CN114818408A - Macroscopic angle modeling method based on porous medium pore structure - Google Patents
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Abstract
The invention relates to the field of porous medium pore size flow simulation, in particular to a macroscopic angle modeling method based on a porous medium pore structure. The method comprises the following steps: s1: aiming at a reservoir core sample, utilizing CT scanning to create a two-dimensional gray image; s2: acquiring pore structure geometric information based on the gray level image, and constructing a gray level image numerical function f (x, y); s3: establishing a two-dimensional simulation region with the same size as the CT image by using a finite element method; s4: initializing parameter values required by pore scale flow simulation; s5: constructing a discretization parameter function from a macroscopic angle; s6: the grid is sub-divided for the whole simulation area based on a gray image numerical function f (x, y); s7: and applying a Brinkman equation to the simulation region, and solving a velocity field and a pressure field of the flow process in the grid divided by S6. The invention provides a method which is reasonable and effective, can accurately simulate the pore-scale flow process of the porous medium and is modeled from a macroscopic view.
Description
Technical Field
The invention relates to a macroscopic angle modeling method based on a porous medium pore structure, and belongs to the technical field of porous medium pore scale flow simulation.
Background
Petroleum and natural gas are important components of energy systems in China, and development and utilization of oil and gas resources are of great importance in high efficiency and reasonability. The flow of hydrocarbons in a subterranean reservoir may be equivalent to a porous media flow. And hydrate mining, geothermal mining, etc. which have been emerging in recent years are also considered to be flow processes within porous media. Accordingly, an increasing number of researchers have conducted extensive research on porous media. The flow characteristics of the porous medium are observed through a physical experiment means, and the flow mechanism is researched through a numerical simulation means.
With the widespread use of computer science, numerical simulation technology has been widely applied to the research of flow simulation of porous media. By utilizing a numerical simulation technology, the flow rule of the fluid in the porous medium under the pore scale can be effectively simulated. With the development of computed tomography (ct) technology, a high-resolution pore structure can be easily obtained by scanning a reservoir core. Many researchers have simulated the fluid phase flow during production based on the pore structure of CT scans. The current porous medium pore size flow simulation method mainly comprises a pore network model, an unstructured grid finite element simulation, a lattice-boltzmann method and the like. However, most of the simulation methods are based on the real pore structure of the reservoir core, so that the complex boundary problem is inevitably processed, and the calculation amount is huge.
The finite element simulation method needs to obtain a pore structure gray-scale image based on core CT scanning, and solves the problem of complex particle pore boundary. In the mesh subdivision process, the boundary between pores and particles needs to be locally encrypted or even processed by a boundary layer, so that the number of meshes in a solution domain is increased, and the complexity of solving partial differential equations is aggravated by a large number of pore particle boundaries. On one hand, the calculation amount is increased, and the requirement on the performance of the computer is too high; on the other hand, the model is difficult to converge, and the solution result is not accurate. And the pore network model firstly obtains a core electron microscope picture through CT scanning and extracts the pore space information of the porous medium. And then reconstructing the digital core through a corresponding mathematical method to obtain the geometric structure data of the digital core, including rock pores and rock skeletons. And extracting key information of the pore structure of the digital core, and replacing pores and roars of the core with a simple pore network model. However, the method does not consider the characteristics of the fluid flowing in the micro-scale channel, and is an ideal model, and the flow of the fluid in the porous medium at the pore scale cannot be accurately described by means of a simplified pore network model. In contrast, the lattice-boltzmann method, which is more suitable for pore scale flow simulation, can be simulated directly on a digital pore structure without solving any partial differential equations. The method assumes that the fluid exists in the form of particles, the fluid is represented by a distribution function of the particles, and the fluid flow process comprises two processes of collision and flow of the particles, and the principle is relatively simple. However, the boundary processing between the lattice-boltzmann pore space and the rock particles is relatively complicated, the default is that the fluid particles collide with the rock framework, a collision boundary condition needs to be applied to each fluid particle, and the calculation amount is large. For example, chinese patent document (application No. CN201510173922.7) discloses a method and an apparatus for simulating the micro-flow of carbonate rock, which mainly utilizes the lattice boltzmann method to simulate the micro-flow of carbonate rock.
