CN111563927A - Pore tortuosity calculation method based on rock micro-CT image - Google Patents
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- 239000011435 rock Substances 0.000 title claims abstract description 77
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- 238000009792 diffusion process Methods 0.000 claims abstract description 23
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- 238000006073 displacement reaction Methods 0.000 claims abstract description 9
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- 239000011159 matrix material Substances 0.000 claims description 6
- 230000035699 permeability Effects 0.000 claims description 3
- 230000011218 segmentation Effects 0.000 claims 1
- 238000003709 image segmentation Methods 0.000 abstract description 2
- 239000012530 fluid Substances 0.000 description 3
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Abstract
The invention provides a pore tortuosity calculation method based on a rock micro-CT image, which comprises the steps of firstly carrying out micro-CT scanning test on a rock sample, obtaining a rock micro-pore structure image, and obtaining a binaryzation image containing a rock framework and pores by combining digital image filtering and image segmentation; carrying out REV analysis of images based on micro CT rock samples to obtain REV sizes of different rock samples; establishing a three-dimensional computational grid model of the rock sample REV by utilizing the one-to-one correspondence relationship between the image pixels and the computational grid; based on a rock REV calculation grid and a random walk theory, a MATLAB toolbox is used for carrying out pore diffusion simulation, the effective diffusion coefficient of a rock pore phase can be obtained by counting the mean square displacement of a random particle swarm and the derivative of time, and then the three-dimensional porosity of the pore in a rock micro CT image is calculated.
Description
Technical Field
The invention relates to the field of seepage mechanics, in particular to a pore tortuosity calculation method based on a rock micro-CT image.
Background
Tortuosity is an important parameter for describing the characteristics of a microscopic seepage channel of porous media such as rock-soil mass and the like, and is defined as the ratio of the actual length of the seepage channel to the apparent length (macroscopic distance) of the seepage channel (as shown in fig. 2), namely the true length of the movement track of particles in a pore channel when the particles of seepage fluid traverse a unit distance of the medium, and can be represented by the following formula:
in the formula, LtIs the distance of the fluid through the pore channel, L0Is the macroscopic distance of the percolating medium.
Both the acoustoelectric and fluid transport properties of porous media are closely related to tortuosity. On the basis of accurately predicting the pore tortuosity of porous media such as rock-soil bodies and the like, the rapid prediction of parameters such as the sound absorption coefficient, the electric conductivity, the heat conductivity, the permeability and the like of the porous media can be realized by combining physical characteristic fitting formulas of different media, so that the relation between the structural characteristics of the microscopic seepage channel of the porous media and the macroscopic transport parameters is established. The traditional rock tortuosity calculation method is mainly obtained by combining a two-dimensional rock slice image or an empirical relation for rock average pore diameter test. A calculation method for obtaining the three-dimensional pore tortuosity of the rock by combining a three-dimensional micro CT image of the rock does not exist. Aiming at the defect, the invention discloses a pore tortuosity calculation method based on a rock micro-CT image.
Disclosure of Invention
The invention aims to provide a method for calculating the tortuosity of a three-dimensional rock pore with high prediction precision and strong usability. In order to achieve the above purpose, the invention mainly comprises the following steps:
step S1: and carrying out micro CT scanning test on the rock sample, obtaining a rock micro-pore structure image, and combining digital image filtering and image segmentation to obtain a binary image containing a rock skeleton and pores.
Step S2: and carrying out REV analysis of the image based on the micro CT rock sample, and obtaining REV sizes of different rock samples by taking the porosity and absolute permeability of the image as reference bases.
Step S3: based on the rock REV image, a three-dimensional calculation grid model of the rock sample REV is established by utilizing the one-to-one correspondence relationship between the image pixels and the calculation grids.
Step S4: based on the rock REV computational grid, a MATLAB toolbox is utilized to carry out pore diffusion simulation based on a random walk theory. Firstly, assuming that a certain number of hypothetical particles randomly walk in a rock pore space, the effective diffusion coefficient of a rock pore phase can be obtained by counting the derivative of the mean square displacement and time of a particle swarm, namely:
in the formula, r2(t) mean square displacement of the particle population, t is time, phi is the volume fraction of the dielectric phase, DeIs the effective diffusivity of the particles in the porous medium. For a three-dimensional rock pore, the mean square displacement in the three directions x, y, z is:
in the formula, n is the number of random particles, and i represents the ith particle.
Step S5: the effective diffusion coefficient of the medium in the rock and the intrinsic diffusion coefficient of the material are analyzed,
wherein τ is tortuosity and D is the intrinsic diffusion coefficient of the medium; . Will DeSubstituting the formula (4) to obtain the three-dimensional porosity of the pore in the rock micro CT image.
Compared with the prior art, the invention has the beneficial effects that: the method for calculating the three-dimensional tortuosity of the rock pore space is feasible, high in precision and high in calculation efficiency.
Drawings
In order to more clearly illustrate the technical solution of the method of the present invention, the following embodiments are further described with reference to the accompanying drawings.
FIG. 1 is a flow chart of a method for calculating three-dimensional porosity based on rock micro-CT images.
