Computer simulation of polyphase multicomponent fluid flow including physics of low-resolution porous structure

Abstract

To provide a computerized technique for performing a fluid simulation of a porous medium.SOLUTION: Techniques includes: searching for representations of three-dimensional porous media, in which the representations include pore space corresponding to the porous medium, and the representations include at least part of a low-resolution pore structure in the porous medium; defining a representative flow model that includes the low-resolution pore structure in the representations; and constructing a fluid force curve corresponding to fluid force in the low resolution pore structure in the representations by a computer system.SELECTED DRAWING: Figure 3

Description

[Background technology]

[0001] Multi-component fluid flow through porous regions is a key characteristic of hydrocarbon reservoir rocks and provides crucial information (input) for the oil and gas industry and other industries.

[0002] Numerical simulations of multi-component fluid flows in porous regions with complex solid structures are crucial for many industrial applications, such as enhanced oil recovery (EOR) and personal protective equipment (PPE). To obtain accurate simulation results, it is essential to capture relevant data from porous structures of all scales.

[0003] In many porous materials, the scale range often spans several orders of magnitude. Furthermore, the scale range is often unevenly distributed in space. Simulating such porous structures at the highest scale resolution (fully scale-resolved) is computationally too costly in terms of both data size and computation time and resources. Therefore, such simulations are often limited to samples that are considerably smaller in size than those of the original porous material under consideration. In the latter type of simulation, statistical representation may be sacrificed, or the types of porous materials investigated may be limited. [Overview of the project]

[0004] According to one embodiment, a computer implementation method for performing fluid simulation of a porous medium includes: searching for a representation of a three-dimensional porous medium using a computing system, wherein the representation includes the pore space corresponding to the porous medium and includes at least a portion of the under-resolved pore structure in the porous medium; defining a representative flow model including the under-resolved pore structure in the representation using the computing system; and constructing a fluid force curve corresponding to the fluid force in the under-resolved pore structure in the representation using the computer system.

[0005] Embodiments of the method may include any one or more of the following features or other features disclosed herein.

[0006] The representation of a three-dimensional porous medium is obtained from a three-dimensional image to which three-dimensional segmentation is applied. Low-resolution pore structures belong to a class of low-resolution pore structures, also called PM types, and the pore structure is represented by a description common to all elements of the class. The method further includes simulating fluid flow through the porous medium, accessing a model of the low-resolution pore structure when detecting the low-resolution pore structure, and applying a hydrodynamic curve to the low-resolution pore structure.

[0007] The application further includes applying a hydrodynamic curve according to local porosity data. Local porosity data includes local porosity and local orientation / spatial gradient of local porosity, obtained from a representation of a three-dimensional porous medium.

[0008] The method further includes using a computing system to calculate a hydrodynamic curve from pre-calculated physical properties, including absolute permeability, relative permeability, and capillary pressure curves, of a low-resolution pore structure in a representation based on local pore space data.

[0009] The calculations further involve computing physical properties, including absolute permeability, relative permeability, and capillary pressure curves, through simulations of the highest resolution subregions of a low-resolution pore scale in a representation based on local pore space data.

[0010] The method further includes storing parameter models of physical properties in a repository or library, which have parameters fitted to simulation data or adjusted according to subject expert matter knowledge.

[0011] The representations pertain to physical rock samples and include pore space and particle space data corresponding to physically porous rock samples, porous particle filters, and similar physically porous media.

[0012] In an additional embodiment, the computer system includes one or more processor devices, memory coupled to one or more processor devices, and storage storing executable computer instructions for performing fluid simulations of a porous medium, wherein the instructions are configured to cause one or more processors to retrieve a representation of a three-dimensional porous medium, the representation includes pore space corresponding to the porous medium, the representation includes at least a portion of the low-resolution pore structure in the porous medium, define a representative flow model including the low-resolution pore structure in the representation, and construct a fluid force curve corresponding to the fluid forces in the low-resolution pore structure in the representation.