The above discussed pore size flow simulation methods all need to process a real digital pore structure, and cannot avoid processing complex pore-particle boundary conditions. And the pore size simulation needs to carry out extremely detailed subdivision on the grids, and the number of equations solved by each grid node is large, so that the calculation amount is large, the simulation time is long, and the requirement on the performance of a computer is high.
However, if modeling from a macroscopic point of view is considered, the boundary processing problem of the pore grains can be effectively avoided. Only the required parameter values need to be assigned to the whole area, and the parameter values required for different points in the area are different. For example, flow simulation requires that parameter values such as porosity and permeability are assigned to the whole region, but the porosity and permeability are generally different at different points in the region. In particular, the permeability of the part of the particles should be given a very small value, which may even be 0. By the discretization assignment method, the relation between the pore and the framework can be effectively processed only by endowing different parameter values to the whole solution domain.
Therefore, the invention provides a discretization function assignment method aiming at porous medium pore scale flow simulation, and different parameter values can be assigned to different points in the region from a macroscopic view. The method can realize the same result as pore size flow simulation, and can avoid the boundary processing problem of pore size simulation and huge calculation amount.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method which is reasonable and effective, can accurately simulate the pore-scale flow process of the porous medium and can be used for modeling from a macroscopic view.
The technical scheme of the invention is as follows:
a macroscopic angle modeling method for porous medium pore scale flow simulation comprises the following steps:
s1: obtaining a core sample by sampling a core of a reservoir; utilizing CT to scan the rock core slice and creating a two-dimensional rock gray level image; wherein black is represented by a value of 0 and white is represented by a value of 1; 0 represents the pore throat, 1 represents the rock skeleton particle;
s2: and acquiring spatial information of the pore structure based on the rock gray-scale image in the S1. Constructing an image numerical function f (x, y),
wherein (x, y) are geometric position coordinates;
s3: according to the size of the two-dimensional rock gray level image scanned by the CT in the S1, establishing a two-dimensional simulation area with the same size as the CT image by using a finite element method so as to perform flow simulation;
s4: setting the global parameter values needed for pore-scale flow simulation, taking porosity and permeability as an example, assuming that the global porosity is phi 0 Global permeability of k 0 ；
S5: to avoid considering the problem of pore-particle complex boundaries, discretized parameter functions are constructed from a macroscopic perspective. This region of porous media is defaulted to a complete region, ignoring the presence of pore structure. The complex position relation of pore particles does not exist in the area, and only different positions of the area have different parameter values, so that the pore and the particles are distinguished by the difference of the parameter values. Taking porosity and permeability as an example, the porosity and permeability of the regions are different at different positions. Therefore, the porosity discretization function is constructed as phi (x, y) ═ phi 0 (1-f (x, y). a), i.e., the porosity at the location of the particles is a minimum value close to 0, and the porosity at the location of the pores is phi 0 (ii) a A discretization function of permeability of
The permeability of the position of the particle is a small value, the permeability of the position of the pore is a large value, and the pore and the particle are distinguished by the permeability;
wherein a and c are constants, and the constants a and c are introduced to avoid phi being 0 or k being infinity; this allows the porosity to be near zero and non-zeroThe permeability is close to infinity and is a calculable value. These two constants ensure that numerical errors are avoided in the numerical calculations. b is a constant, and the constant b is used for ensuring the permeability of the particles
The permeability is a smaller value, and the value of the permeability at the position can be determined by adjusting the size of b.
Preferably, a is phi so as to avoid phi being 0, so a is 0 Nineteen percent, c is to avoid k ═ infinity, so c is taken to be k 0 B is to ensure that the permeability of the particles is a small value, so b is k 0 Ten percent.
S6: the position relation of the pores and the particles is successfully distinguished through S5, and the geometric position information of the pore structure is determined in a discretization assignment function mode; then, mesh subdivision is carried out on the whole two-dimensional rock gray level image area where the model is located, the mesh subdivision is assisted based on a numerical function of the gray level image, the mesh needs to be refined in the area where f (x, y) is 0, the particle area where f (x, y) is 1 is not involved in calculation, and the mesh can be coarsened. Therefore, the number of grids in the area and the time of simulation calculation can be greatly saved, and the complex problem of grid subdivision on the pore-particle boundary is effectively avoided.
