CN109977469B - Two-dimensional porous medium model construction method based on Voronoi diagram - Google Patents
Two-dimensional porous medium model construction method based on Voronoi diagram Download PDFInfo
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Abstract
The invention relates to a two-dimensional porous medium model construction method based on a Voronoi diagram, which comprises the following steps of: (1) Giving a two-dimensional porous medium area, and randomly arranging discrete points in a given target area to obtain a discrete point data file; (2) obtaining the Delaunay triangular mesh information of the target area; (3) constructing a Voronoi diagram; (4) updating the Voronoi diagram; (5) And endowing each grid edge with a certain width to form a flow channel, and connecting the flow channels into a network to form a two-dimensional porous medium model. The invention can form the aperiodic distribution of the porous medium solid framework, thereby leading the constructed porous medium model to better accord with the structural characteristics of a real porous medium. The invention has the characteristics of low porosity, low permeability and high communication performance, and is suitable for researching the flow mechanism and the flow rule of oil gas water in compact rocks.
Description
Technical Field
The invention relates to a two-dimensional porous medium model construction method based on a Voronoi diagram, and belongs to the field of porous medium micro-flow mechanism research.
Background
The occurrence and seepage mechanism of single-phase and multi-phase fluid in a porous medium is researched on the pore scale, and the method has important significance for researching the underground resource development processes such as a water flooding process, a shale oil-gas flow mode and the like. An analysis experiment based on a real stratum core is an important means for researching the seepage rule of a porous medium. The core experiment provides important basis for understanding stratum related physical property parameters such as stratum permeability, porosity, clay content and the like. However, the real core cannot independently change the rock-related physical parameters such as porosity, pore wall surface wettability, connectivity and the like, and it is difficult to directly observe the flow process of the fluid in the core and only count the macroscopic parameters such as flow pressure and the like at the input end, and these limitations make the core experiment unable to provide a mechanism explanation of the fluid flow in the pore size.
The numerical simulation of the pore size can overcome the defects of core experiments, can perform single factor change on the physical parameters of the porous medium so as to perform sensitivity analysis, and can perform visual analysis on the fluid flow in the porous medium, thereby becoming an important means for researching the internal seepage mechanism of the porous medium. The construction of the porous medium experimental model is the premise and the basis for developing the numerical simulation of the pore size. At present, porous medium models for microscale seepage mechanism research in the field of numerical simulation can be mainly divided into porous medium models constructed based on real core information and artificially constructed porous medium models. The porous medium based on the real core information usually depends on microscopic equipment such as a CT (computed tomography) and a scanning electron microscope to obtain the real core information, so that a porous medium model containing real pore space information, such as a pore network model and a digital core, is constructed. However, when the porous medium model is constructed based on the real rock core, the rock itself needs to be processed and the pore information needs to be extracted, so that the construction cost is high and the time is consumed. In addition, the porous medium model constructed based on the real core information has a complex structure, is suitable for analyzing the seepage characteristics and the flow rules of specific stratum rocks, and is less used for researching the commonly-applied seepage mode and flow mechanism.
In the research of domestic and foreign documents, a large number of two-dimensional artificially-constructed porous medium models with simpler structures are applied to the research of pore-scale single-phase and multi-phase seepage mechanisms, such as capillary bundle models, small ball accumulation models and the like, but the two-dimensional porous medium formed on the basis of regularly or randomly arranged squares or spheres has the following problems: firstly, the porous medium often has a periodic geometric structure, and the distribution and the shape of the solid particles of the real porous medium have randomness; secondly, the porosity of the model is higher and is generally larger than 0.2, and the porosity of the model is larger than 0.5 in partial research. This is far from the actual porous media, especially dense porous media. However, a great deal of research shows that the porosity is an important influence factor for the seepage of the porous medium.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a two-dimensional porous medium model construction method based on a Voronoi diagram, which overcomes the defects that the geometric structure of the two-dimensional porous medium model used for the research of the micro-scale seepage mechanism is periodically distributed, and the porosity is inconsistent with the actual porous medium.
