KR101661336B1 - Apparatus and method for calculating permeability and porosity of rock using image of slice of rock - Google Patents

Abstract

The present invention relates to an apparatus and method for calculating the permeability and porosity of a rock using a slice image of a rock, in which a three-dimensional pore structure is obtained by using a slice image of a rock, and the permeability and porosity of the rock are calculated by using the lattice Boltzmann method . The apparatus for calculating the permeability and porosity of a rock using a slice image of a rock according to the present invention comprises a microscope equipped with a digital camera and configured to acquire a two-dimensional thin film image by photographing a rock slice sample, A control means configured to acquire a three-dimensional pore structure by inputting, calculate a permeability and porosity of the rock by using the lattice Boltzmann method in the pore structure, and output a display control signal corresponding thereto; And a display unit for receiving and displaying.

Description

TECHNICAL FIELD The present invention relates to a method of calculating a porosity and a porosity of a rock using a slice image of a rock,

The present invention relates to an apparatus and method for calculating the permeability and porosity of a rock using a slice image of a rock, and more particularly, to a three-dimensional pore structure using a slice image of a rock, and using the lattice Boltzmann method, The present invention relates to a method for calculating a porosity and a porosity of a rock using a slice image of a rock.

Typically, measuring or predicting the permeability of rocks is a very important and fundamental task for so-called "geological characterization" in areas such as groundwater research, civil engineering foundations, oil and gas exploration, and greenhouse gas underground storage.

Conventional measurements of rock permeability are based on the assumption that rocks and soil samples are obtained in a columnar form and are actually measured in a laboratory or formed and processed into rock and soil samples to produce cylindrical microstructures, A cylindrical rock sample was taken by CT to acquire the three - dimensional rock structure and the permeability was measured.

However, there is a problem in that, in the conventional method of measuring the permeability of water, the method of acquiring a rock and soil sample in a cylindrical shape and actually measuring it in a laboratory has a problem that a measurement time in a laboratory is long, The method using the accelerator has a problem in that it is not easy to acquire the sample of the cylindrical rock and the X-ray accelerator is used, so that the cost is high and the time is long.

Also, in the conventional permeability measurement method, in order to grasp the characteristics of the permeability of a certain rock (stratum), it is necessary to acquire the fitting curve by grasping the change of the permeability due to the change of the natural porosity, There is a problem in that it takes a lot of time and costs a lot because it needs to be measured as a target.

SUMMARY OF THE INVENTION It is therefore an object of the present invention to provide a method and apparatus for measuring rock mass and porosity of a rock, And a method for calculating the porosity and porosity of a rock using the same.

In order to accomplish the above object, there is provided an apparatus for calculating the permeability and porosity of a rock using a slice image of a rock according to an embodiment of the present invention includes a digital camera equipped with a digital camera configured to acquire a two- A control means configured to obtain a three-dimensional void structure by receiving a two-dimensional thin film image from the microscope, calculate a permeability and porosity of the rock by using the lattice Boltzmann method in the void structure, and output a display control signal corresponding thereto; And a display unit for receiving and displaying a display control signal output from the control unit.

In the permeability and porosity calculating device of rock using the slice image of rock according to the one embodiment, the control means calculates the autocorrelation length by inputting the two-dimensional thin film image and performing image analysis And an input image having the optimal resolution is generated for each of the porosity and the particle, and an equiprobable three-dimensional void structure for each of the generated input images is obtained by using a three-dimensional structure generation program, The permeability is calculated by applying the result of the fluid computer simulation to the equation, and when the permeability and porosity of all the input images are calculated, And outputs a display control signal according to the variation of the porosity and the porosity calculated for each image, And calculating a representative permeability and a representative porosity by averaging the permeability and porosity calculated for each input image, and outputting a corresponding display control signal.

