Fractal dimension prediction method for rock pore tortuosity based on nuclear magnetic resonance image

Abstract

The application discloses a rock pore tortuosity fractal dimension prediction method based on a nuclear magnetic resonance image, and comprises the following steps: after pretreatment of a rock sample, T2 spectrum testing is performed, and a pore size distribution curve is obtained through inversion; an MRI image is acquired by using a nuclear magnetic resonance imaging module, and rock pore distribution fractal dimension is calculated based on the image; the rock pore space is simplified into capillary tubes with different pore sizes and tortuosity, and the number of capillary tubes under different tortuosity is determined; a mathematical relationship between the tortuosity fractal dimension and the pore distribution fractal dimension is established according to the scaling relationship between the pore distribution and the number of capillary tubes, and the tortuosity fractal dimension is solved. The method uses nuclear magnetic resonance technology as an experimental means, directly obtains the pore distribution dimension representing the two-dimensional plane of the pore space through the nuclear magnetic image, takes the dimension as a target parameter, combines the pore size distribution information of the T2 spectrum, calculates the tortuosity fractal dimension, and provides a basis for quantitatively describing the rock pore structure and the permeability characteristics.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of oil and gas exploration and development, and particularly relates to a rock pore tortuosity fractal dimension prediction method based on nuclear magnetic resonance imaging technology. BACKGROUND

[0002] In the field of oil and gas exploration and development, the rock micro-pore structure is the channel for gas-water two-phase flow and diffusion, and the tortuosity fractal dimension as a quantitative characterization parameter of the pore structure bending degree reflects the difficulty of fluid passing through the rock solid matrix and is the basis for evaluating the oil and gas exploitation efficiency.

[0003] At present, the calculation of the rock pore tortuosity fractal dimension at home and abroad is mainly based on the empirical expression of the macroscopic parameter porosity obtained from the completely self-similar Sierspinski carpet, and the characteristic parameters such as the average pore radius, the average tortuosity and the capillary characteristic length need to be determined. For rock samples, the pore structure distribution is not an accurate self-similar model, and the influence of the pore structure on the rock pore tortuosity is discussed through the macroscopic parameter-porosity, which ignores the influence of the internal pore arrangement mode on the rock tortuosity. Different pore distributions have a crucial influence on the rock tortuosity fractal dimension, and even rock samples with similar porosities may have different pore distributions and capillary numbers, resulting in significant differences in the rock pore tortuosity fractal dimension. SUMMARY

[0004] The purpose of the present application is to provide a rock pore tortuosity fractal dimension prediction method based on nuclear magnetic resonance images, to obtain the pore distribution dimension representing the two-dimensional plane of the pore space directly through the nuclear magnetic image by taking the nuclear magnetic resonance technology as an experimental means, and to calculate the tortuosity fractal dimension by taking the pore distribution dimension as a target parameter and combining the pore size distribution information of the T2 spectrum, so as to accurately estimate the pore structure and permeability characteristics of different rocks.

[0005] In order to achieve the above purpose, the solution of the present application is as follows:

[0006] A rock pore tortuosity fractal dimension prediction method based on nuclear magnetic resonance images, comprising the following steps:

[0007] Step 1, pretreating the rock sample;

[0008] Step 2, testing the rock sample by T2 spectrum and obtaining the pore size distribution curve by inversion;

[0009] Step 3, obtaining the MRI image of the rock sample by using the nuclear magnetic resonance imaging module, and calculating the rock pore distribution fractal dimension based on the image;

[0010] Step 4, the rock pore space is simplified as capillary tubes with different pore sizes and tortuosity, and the number of capillary tubes under different tortuosity is determined;

[0011] Step 5, according to the scaling relationship between the pore distribution and the number of capillary tubes, the mathematical relationship between the tortuosity fractal dimension and the pore distribution fractal dimension is established, and the tortuosity fractal dimension is solved.

[0012] The specific content of the above step 1 is to process the rock sample into a cylinder conforming to the international mechanics society standard, and after vacuumizing treatment, to pressurize and saturate for not less than 24 hours.

[0013] In the above step 2, the rock sample is tested by using a measurement system to obtain a T2 spectrum, and the measurement system is debugged before testing. The FID sequence is selected to automatically find the center frequency and the hard pulse width to initially debug the system. The CPMG sequence is selected to test the T2 spectrum of the rock sample.

[0014] In the above step 3, before the MRI image is collected by using the nuclear magnetic resonance imaging module, the nuclear magnetic resonance imaging module is parameterized, the SE sequence is selected for imaging, and the parameters are set.

[0015] In the above step 3, before the pore distribution fractal dimension of the rock is calculated, the MRI image is preprocessed, including image splicing, filtering and noise reduction processing of the image by using the ImageJ software, and threshold value determination and binarization processing of the image by using the Matlab program.

[0016] In the above step 3, the box-counting method is used to calculate the pore distribution fractal dimension D f Different length boxes are respectively covered on the surface of the MRI image, the number N(d) of the boxes containing pores is counted, then the length d of the box is continuously reduced until the smallest box length reaches the pixel, according to the scaling relationship formula of the fractal ln[N(d)]=-D f ln d, the linear fitting of different size boxes and the number of boxes containing pores in the logarithmic coordinate system is established, and the slope k of the fitting straight line is the fractal dimension representing the pore structure distribution.

