Computer simulation of multiphase and multicomponent fluid flows including the physical properties of under-resolved porous structures

Abstract

The present application relates to computer simulation of multiphase, multicomponent fluid flows including physical properties of under-resolved porous structures. Computer-implemented techniques for performing fluid simulations of porous media are disclosed. These techniques involve retrieving a representation of a three-dimensional porous medium, the representation including pore space corresponding to the porous medium, and the representation including at least a portion of an under-resolved pore structure in the porous medium, defining a representative flow model including the under-resolved pore structure in the representation, and constructing, by a computer system, a fluid force curve corresponding to a fluid force in the under-resolved pore structure in the representation.

Description

Background Art

[0001] The flow of multicomponent fluids through porous zones is an important property of hydrocarbon reservoir rocks and is a vital input to the oil and gas industry and other industries.

[0002] Numerical simulations of multicomponent fluid flows in porous regions with complex solid structures are very important in many industrial applications, such as enhanced oil recovery (EOR) and personal protective equipment (PPE). In order to obtain accurate simulation results, it is important to capture relevant data from all scales of the porous structure.

[0003] For many porous materials, the scale range often spans many orders of magnitude in size. Furthermore, the scale range is often heterogeneously distributed in space. Full-scale resolved simulations of such porous structures are computationally prohibitive in terms of data size, computational time, and computational resources. Therefore, such simulations are often limited to samples that are significantly smaller in size than the original porous material of interest. The latter may compromise or limit the type of porous material studied in terms of statistical representation. Summary of the invention

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

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

[0006] A representation of the three-dimensional porous medium is obtained from the three-dimensional image to which the three-dimensional segmentation is applied. The under-resolved pore structure belongs to a class of under-resolved pore structures represented by a common description of all elements of the class, also referred to as a PM type. The method also includes simulating fluid flow through the porous medium, and when the under-resolved pore structure is detected, accessing a model of the under-resolved pore structure and applying a fluid force curve to the under-resolved pore structure.

[0007] The application also includes applying the fluid force curve based on the local pore space data. The local pore space data includes the local porosity, the local orientation / spatial gradient of the local porosity obtained from the representation of the three-dimensional porous medium.

[0008] The method also includes calculating, by a computing system, a fluid force curve based on pre-calculated physical properties including absolute permeability, relative permeability, and a capillary pressure curve based on an under-resolved pore structure in a representation of the local pore space data.

[0009] The calculations also include calculating physical properties including absolute permeability, relative permeability, and capillary pressure curves via simulation of a set of fully resolved subdomains at under-resolved pore scales in a representation based on local pore space data.

[0010] The method also includes storing the parametric model of the physical properties with parameters adapted to the simulation data or adjusted based on subject matter expert knowledge in a repository or library.

[0011] The representation is a representation of a physical rock sample that includes pore space and grain space data corresponding to physical porous rock samples, porous particle filters, and similar physical porous media.

[0012] According to another aspect, a computer system includes one or more processor devices, a memory coupled to the one or more processor devices, and a storage device storing executable computer instructions for performing fluid simulation of a porous medium, the instructions being used to configure the one or more processors to: retrieve a representation of a three-dimensional porous medium, the representation including a pore space corresponding to the porous medium, and the representation including at least a portion of an under-resolved pore structure in the porous medium; define a representative flow model including the under-resolved pore structure in the representation; and construct a fluid force curve corresponding to the fluid force in the under-resolved pore structure in the representation.

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

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

[0015] The system is also configured to simulate fluid flow through the porous medium and, when an under-resolved pore structure is detected, access a model of the under-resolved pore structure and apply the fluid force curve to the under-resolved pore structure.

[0016] The local pore space data includes the local porosity, the local orientation / spatial gradient of the local porosity obtained from the representation of the three-dimensional porous medium.

[0017] According to another aspect, a computer program product tangibly stored on a computer-readable, non-transitory storage device storing executable computer instructions for performing fluid simulation of a porous medium, the instructions being used to cause a computing system to: retrieve a representation of a three-dimensional porous medium, the representation including pore space corresponding to the porous medium and the representation including at least a portion of an under-resolved pore structure in the porous medium; define a representative flow model including the under-resolved pore structure in the representation; and construct a fluid force curve corresponding to the fluid forces in the under-resolved pore structure in the representation.