In the apparatus for calculating a porosity and a porosity of a rock using a slice image of a rock according to the one embodiment, the input image generated by the porosity and the particle is divided into a compression band generated due to the deformation of the rock, And a total of six regions (regions of well-classified small particles, regions of well-classified small particles, regions of poorly classified particles), each of which is classified into three regions in the compression band and the matrix region Region. ≪ / RTI >

The method for calculating the percentage of permeability and the porosity of a rock using a slice image of a rock according to another embodiment of the present invention comprises the steps of: capturing a rock slab sample to obtain a two-dimensional slice image; Calculating an autocorrelation length and deriving an optimum resolution, generating an input image having the optimal resolution for each of the porosity and the particle, and generating a three-dimensional pore structure for each input image using the three- Calculating a permeability by applying the result of the fluid computer simulation to the equation, and calculating a permeability of the fluid, Judging whether or not the permeability and porosity of all of the input images have been calculated, If the permeability and porosity of all the input image generated based on the calculation it is characterized in that it comprises the step of displaying a change of the permeability and porosity calculated by the input image.

The method for calculating a permeability and a porosity of a rock using the slice image of a rock according to another embodiment of the present invention is characterized in that after the step of displaying the change in the permeability and the porosity, the permeability and porosity calculated for each input image are averaged, Calculating the porosity and displaying it.

If the permeability and porosity of all input images generated in the determination step are not calculated using the slice image of the rock according to another embodiment of the present invention, And acquiring the porosity.

In the method of calculating a porosity and a porosity of a rock using a slice image of a rock according to another embodiment of the present invention, the input image generated by the porosity and the particle is generated by a compression band generated by the influence of deformation of the rock, And a total of six regions (a region of a well-classified large particle, a region of a well-classified small particle, a region of an undesirably classified particle) each of which is classified as a metric region, As shown in FIG.

According to the apparatus and method for calculating the permeability and porosity of a rock using a slice image of a rock according to an embodiment of the present invention, since a sample of a rock slab obtained from a rock mass, which is commonly used in general geological survey, is used, The sample can be obtained easily and quickly.

Further, according to the permeability and porosity calculating apparatus and method for calculating the rock permeability of a rock using a rock slice image according to an embodiment of the present invention, a three-dimensional pore structure is obtained by using a two-dimensional flake image, and the lattice Boltzmann method There is another effect that the permeability and porosity of the rock can be calculated efficiently without costly and time-consuming cost as compared with the conventional permeability measuring method since it is a method of calculating the permeability and porosity of the rock.

FIG. 1 is a block diagram of a permeability and porosity calculating apparatus of a rock using a slice image of a rock according to an embodiment of the present invention.
2 is a flow chart showing a method of calculating a porosity and a porosity of a rock using a slice image of a rock according to an embodiment of the present invention.
3 is a view showing an image of a flake obtained using a microscope equipped with a digital camera.
FIG. 4A is a diagram showing a two-dimensional autocorrelation function of a thin film image, and FIG. 4B is a diagram showing two one-dimensional autocorrelation functions extracted from the two-dimensional autocorrelation function.
5 is a diagram showing the entire area of the thin film image having the optimum resolution.
FIG. 6 is a view showing an input image for each region selected in the entire region of FIG. 5 to observe the calculation of the permeability and the change pattern.
FIG. 7 is a diagram showing a three-dimensional void structure generated by using a three-dimensional structure generation program. FIG.
8 is a diagram showing a structure of a velocity vector used in the lattice Boltzmann method.
9 is a view showing a flow of fluid in a three-dimensional pore structure.
10 is a graph showing the distribution of porosity and permeability predicted for each group.
FIG. 11 is a diagram showing a change in the permeability according to the porosity per group.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of a permeability and porosity calculating apparatus for rocks using a slice image of rock according to an embodiment of the present invention. FIG. 1 is a graph showing the permeability and porosity of a rock using a slice image of a rock according to an embodiment of the present invention. A microscope 100 equipped with a digital camera, a control unit 200, and a display unit 300. [

A microscope (100) equipped with a digital camera is configured to acquire a two-dimensional flake image by photographing a rock flake sample.

