CN114818408A - Macroscopic angle modeling method based on porous medium pore structure - Google Patents

Abstract

The invention relates to the field of pore-scale flow simulation of porous media, in particular to a macro-angle modeling method based on the pore structure of porous media. The method includes the following steps: S1: for the reservoir core sample, use CT scanning to create a two-dimensional gray image; S2: obtain pore structure geometric information based on the gray image, and construct a gray image numerical function f(x, y); S3: Use the finite element method to establish a two-dimensional simulation area with the same size as the CT image; S4: Initialize the parameter values required for pore-scale flow simulation; S5: Construct the discretized parameter function from a macroscopic perspective; S6: The entire simulation area is based on grayscale images The numerical function f(x,y) assists in meshing; S7: Apply the Brinkman equation to the simulation area, and solve the velocity field and pressure field of the flow process in the mesh meshed by S6. The invention provides a reasonable and effective method that can accurately simulate the pore scale flow process of a porous medium and model from a macroscopic point of view.

Description

A Macroscopic Angle Modeling Method Based on Porous Media Pore Structure

technical field

The invention relates to a macro-angle modeling method based on a porous medium pore structure, and belongs to the technical field of porous medium pore scale flow simulation.

Background technique

Oil and natural gas are an important part of my country's energy system, and it is very important to develop and utilize oil and gas resources efficiently and rationally. The flow of oil and gas in underground reservoirs can be equivalent to the flow of porous media. Moreover, hydrate mining and geothermal mining, which have emerged in recent years, can also be considered as flow processes in porous media. Therefore, more and more scholars have done a lot of research on porous media. The flow characteristics of porous media are not only observed by physical experiments, but also the flow mechanism is studied by numerical simulation.

With the widespread application of computer science, numerical simulation technology has been widely used in the study of flow simulation of porous media. Using numerical simulation technology, the flow law of fluid in porous media at the pore scale can be effectively simulated. And with the development of computer tomography (Computed Tomography) technology, high-resolution pore structure can be easily obtained by scanning reservoir cores. Many scholars simulate the fluid phase flow during the production process based on the pore structure of CT scanning. At present, the flow simulation methods at the pore scale of porous media mainly include pore network model, unstructured mesh finite element simulation and lattice-Boltzmann method. However, most of these simulation methods are based on the real pore structure of the reservoir core, which inevitably deals with complex boundary problems and requires a huge amount of calculation.

The finite element simulation method needs to obtain the grayscale image of the pore structure based on the CT scan of the core, and deal with the complex particle pore boundary problem. This requires local refinement of the boundary between pores and particles or even boundary layer processing during the meshing process, which not only increases the number of meshes in the solution domain, but also aggravates the complexity of solving partial differential equations due to a large number of pores and particle boundaries. On the one hand, the amount of calculation is increased, and the computer performance requirements are too high; on the other hand, it is very likely that the model is difficult to converge and the solution results are inaccurate. The pore network model first obtains the core electron microscope image through CT scanning, and extracts the pore space information of the porous medium. The digital core is then reconstructed by corresponding mathematical methods to obtain the geometric structure data of the digital core, including rock pores and rock skeleton. Then, the key information of the pore structure of the digital core is extracted, and the pores and roars of the core are replaced by a simple pore network model. However, this method does not consider the characteristics of fluid flow in micro-scale channels, and is an idealized model. Relying on a simplified pore network model cannot accurately describe the flow of fluid in porous media at the pore scale. In contrast, the Lattice-Boltzmann method is more suitable for pore-scale flow simulation, and the Lattice-Boltzmann method can be directly simulated on the digital pore structure without solving any partial differential equations. This method assumes that the fluid exists in the form of particles, the fluid is represented by the distribution function of the particles, and the fluid flow process includes two processes of particle collision and flow, and the principle is relatively simple. However, the boundary processing between the pores and rock particles of Lattice-Boltzmann is relatively cumbersome. The default is that the fluid particles collide with the rock skeleton. It is necessary to apply collision boundary conditions to each fluid particle, which requires a large amount of calculation. For example, a Chinese patent document (application number CN201510173922.7) discloses a method and device for simulating the microscopic flow of carbonate rock, mainly using the lattice Boltzmann method to simulate the microscopic flow of carbonate rock.