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

[0019] The computer program product also includes instructions for calculating a fluid force curve based on pre-calculated physical properties including absolute permeability, relative permeability, and capillary pressure curves based on under-resolved pore structures in a representation of the local pore space data.

[0020] The computer program product also includes instructions for calculating physical properties including absolute permeability, relative permeability, and capillary pressure curves via simulation of a set of fully resolved subdomains at under-resolved pore scales in the representation of the local pore space data.

[0021] The computer program product also includes instructions for storing the parametric model of the physical properties with parameters adapted to the simulation data or adjusted based on subject matter expert knowledge in a repository or library.

[0022] The computer program product also includes instructions for: simulating fluid flow through the porous medium; and when an under-resolved pore structure is detected, accessing a model of the under-resolved pore structure and applying the fluid force curve to the under-resolved pore structure.

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

[0024] The numerical method described herein enables multicomponent fluid flow simulations for multiscale porous structures while avoiding the extremely expensive computational costs inherent in full-scale resolved simulations of multiscale porous structures. This numerical method uses a complete set of pre-computed physical properties (one or more) applicable to the under-resolved regions (one or more) of the multiscale porous structure, introducing local appropriate forces acting on the fluid components. Typically, the use of the physical properties of representative porous structures saves a lot of computational costs while maintaining reasonable accuracy.

[0025] The proposed method 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. The physical properties stored in the representative solid structure can be widely used in any spatial scale and various fluid conditions, such as viscosity, surface tension and surface wettability, because these properties can be stored in a phenomenological dimensionless form.

[0026] Other features and advantages of the invention will be apparent from the following description, and from the claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Described is a system for simulating a multiscale porous structure using a model with locally appropriate forces applicable to under-resolved region(s) of the multiscale porous structure.

[0028] Figure 2A , Figure 2B Depicts a cross-section of a carbonate rock, where the original scan image ( Figure 2A ) and segmented image ( Figure 2B ) shows the small-scale porous regions marked in grey.

[0029] Figure 3 A flow chart showing operations for a multicomponent fluid flow simulation with an under-resolved porous structure is depicted.

[0030] Figure 4 Images showing different types of under-resolved porous structures are depicted.

[0031] Figure 5 The relationship between permeability and porosity is depicted.

[0032] Figure 6 Model curves of displacement / imbibition capillary pressure versus water saturation are plotted. DETAILED DESCRIPTION

[0033] refer to Figure 1 The system 10 is used to simulate a multi-scale porous material having (one or more) under-resolved regions of the multi-scale porous material. The simulation can be used for various purposes, such as for simulating a "wettability recovery" or "aging" process representative of underground reservoir conditions, i.e., "numerical aging". Other simulations can include the effects of vapor flow on PPE, etc.

[0034] The focus of this discussion will be the simulation of multi-scale porous materials with (one or more) under-resolved regions. Typically, the system 10 in this implementation is based on a client-server or cloud-based architecture and includes a (standalone or cloud-based) server system 12 and a client system 14 implemented as a massively parallel computing system 12. The server system 12 includes a memory 18, a bus system 11, an interface 20 (e.g., a user interface / network interface / display or monitor interface, etc.) and a processing device 24.

[0035] For the example of wettability changes, in memory 18 there is a numerical aging engine 32 that operates on a digital representation of a physical rock sample that digitally represents the pore spaces and grain spaces of a digital representation of a physical material, e.g., a physical rock sample (digital rock sample). Also in memory is a simulation engine 34 that simulates wettability changes using a simulation of a multi-scale porous material with under-resolved region(s).

[0036] In some embodiments, multiphase flow behavior is simulated through reservoir rock adjacent to a gas or oil well (e.g., drilling rig 37) using simulations of multiscale porous materials with under-resolved region(s). Determining multiphase flow behavior includes determining wettability changes of the physical rock sample.

[0037] The digital representation of the physical rock sample may be a third party application executed on a different system than the server 12. The system 10 requires only the digital representation 32' of the physical rock sample in order for the numerical aging engine to digitally prepare the digital representation of the physical rock sample. One method of providing the digital representation 32' of the rock sample is to obtain the representation 32', for example, from a 3D image generated by a micro-CT scan of the rock sample.