The control means 200 receives a two-dimensional flaky image from the microscope 100 equipped with a digital camera and obtains a three-dimensional air gap structure. In the air gap structure, the permeability and porosity of the rock are calculated using the grid Boltzmann method, And outputs a display control signal. The control unit 200 may be a mobile terminal (e.g., a notebook, a personal computer, a PDA, a PMP, a smart phone, or the like) capable of wireless communication with the microscope 100 or the display unit 300 equipped with a digital camera. The method of calculating the permeability and the porosity of the rock using the slice image of the rock performed by the control means 200 will be described later.

The display unit 300 may be a display device such as a monitor, an LCD, and a PDP that receives and displays a display control signal output from the control unit 200.

Hereinafter, the percentage of permeability and porosity of a rock using a slice image of a rock according to another embodiment of the present invention, using the permeability and porosity of the rock using the slice image of the rock according to the embodiment of the present invention, Will be described.

First, a rock flake sample is photographed using a microscope 100 equipped with a digital camera to obtain a two-dimensional flake image as shown in FIG. 3 (S1). In Fig. 3, the blue portion represents a void and the gray series represents particles. It can be seen that the difference in the size of the particles and the amount of pores is remarkable depending on the position.

Then, the control means 200 receives the obtained 2D flake image from the microscope 100 equipped with the digital camera, calculates the autocorrelation length? Through image analysis, and derives the optimal resolution (S2) . The step S2 will be described in more detail. In order to determine an appropriate resolution, the two-dimensional flaky image is configured as a two-dimensional function f (r), and the autocorrelation function A (h) do. The equation is as follows.

[Equation 1]

A (h) = < f (r) f (r + h)

[Where h is the interval (Lag), <> means the average]

Next, a one-dimensional autocorrelation function is extracted from the X-axis component and the Y-axis component of the calculated autocorrelation function A (h), and this function is fitted to the following model function The autocorrelation length α in the model function is determined.

&Quot; (2) "

[Where? Is the porosity]

The autocorrelation length α is related to the average particle size of the flakes. For efficient permeability prediction, the resolution of the image is adjusted to be between 10 and 20 pixels per autocorrelation length α, . FIG. 4A is a diagram showing a two-dimensional autocorrelation function of a thin film image, FIG. 4B is a diagram showing two one-dimensional autocorrelation functions extracted from the two-dimensional autocorrelation function, and FIG. The direction function, and the model function using the model function to obtain the autocorrelation length (α).

In step S3, the control means 200 generates an input image having the optimal resolution for each porosity and particle. FIG. 5 is a view showing an entire region of a thin film image having an optimal resolution, and FIG. 6 is a view showing an input image for each region selected in the entire region of FIG. 5 in order to observe the calculation of permeability and the change pattern. As shown in FIGS. 5 and 6, the input image generated by the porosity and the particle is classified into a compression band generated by the influence of deformation of the rock and a matrix section on both sides of the compression band, Which is an image obtained in a total of six regions, each of which is three regions (well-classified large particle region, well-classified small particle region, and poorly classified particle region) in the interval.

Next, the control unit 200 acquires a three-dimensional pore structure (see FIG. 7) for each input image generated in step S3 using the three-dimensional structure generation program (S4).

와 위치

에서의 입자 밀도 분포는

로 나타낸다.

는 각 방향의 속도 벡터를 의미하며,

는 각각의 방향을 의미한다. 각 방향은 2차원에서 도 8에 도시된 바와 같은 격자모델(face-centered hypercube grid)로 나타내며, 8개의 속도 방향을 갖는다. 각 노드에서의 초기밀도의 값인 로컬 질량 밀도

, 운동량 밀도

, 그리고 운동량 속 텐서(momentum flux tensor)

는 다음과 같이 나타낸다.
In step S5, the control unit 200 performs fluid computer simulation using the lattice Boltzmann method in the three-dimensional void structure obtained in step S4. More specifically, we used the lattice Boltzmann method to calculate the permeability considering complex three-dimensional pore structure. The lattice Boltzmann method is based on the theory of cellular automata, which is characterized by the ability to easily describe the interaction of a complex system of large numbers of cells using simple local rules. It also has the advantage of being able to quickly adapt to any discrete geometry conditions or other computing environments. The lattice Boltzmann method is used to approximate the solution of the Navier-Stokes equations through conservation of mass and conservation of momentum. time

And location

The particle density distribution in

Respectively.