Several pore-scale flow simulation methods discussed above all need to deal with the real digital pore structure, and cannot avoid dealing with complex pore-particle boundary conditions. Moreover, pore-scale simulation requires extremely fine mesh division, and the number of equations to be solved for each mesh node is large, so the calculation amount is large, the simulation time is long, and the computer performance is required to be high.

However, if the modeling is considered from a macroscopic point of view, the problem of boundary processing of pore particles can be effectively avoided. It is only necessary to assign the required parameter values to the entire area, and different points in the area require different parameter values. For example, flow simulation needs to assign parameter values such as porosity and permeability to the entire region, but different points in the region generally have different porosity and permeability. Specifically, the permeability of the part where the particles are located should be given a very small value, even zero. Through this discretization assignment method, the relationship between pores and skeleton can be effectively dealt with by assigning different parameter values to the entire solution domain.

Therefore, the present invention proposes a method for assigning discrete functions for pore-scale flow simulation of porous media, which can assign different parameter values to different points in a region from a macroscopic perspective. It can not only achieve the same results as pore-scale flow simulation, but also avoid the boundary processing problems and huge calculation amount of pore-scale simulation.

SUMMARY OF THE INVENTION

Aiming at the deficiencies of the prior art, the present invention provides a method that is reasonable and effective, can accurately simulate the flow process at the pore scale of a porous medium, and model from a macroscopic perspective.

The technical scheme of the present invention is as follows:

A macro-angle modeling method for pore-scale flow simulation in porous media, comprising the following steps:

S1: Obtain core samples by sampling the cores of the reservoir; use CT to scan the core slices to create a two-dimensional rock grayscale image; in which, black is represented by a value of 0, and white is represented by a value of 1; 0 represents pore roars, and 1 represents rock skeleton particles;

其中(x,y)是几何位置坐标；S2: Based on the rock grayscale image in S1, the spatial information of the pore structure is obtained. Construct the image numerical function f(x,y),

Where (x, y) is the geometric position coordinate;

S3: According to the size of the two-dimensional rock grayscale image scanned by the CT scan in S1, a two-dimensional simulation area with the same size as the CT image is established by the finite element method for flow simulation;

S4: Set the global parameter values required for pore-scale flow simulation, taking porosity and permeability as an example, assuming that the global porosity is φ ₀ and the global permeability is k ₀ ;

即颗粒所在位置其渗透率为一个较小值，而孔隙所在位置其渗透率极大，以渗透率的大小区分孔隙与颗粒；S5: In order to avoid considering the complex boundary problem of pores-particles, a discretized parameter function is constructed from a macroscopic point of view. The porous media region is assumed to be a complete region by default, ignoring the existence of pore structure. It is assumed that there is no complex positional relationship between pores and particles in this region, but only that different positions in the region have different parameter values, and the pores and particles are distinguished by the different parameter values. Taking porosity and permeability as an example, different positions of the region have different porosity and permeability. Therefore, the porosity discretization function is constructed as φ(x,y)=φ ₀ (1-f(x,y)·a), that is, the porosity at the location of the particle is a minimum value close to 0, and the porosity at the location of the pore is is φ ₀ ; the permeability discretization function is

That is, the permeability of the particle location is a small value, while the permeability of the pore location is extremely large, and the pores and particles are distinguished by the size of the permeability;

是一个较小值，可以通过调整b的大小，确定该处渗透率的取值。Among them, a and c are constants. In order to avoid φ=0 or k=∞, constants a and c are introduced; this makes the porosity a value close to zero and non-zero, and the permeability close to infinity and a computable value. value. These two constants ensure that numerical errors are avoided in numerical calculations. b is a constant, in addition, the constant b is to ensure the permeability of the particles

is a small value, and the value of the permeability can be determined by adjusting the size of b.

Preferably, a is to avoid φ=0, so a is 99% of φ ₀ , c is to avoid k=∞, so c is 1/10,000 of k ₀ , b is to ensure the penetration of particles The rate is a small value, so b takes ten percent of k ₀ .

S6: The positional relationship between pores and particles has been successfully distinguished through S5, and the geometrical position information of the pore structure is determined by means of a discretized assignment function; The gray-scale image-based numerical function assists the mesh division. The area where f(x,y) is 0 needs to refine the grid, while the area where f(x,y) is 1 is the particle area, which does not participate in the calculation and can be coarsened. grid. In this way, the number of meshes in the region and the time of simulation calculation can be greatly saved, and the complex problem of meshing on the pore-particle boundary can be effectively avoided.