[0038] For complete details of the simulation process, please refer to U.S. Patent Application Serial No. 15 / 880,867, filed on January 26, 2018, entitled "Multi-Phase Flow Visualizations Based on Fluid Occupation Time", and assigned to the assignee of the present application. For other exemplary cases, please refer to U.S. Patent Application Serial No. 16 / 243,285, filed on January 9, 2019, entitled "Determining Fluid Flow Characteristics Of Porous Media"; or U.S. Patent Application Serial No. 16 / 545,387, filed on August 20, 2019, entitled "Determination Of Oil Removed By Gas Via Miscible Displacement In Reservoir Rock", both of which are assigned to the assignee of the present application.

[0039] The memory 18 may store parameters used by the engine 32. In particular, specific parameters for the case entitled: "Determination Of Oil Removed By Gas Via Miscible Displacement In Reservoir Rock" may include particle surface properties obtained by assigning mineral types 33a to particles to determine surface properties of each of those mineral types, as well as surface texture and roughness properties, for one or more of the above-mentioned applications for the disclosed subject matter. The memory 18 may also store parameters such as fluid properties 33b, for example, fluid density and viscosity and fluid-fluid interfacial tension properties for each expected fluid (e.g., two or more of water, gas, oil). The memory 18 also stores parameters such as chemical composition data 33c and affinity data 33d for fluid components of a particular mineral type. The memory 18 also stores a separation pressure 33e for each mineral type combined with the fluid, and a selected aging time 33f used by the aging engine 32. In addition, reservoir pressure and temperature data are also stored. The mineral types assessed may be the mineral types found or expected at the actual site of the reservoir.

[0040] The simulation engine 34 includes a module for setting up a rock sample simulation environment, a module for performing a drainage / imbibition simulation, 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 multi-scale porous materials with (one or more) under-resolved regions.

[0041] The system 10 accesses a data repository 38 storing 2D and / or 3D grids, coordinate systems, and libraries that can be used for displacement / imbibition simulations using any well-known computational technique, such as computational fluid dynamics or the so-called lattice Boltzmann method. In addition, the system 10 accesses a library 50a that includes a model 50b representing an under-resolved region.

[0042] Figure 2A and Figure 2B An example of a porous medium with under-resolved regions obtained from a subsurface porous medium for oil and gas applications is illustrated. Figure 2A is the original scanned image. Figure 2A A typical cross section of a carbonate rock sample 40 is shown, the sample having solid structures at a number of different scales, and showing small scale porous structures, three of which are indicated at 42 .

[0043] Figure 2B Carbonate rock sample 40 ( Figure 2A ), which shows small-scale porous structures, three of which are represented as 42' marked in gray. The length scale difference between the black and gray structures is about 10 times. Since the gray small-scale porous areas may significantly affect the flow behavior, it is necessary to properly consider their contribution. Figure 2B A portion of is represented by imaginary line 44' and is Figure 4 Further discussion in.

[0044] However, resolving all such small-scale details requires very fine resolution, which results in very expensive computational simulations. By simulating the gray area, the cost of such simulations can increase by tens of thousands times compared to the unresolved case, as the number of 3D cells increases and the time increment decreases. Therefore, such fully resolved simulations are impractical for most industrial applications.

[0045] The process 50 simulates an original porous material having various sizes including under-resolved small scales without resolving all under-resolved small scales involved in the original porous material. The physical properties of these under-resolved small scales are appropriately incorporated into the process setup described below.

[0046] The process 50 for addressing the above challenges of multicomponent fluid flow simulation with under-resolved porous structures involves a novel workflow in which the fluid flow simulation only resolves the porous sample to a certain scale level. However, the numerical model takes into account the under-resolved porous region 42' ( Figure 2B The basic idea is to recognize that the influence of the under-resolved porous region on the flow is a set of forces, such as viscosity, pressure, and capillary forces. The numerical model reproduces such forces as acting on the resolved fluid by using local representative physical properties such as absolute permeability, relative permeability, and capillary pressure saturation curves.