Interpretation of terms:
a Voronoi diagram, also called Thiessen polygon or Dirichlet diagram, is composed of a set of continuous polygons made up of perpendicular bisectors connecting two adjacent point lines.
The technical scheme of the invention is as follows:
a two-dimensional porous medium model construction method based on Voronoi diagrams comprises the following steps:
(1) Setting the length and width of the two-dimensional porous medium region as L respectively x 、L y Establishing a two-dimensional coordinate system, and randomly arranging discrete points in a given porous medium area to obtain a discrete point data file, wherein the discrete point data file comprises coordinate values of all the discrete points;
(2) Obtaining the Delaunay triangular mesh information of a target area based on the discrete point data file obtained in the step (1); the Delaunay triangular grid information of the target area comprises coordinate values of grid nodes and coordinate axis information of grid edges, wherein the coordinate axis information of the grid edges refers to the coordinate values of two end points of the grid edges;
(3) Obtaining a Voronoi diagram by connecting the circumscribed circle centers of the adjacent triangles based on the Delaunay triangular mesh information of the target area obtained in the step (2);
(4) Judging the distance between every two adjacent grid nodes in the Voronoi diagram obtained in the step (3), if the distance between every two adjacent grid nodes is smaller than or equal to a critical value r, merging the adjacent grid nodes, and updating the Voronoi diagram, otherwise, not changing; the critical value r is selected according to the pore diameter of the porous medium under study, and generally, the pore diameter of the porous medium is used as the critical value.
(5) And (4) endowing each grid edge in the Voronoi diagram obtained in the step (4) with a certain width to characterize pore channels in the porous medium, wherein the formed channel width is equal to the pore diameter of the porous medium. Connecting the channels into a network to form a two-dimensional porous medium model, endowing grid edges with width as pore space, and making a geometric polygon in a target area as a solid skeleton;
according to the present invention, preferably, in the step (2), delaunay triangulation algorithm is adopted to obtain the Delaunay triangulation mesh information of the target area. The Delaunay triangulation algorithm technology reference document is as follows: tsai, victor J D. Delaunay triangle in TIN creation: an overview and a line-time algorithm [ J ]. International journal of geographic information systems,1993,7 (6): 501-524.
Preferably, in step (3), a Delaunay triangulation algorithm is used to obtain the Voronoi diagram by connecting the circumcircle centers of adjacent triangles. The Voronoi diagram includes coordinate axis information of the grid nodes and the grid edges. The Voronoi graph algorithm is constructed as a Delaunay triangulation algorithm, and the reference documents are as follows: tsai, victor J D. Delaunay triangle in TIN creation: an overview and a line-time algorithm [ J ]. International journal of geographic information systems,1993,7 (6): 501-524.
Preferably, in step (3), the distance between adjacent grid nodes is calculated according to formula (I):
in the formula (I), I and j refer to any two adjacent grid nodes in the Voronoi graph; (x) j ，y j ) Is the coordinate value of grid node j; (x) i ，y i ) Is the coordinate value of the grid node i; l is the distance between any two adjacent mesh nodes i, j.
Preferably, in the step (3), when l is less than or equal to r, a calculation formula of coordinates (x, y) of a new node after two adjacent grid nodes are merged is shown as formula (II):
according to the present invention, in the step (4), the critical value r is the pore diameter of the porous medium.
The invention has the beneficial effects that:
1. the two-dimensional porous medium model construction method based on the Voronoi diagram can avoid the periodic distribution of the solid skeleton of the porous medium, so that the constructed porous medium model is more in line with the structural characteristics of a real porous medium (such as stratum rock).
2. The porous medium constructed by the invention overcomes the defect of larger porosity of a two-dimensional porous medium used in the traditional research, has the characteristics of low porosity, low permeability and high communication, and is suitable for researching the flow mechanism and the flow rule of oil gas water in dense rock.