[0013] Embodiments of a computer system may include any one or more of the following features or other features disclosed herein.

[0014] The representation of a three-dimensional porous medium is obtained from a three-dimensional image to which three-dimensional segmentation is applied.

[0015] The system is further configured to simulate fluid flow through a porous medium, detect low-resolution pore structures, access models of low-resolution pore structures, and apply hydrodynamic curves to these low-resolution pore structures.

[0016] Local porosity data includes local porosity and local orientation / spatial gradient of local porosity, obtained from a representation of a three-dimensional porous medium.

[0017] In an additional embodiment, the computer program product is tangibly stored in a computer-readable non-temporary storage device that stores executable computer instructions for performing fluid simulations of a porous medium, wherein the instructions cause a computing system to retrieve a representation of a three-dimensional porous medium, the representation includes a pore space corresponding to the porous medium, the representation includes at least a portion of the low-resolution pore structure in the porous medium, the representation defines a representative flow model including the low-resolution pore structure in the representation, and the computer program product constructs a fluid force curve corresponding to the fluid forces in the low-resolution pore structure in the representation.

[0018] Embodiments of a computer program product may include any one or more of the following features or other features disclosed herein.

[0019] The computer program product further includes instructions for calculating hydrodynamic curves from pre-calculated physical properties, including absolute permeability, relative permeability, and capillary pressure curves of low-resolution pore structures in representations based on local pore space data.

[0020] The computer program product further includes instructions for calculating physical properties, including absolute permeability, relative permeability, and capillary pressure curves, through simulation of a set of the highest resolution subregions of a low-resolution pore scale in a representation based on local pore space data.

[0021] The computer program product further includes instructions for storing in a repository or library a parameter model for physical properties having parameters fitted to simulation data or adjusted according to the expertise of the subject matter.

[0022] The computer program product further includes instructions for simulating fluid flow through a porous medium, accessing a model of a low-resolution pore structure when detecting the low-resolution pore structure, and applying a fluid force curve to the low-resolution pore structure.

[0023] One or more of the above aspects may provide one or more of the following advantages.

[0024] The numerical approach described herein enables multi-component fluid flow simulation in a multi-scale porous structure while avoiding the extremely high computational cost associated with simulation of the highest scale resolution of the multi-scale porous structure. This numerical approach locally introduces appropriate forces acting on the fluid components using a complete set of pre-computed physical properties applicable to the low-resolution regions of the multi-scale porous structure. By using the physical properties of representative porous structures, generally, the computational cost is greatly reduced while maintaining reasonable accuracy.

[0025] The proposed method is applicable to other computational fluid dynamics methods including the lattice Boltzmann method and other methods such as the finite volume method and the finite element method. The stored physical properties of the representative solid structures can be widely applied to any spatial scale and various fluid conditions such as viscosity, surface tension, and surface wettability because the properties can be stored in a phenomenologically dimensionless form.

[0026] Other features and advantages of the present invention will become apparent from the following description and from the claims.

Brief Description of the Drawings

[0027] [Figure 1]This is a diagram of a system for simulating multiscale porous structures using a model with locally appropriate forces applicable to the low-resolution region of the multiscale porous structure. [Figure 2A-B] This is a cross-sectional view of a carbonate rock, showing the original scanned image (Figure 2A) and a segmented image (Figure 2B) showing small-scale porous regions marked in gray. [Figure 3] This is a flowchart showing the operation of a multi-component fluid flow simulation for a low-resolution porous structure. [Figure 4] This image shows various types of low-resolution porous structures. [Figure 5] This is a diagram showing the relationship between permeability and porosity. [Figure 6] This is a model curve of discharge / intake capillary pressure versus water saturation rate. [Modes for carrying out the invention]

[0028] Referring to Figure 1, System 10 is used to simulate a multiscale porous material having a low-resolution region. The purpose of the simulation can vary, such as simulating the "wettability recovery" or "aging" process that represents underground reservoir conditions, i.e., "numerical aging." Other simulations may include the effect of steam flow on PPE.

