk modulus, and shear tests can be performed to measure shear modulus. Table 2 summarizes the results. Table 2. Volume and shear moduli of sphere packings [Table 2] The parametric cohesive contact engine at C=0 yields elastic moduli very similar to free-particle contacts. See Z. Sun, R. Salazar-Tio, L. Duranti, B. Crouse, A. Fager, and G. Balasubramanian, Prediction of Rock Elastic Moduli Based on a Micromechanical Finite Element Model, Comput. Geotech. 135, 104149 (2021). Results are not expected to be identical, given that the numerical simulations are based on different contact mechanisms.

[0058] The Grosmont Carbonates are a good example of fixed particle-particle contact behavior, given that carbonates are typically recrystallized by diagenesis. Thus, all particles behave as a solid framework. In this section, we perform particle compartmentalization to demonstrate that cohesive contacts can mimic the behavior of fixed particle contacts when C = 1.

[0059] Figure 7A is the original binary micro-CT image of the Grosmont carbonate, Figure 7B is the segmented particles shown by different shades of grey, and Figure 7C is the particle mesh for the FE solver (only the outer edges are shown for better visualization).

[0060] Table 3 summarizes the specifications for Grosmont Carbonate. Material properties for Grosmont Carbonate, 50% calcite and 50% dolomite, with a density of 2.79 g / cm 3 , bulk modulus 81.6 GPa, and shear modulus 36.7 GPa. The consolidation level C is equal to 1 for rigid particle contacts, and stiffness K is a calibrated parameter. Table 3. Grosmont Carbonate Specifications [Table 3]

[0061] Table 4 shows the results of a comparison of this model with our previous simulations, showing that the parametric cohesive contact engine with C = 1 results in moduli very similar to fixed particle contacts. Table 4. Bulk and shear moduli of Grosmont carbonates [Table 4]

[0062] Many sedimentary rock samples can exhibit different levels of compaction as sediments are compressed and cemented under various geotechnical and geochemical conditions. In this section, we focus on an intermediately compacted rock, the Fontainebleau Sandstone.

[0063] For illustrative purposes, the parametric cohesive contact engine 32 is applied to the Fontainebleau model, using a relatively small volume of 100 x 100 x 100 voxels and a voxel size of 7.3 μm. In Figures 8A-8C, Figure 8A shows the binary voxelized image, Figure 8B shows the segmented particles, and Figure 8C shows the conformal particle mesh used in the FE solver. The specified material properties are for quartz, as in the sphere packing case.

[0064] Uniaxial strain tests were performed on this Fontainebleau model, which required incremental strain in the vertical direction and zero strain in the horizontal direction. Figure 9A shows the stress-strain behavior for various consolidation levels C. When C = 0 and C = 1, the cohesive contact model 32 is able to reproduce the elastic moduli of free and fixed particle contacts, respectively. The elastic moduli show an increase as the consolidation level C increases.

[0065] Figure 9B shows the normalized modulus, [M(C)-M(0)] / [M(1)-M(0)], as a function of compaction level. The modulus tends to asymptotically approach two extremes. The data can be well fitted by a logistic function.

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[0066] Using knowledge gained from simulations on the small Fontainebleau model, the parametric cohesive contact engine 32 is applied to a larger Fontainebleau sandstone micro-CT model of 288 x 288 x 300 voxels. The voxel size is 7.5 μm. The sample porosity is 14.7%. The material properties are specified as quartz. Figure 10A shows the voxelized image, Figure 10B shows the segmented particles, and Figure 10C shows the conformal particle mesh.

[0067] Hydrostatic compression tests are performed to measure the bulk modulus. Figure 11A shows the stress-strain response for various consolidation levels C. Figure 11B shows the normalized modulus as a function of consolidation level. The results can be fitted by a logistic function (Equation 8) that describes the stress-strain behavior for various consolidation levels C. The parametric cohesive contact engine can reproduce the moduli of fixed and free particle contacts when C = 1 and C = 0, respectively. Two intermediate consolidation levels result in moduli in between. The parameters k and x0 of the above logistic fitting function (Equation 8) are 15.9 and 0.5, respectively.