Roughening the mesh of the model and refining the mesh is a basic concept in the field of fluid mechanics computer simulation, which refers to the number of meshes used to characterize the constructed model participating in the calculation. Considering that the sizes of different models are different, the coarsening and refining of this application are a relative concept proposed in the same model and in the same scene. In this step of the present invention, it refers to, f(x , y) is 0 and the number of meshes is more than that where f(x, y) is 1.

S7: Apply the Brinkman equation for flow simulation to the simulation area established by S3, set the initial boundary conditions, and solve the velocity field and pressure field of the flow process in the mesh divided by S6; Scale flow simulation equations. Note that the Brinkman flow equation mentioned in S7 is a mature theoretical equation, which does not belong to the content of the present invention, and will not be repeated here.

Preferably, the initial boundary conditions in S7 are: the inlet boundary P=P ₀ , the outlet boundary P=0, the other two boundaries are set to u·n=0, u is the velocity vector, n is the normal vector, and u·n=0 means is no flow velocity perpendicular to the boundary, that is, no flow boundary.

More preferably, the P ₀ value is 0.715Pa.

When simulating microscopic flow, the present invention does not process the complex boundary relationship between particles and pores, but uses discrete numerical functions to assign different values in different regions, and realizes microscopic boundary processing from the perspective of macroscopic modeling.

The beneficial effects of the present invention are:

1. The macro-angle modeling method for pore-scale flow simulation in porous media proposed by the present invention includes constructing an image numerical function of a CT scan image of a rock slice, a discretized parameter assignment function of the entire area, and an image numerical function-assisted subdivision area network. method, etc. Based on CT scanning images, the invention can truly restore the distribution of pore roars of rock particles, obtain a real physical model of porous media, and discretize and assign simulation parameters in the real porous media area. Compared with the complexity of pore scale simulation, the macro modeling method proposed in the present invention avoids the problem of particle-pore boundary processing by pore scale, and greatly eliminates the uncertainty caused by the boundary problem in numerical calculation. Moreover, the macro-angle modeling reduces the number of meshes for the model, and avoids the problem of local refinement and fine meshing at the pore-particle boundary. That is, the macro-angle modeling method for porous media involved in the present invention can greatly reduce the amount of calculation and reduce the time of numerical simulation. The results of pore-scale flow simulation can be achieved while avoiding the inadequacies of pore-scale simulation.

2. The macro-angle modeling method proposed by the present invention can be used to study the flow simulation of porous media at the micro-scale, to study the influence of the distribution of pore roars on the velocity field of the flow process at the pore scale, and to further study the micro-flow in the flow process. Line distribution, calculation of tortuosity and permeability and other parameters.

3. The macro-angle modeling method involved in the present invention greatly reduces the calculation amount of pore flow numerical simulation, and has the advantages of fast numerical calculation speed and high precision. And the proposed parameter discretization function can effectively assign corresponding parameters to the model according to the actual pore roar distribution of porous media. The principle is simple and easy to operate. Therefore, this method can be effectively applied to the research of porous media flow simulation, and provides technical support for porous media flow research from the perspective of numerical simulation.

Description of drawings

FIG. 1 is a technical flow chart of the present invention.

Figure 2. Two-dimensional grayscale image of CT scan of core sample.

Fig. 3a and Fig. 3b are the porosity and permeability discretization parameter function assignment diagrams. Figure 3a is the discretized value of porosity in the model area; Figure 3b is the discretized value of permeability in the model area.

FIG. 4 is the initial boundary condition set by the present invention.

Figure 5 shows the flow results simulated by the macro-angle modeling method for porous media of the invention.

Detailed ways

In order to enable those skilled in the art to better understand the present invention, the present invention will be further described below with reference to the embodiments and accompanying drawings, but not limited thereto.

In the present invention, the reservoir core sample is first obtained by core sampling, and the grayscale image of the core sample is obtained by using the CT scanning technology. After obtaining confidence in the geometrical position of the pore structure, a numerical function of the image is constructed. In order to avoid considering the complex boundary problem between pores and particles, a discretized parameter function is constructed from a macroscopic point of view. By default, there is no distinction between pores and rock skeletons in the entire area, only the difference in the corresponding parameter values. Finally, according to the numerical function of the gray image, the subdivision is used to solve the area grid, and the flow equation is calculated. It is possible to model the pore-scale flow simulation of porous media from a macroscopic point of view, and to carry out further research on the basis of this method.