[0047] These physical properties are obtained via simulations of much smaller fully resolved subdomains of the original porous material, which represent small-scale unresolved gray porous regions, or are generated in the form of user-calibrated parameter functions. A collection of these physical properties is stored in a library. Each set of physical properties represents the flow type of a specific under-resolved porous structure. In each gray region, a set of physical properties of the porous type is selected from the library and assigned to the model during simulations for the under-resolved porous structure. By considering the local porous geometric information including the porosity (ratio of pore space to total volume) and directionality of the structure, the locally under-resolved flow behavior can be appropriately reproduced.

[0048] Reference now Figure 3 , a process 50 for performing a multicomponent fluid flow simulation for an under-resolved porous structure is shown. The process 50 uses a simulation of a porous rock sample as an example. The process 50 includes performing 52 a geometric analysis of a typical porous structure, using scanned images to identify various types of under-resolved porous structures encountered in the porous structure being studied. The type of under-resolved porous structure is used to define 54 a representative flow model for each gray area. When defining the model, the defined model is compared to existing models stored in a model library. Essentially, the model is defined to include a set of physical properties. If a corresponding set of physical properties already exists in the library 56, the model including the set of physical properties is retrieved 58 from the library.

[0049] If the set of properties does not exist, the process performs 60 a fully resolved simulation 62 in a representative subdomain of the gray area and calculates 64 a new set of physical properties, including absolute permeability, relative permeability, and capillary pressure saturation curves for the particular type of porous structure being modeled. These sets of physical properties describe the effective multiphase flow behavior of the porous media structure. When calculating this new set of physical properties, the now calculated model is added 66 to the library and marked as being used for the particular under-resolved simulation being performed.

[0050] The process 50 uses the local geometry information and physical properties to determine 66 whether all under-resolved sites have been completed (finished). These appropriate fluid forces correspond to the viscosity, pressure, and capillary forces from the under-resolved solid structure.

[0051] segmentation

[0052] Reference now Figure 4 There are various ways to define numerical models of fluid forces in under-resolved regions. Through image analysis (segmentation), 3D image analysis can define different types of under-resolved porous regions. 3D image analysis (segmentation) is applied to 3D images. Figure 4 As shown, during segmentation, the under-resolved porous regions 42a' to 42d' are divided into Figure 2B A portion of is shown.

[0053] Different materials have different X-ray attenuation coefficients. The grayscale value can be used to classify pixels according to material type (e.g., mineral, fluid, etc.). When a pixel contains sub-resolution pores, the X-ray attenuation is the average of the solid and pore fractions within the pixel (partial volume effect).

[0054] Additional texture features can be used to segment pixels into different porous media (PM) types, such as:

[0055] Honeycomb structure (42a')

[0056] Fiber structure (42b')

[0057] Microporous clay (42c')

[0058] Microporous dolomite (42d')

[0059] Absolute permeability

[0060] For example, absolute permeability is simulated by a single-phase flow Lattice Boltzmann (LB) solver. Typically, the simulation output of a macroscopic 3D model is a permeability tensor with 3x3 values. Typically, the similarity established between the macroscopic output and the microscopic PM pixel input should also be a tensor. However, in most cases, the tensor can be obtained by a single permeability and porosity function. is approximated, sometimes supplemented by local orientations that can be computed from the image itself.

[0061] For example, in the "microporous dolomite" PM type (42d'), 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 fully described by a single curve. The PM permeability tensor for this pixel will be the identity matrix multiplied by

[0062] If a nanoscale model of a “microporous clay” PM type is available (e.g. from a focused ion beam (FIB) image), permeability simulations of different subvolumes can be used to generate a permeability versus porosity relationship, (φ), such as Figure 5 shown.

[0063] In another example, a "single channel" PM type, there is a strong orientation dependence for the permeability. The preferred orientation will vary locally, depending on the local orientation of the sub-resolution channel in the image. The local orientation can be calculated from the image itself, for example, from the local derivative of the grayscale value.

[0064] Also in this case, a single permeability curve may be used as input, and the local image orientation information will be used to modulate the value in a given direction.

[0065] To account for arbitrarily oriented flows, the LB flow solver needs to compute all contributions to the flow. The local resistivity associated with the velocity and pressure gradients in different directions can be used to implement the permeability tensor effect in the PM pixel. For example, for flow in the y direction caused by a pressure gradient in the x direction, we use the resistivity coefficient Ryx: it is directly related to the corresponding permeability tensor element kyx. Here ρ is the fluid density and v is the dynamic viscosity.