[0029] The focus of the discussion herein is on the simulation of multiscale porous materials having low-resolution regions. Generally, the system 10 in this embodiment is based on a client-server or cloud-based architecture and includes a server system 12 and a client system 14, which are implemented as a large-scale parallel computing system 12 (standalone or cloud-based). The server system 12 includes memory 18, a bus system 11, interfaces 20 (e.g., user interface / network interface / display or monitor interface, etc.), and processing devices 24.

[0030] As an example of a change in wettability, memory 18 contains a numerical aging engine 32 that manipulates a digital representation of a physical rock sample (digital rock sample), which digitally represents the pore space and granular space of a physical material, such as a physical rock sample. Memory also contains a simulation engine 34 that simulates changes in wettability using a simulation of a multiscale porous material with low-resolution regions.

[0031] In some embodiments, the simulation of multiphase flow behavior is performed through a reservoir rock adjacent to a gas or oil well (e.g., drilling rig 37) using simulations that utilize multiscale porous materials with low-resolution regions. Determining the multiphase flow behavior includes determining the changes in wettability of physical rock samples.

[0032] The digital representation of the physical rock sample may be a third-party application running on a system different from server 12. System 10 only needs the digital representation of the physical rock sample 32' for the numerical aging engine to prepare the digital representation of the physical rock sample digitally. One method for providing the digital representation 32' of the rock sample is to obtain the representation 32' from a 3D image generated from a micro-CT scan of the rock sample, for example.

[0033] For complete details of the simulation process, see U.S. Patent Application No. 15 / 880,867, filed January 26, 2018, entitled "Multi-Phase Flow Visualizations Based On Fluid Occupation Time," which is assigned to the assignee of this application. For other exemplary cases, see U.S. Patent Application No. 16 / 243,285, filed January 9, 2019, entitled "Determining Fluid Flow Characteristics Of Porous Mediums," or U.S. Patent Application No. 16 / 545,387, filed August 20, 2019, entitled "Determination Of Oil Removed By Gas Via Miscible Displacement In Reservoir Rock," which is also assigned to the assignee of this application.

[0034] Memory 18 may store parameters used by the engine 32. In particular, the parameters used in the case of the title “Determination of Oil Removed By Gas Via Miscible Displacement In Reservoir Rock” may include granular surface properties obtained by assigning mineral types 33a to granules and determining surface properties for each of those mineral types, as well as surface texture and roughness properties, with respect to one or more of the above-mentioned applications of the disclosed subject. Memory 18 may also store parameters such as fluid properties 33b of each expected fluid (e.g., two or more of water, gas, and oil), such as fluid density and viscosity, as well as fluid-fluid interfacial tension properties. Memory 18 also stores parameters such as chemical composition data 33c of the fluid and affinity data 33d of the fluid components for a particular mineral type. Memory 18 also stores the separation pressure 33e for each mineral type and fluid combination, and the selected aging time 33f used by the aging engine 32. Furthermore, reservoir pressure and temperature data are also stored. The mineral types evaluated may be those found or expected to be found at the actual location of the reservoir.

[0035] The simulation engine 34 includes a module for setting up the simulation environment for rock samples, a module for performing discharge / intake simulations, and a module for calculating the local curvature of the surface in the pore space. The simulation engine also includes a module 50 for performing processing of multiscale porous materials with low-resolution regions.

[0036] System 10 accesses a data repository 38 that stores 2D and / or 3D meshes, coordinate systems, and libraries that can be used for emission / intake simulations using computational fluid dynamics or any well-known computational technique such as the so-called lattice Boltzmann method. Furthermore, System 10 accesses a library 50a that includes a model 50b representing a low-resolution region.

[0037] Figures 2A and 2B illustrate examples of porous media with low-resolution regions, obtained from underground porous media for oil and gas applications. Figure 2A is the original scanned image. Figure 2A shows a typical cross-section of a carbonate rock sample 40 having solid structures of several different scales, including small-scale porous structures, three of which are shown as 42.