Drawings
FIG. 1 is a flow chart of a two-dimensional porous medium model construction method based on a Voronoi diagram.
FIG. 2 is a schematic diagram of randomly assigning discrete points in a target region according to step (1) of the embodiment.
Fig. 3 is a schematic diagram of the Delaunay triangular mesh formed according to the discrete points in the step (2) of the embodiment.
Fig. 4 is an initial Voronoi diagram of the target region of example step (3).
Fig. 5 is a schematic diagram of a portion (circled portion) of the Voronoi diagram of the target region to be updated in the step (4) of the embodiment.
FIG. 6 is a schematic diagram of a two-dimensional porous medium model generated based on a Voronoi diagram in example step (5).
FIG. 7 is a schematic diagram of a prior art artificially constructed two-dimensional porous medium model.
Detailed Description
The invention is further defined in the following description, without being limited thereto, by reference to the drawings and examples.
Example 1
A two-dimensional porous medium model construction method based on Voronoi diagrams is disclosed, as shown in figure 1, and comprises the following steps:
(1) Setting the length and width of the two-dimensional porous medium region as L x 、L y ，L x Is 1mm, L y And 1mm, as shown in fig. 2, establishing a two-dimensional coordinate system, wherein the X axis is one side below the two-dimensional porous medium region, the Y axis is one side on the left side of the two-dimensional porous medium region, and the intersection point of the lower left corner is the origin. Randomly arranging discrete points in a given porous medium area to obtain a discrete point data file, wherein the discrete point data file comprises coordinate values of all the discrete points;
(2) Obtaining the Delaunay triangular mesh information of a target area by adopting a Delaunay triangular segmentation algorithm based on the discrete point data file obtained in the step (1); the target area Delaunay triangular grid information comprises coordinate values of grid nodes and coordinate axis information of grid edges, wherein the coordinate axis information of the grid edges refers to the coordinate values of two end points of the grid edges; as shown in fig. 3. The Delaunay triangulation algorithm technology reference document is as follows: tsai, vector J D. Delaunay triangularities in TIN creation an overview and a linear-time algorithm [ J ]. International journal of geographic information systems,1993,7 (6): 501-524.
(3) Obtaining a Voronoi diagram by connecting the circumscribed circle centers of the adjacent triangles based on the Delaunay triangular mesh information of the target area obtained in the step (2); as shown in fig. 4. The Voronoi diagram includes coordinate axis information of the grid nodes and the grid edges. The Voronoi graph algorithm is constructed as a Delaunay triangulation algorithm, and the reference documents are as follows: tsai, victor J D. Delaunay triangle in TIN creation: an overview and a line-time algorithm [ J ]. International journal of geographic information systems,1993,7 (6): 501-524.
(4) Judging the distance between every two adjacent grid nodes in the Voronoi diagram obtained in the step (3), if the distance between every two adjacent grid nodes is smaller than or equal to a critical value r, merging the adjacent grid nodes, and updating the Voronoi diagram, otherwise, not changing; as shown in fig. 5. The critical value r is selected according to the pore diameter of the porous medium under study, and generally, the pore diameter of the porous medium is used as the critical value.
(5) And (4) endowing each grid edge in the Voronoi diagram obtained in the step (4) with a certain width to characterize pore channels in the porous medium, wherein the formed channel width is equal to the pore diameter of the porous medium. Connecting the channels into a network to form a two-dimensional porous medium model, endowing grid edges with width as pore space, and making a geometric polygon in a target area as a solid skeleton; as shown in fig. 6.
The horizontal and vertical coordinates in fig. 2-6 are the length and width of the two-dimensional porous medium region, respectively.