Denotes a velocity vector in each direction,

Quot; refers to each direction. Each direction is represented in two dimensions by a face-centered hypercube grid as shown in Fig. 8, and has eight velocity directions. The local mass density, which is the value of the initial density at each node

, Momentum density

, And momentum flux tensor

Is expressed as follows.

&Quot; (3) "

&Quot; (4) "

&Quot; (5) "

는 속도벡터

의

성분

또는

성분

이다]
[here

Is a velocity vector

of

ingredient

or

ingredient

to be]

는 불연속 볼츠만 방정식인 수학식 6과 같이 나타낸다.
Distribution function over time

Is expressed by Equation 6, which is a discontinuous Boltzmann equation.

&Quot; (6) "

는 충돌 연산자이고,

는 다음 시간 단계에서의 질량 밀도 분포를 의미한다]
[here,

Is a conflict operator,

Means the mass density distribution at the next time step)

에서의 분포는 이웃 위치에서

로 나타낸다. 수학식 6은 충돌 연산자를 선형화하고 고유방정식(eigen equations)을 풀면 수학식 7로 표시된다.
The distribution function according to time evolution consists of collision step and propagation step, and redistributes the mass and momentum of each lattice node in the collision step. Also,

The distribution at

Respectively. Equation (6) linearizes the collision operator and solves the eigen equations, which is expressed by Equation (7).

&Quot; (7) "

는 갱신된 운동량 속 텐서이다]
[here

Is an updated momentum tensor]

그리고

과 같은 계수가 결정된다. 충돌과 전파는 정류상태가 될 때까지 지속되며, 로컬 속(local flux)(

)는 수학식 8과 같이 계산된다.
The new distribution depends on the nature of the fluid

And

Is determined. Collisions and propagation continue until they are rectified, and local flux (

) Is calculated as shown in Equation (8).

&Quot; (8) "

Using this method, the present invention uses a program developed by the inventor using the C language. The velocity distribution of the local fluid calculated by applying this method to the three-dimensional cavity structure in step S4 is as shown in Fig.

를 계산하고, 적용한 압력구배

, 그리고 유체의 점도

를 이용하면 투수율

는 다음의 수학식 9와 같은 다시(Darcy) 식으로 표시된다.
Next, the control unit 200 calculates the permeability by applying the result of the fluid computer simulation performed in step S5 to the Darcy equation (S6). More specifically, from the velocity distribution of the local fluid obtained previously,

And the applied pressure gradient

, And the viscosity of the fluid

The permeability

(Darcy) equation as shown in the following equation (9).

&Quot; (9) "

Subsequently, in step S7, the control means 200 determines whether or not the permeability and porosity of all of the input images generated in step S3 have been calculated.

If the water permeability and porosity of all input images have been calculated in step S7 (YES), the flow proceeds to step S8 to display the change in the permeability and porosity calculated for each input image through the display unit 300. FIG. 11 shows changes in the percentage of permeability and porosity calculated for each input image.

In step S9, the control unit 200 calculates the representative permeability and the representative porosity by averaging the permeability and the porosity calculated for each input image, and displays the representative permeability and the representative porosity through the display unit 300. FIG. 10 is a diagram showing the distribution of the porosity and permeability predicted for each group, with the large circle representing the average value and the detailed value being displayed on the right. The small dots reflect the statistical distribution of these values to the values obtained from each dynamically probable three-dimensional structure. The experimental data do not reflect the detailed permeability and porosity values of these complex structures.

On the other hand, if the water permeability and porosity of all input images have not been calculated in step S7 (NO), the flow proceeds to step S4.