[0068] The experimentally measured bulk modulus is about 22.2 GPa, which corresponds to a consolidation level C of 0.56 based on the simulation results in Figure 11B. Shear tests can be performed to measure the shear modulus when C = 0.56, which obtains a shear modulus of 24.9 GPa, which is also close to the laboratory measured shear modulus.

[0069] The parameterized cohesive contact model 32 allows the user to select the level of compaction as an input parameter based on their knowledge of the diagenetic history of the sedimentary rock sample.

[0070] Rock failure behavior clearly demonstrates the importance of well-capturing the consolidation level. Unconfined compression tests are widely used to determine the uniaxial compressive strength (UCS) and deformability of rock samples. The test sample is loaded axially without radial confinement. The height / diameter ratio of the sample is typically 2-3. Ratios smaller than 2 result in high uniaxial compressive strengths.

[0071] In this section, uniaxial compression tests are performed on cylindrical volumes from the Fontainebleau model used above at various compaction levels C. All other model parameters remain unchanged. The specimens have a height of 500 voxels and a diameter of 250 voxels. The voxel size is 7.3 μm. Figure 12A shows a voxelized image of the segmented grain, and Figure 12B shows the corresponding grain mesh used in the FE simulation of the uniaxial compression tests.

[0072] Figure 13 shows the evolution of the vertical displacement field from the initial state to the intermediate state as the sample is compressed vertically (C = 0.2). The Fontainebleau sample is initially intact and eventually ruptures due to shear bands.

[0073] Figure 14 shows normal stress as a function of normal strain for various levels of compaction, C. When C = 1, the particles are fused together and the sample behaves elastically with infinite strength. When C = 0, the particles are unconsolidated and the sample fails when the normal stress reaches the uniaxial compressive strength, with friction as the only remaining force. Intermediate values ​​of C result in stress-strain curves intermediate between the two end-member scenarios.

[0074] When C is relatively small (e.g., C = 0.2), the stress-strain curve is very close to the result for C = 0 due to the asymptotic properties of equation (8) and shown in Figures 9B and 11B. Simulation results show that rock failure behavior is conditioned by the consolidation level, which is parameterized in the cohesive contact model 32.

[0075] Figure 14 shows the normal stress as a function of normal strain for various levels of compaction, C. Larger values ​​of C result in greater uniaxial strength and modulus.

[0076] Table 6 summarizes the Young's modulus and unconfined compressive strength based on the results shown in FIG. Table 6. Bulk and shear moduli of Fontainebleau sandstone [Table 5]

[0077] A larger consolidation level parameter C results in a larger Young's modulus and unconfined compressive strength. Numerical simulations for this particular Fontainebleau model produce reasonable values ​​for Young's modulus and unconfined compressive strength compared to the referenced experimental data.

[0078] In addition to the compaction level, contact friction is another parameter for rock failure. Applying the so-called "Coulomb friction model," which relates the maximum allowable frictional stress across a particle contact to the contact pressure between the particles, results in a frictional stress at which contact slippage begins that is proportional to the product of the friction coefficient and the contact pressure. A friction coefficient of 0.2 is assumed. In addition, non-smooth contact boundaries can also add friction to particle contacts.

[0079] Referring now to Figures 15A-15C, these figures show the measured and simulated bulk moduli for sphere packing (Figure 15A), Grosmont carbonate (Figure 15B), and Fontainebleau sandstone (Figure 15C).

[0080] For sphere packing (Figure 15A), the particle contact model allows for free particle-particle contact, resulting in a bulk modulus that is much closer to the laboratory data than other numerical simulations that only allow fixed particle-particle contact. Sphere packing is a very good example of free particle-particle contact behavior. Numerical simulations based directly on image voxels and that only allow fixed particle-particle contact tend to overestimate the elastic properties.

[0081] The described micromechanical finite element model allows for particle redistribution, resulting in elastic moduli that are very close to "laboratory" data (solutions from fine-grained dynamic simulations), see Z. Sun, R. Salazar-Tio, L. Duranti, B. Crouse, A. Fager, and G. Balasubramanian, Prediction of Rock Elastic Moduli Based on a Micromechanical Finite Element Model, Comput. Geotech. 135, 104149 (2021).