Example 2
According to the two-dimensional porous medium model construction method based on the Voronoi diagram in the embodiment 1, the difference is that,
in the step (3), a distance calculation formula between each adjacent grid node is shown as a formula (I):
in the formula (I), I and j refer to any two adjacent grid nodes in the Voronoi graph; (x) j ，y j ) Is the coordinate value of grid node j; (x) i ，y i ) Is the coordinate value of grid node i; l is the distance between any two adjacent mesh nodes i, j.
In the step (3), when l is less than or equal to r, a calculation formula of coordinates (x, y) of a new node after two adjacent grid nodes are combined is shown as a formula (II):
comparative example 1
Under the same conditions, a two-dimensional porous medium model artificially constructed in the prior art is formed by stacking small spheres as shown in fig. 7, wherein the white spheres are solid skeletons, and the black areas are pore spaces.
Compared with the method shown in the figure 7, the two-dimensional porous medium model construction method based on the Voronoi diagram can avoid the periodic distribution of the solid skeleton of the porous medium, so that the constructed porous medium model is more consistent with the structural characteristics of a real porous medium (such as stratum rock). The porous medium constructed by the invention overcomes the defect of larger porosity of a two-dimensional porous medium used in the traditional research, and has the characteristics of low porosity, low permeability and high connectivity.
Claims (5)
1. A two-dimensional porous medium model construction method based on a Voronoi diagram is characterized by comprising the following steps:
(1) Setting the length and width of the two-dimensional porous medium region as L x 、L y Establishing a two-dimensional coordinate system, and randomly arranging discrete points in a given porous medium area to obtain a discrete point data file, wherein the discrete point data file comprises coordinate values of all the discrete points;
(2) Obtaining the Delaunay triangular mesh information of a target area based on the discrete point data file obtained in the step (1); the Delaunay triangular grid information of the target area comprises coordinate values of grid nodes and coordinate axis information of grid edges, wherein the coordinate axis information of the grid edges refers to the coordinate values of two end points of the grid edges;
(3) Obtaining a Voronoi diagram by connecting the circumscribed circle centers of the adjacent triangles based on the Delaunay triangular mesh information of the target area obtained in the step (2);
(4) Judging the distance between every two adjacent grid nodes in the Voronoi graph obtained in the step (3), if the distance between every two adjacent grid nodes is smaller than or equal to a critical value r, combining the adjacent grid nodes, and updating the Voronoi graph, otherwise, not changing, wherein the critical value r needs to be selected according to the pore diameter of the porous medium to be researched, and the critical value r is the pore diameter of the porous medium;
(5) And (3) endowing each grid edge in the Voronoi diagram obtained in the step (4) with a certain width to represent pore channels in the porous medium, wherein the width of the formed channel is equal to the pore diameter of the porous medium, the channels are connected into a network to form a two-dimensional porous medium model, the grid edge endowed with the width is a pore space, and a geometric polygon in the target area is a solid skeleton.
2. The Voronoi diagram-based two-dimensional porous medium model construction method according to claim 1, wherein in the step (2), delaunay triangulation algorithm is adopted to obtain Delaunay triangular mesh information of the target region.
3. The method for constructing the two-dimensional porous medium model based on the Voronoi diagram as claimed in claim 1, wherein in the step (3), the Voronoi diagram is obtained by connecting the circumcircle centers of the adjacent triangles by using a Delaunay triangulation algorithm.
4. The two-dimensional porous medium model construction method based on the Voronoi diagram in claim 1, wherein in the step (3), the calculation formula of the distance between each two adjacent grid nodes is shown as formula (I):
in the formula (I), I and j refer to any two adjacent grid nodes in the Voronoi diagram; (x) j ，y j ) Is the coordinate value of grid node j; (x) i ，y i ) Is the coordinate value of grid node i; l is the distance between any two adjacent mesh nodes i, j.
5. The two-dimensional porous medium model construction method based on the Voronoi diagram as claimed in claim 4, wherein in the step (3), when l is less than or equal to r, the calculation formula of the coordinates (x, y) of the new node after the two adjacent grid nodes are merged is shown as formula (II):
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