[0038] Figure 2B is the corresponding segmented image 40' of carbonate rock sample 40 (Figure 2A), which shows small-scale porous structures, three of which are shown at 42' and marked in gray. The difference in length scale between the black and gray structures is approximately 10 times. The gray small-scale porous regions can significantly affect flow behavior, so their contributions should be appropriately considered. Part of Figure 2B is shown by a dashed line 44', which will be discussed further in Figure 4.

[0039] However, resolving all such small-scale details requires extremely fine resolution, resulting in significantly higher computational costs for simulations. The cost of such simulations can increase tens of thousands of times compared to unresolved simulations, due to the increased number of 3D cells and the decrease in time increments caused by simulating gray areas. Therefore, simulations at such high resolutions are not practical for most industrial applications.

[0040] Process 50 simulates the original porous material with various sizes, including low-resolution subscales, but it is not necessary to resolve all of the low-resolution subscales contained in the original porous material. These low-resolution subscale physical features are appropriately incorporated when establishing the process described below.

[0041] Process 50, which addresses the aforementioned challenges of multi-component fluid flow simulations for low-resolution porous structures, involves a novel workflow where the fluid flow simulation only resolves porous samples to a certain scale level. However, numerical models take into account data contributions from low-resolution porous regions 42' (gray area in Figure 2B). The essential idea is to recognize that the effect of low-resolution porous regions on the flow is a set of forces, such as viscous forces, pressure, and capillary forces. Numerical models reproduce such forces acting on the resolved fluid by using local representative physical properties such as absolute permeability, relative permeability, and capillary pressure saturation curves.

[0042] These physical properties are obtained through simulations of much smaller subregions of the original porous material at the highest resolution, representing small-scale unresolved gray porous regions, or generated by a user-calibrated parameter function. These sets of physical properties are stored in a library. Each set of physical properties represents a type of flow for a particular low-resolution porous structure. In each gray region, during the simulation of the low-resolution porous structure, a set of physical properties for that type of porous structure is selected from the library and assigned to the model. By taking into account local porous geometry information, including the porosity (ratio of pore space to total volume) and directionality of the structure, local low-resolution flow behavior can be adequately reproduced.

[0043] Referring here to Figure 3, a process 50 for performing a multi-component fluid flow simulation for a low-resolution porous structure is shown. Process 50 uses a simulation of a porous rock sample as an example. Process 50 includes performing a geometric analysis of a typical porous structure using scanning images 52 to identify the various types of low-resolution porous structures encountered in the porous structure under investigation. The types of low-resolution porous structures are used to define a model 54 for the representative flow of each gray region. Once the model is defined, the defined model is compared to an existing model stored in the model library. Essentially, a model is defined as containing a set of physical properties. If a corresponding set of physical properties already exists in the library 56, a model containing the set of physical properties is retrieved from the library 58.

[0044] If a set of properties does not exist, the process performs a high-resolution simulation in a representative sub-region of the gray area6260 to compute a new set of physical properties for a specific type of porous structure being modeled, including absolute permeability, relative permeability, and capillary pressure saturation curves64. These sets of physical properties describe the effective multiphase flow behavior of the porous media structure. Once the new set of physical properties is computed, the computed new model is added to the library66 and labeled for that particular low-resolution simulation being performed.

[0045] Process 50 uses local geometric information and physical properties to determine whether all low-resolution parts are finished (completed) 66. These appropriate fluid forces correspond to viscous forces, pressure, and capillary forces from the low-resolution solid structure.

[0046] Segmentation Referring to Figure 4, various methods exist for defining numerical models of fluid forces in low-resolution regions. Through image analysis (segmentation), 3D image analysis can define various types of low-resolution porous regions. 3D image analysis (segmentation) is applied to 3D images. As shown in Figure 4, after segmentation, the low-resolution porous regions 42a'~42d' are illustrated from a portion of Figure 2B.