FIG. 2 is a schematic diagram illustrating the definition of rock pore tortuosity according to the present invention.
Fig. 3 is a schematic diagram of rock micro-CT scanning rock sample preparation according to an embodiment of the present invention.
FIG. 4 is a cross-sectional binarized image of a rock sample provided by an embodiment of the present invention.
FIG. 5 is a rock sample S1-S4 micro skeleton reconstruction grid model provided by the embodiment of the invention.
Detailed Description
In order to facilitate the description of the technical means, the achievement purpose and the model efficacy of the implementation of the present invention, the technical solutions in the embodiments of the present application are described in detail below with reference to the accompanying drawings and the embodiments. It should be understood that the embodiments described are only some of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by other persons skilled in the art from the embodiments of the present application without further inventive efforts, shall fall within the scope of protection of the present application.
FIG. 1 is a flow chart of a method for measuring and calculating micro-scale strength and residual strength of rock, which comprises the following steps:
step S1: the cores drilled from the original rock samples (5 cm. times. phi.2.5 cm) were 6mm in diameter and 5mm in height, as shown in FIG. 3. The prepared rock sample is placed on the object stage, the outer cover of the sample is closed, the device is opened for scanning, and one rock sample is scanned for 15-20 h in a common condition.
The ImageJ software is utilized to perform median filtering and binarization on the obtained rock micro CT graph, and then part of rock samples are shown in figure 4, wherein black is a rock skeleton, and white is a pore space.
Step S2: based on the segmented rock sample micro-CT binary image, the segmented image is converted into a corresponding three-dimensional array matrix by using MATLAB software, the gray values of pores and skeleton pixels are respectively represented by '0' and '1', and the volume fraction phi of rock pore phases can be obtained by counting the proportion of '0' in the matrix.
A cube of 100-800 pixels is extracted from the center of an original three-dimensional cylindrical rock sample image and then gradually expanded to the surrounding area, the porosity parameter gradually tends to be stable along with the increase of the size of the rock sample, and the size at the moment is the RVE size. The analysis results showed that REV sizes of S1 and S2 were 300 pixels, and REV sizes of S3 and S4 were 400 pixels.
Step S3: importing the rock sample REV image data file into MATLAB to be stored in a matrix form, searching the position of 1 (pore) or 0 (skeleton) in the matrix, and replacing the skeleton and pore image body in the digital image based on the idea that the finite element grid and the rock microscopic image body are in one-to-one correspondence, thereby obtaining a rock skeleton model and a rock pore model which are stored in an inp file format. The generated solid skeleton mesh models of the rock samples S1-S4 are shown in FIG. 5.
Step S4: and importing the generated data matrix of the rock skeleton and the pore grid model into MATLAB software, and carrying out pore diffusion simulation based on a random walk theory. Firstly, a certain number of hypothetical particles are randomly distributed in rock pores, and each particle randomly moves to any adjacent grid at the next time step; and if the particles move to the solid grid, returning to the original position, and waiting for the next time step to repeat the random motion behavior. Along with the calculation time, the hypothetical particle swarm randomly walks in the rock pore space, and the effective diffusion coefficient of the rock pore phase can be obtained by counting the derivative of the mean square displacement and the time of the particle swarm, namely:
in the formula, r2(t) mean square displacement of the particle population, t is time, phi is the volume fraction of the dielectric phase, DeIs the effective diffusivity of the particles in the porous medium. For a three-dimensional rock pore, the mean square displacement in the three directions x, y, z is:
in the formula, n is the number of random particles, and i represents the ith particle.
Step S5: the effective diffusion coefficient of the medium in the rock and the intrinsic diffusion coefficient of the material are analyzed,
where τ is tortuosity and D is the intrinsic diffusion coefficient of the medium. And (3) obtaining the effective diffusion coefficient of the medium in the porous medium by combining the formulas (2) and (3) to obtain the three-dimensional pore tortuosity in the rock micro-CT image. Combine phi and r calculated in steps S2 and S42(t) the three-dimensional tortuosity of the pores of the rock samples S1-S4 can be respectively obtained, and the tortuosity value calculated by the method and the tortuosity value estimated by an empirical formula are shown in Table 1.
TABLE 1 calculation of three-dimensional tortuosity of pores
| Model (model) | Porosity/%) | In the X direction | Y direction | In the Z direction | Empirical value |
| S1 | 17 | 5.2 | 3.76 | 4.5 | 3.33 |
| S2 | 23 | 2.56 | 6.78 | 5.36 | 2.67 |
| S3 | 38.6 | 1.95 | 2.1 | 3.46 | 1.69 |
| S4 | 40.3 | 2.95 | 3.15 | 1.83 | 1.62 |
The above description is only a preferred embodiment of the present invention, and is intended to describe the basic principles, features and main advantages of the present invention, and not to limit the present invention, and all modifications, equivalent variations and modifications made to the above embodiments according to the technical spirit of the present invention are within the scope of the technical solution of the present invention.