[0082] For the Grosmont carbonates (Fig. 15B), all conventional numerical methods and particle contact models assume rigid particle-particle contact and yield similar predictions of the bulk modulus.

[0083] For the Fontainebleau sandstone (Figure 15C), numerical simulations were performed for both free and fixed particle-particle contacts, which serve as two end-member case scenarios. The actual particle-particle contact behavior of the Fontainebleau sandstone lies between these two end-member scenarios, which is accurately reproduced by our parametric cohesive contact model with C = 0.56. Because sediments are compacted and cemented under a variety of geotechnical and geochemical conditions, many sedimentary rock samples can exhibit different levels of compaction.

[0084] In Figures 15B and 15C, the upper and lower dashed lines serve as a reference for the numerical results. The upper and lower dashed lines correspond to the upper and modified lower Hashin-Shtrikman bounds (soft sand model). The solid line represents the stiff sand model.

[0085] Embodiments of the present subject matter and the functional operations described herein may be implemented in digital electronic circuitry, tangibly embodied computer software or firmware, computer hardware (including structures disclosed herein and their structural equivalents), or one or more combinations thereof. Embodiments of the present subject matter described herein may be implemented as one or more computer programs (i.e., one or more modules of computer program instructions encoded on a tangible, non-transitory program carrier for execution by, or to control the operation of, a data processing apparatus). A computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or one or more combinations thereof.

[0086] A computer program, which may also be referred to or described as a program, software, software application, module, software module, script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and can be deployed in any form including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program, or in multiple coordinated files (e.g., files storing one or more modules, subprograms, or portions of code)). A computer program can be deployed so that the program is executed on one computer or on multiple computers located at one site or distributed across multiple sites and interconnected by a data communications network.

[0087] A computer suitable for running a computer program can be based on a general-purpose or dedicated microprocessor, or both, or any other type of central processing unit. Typically, the central processing unit will receive instructions and data from a read-only memory, a random-access memory, or both. The essential elements of a computer are a central processing unit for performing or executing instructions, and one or more memory devices for storing instructions and data. Typically, a computer will also include one or more mass storage devices (e.g., magnetic, magneto-optical, or optical disks) for storing data, or be operatively coupled to receive data from or transfer data to them, although it is not necessary for a computer to have such devices.

[0088] Computer-readable media suitable for storing computer program instructions and data include all forms of non-volatile memory on media and memory devices, including, by way of example, semiconductor memory devices (e.g., EPROM, EEPROM, and flash memory devices), magnetic disks (e.g., internal hard disks or removable disks), magneto-optical disks, and CD-ROM and DVD-ROM disks. The processor and memory can be supplemented by, or incorporated in, special purpose logic circuitry.

Claims

1. 1. A computer-implemented method for simulating physical properties of porous media, comprising: receiving, by a computer, a microCT 3D image capturing a representative elemental volume of the porous medium, the porous medium being defined as having mineral species and fluid species with individual particles and particle-to-particle contacts; labeling, by the computer, the microCT 3D image as individual voxels according to mineral and fluid type; labeling, by the computer, the mineral species voxels as belonging to separated and fixed individual particles; converting, by the computer, the labeled voxels into an unstructured conformal mesh representation for every particle; applying the unstructured conformal mesh representation to a parametric cohesive contact engine, the parametric cohesive contact engine comprising a critical separation δ conditioned according to an adjustable parameter, compaction level; 0 Implementing a parametric cohesive contact model with Including, The method wherein the critical separation δ 0 is a length.

2. The method described in claim 1, wherein labeling the mineral species voxels as belonging to separated and fixed individual particles is performed by the watershed method.

3. The method of claim 1 , wherein the microCT 3D images have sufficient resolution to distinguish individual grains and associated pore geometries.

4. The method of claim 1 , wherein the particles are in free particle contact, where only friction is modeled between the particles, or in fixed particle contact, where the particles are fully fused together.

5. Transforming the labeled voxelized 3D image includes: Optimizing elements of the same particle for a finite element simulation, wherein the elements on each side of a contact between particles fit together without gaps or overlaps at the contact boundary. The method of claim 1 further comprising:

6. The parametric coagulation catalytic engine 0 relates to the compaction level, defined as C, by the following equation: [Equation 1] However, Δx is the same as δ 0 The method of claim 1 , wherein the characteristic length has units of .