[0047] Different materials have different X-ray attenuation coefficients. Grayscale values ​​can be used to classify pixels according to the type of material (e.g., minerals, fluids, etc.). If a pixel contains sub-resolution pores, the X-ray attenuation is the average value of the solid and pore portions within that pixel (partial volume effect).

[0048] Additional texture features can be used to segment pixels into different porous media (PM) types, for example: Cellular structure (42a') Fibrous structure (42b') Microporous clay (42c') Microporous dolomite (42d')

[0049] Absolute penetration rate Absolute permeability is simulated, for example, by a single-phase flow lattice Boltzmann (LB) solver. Generally, the simulation output for a macroscopic 3D model is a permeability tensor with 3x3 values. The established similarity between the macroscopic output and the microscopic PM pixel input should generally also be a tensor. However, in the vast majority of cases, it is a function of a single permeability versus porosity. The tensor can be approximated by TIFF2022104831000002.tif6170. In some cases, local orientation can be interpolated by calculations performed on the image itself.

[0050] For example, in the PM type (42d') of "microporous dolomite," the pores are small compared to the pixel size, and the internal structure is homogeneous and isotropic. In this case, there is no preferred direction, and the PM permeability can be completely described by a single curve, and the PM permeability tensor for this pixel is given by the identity matrix. This is the result of multiplying by TIFF2022104831000003.tif6170.

[0051] For example, if a nanoscale model of the PM type with "microporous viscosity" is available from focused ion beam (FIB) images, the relationship between permeability and porosity, as shown in Figure 5, can be obtained by using permeability simulations for various subvolumes. It is possible to generate TIFF2022104831000004.tif6170.

[0052] As another example, in the "single-channel" PM type, there is a strong directional dependence with respect to permeability. The preferred direction tends to change locally, depending on the local orientation of the sub-resolution channels in the image. The local orientation can be calculated from the image itself, for example, from the local derivative of the grayscale values.

[0053] In this case as well, a single permeability curve can be used as input, and local orientation information of the image will be used to adjust the values ​​in a given direction.

[0054] To describe the flow for any orientation, the LB flow solver needs to calculate all contributions to the flow. To implement the permeability tensor effect in the PM pixel, local resistivity coefficients related to velocity and pressure gradients in various directions can be used. For example, for a flow in the y direction induced by a pressure gradient in the x direction, the resistivity coefficient Ryx is used, which is directly related to the corresponding permeability tensor element kyx, where ρ is the fluid density and ν is the mechanical viscosity.

[0055]

number

[0056]

number

[0057] Process 50 then uses a set of physical properties related to the PM region to simulate the physical properties of the multiscale model.

[0058] viscous force One possible example related to TIFF2022104831000007.tif6150 is absolute penetrant K0 and relative penetrant Using TIFF2022104831000008.tif6150,

number

[0059] The solver can be viewed as an extension of Brinkman's formula.

[0060] Capillary pressure To determine the capillary pressure behavior of porous media independently of wettability effects, mercury-impacted capillary pressure (MICP) measurements are typically used.

[0061] Generally, when a reservoir fluid (oil / water) is used instead of mercury and wettability is considered, there will be an irreducible water saturation Sw for discharge and some residual oil saturation Sor for inhalation. For various pressure gradients Po-Pw=Pc(Sw), the amount of water / oil fluid Sw+So=1 present in the PM pixel is given by the capillary radius r c It depends on the size distribution and wettability fluid-solid properties.

[0062] In the model curve shown in Figure 6, Pc* represents the discharge threshold pressure and ΔPc* represents the width of the pore size distribution. A second curve with different threshold pressures and corresponding widths is included to model the intake behavior.

[0063] Several capillary pressure-saturation rate models exist in the literature. For example, there are Thomeer's model, Brooks and Corey's model, and Bentsen and Anli's model. For instance, in Thomeer's model, the relationship between capillary pressure and saturation rate is as follows:

number

[0064] The capillary pressure behavior of each PM type can be represented by such parameterized curves, and, as with the example of absolute permeability, may be based on partial volume capillary simulation results of the highest resolution model for that PM type.