[0066]

[0067]

[0068] Process 50 sequentially simulates the physical properties of the multiscale model using the set of physical properties for the PM region.

[0069] A possible example, for the viscosity force The absolute permeability K0 and relative permeability can be used Defined as,

[0070]

[0071] where σ is the index of the component and ν is the kinematic viscosity. Here, ρ and are the density and velocity of the fluid flow, respectively. In addition, K0 and is a function of the porosity φ and the density ratio of the fluid components under the assumption of a homogeneous solid structure in the under-resolved porous region.

[0072] The solver can be viewed as an extension of the Brinkman equation.

[0073] Capillary pressure

[0074] Mercury capillary pressure (MICP) measurements are often used to determine the capillary pressure behavior of porous media independent of wettability effects.

[0075] Generally, when wettability is considered and reservoir fluid (oil / water) is used instead of mercury, there should be an irreducible water saturation Swi for displacement and some residual oil saturation S for imbibition. or . For different pressure gradients P o –P w =P c (S w ), fluid volume S w +S o = 1 water / oil exists in the PM pixel, which depends on the capillary radius r c Size distribution and wettability fluid-solid properties.

[0076] exist Figure 6 In the model curve depicted in , Pc* represents the expulsion threshold pressure and ΔPc* represents the spread in the pore size distribution. To model the imbibition behavior, a second curve with a different threshold pressure and corresponding spread is included.

[0077] There are several capillary pressure-saturation models in the literature. For example, there are the Thomeer, Brooks and Corey, Bentsen, and Anli models. For example, in the Thomeer model, the capillary pressure is related to the saturation in the following way:

[0078]

[0079] Similar to the absolute permeability example, the capillary pressure behavior of each PM type can be represented by a parameterized curve like this, perhaps based on the results of subvolume capillary simulations of a fully analytical model of the PM type.

[0080] To model the variation in porosity within a given PM type (similar to permeability), we can use the LeverettJ function (S w ), which integrates the capillary curves from different samples of the same rock type into a single curve:

[0081]

[0082] Usually, the J function (S w ) should be given for each PM type. Then, for each individual PM pixel with sub-resolution porosity φ, the corresponding permeability is given by Using these two values, at the desired saturation S w In this case, the individual Pc can be estimated from the J function of this PM type.

[0083] Furthermore, in the case of non-isotropic properties, such as the “single-channel” PM type, the anisotropic P(Sw ) can be calculated for each direction by using the corresponding element of the permeability tensor in the J-function calculation.

[0084] Therefore, for pores smaller than the pixel size, the capillary pressure behavior can be described by using the PM-type-specific relation Pc(S w )The calibrated J function is modeled.

[0085] Solver implementations can include the flow direction with P(S w ) is proportional to the additional force, so that the oil / water saturation S in each PM pixel o , S w satisfy

[0086] P o -P w =P c (S w )S w +S o =1

[0087] for displacement, and satisfies another relation for imbibition, if P o >P w .

[0088] Capillary force An example of the definition of can be written as,

[0089]

[0090] The symbol "hat" indicates the unit vector, and θ is the contact angle of the underresolved porous solid. Here, J is the Leverett J function That is, the normalized capillary function of the fluid component density ratio, and σ1 is the index of the corresponding component. Function G is a "switching function" that depends on the local multi-component interface information. Here,

[0091]

[0092] The switch function 'G' is used for multicomponent models of diffusion, as its non-zero interface thickness may lead to excessive artificial forces. In addition, this definition may not cover the case where the component fluids are confined in under-resolved cells. To alleviate this problem, an additional model can be implemented using the Leverett J function and local pressure.

[0093] Relative permeability

[0094] Following the same approach as for absolute permeability and capillary pressure, relative permeability curves for PM types can be calculated from the nanoscale model and used as library input for PM pixel behavior.

[0095] The Corey model is a common parameterization of the relative permeability curve, where:

[0096]

[0097]

[0098] And, k rw,ro is the residual oil saturation S or The relative permeability of water at ro,wi is the bound water saturation S wi The relative permeability of oil at .

[0099] When applying physical properties from a representative porous structure to under-resolved sites, the local preferential orientation of the structure can be considered in the following way.