Example 1

In order to further illustrate the effectiveness of this technical method, the CT scan image of a real core sample is taken as an example to further illustrate the macro-angle modeling method of porous media proposed by the present invention. It can be seen from the flow chart of the technical route in Fig. 1 that the specific steps of the present invention are as follows :

S01: CT scan is performed on the real reservoir core sample to obtain a two-dimensional rock scan grayscale image (see Figure 2).

其中(x,y)是几何位置坐标。S02: Based on the core scanning grayscale image in S01, the spatial information of the pore structure is obtained. Construct the image numerical function f(x,y),

where (x, y) are the geometric position coordinates.

S03: According to the size of the CT image (360 μm×360 μm), use the conventional finite element method to establish a two-dimensional simulation area (360 μm×360 μm) of the same size as the CT image for flow simulation.

S04: Initialize and set the global parameter values required for pore-scale flow simulation. For the convenience of explanation, two basic parameters, porosity and permeability, are used as examples here. Suppose initial porosity φ ₀ =1, permeability k ₀ =1000 millidarcy;

S05: In order to avoid the complex boundary problem of pores-particles, a discretized parameter function is constructed from a macroscopic perspective. It is assumed that there is no complex positional relationship between pores and particles in the entire region of the model, only that different positions in the region have different parameter values, and the pores and particles are distinguished by the different parameter values. Taking porosity and permeability as an example, here we only take porosity and permeability as an example. In actual operation, a discretized parameter function can be selectively used for the parameters involved;

即颗粒所处位置渗透率约等于10毫达西，孔隙所处位置渗透率为10000毫达西(见图3b)；模型的整个区域内以孔隙度、渗透率参数值的大小区分颗粒与孔隙。注：本步骤对a、b所设定的具体常数值并不是固定的，这里仅作为参考，可根据实际物理背景赋予更贴切真实的值。Assuming that the porosity and permeability in the model solution area are different due to different positions, the constructed porosity discretization function is φ(x,y)=1-0.99×f(x,y), that is, the porosity of the particle position is 0.01, the porosity of the pore position is 1 (see Figure 3a); the constructed permeability discretization function is

That is, the permeability of the particle location is about 10 millidarcy, and the permeability of the pore location is 10000 millidarcy (see Figure 3b); in the whole area of the model, the size of the porosity and permeability parameters are used to distinguish the particle and the pore . Note: The specific constant values set for a and b in this step are not fixed, and are only used for reference here, and more appropriate and real values can be given according to the actual physical background.

S06: Through S05, the positional relationship between pores and particles has been successfully distinguished, and the geometrical position information of the pore structure is determined by means of discretized parameter assignment function. Then, based on the gray image numerical function f(x, y), the auxiliary grid is divided, the position of f(x, y) = 0 is refined, and the partial non-parametric model of f(x, y) = 1 is calculated. , the mesh can be coarsened. This can greatly reduce the number of meshes in the model area and the numerical computation time, while also avoiding the processing of particle-pore boundaries.

S07: Apply the Brinkman equation of flow simulation to the simulation area established in S03, set the initial boundary conditions (as shown in Figure 4), the inlet boundary P=P ₀ , the outlet boundary P=0, and the other two boundaries are set to u·n=0, u is the velocity vector, n is the normal vector, u·n=0 means that there is no flow velocity perpendicular to the boundary, that is, no flow boundary, where the value of P ₀ is 0.715Pa, and the flow process is solved in the grid divided by S06. Velocity field and pressure field. The velocity field distribution solved by S01-S07 is shown in Figure 5. It can be seen from Figure 5 that the flow process occurs in the pore roar, and the flow channel can be clearly seen in the figure.

Through this implementation case, it is further verified that the discrete parameter assignment function proposed by the present invention realizes the flow simulation process of the pore scale of the porous medium by modeling from the macroscopic point of view. This method is suitable for pore-scale flow simulation in porous media, which can not only subtly avoid dealing with complex pore-particle boundary problems, but also reduce the number of meshes for model division and the computation time.

On the basis of the macro-angle modeling method provided by the present invention, further research can be carried out. After the pore-scale flow simulation is realized, the streamline of the model can be drawn, and parameters such as tortuosity and permeability can be calculated. Therefore, the method provided by the present invention has excellent generality.

It should be noted that the above examples are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand; The discretization parameter function and the macro-angle modeling method are simple to operate, and those related in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements , does 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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