As described above, according to the apparatus and method for calculating the permeability and porosity of a rock using a slice image of a rock according to an embodiment of the present invention, since a sample of rock flake, which can be obtained from a rock mass commonly used in general geological survey, is used, The sample can be obtained easily and quickly as compared with the measuring method. According to the apparatus for calculating the porosity and permeability of a rock using a slice image of rock according to an embodiment of the present invention, a three-dimensional pore structure can be obtained by using a two-dimensional flake image, and the lattice Boltzmann method The permeability and the porosity of the rock can be calculated efficiently because the permeability and the porosity of the rock are calculated. Therefore, the permeability and the porosity of the rock can be calculated efficiently without costly and time-consuming as compared with the conventional permeability measurement method.

Although the best mode has been shown and described in the drawings and specification, certain terminology has been used for the purpose of describing the embodiments of the invention and is not intended to be limiting or to limit the scope of the invention described in the claims. It is not. Therefore, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the scope of the present invention. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

100: Digital camera mounting microscope 200: Control means
300:

Claims (7)

A microscope equipped with a digital camera configured to capture a two-dimensional flaky image by photographing a rocky flake sample;
A control means configured to acquire a three-dimensional void structure by receiving a two-dimensional flaky image from the microscope, to calculate a permeability and porosity of the rock by using the lattice Boltzmann method in the void structure, and to output a corresponding display control signal; And
And a display unit for receiving and displaying a display control signal output from the control unit,
Wherein the control means calculates the autocorrelation length through the image analysis, derives the optimum resolution, generates the input image having the optimal resolution for each of the porosity and the particle, Acquiring an equiprobable three-dimensional pore structure for each of the generated input images using the generated program, obtaining a porosity, performing fluid computer simulation using the lattice Boltzmann method in the obtained three-dimensional pore structure, The permeability is calculated by applying the result of the computer simulation to the equation again. When the permeability and porosity of all the input images are calculated, the display control signal according to the change of the permeability and porosity calculated for each input image is output. The calculated permeability and porosity are averaged to calculate the representative permeability and the representative porosity. The permeability and porosity of the device for computing the rock using a foil image of the rock, characterized in that configured to output a display control signal. delete The method according to claim 1,
The input image generated by the porosity and the particle is classified into a compression band generated due to the deformation of the rock and a matrix region on both sides of the compression band, and three regions (well-classified) in the compression band and the matrix region A region of large particles, a region of well-sorted small particles, and a region of particles not well classified), wherein the image is obtained from a total of six regions. . Acquiring a two-dimensional flaky image by photographing a rock flake sample;
Calculating an autocorrelation length by inputting the 2D flake image and analyzing the image and deriving an optimal resolution;
Generating an input image having the optimal resolution for each of the porosity and the particle;
Obtaining an equiprobable three-dimensional void structure for each of the input images using the three-dimensional structure generation program and obtaining a void ratio;
Performing fluid computer simulation using the lattice Boltzmann method in the obtained three-dimensional void structure;
Applying the result of the fluid computer simulation to the equation to calculate the permeability;
Determining whether a permeability and a porosity of all of the generated input images have been calculated; And
And displaying the change in the percentage of permeability and porosity calculated for each input image if the permeability and porosity of all the input images generated in the determination step are calculated. Calculation method. 5. The method of claim 4,
Calculating a representative permeability and a representative porosity by averaging the permeability and the porosity calculated for each of the input images after displaying the aspect ratio of the permeability and porosity, Method of calculating permeability and porosity of used rocks. 5. The method of claim 4,
Wherein if the percentages of permeability and porosity of all the input images generated in the determination step are not calculated, the step of acquiring the three-dimensional pore structure and obtaining the porosity of the input image is performed. Method of calculating permeability and porosity of rock. 7. The method according to any one of claims 4 to 6,
The input image generated by the porosity and the particle is classified into a compression band generated due to the deformation of the rock and a matrix region on both sides of the compression band, and three regions (well-classified) in the compression band and the matrix region A region of large particles, a region of well-sorted small particles, a region of undesirably classified particles), wherein the image is obtained in a total of six regions. The method of calculating the porosity and porosity of a rock using the slice image of the rock .

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