[0065] To model the variability of porosity within a given PM type (similar to permeability), the Leverett J function (Sw) can be used, which provides a single curve for the capillary curves of different samples from the same rock type:

number

[0066] In general, the J function (Sw) should be given for each PM type. In that case, the sub-resolution porosity For each individual PM pixel having TIFF2022104831000015.tif6170, the corresponding permeability This is estimated from TIFF2022104831000016.tif6170. Using these two values, the individual Pc values ​​at the required saturation rate Sw can be estimated from the J function for this PM type.

[0067] Furthermore, in the case of anisotropy, similar to the PM types for "single channel," the anisotropic (P(Sw)) can be calculated for each direction by using the corresponding elements of the permeability tensor in the calculation of the J function.

[0068] Thus, for pores smaller than the pixel size, the capillary pressure behavior is related to a specific type of PM P. c (S w It can be modeled by a J function calibrated using ).

[0069] The solver embodiment determines the oil / water saturation rate So, Sw in each PM pixel with respect to emissions. P o -P w =P c (S w ) Sw +S o =1 For Po > Pw and satisfying another relationship for inhalation, it can include an additional force in the flow direction proportional to P(S w ).

[0070] Capillary force An example of the definition of TIFF2022104831000017.tif6150, [Number] can be written as, in the above formula, the symbol "hat" TIFF2022104831000019.tif8170 indicates a unit vector, and θ is the contact angle of the low-resolution porous solid. In the above formula, J is the Leverett J function, which is a capillary function of the normalized density ratio of the fluid components TIFF2022104831000020.tif7170, and σ1 is the index of the corresponding component. The function G is a "switch function" that depends on the local multi-component interface information. In the above formula, [Number] is.

[0071] The switch function "G" is used in the diffusive multi-component model because its non-zero interface thickness may result in excessive artificial forces. Furthermore, this definition may not cover the scenario where the component fluids are confined within low-resolution cells. To mitigate this problem, an additional model using the Leverett J function and local pressure can be implemented.

[0072] Relative permeability [[ID=第41]]Following the same approach as in the case of absolute permeability and capillary pressure, a relative permeability curve corresponding to the type of PM can be calculated from the nanoscale model and used as library input for PM pixel behavior.

[0073] The Corey model is a general parameterization of the relative permeability curve, and in this model,

number

number

[0074] When the physical properties of a representative porous structure are applied to low-resolution areas, the local preferred direction of the structure can be taken into consideration in the following manner.

[0075] The orientation of local solid structures can be calculated from images, for example, from the local derivative of grayscale values. By comparing such structural orientation with the orientation of the principal axes of permeability, the physical properties can be adjusted in appropriate directions. The following discussion shows the case for absolute permeability.

[0076] The absolute penetration rate (K) of the tuned tensor form in 3 dimensions. 0,αβ )teeth,

number

number

[0077] Here, this equation is written in Einstein notation using the spatial subscripts α and β, rather than vector notation. The matrix in the denominator represents the inverse matrix.

[0078] The numerical approach described herein enables multi-component fluid flow simulations in multi-scale porous structures while avoiding the extremely high computational costs associated with high-scale resolution simulations of such structures. This numerical approach locally introduces appropriate forces acting on the fluid components using a complete set of pre-calculated physical properties applicable to the low-resolution regions of the multi-scale porous structure. Multi-scale simulations become possible without a significant sacrifice of computational efficiency, while achieving relative accuracy compared to either high-scale resolution simulations or avoiding multi-scale simulations altogether in such multi-scale porous structures.

[0079] By using the physical properties of several representative porous structures across a wide range of low-resolution regions, computational costs are generally significantly reduced while maintaining reasonable accuracy. This accuracy is achieved because the numerical approaches described herein all take into account the local variability of individual structures through adjustments based on local porosity and orientation directly estimated from the images.