7. The method of claim 6, wherein Δx is estimated from particle size distribution or particle-particle contact area distribution as extracted from the microCT 3D image.

8. 10. The method of claim 1, wherein the compaction level is a dimensionless value that varies from 0 to 1 with increasing levels of compaction.

9. The compaction level is defined as C and δ 0 =∞, C=1, δ 0 2. The method of claim 1, wherein C=0 for .times. ...

10. The porous medium is a porous rock sample, and the method comprises: applying the parametric cohesive contact engine to a finite element solver with prescribed strain / stress boundary conditions and particle-particle contact according to the parametric cohesive contact model; determining contact behavior at different levels of particle coagulation to convert the parametric coagulation contact engine into a net confinement pressure model; performing a flow simulation for the net confining pressure model; The method of claim 1 further comprising:

11. 1. A computer system comprising: one or more processor devices; a memory coupled to the one or more processor devices; and storage storing executable computer instructions for performing a porous media fluid simulation, the instructions causing the one or more processors to: receiving a microCT 3D image capturing a representative elemental volume of the porous medium, the porous medium being defined as having mineral species and fluid species with individual particles and particle-to-particle contacts; labeling the microCT 3D images as individual voxels according to mineral and fluid species; labeling said mineral species voxels as belonging to separated and fixed individual particles; converting the labeled voxels into an unstructured conformal mesh representation for every particle; applying the unstructured conformal mesh representation to a parametric cohesive contact engine, the parametric cohesive contact engine comprising a critical separation δ conditioned according to an adjustable parameter, compaction level; 0 Implementing a parametric cohesive contact model with and The critical separation δ 0 is a length.

12. 12. The computer system of claim 11, wherein the compaction level is a dimensionless value that varies from 0 to 1 with increasing levels of compaction.

13. Transforming the labeled voxelized 3D image includes: Optimizing elements of the same particle for a finite element simulation, wherein the elements on each side of a contact between particles fit together without gaps or overlaps at the contact boundary.

12. The computer system of claim 11, further comprising instructions for:

14. The parametric coagulation catalytic engine 0 relates to the compaction level, defined as C, by the following equation: [Equation 2] However, Δx is the same as δ 0 12. The computer system of claim 11, wherein the characteristic length has units of .

15. the porous medium is a porous rock sample, and the instructions include: applying the parametric cohesive contact engine to a finite element solver with prescribed strain / stress boundary conditions and particle-particle contact according to the parametric cohesive contact model; determining contact behavior at different levels of particle coagulation to convert the parametric coagulation contact engine into a net confinement pressure model; performing a flow simulation for the net confining pressure model; 12. The computer system of claim 11, further comprising instructions for:

16. 1. A computer program product tangibly stored on a computer-readable non-transitory storage device storing executable computer instructions for performing a porous media fluid simulation, the instructions comprising: receiving a microCT 3D image capturing a representative elemental volume of the porous medium, the porous medium being defined as having mineral species and fluid species with individual particles and particle-to-particle contacts; labeling the microCT 3D images as individual voxels according to mineral and fluid species; labeling said mineral species voxels as belonging to separated and fixed individual particles; converting the labeled voxels into an unstructured conformal mesh representation for every particle; applying the unstructured conformal mesh representation to a parametric cohesive contact engine, the parametric cohesive contact engine comprising a critical separation δ conditioned according to an adjustable parameter, compaction level; 0 Implementing a parametric cohesive contact model with Let them do this, The critical separation δ 0 is a length.

17. The parametric coagulation catalytic engine 0 relates to the compaction level, defined as C, by the following equation: [Equation 3] However, Δx is the same as δ 0 17. The computer program product of claim 16, wherein the characteristic length has units of .

18. 18. The computer program product of claim 17, wherein Δx is estimated from the particle size distribution or particle-particle contact area distribution as extracted from the microCT 3D image.

19. 17. The computer program product of claim 16, wherein the compaction level is a dimensionless value that varies from 0 to 1 with increasing levels of compaction.

20. The compaction level is defined as C and δ 0 =∞, C=1, δ 0 17. The computer program product of claim 16, wherein C=0 for .times. ...

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