The mesh coarsening and mesh refinement of the model are a basic concept in the field of fluid mechanics computer simulation, and refer to the number of meshes used for characterizing the constructed model to participate in calculation. Considering that the sizes of different models are different, the coarsening and the refining of the application are relative concepts provided in the same model and the same scene, and in the step of the invention, the number of meshes of a region where f (x, y) is 0 is more than the number of meshes of a position where f (x, y) is 1.
S7: applying a Brinkman equation of flow simulation to the simulation region established in S3, setting an initial boundary condition, and solving a velocity field and a pressure field of the flow process in the grid split in S6; the pore-scale flow simulation equation is realized through S1-S7, namely from a macroscopic view. Note that the Brinkman flow equation mentioned in S7 is a well-established theoretical equation and is not part of the present invention, and will not be described herein.
Preferably, the initial boundary conditions in S7 are: entry boundary P ═ P 0 The exit boundary P is 0, and u · n is 0, u is a velocity vector, n is a normal vector, and u · n is 0, meaning that there is no flow velocity perpendicular to the boundary, i.e. no flow boundary.
Further preferred, wherein P 0 The value was 0.715 Pa.
When the method is used for simulating the micro flow, the complex boundary relation between particles and pores is not processed, but different values are assigned in different areas by using a discretized numerical function, and the micro boundary processing is realized from the macroscopic modeling angle.
The invention has the beneficial effects that:
1. the invention provides a macroscopic angle modeling method for porous medium pore size flow simulation, which comprises the steps of constructing an image numerical function of a rock slice CT scanning image, a discretization parameter assignment function of the whole area, an image numerical function auxiliary area mesh generation method and the like. The method can truly restore the distribution of rock particle pore throat based on CT scanning images, acquire a real porous medium physical model, and endow simulation parameters in a real porous medium region in a discretization manner. Compared with the complexity of pore scale simulation, the macro modeling method provided by the invention avoids the problem of particle-pore boundary processing by the pore scale, and greatly eliminates the uncertainty of the boundary problem in numerical calculation. Moreover, the macro angle modeling reduces the number of meshes for model subdivision, and avoids the problem of partial encryption fine mesh subdivision at the pore-particle boundary. Namely, the porous medium macroscopic angle modeling method can greatly reduce the calculated amount and reduce the numerical simulation time. The simulation result of pore size flow can be realized, and the defects of pore size simulation can be avoided.
2. The macroscopic angle modeling method provided by the invention can be used for researching the flow simulation of a porous medium at a microscopic scale, researching the influence of the distribution of pore roar channels under the pore scale on a flow process speed field, and further researching the parameter values of microscopic streamline distribution, tortuosity calculation, permeability calculation and the like in the flow process.
3. The macroscopic angle modeling method provided by the invention greatly reduces the calculation amount of numerical simulation of pore flow, and has the advantages of high numerical calculation speed, high precision and the like. And the proposed parameter discretization function can effectively endow the model with corresponding parameters according to the actual pore throat distribution of the porous medium, and the principle is simple and easy to operate. Therefore, the method can be effectively applied to the research of the flow simulation of the porous medium, and the technical support is provided for the flow research of the porous medium from the angle of numerical simulation.
Drawings
FIG. 1 is a technical flow chart of the present invention.
Fig. 2 core sample CT scan two-dimensional grayscale image.
Fig. 3a and 3b are diagrams of porosity and permeability discretization parameter function assignment. FIG. 3a is a discretized value of the porosity of a model region; FIG. 3b is a discretized value of permeability within a modeled region.
Fig. 4 illustrates the initial boundary conditions set by the present invention.
FIG. 5 shows the flow results of the inventive porous medium macroscopic angle modeling method simulation.
Detailed Description
In order that those skilled in the art can better understand the present invention, the present invention will be further described below by way of examples, but not limited thereto, in conjunction with the accompanying drawings.