[0100] The orientation of the local solid structure is calculated from the image, for example, from the local derivative of the grayscale values. By comparing such structural orientation with the orientation of the principal axis of permeability, the physical properties are modulated in the appropriate direction. In the following discussion, the case of absolute permeability is shown.

[0101] The modulated tensor forms the three-dimensional absolute permeability K 0，αβ is calculated as,

[0102]

[0103] where e ij are the elements of the three-dimensional local rotation matrix, and the value k i is the absolute permeability value along the principal axis. Calculate e ij One way to consider the three-dimensional rotation from the principal axis to the local orientation axis is to consider the relative permeability and the LeverettJ function are also modulated. Therefore, the viscous force is calculated as:

[0104]

[0105] Here, the equation is written in Einstein notation rather than vector notation using spatial direction indices (α and β). The matrix in the denominator indicates the inverse matrix.

[0106] The numerical method described herein realizes multi-component fluid flow simulation in multi-scale porous structure, while avoiding the extremely expensive computational cost inherent in the full-scale analytical simulation of such multi-scale porous structure. This numerical method uses (one or more) complete pre-calculated physical property sets applicable to (one or more) under-resolved regions of the multi-scale porous structure, introducing local appropriate forces acting on the fluid components. Compared with the full-scale analytical simulation in such multi-scale porous structure or avoiding the multi-scale simulation in such multi-scale porous structure, multi-scale simulation becomes feasible without sacrificing significant computational efficiency, while achieving relative accuracy.

[0107] For large under-resolved regions, it is often more efficient to use the physical properties of a few representative porous structures, saving significant computational cost while maintaining reasonable accuracy. The accuracy arises because the numerical method described here takes into account local variations of individual structures via modulations based on local porosity and directionality, both of which are estimated directly from the image.

[0108] A single fluid dynamics solver can be used to perform both under-resolved simulations with coarse resolution for capturing physical properties and previously fully resolved simulations in sub-gray areas with fine resolution. Using a single fluid dynamics solver is highly beneficial in terms of consistency of the simulation process. Namely, because any computational method exhibits more or less unique numerical aspects, this can lead to problems when these methods are connected with other methods. Such problems can be effectively circumvented by using a consistent solver during the simulation process.

[0109] The proposed method 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.

[0110] The physical properties stored in the representative solid structure can be widely applied to any spatial scale and various fluid conditions, such as viscosity, surface tension, and surface wettability, because these properties can be stored in a phenomenological, dimensionless form. Phenomenological means that the properties are constructed from the results of experiments and / or simulations. The simulated physical properties in a multiscale solid structure can be used as input to a larger scale situation. Therefore, by detecting hierarchical structures and classifying the structure types, this method can be widely applied to highly complex geometric constructions with structures at various scales.

[0111] Embodiments of the subject matter and functional operations described in this specification may be implemented in digital electronic circuits, tangibly embodied computer software or firmware, computer hardware (including the structures disclosed in this specification and their structural equivalents), or a combination of one or more of them. Embodiments of the subject matter described in this specification may be implemented as one or more computer programs (i.e., one or more computer program instruction modules encoded on a tangible, non-transitory program carrier for execution by a data processing apparatus or for controlling the operation of a data processing apparatus). Computer storage media may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them.

[0112] A computer program, which may also be referred to or described as a program, software, software application, module, software module, script, or code, may be written in any form of programming language (including compiled or interpreted languages, or declarative or procedural languages), and it may 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 may 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, a single file dedicated to a related program, or multiple coordinated files (e.g., files storing one or more modules, subroutines, or code portions)). A computer program may be deployed so that it 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.

[0113] Computers suitable for executing computer programs may be based on general or special purpose microprocessors or both, or any other kind of central processing unit. Typically, the central processing unit will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a central processing unit for executing or implementing 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 disks, magneto-optical disks, or optical disks) for storing data or be operatively coupled to receive data from or transfer data to one or more mass storage devices or both for storing data, however, a computer need not have such a device.

[0114] Computer-readable media suitable for storing computer program instructions and data include all forms of nonvolatile memory on media and memory devices, including, for 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 may be supplemented by, or incorporated in, special purpose logic circuits.

Claims

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

2. The method of claim 1, wherein performing image processing on the accessed three-dimensional digital image comprises: Three-dimensional segmentation is applied to the three-dimensional digital image.