[0080] Both low-resolution simulations with coarse resolution and high-resolution simulations with finer resolutions to capture physical properties in non-gray areas can be performed using a single fluid dynamics solver. Using a single fluid dynamics solver is highly beneficial from the standpoint of consistency in the simulation process, because any calculation method exhibits its own unique numerical aspects to varying degrees, and these can cause problems when combined with other methods. Using a consistent solver in the simulation process effectively avoids such problems.

[0081] The proposed method is applicable to other computational fluid dynamics methods, including the lattice Boltzmann method, as well as the finite volume method, the finite element method, and so on.

[0082] The memorized physical properties of a representative solid structure can be broadly applied to arbitrary spatial scales, as well as various fluid conditions such as viscosity, surface tension, and surface wettability, because the properties can be memorized in a phenomenological, dimensionless form. Phenomenological means that the properties are constructed from experimental and / or simulation results. The simulated physical properties of a particular multiscale solid structure can be used as input for cases at even larger scales. Therefore, by detecting hierarchical structures and classifying structure types, this method can be broadly applied to very complex geometries with structures at various scales.

[0083] The embodiments and functional operations of the subject matter described herein can be implemented in digital electronic circuits, tangibly embodied computer software or firmware, computer hardware (including structures disclosed herein and their structural equivalents), or one or more combinations thereof. The embodiments of the subject matter described herein can be implemented as one or more computer programs (i.e., one or more modules of computer program instructions encoded on a tangible, non-temporary program carrier for execution by or control of the operation of a data processing device). Computer storage media can be machine-readable storage devices, machine-readable storage boards, random or serial access memory devices, or one or more combinations thereof.

[0084] Computer programs may also be called or described as programs, software, software applications, modules, software modules, scripts, or code, and 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, as standalone programs or as modules, components, subroutines, or other units suitable for use in a computing environment. Computer programs may, but are not required, correspond to files in a file system. A program may be stored in a single file dedicated to it, as part of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), or in a series of interconnected files (e.g., a file that stores one or more modules, subprograms, or code sections). A computer program may be deployed so that it runs on one computer, or on multiple computers located in one place or distributed across multiple locations and interconnected by a data communication network.

[0085] A computer suitable for running computer programs may utilize a general-purpose microprocessor, a dedicated microprocessor, or both, or any other type of central processing unit. Generally, a central processing unit receives instructions and data from read-only memory, random-access memory, or both. Essential elements of a computer are a central processing unit for executing or running instructions, and one or more memory devices for storing instructions and data. Generally, a computer also includes, or is operablely coupled to, one or more mass storage devices (e.g., magnetic, magneto-optical disks, or optical disks) for storing data, or for receiving data from them, or for transferring data to them, or both, but such devices are not required of a computer.

[0086] Computer-readable media suitable for storing computer program instructions and data include, for example, all forms of non-volatile memory on media or memory devices, including 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. Processors and memory can be complemented by or incorporated into dedicated logic circuits.

Claims

1. A computer-implemented method for performing a fluid dynamics simulation of a porous medium, comprising: accessing from a memory a three-dimensional digital image of the three-dimensional porous medium; performing image processing on the accessed three-dimensional digital image by a computer system; generating, by the computer system, a representation of the three-dimensional porous medium based on performing the image processing, the representation including pore space corresponding to the porous medium; determining, by the computer system, that the representation includes at least a portion of a low resolution pore structure in the porous medium, the low resolution pore structure having a pore size smaller than a resolution of the fluid simulation; digitally constructing, by said computer system, a visual representation of a fluid force curve corresponding to the fluid forces in said low resolution pore structure in said representation; A method comprising:

2. The method of claim 1 , wherein performing image processing on the accessed three-dimensional digital image comprises applying a three-dimensional segmentation to the three-dimensional digital image.

3. 2. The method of claim 1, wherein the low resolution pore structure belongs to a class of low resolution pore structures, also called PM types, and the pore structure is represented by a description common to all members of the class.