The method comprises the steps of firstly obtaining a reservoir core sample through core sampling, and obtaining a gray image of the core sample by utilizing a CT scanning technology. And after acquiring the geometric position confidence of the pore structure, constructing an image numerical function. To avoid considering the pore-particle complex boundary problem, the discretization parameter function is constructed from a macroscopic perspective. The whole area is not distinguished by pores and rock skeletons by default, and only the corresponding parameter values are different. And finally, dividing and solving area grids under the assistance of a numerical function of the gray level image, and calculating a flow equation. The porous medium pore size flow simulation can be realized by modeling from a macroscopic angle, and the next step of research can be carried out on the basis of the method.
Example 1
In order to further explain the effectiveness of the technical method, the method for modeling the macroscopic angle of the porous medium provided by the invention is further explained by taking a real core sample CT scanning image as an example, and as can be seen from a technical route flow chart in FIG. 1, the specific steps of the method are as follows:
s01: and (3) performing CT scanning on the real reservoir core sample to obtain a two-dimensional rock scanning gray image (see figure 2).
S02: and acquiring spatial information of the pore structure based on the core scanning gray-scale image in the S01. Constructing an image numerical function f (x, y),
where (x, y) are the geometric position coordinates.
S03: a two-dimensional simulation region (360 μm) of the same size as the CT image was created using a conventional finite element method according to the CT image size (360 μm) for flow simulation.
S04: the initialization sets the global parameter values required for pore-scale flow simulation, and for convenience of explanation, two basic parameters of porosity and permeability are taken as examples. Suppose that the porosity φ is initialized 0 1, permeability k 0 1000 millidarcy;
s05: to avoid the pore-particle complex boundary problem, the discretization parameter function is constructed from a macroscopic perspective. The pore and the particle are distinguished by the difference of the parameter values on the assumption that the complex pore-particle position relation does not exist in the whole area of the model, and only different positions of the area have different parameter values. Taking porosity and permeability as examples, and taking porosity and permeability as examples only, a discretization parameter function can be selectively adopted for related parameters in actual operation;
assuming that the porosity and permeability in the model solution area are different due to different positions, the constructed porosity discretization function is phi (x, y) 1-0.99 xf (x, y), that is, the porosity of the particle at the position is 0.01, and the porosity of the pore at the position is 1 (see fig. 3 a); constructed discretization function of permeability as
I.e. the permeability of the particles is equal to about 10 millidarcy and the permeability of the pores is 10000 millidarcy (see figure 3 b); the particles and the pores are distinguished in the whole area of the model according to the sizes of the porosity and permeability parameter values. Note: the specific constant values set for a and b in the step are not fixed, and are only used as reference, and a more actual value can be given according to the actual physical background.
S06: the position relation of the pore and the particle is successfully distinguished through S05, and the geometric position information of the pore structure is determined in a way of discretizing a parameter assignment function. And then assisting the mesh division based on a gray image numerical function f (x, y), refining the mesh division at the position where f (x, y) is 0, and coarsening the mesh by partial non-parametric model calculation where f (x, y) is 1. This can greatly reduce the number of meshes and the numerical computation time in the model region, while also avoiding the process of particle-pore boundary processing.
S07: the Brinkman equation of the flow simulation is applied to the simulation region established at S03, and initial boundary conditions (as shown in fig. 4) are set, with the entry boundary P ═ P 0 The exit boundary P is 0, the other two boundaries are set to u · n is 0, u is the velocity vector, n is the normal vector, u · n is 0 means no flow velocity perpendicular to the boundary, i.e. no flow boundary, where P is 0 0 The numerical value is 0.715Pa, and the velocity field and the pressure field of the flow process are solved in the grid split in S06. The velocity field distribution solved by S01-S07 is shown in FIG. 5. As can be seen in fig. 5, the flow process occurs in the pore throat, and the flow path is clearly seen.
Through the implementation case, the flow simulation process of the pore size of the porous medium is realized by modeling the discretization parameter assignment function from a macroscopic view. The method is suitable for porous medium pore size flow simulation, can skillfully avoid processing the complex boundary problem of pore-particle, and can reduce the mesh number of the model subdivision and reduce the operation time.
On the basis of the macro angle modeling method provided by the invention, further research can be carried out. After the pore size flow simulation is realized, the streamline of the model can be drawn, and the parameters such as tortuosity and permeability can be calculated. Therefore, the method provided by the invention has excellent universality.