3. The method of claim 1, wherein the under-resolved pore structure belongs to a class of under-resolved pore structures represented by the common description of all elements of the class, which class is also called porous media PM type.

4. The method of claim 1, further comprising: simulating fluid flow through the porous medium; and when an under-resolved pore structure is detected, accessing a model of the under-resolved pore structure; as well as The fluid force curves are applied to the under-resolved pore structure.

5. The method of claim 4, wherein applying further comprises: The fluid force curve is applied based on the local pore space data.

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

7. The method of claim 6, further comprising: A fluid force curve is calculated by the computer system based on pre-calculated physical properties including absolute permeability, relative permeability, and capillary pressure curves based on the under-resolved pore structure in the representation of local pore space data.

8. The method of claim 7, wherein calculating further comprises: Physical properties including absolute permeability, relative permeability, and capillary pressure curves are calculated via simulation of a set of fully resolved subdomains based on under-resolved pore scales in the representation of local pore space data.

9. The method of claim 7, further comprising: Parametric models of the physical properties with parameters adapted to the simulation data or adjusted according to subject matter expert knowledge are stored in a repository or library.

10. The method of claim 1, wherein the representation is a representation of a physical rock sample, the representation including pore space and grain space data corresponding to the physical rock sample, a porous particle filter, and a physical porous medium.

11. The method of claim 1 , further comprising: A representative flow model of the under-resolved pore structure is defined by the computer system, the representative flow model comprising one or more physical properties of the under-resolved pore structure in the representation.

12. A computer system comprising: one or more processor devices; a memory coupled to the one or more processor devices; A storage device storing executable computer instructions for performing fluid simulation of porous media, the instructions for configuring the one or more processors to: accessing a three-dimensional digital image of the three-dimensional porous medium from a memory; 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 pore spaces corresponding to the porous medium; determining that the representation includes at least a portion of an under-resolved pore structure in the porous medium, the under-resolved pore structure having a pore size smaller than a resolution of the fluid simulation; as well as A visual representation of a fluid force curve corresponding to the fluid forces in the under-resolved pore structure in the representation is digitally constructed.

13. The system of claim 12, wherein the instructions for performing image processing on the accessed three-dimensional digital image include: Three-dimensional segmentation is applied to the three-dimensional digital image.

14. The system of claim 12, wherein the instructions are further configured to configure the one or more processors to: simulating fluid flow through the porous medium; and when an under-resolved pore structure is detected, accessing a model of the under-resolved pore structure; and The fluid force curves are applied to the under-resolved pore structure.

15. The system of claim 14, wherein: Applying further comprises applying the fluid force curve based on local pore space data, the local pore space data comprising a local porosity, a local orientation / spatial gradient of the local porosity obtained from the representation of the three-dimensional porous medium.

16. A computer program product tangibly stored on a computer readable non-transitory storage device storing executable computer instructions for performing fluid simulation of porous media, the instructions for causing a computing system to: accessing a three-dimensional digital image of the three-dimensional porous medium from a memory; 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 pore spaces corresponding to the porous medium; determining that the representation includes at least a portion of an under-resolved pore structure in the porous medium, the under-resolved pore structure having a pore size smaller than a resolution of the fluid simulation; and A visual representation of a fluid force curve corresponding to the fluid forces in the under-resolved pore structure in the representation is digitally constructed.

17. The computer program product of claim 16, further comprising instructions for: A fluid force curve is calculated based on pre-calculated physical properties including absolute permeability, relative permeability, and capillary pressure curves based on the under-resolved pore structure in the representation of local pore space data.

18. The computer program product of claim 16, further comprising instructions for: Physical properties including absolute permeability, relative permeability, and capillary pressure curves are calculated via simulation of a set of fully resolved subdomains based on under-resolved pore scales in the representation of local pore space data.

19. The computer program product of claim 18, further comprising instructions for: Parametric models of the physical properties with parameters adapted to the simulation data or adjusted according to subject matter expert knowledge are stored in a repository or library.

20. The computer program product of claim 16, further comprising instructions for: simulating fluid flow through the porous medium; and when an under-resolved pore structure is detected, accessing a model of the under-resolved pore structure; and The fluid force curves are applied to the under-resolved pore structure.

Images