4. simulating fluid flow through said porous medium and detecting a low-resolution pore structure; accessing said low resolution pore structure model; applying the fluid force curve to the low resolution pore structure; The method of claim 1 further comprising:

5. To apply, The method of claim 4 further comprising applying the hydraulic force curve according to local pore space data.

6. The method of claim 5 , wherein the local pore space data includes local porosity, local orientation / spatial gradients of the local porosity obtained from the representation of the three-dimensional porous medium.

7. calculating, by said computing system, hydraulic force curves from pre-computed physical properties including absolute permeability, relative permeability, and capillary pressure curves of said low resolution pore structure in said representation based on local pore space data; The method of claim 6 further comprising:

8. The method of claim 7, wherein the calculating further comprises calculating physical properties including absolute permeability, relative permeability, and capillary pressure curves via simulation of a set of highest resolution sub-regions of the low resolution pore scale in the representation based on local pore space data.

9. storing in a repository or library parametric models for said physical properties, with parameters fitted to simulation data or adjusted according to subject matter expertise; The method of claim 7 further comprising:

10. The method of claim 1 , wherein the representation is of a physical rock sample, the representation including pore space and grain space data corresponding to physical rock samples, porous particulate filters, and similar physical porous media.

11. 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: accessing from the memory a three-dimensional digital image of the three-dimensional porous medium; performing image processing on the accessed three-dimensional digital image; generating a representation of the three-dimensional porous medium based on performing the image processing, the representation including a pore space corresponding to the porous medium; determining that the representation includes at least a portion of a low resolution pore structure in the porous medium, the low resolution pore structure having a pore size smaller than a resolution of the fluid simulation; and configuring said digitally constructing a visual representation of a fluid force curve corresponding to the fluid forces in said low resolution pore structure in said representation. Computer system.

12. The system of claim 11 , wherein the instructions for performing image processing on the accessed three-dimensional digital image include applying a three-dimensional segmentation to the three-dimensional digital image.

13. simulating fluid flow through said porous medium and detecting low-resolution pore structure; accessing said low resolution pore structure model; applying the fluid force curve to the low resolution pore structure; The system of claim 11 further configured to:

14. The system of claim 13, wherein applying further comprises applying the fluid force curve in accordance with local pore space data, the local pore space data including local porosity, local orientation / spatial gradient of the local porosity obtained from the representation of the three-dimensional porous medium.

15. 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 being configured to: accessing from the memory a three-dimensional digital image of the three-dimensional porous medium; performing image processing on the accessed three-dimensional digital image; generating a representation of the three-dimensional porous medium based on performing the image processing, the representation including a pore space corresponding to the porous medium; determining that the representation includes at least a portion of a low resolution pore structure in the porous medium, the low resolution pore structure having a pore size smaller than a resolution of the fluid simulation; A computer program product that digitally constructs a visual representation of fluid force curves corresponding to fluid forces in the low resolution pore structure in the representation.

16. Calculating hydraulic force curves from pre-computed physical properties including absolute permeability, relative permeability, and capillary pressure curves of said low-resolution pore structure in said representation based on local pore space data.

20. The computer program product of claim 15, further comprising instructions for:

17. Calculating physical properties including absolute permeability, relative permeability, and capillary pressure curves through simulation of a set of low-resolution pore-scale highest resolution subregions in said representation based on local pore space data.

20. The computer program product of claim 15, further comprising instructions for:

18. storing, in a repository or library, parametric models for said physical properties, with parameters fitted to simulation data or adjusted according to subject matter expertise; 20. The computer program product of claim 17, further comprising instructions for:

19. simulating fluid flow through said porous medium and detecting low-resolution pore structure; accessing said low resolution pore structure model; applying the fluid force curve to the low resolution pore structure; 20. The computer program product of claim 15, further comprising instructions for:

20. The computer-implemented method of claim 1, further comprising: defining, by the computer system, a representative flow model of the low-resolution pore structure including one or more physical properties of the low-resolution pore structure in the representation.

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