It should be noted that the above examples are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, those skilled in the art will appreciate that; in view of the simplicity in operation of the discretization parameter function and the macroscopic angle modeling method provided by the invention, the relevant person in the art can still modify the technical solutions described in the foregoing embodiments, or equivalently replace some or all of the technical features; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (9)
1. A macroscopic angle modeling method based on a porous medium pore structure is characterized by comprising the following steps: the method comprises the following steps:
s1: creating a two-dimensional rock gray level image according to a preset method;
s2: constructing an image numerical function f (x, y) based on the two-dimensional rock gray level image obtained by S1 according to a preset method;
s3: according to the size of the two-dimensional rock gray level image scanned by the CT in the S1, establishing a two-dimensional simulation area with the same size as the CT image by using a finite element method;
s4: setting the global parameter value required by pore size flow simulation, and setting the global porosity as phi 0 Global permeability of k 0 ；
S5: constructing a discretization parameter function from a macroscopic angle according to a preset method;
s6: the geometrical position relation of pores and particles can be successfully distinguished by using the S5 in a discretization assignment function mode, and then the whole two-dimensional rock gray image area is subjected to auxiliary mesh subdivision based on a gray image numerical function f (x, y) according to a preset method;
s7: applying a Brinkman equation of flow simulation to the simulation region established in S3, setting an initial boundary condition, and solving a velocity field and a pressure field of the flow process in the grid split in S6; the pore-scale flow simulation equation is realized through S1-S7, namely from a macroscopic view.
2. The porous media pore structure-based macroscopic view modeling method of claim 1, wherein: the creating of the two-dimensional rock gray level image according to the preset method in S1 specifically includes the following steps:
sampling a reservoir core to obtain a reservoir core sample; scanning a rock slice by utilizing CT (computed tomography), and creating a two-dimensional rock gray level image; wherein black is represented by a value of 0 and white is represented by a value of 1; 0 represents the pore throat and 1 represents the rock skeleton grain.
3. The porous media pore structure-based macroscopic view modeling method of claim 1, wherein: the image numerical function f (x, y) constructed in S2 is specifically:
constructing an image numerical function f (x, y) based on the core scan gray scale image in S1,
where (x, y) are the geometric position coordinates.
4. The porous media pore structure-based macroscopic view modeling method of claim 1, wherein: the step of constructing the discretization parameter function from the macroscopic view in the step S5 specifically includes the following steps:
constructing a porosity discretization function of phi (x, y) to phi 0 (1-f (x, y). a) a discretization function of permeability of
Wherein a, b and c are constants.
5. The method for macroscopic modeling based on porous medium pore structure according to claim 4, characterized in thatCharacterized in that: a takes phi 0 Nineteen percent, c is k 0 One ten thousandth of (b) is k 0 Ten percent.
6. The porous media pore structure-based macroscopic view modeling method of claim 1, wherein: the step S6 specifically includes the following steps:
and (3) assisting to subdivide the grid based on a numerical function of a two-dimensional rock gray level image, wherein the grid needs to be refined in a region where f (x, y) is 0, and the grid is coarsened in a region where f (x, y) is 1.
7. The method of claim 6, wherein the number of meshes of the area where f (x, y) is 0 is greater than the number of meshes of the position where f (x, y) is 1.
8. The method for macroscopic modeling according to claim 1, wherein the initial boundary conditions in S7 are respectively: entry boundary P ═ P 0 The exit boundary P is 0, and u · n is 0, u is a velocity vector, n is a normal vector, and u · n is 0, meaning that there is no flow velocity perpendicular to the boundary, i.e. no flow boundary.
9. The porous media pore structure-based macroscopic modeling method of claim 8, wherein P is 0 The value was 0.715 Pa.
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| 齐宁;陈国彬;李振亮;梁冲;何龙;: "基于分步算法的裂缝性碳酸盐岩油藏大尺度酸化数值模拟", 石油学报, no. 03, 15 March 2020 (2020-03-15) * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116882255A (en) * | 2023-06-02 | 2023-10-13 | 哈尔滨工业大学 | Method and system for randomly generating porous medium model based on Fourier series |
| CN116882255B (en) * | 2023-06-02 | 2024-04-19 | 哈尔滨工业大学 | Method and system for randomly generating porous medium model based on Fourier series |
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