Claims (7)
1. A pore tortuosity calculation method based on a rock micro CT image is characterized by comprising the following steps:
(1) constructing a grid unit model for diffusion simulation by using a rock core micro-CT image as a basis and through the one-to-one correspondence relationship between image pixels and grid units on the basis of image REV analysis;
(2) carrying out pore diffusion simulation by using a constructed rock core REV grid unit model and adopting an MATLAB tool box based on a random walk theory, and calculating an effective diffusion coefficient;
(3) and (4) combining the intrinsic diffusion coefficient of the rock sample and the effective diffusion coefficient analysis obtained by simulation, and calculating the three-dimensional tortuosity of the rock core.
2. The method for calculating pore tortuosity based on rock micro-CT images as claimed in claim 1, characterized in that in the step (1), based on the core micro-CT image, a binary image containing the core skeleton and the pore information is extracted by image processing techniques such as noise reduction, filtering and segmentation.
3. The method for calculating the pore tortuosity based on the rock micro-CT image as claimed in claim 1, wherein in the step (1), based on the obtained core binarized image, the REV size of the sample is calculated by taking parameters such as porosity and permeability as reference bases.
4. The method for calculating pore tortuosity based on rock micro-CT images as claimed in claim 1, wherein in the step (1), based on the one-to-one spatial correspondence relationship between image pixels and grid cells, a REV three-dimensional calculation grid model of the sample is reconstructed by a pixel replacement method.
5. The method for calculating pore tortuosity based on rock micro-CT images as claimed in claim 1, wherein in the step (2), the skeleton of the reconstructed core REV grid model and the pore phase grid data matrix are imported into MATLAB, and pore diffusion simulation is carried out based on the random walk theory.
6. The method for calculating pore tortuosity based on rock micro-CT images as claimed in claim 1, wherein in the step (2), the diffusion simulates the repeated random motion behavior of the hypothetical particles in the pore space at different time steps, and the effective diffusion coefficient D of the model is calculated by counting the mean square displacement and the time derivative of the particle swarme。
7. The method for calculating pore tortuosity based on rock micro-CT images as claimed in claim 1, wherein in the step (3), the relationship between the intrinsic diffusion coefficient D and the effective diffusion coefficient of the rock is analyzed, and the three-dimensional tortuosity of the rock can be calculated by combining the parameters such as the mean square displacement of the particle swarm and the porosity obtained in the above step.
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Cited By (7)
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| CN112557254A (en) * | 2020-11-25 | 2021-03-26 | 东南大学 | Method for predicting effective diffusion coefficient of chloride ions in cement slurry |
| CN113029899A (en) * | 2021-02-24 | 2021-06-25 | 西南石油大学 | Sandstone permeability calculation method based on microscopic image processing |
| CN113984589A (en) * | 2021-11-01 | 2022-01-28 | 大连理工大学 | Method for calculating tortuosity and gas diffusion coefficient of rock |
| CN113984590A (en) * | 2021-11-01 | 2022-01-28 | 大连理工大学 | Method for calculating spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rock |
| CN116879129A (en) * | 2023-07-11 | 2023-10-13 | 中国矿业大学 | Rock-soil material effective seepage path characterization method based on three-dimensional microscopic image |
| CN117451582A (en) * | 2023-10-26 | 2024-01-26 | 中国科学院武汉岩土力学研究所 | Core hydrogen diffusion coefficient simulation calculation method and related equipment |
| CN118095021A (en) * | 2024-04-28 | 2024-05-28 | 中国石油大学(华东) | Efficient calculation method for permeability of large-size digital rock core |
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Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112557254A (en) * | 2020-11-25 | 2021-03-26 | 东南大学 | Method for predicting effective diffusion coefficient of chloride ions in cement slurry |
| CN112557254B (en) * | 2020-11-25 | 2022-04-15 | 东南大学 | Method for predicting effective diffusion coefficient of chloride ions in cement slurry |
| CN113029899A (en) * | 2021-02-24 | 2021-06-25 | 西南石油大学 | Sandstone permeability calculation method based on microscopic image processing |
| CN113984589A (en) * | 2021-11-01 | 2022-01-28 | 大连理工大学 | Method for calculating tortuosity and gas diffusion coefficient of rock |
| CN113984590A (en) * | 2021-11-01 | 2022-01-28 | 大连理工大学 | Method for calculating spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rock |
| CN116879129A (en) * | 2023-07-11 | 2023-10-13 | 中国矿业大学 | Rock-soil material effective seepage path characterization method based on three-dimensional microscopic image |
| CN116879129B (en) * | 2023-07-11 | 2024-03-22 | 中国矿业大学 | Rock-soil material effective seepage path characterization method based on three-dimensional microscopic image |
| CN117451582A (en) * | 2023-10-26 | 2024-01-26 | 中国科学院武汉岩土力学研究所 | Core hydrogen diffusion coefficient simulation calculation method and related equipment |
| CN117451582B (en) * | 2023-10-26 | 2024-05-28 | 中国科学院武汉岩土力学研究所 | Core hydrogen diffusion coefficient simulation calculation method and related equipment |
| CN118095021A (en) * | 2024-04-28 | 2024-05-28 | 中国石油大学(华东) | Efficient calculation method for permeability of large-size digital rock core |
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