[0017] The specific process of the above step 4 is as follows:

[0018] The capillary volume V i of a specific pore size r i is calculated according to the following formula:

[0019]

[0020] Wherein, V is the volume of a single capillary tube with a specific pore size r i , V i is the capillary volume of a specific pore size ri the total volume of the capillary tube;

[0021] The volume of the capillary tube is calculated according to the following formula:

[0022] V = πr 2 L t (r)

[0023] wherein r represents the capillary tube radius, L t (r) represents the length of the tortuous capillary tube;

[0024]

[0025] wherein D t is the tortuosity fractal dimension, varying from 1-2 in two-dimensional space, L0 is the characteristic length of the capillary tube, (2r) 1-Dt represents the (1-D t ) power of 2r;

[0026] The number of capillary tubes N i with a capillary tube volume V i of a specific pore size r i is represented as:

[0027]

[0028] The number of capillary tubes with a radius greater than r i is represented as:

[0029]

[0030] wherein n represents the number of capillary tubes with a pore size r i .

[0031] The specific content of the above step 5 is:

[0032] According to fractal theory, the number of capillary tubes with a size greater than r and the pore size r have the following power function relationship:

[0033]

[0034] wherein D f is the fractal dimension of pore distribution, r max is the maximum capillary tube diameter;

[0035] According to the principle of nuclear magnetic resonance, each nuclear magnetic resonance transverse relaxation time T2 represents a specific capillary tube radius r, and the signal amplitude represents the capillary tube volume V i with a capillary tube radius r i . The transverse relaxation time T2 and the pore size have the following relationship:

[0036]

[0037] wherein, p is the relaxation rate, r is the pore radius, F S is the geometric shape factor, for capillary with tortuosity, F S = 2;

[0038] Combining the above relationship, we have:

[0039]

[0040] wherein, T 2i represents the capillary radius r i corresponding to the transverse relaxation time;

[0041] Taking the logarithm of both sides of the above formula, we have:

[0042]

[0043] Taking different tortuosity fractal dimensions into the above formula for iterative calculation until the pore distribution fractal dimension is equal to the fractal dimension calculated by the box counting method, at this time, the tortuosity fractal dimension is the characterization parameter of the capillary tortuosity.

[0044] After adopting the above scheme, the present application carries out slice imaging experiment by using nuclear magnetic resonance imaging technology, determines the pore distribution fractal dimension by using the box counting method, and then calculates the pore tortuosity fractal dimension by taking the same as the target parameter. Compared with the traditional method, the present application obtains the tortuosity fractal dimension by combining the experimental means with the theoretical derivation, no longer depends on the characteristic values such as the average pore radius and the average tortuosity, can quantitatively characterize the tortuosity difference caused by the pore arrangement distribution, and provides the basis for quantitatively describing the rock pore structure and the permeability characteristics. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 is the flow chart of the present application;

[0046] Figure 2 is the pore size distribution curve schematic diagram of four sandstone samples;

[0047] Figure 3 is the capillary model schematic diagram with tortuosity;

[0048] Figure 4 is the slice position schematic diagram of the rock sample;

[0049] Figure 5 is the pore distribution image of the sandstone sample 1 in different slices;

[0050] Figure 6 is the MRI image processing schematic diagram;

[0051] Figure 7is the pore distribution fractal dimension of 4 sandstone samples;

[0052] Figure 8 is the fractal dimension of tortuosity determined by combining the pore distribution fractal dimension;

[0053] Figure 9 is the fractal dimension of tortuosity calculated by different methods. DETAILED DESCRIPTION

[0054] The technical solutions and beneficial effects of the present application will be described in detail below in combination with the drawings.

[0055] As shown in Figure 1 , the present application provides a rock pore tortuosity fractal dimension prediction method based on nuclear magnetic resonance image, which is described below taking sandstone as an example, including the following steps:

[0056] Step 1, for the samples obtained by sampling the cores in the engineering target area, according to the standard of the International Mechanics Society, the sandstone sample is processed into a 50*100mm cylinder, and the sandstone sample is subjected to vacuum treatment using a vacuum saturation instrument, and then pressurized saturation, the time is generally not less than 24h; In this embodiment, 4 sandstone samples were collected;

[0057] Step 2, use the measurement system to test the T2 spectrum of the sandstone sample, and obtain the pore size distribution curve by inversion, which can be combined with Figure 2 as shown;

[0058] Step 3, use the nuclear magnetic resonance imaging module to obtain the MRI image of the sandstone sample, and calculate the rock pore distribution fractal dimension based on the image;

[0059] Step 4, simplify the rock pore space into capillary tubes with different pore sizes and tortuosity, determine the number of capillary tubes under different tortuosity, and the model diagram is as shown in Figure 3 ;

[0060] Step 5, according to the scaling relationship between the pore distribution and the number of capillary tubes, establish the mathematical relationship between the tortuosity fractal dimension and the pore distribution fractal dimension, and solve the tortuosity fractal dimension.

[0061] In step 2, before obtaining the T2 spectrum of the sandstone sample by using the measurement system, the measurement system needs to be pre-adjusted, specifically, the computer control system is opened, the FID sequence is selected to automatically find the center frequency and the hard pulse width to perform initial adjustment of the system; select the CPMG sequence to test the T2 spectrum of the rock sample, for the sandstone type, determine the CPMG parameters: magnetic field strength is 0.3T, center frequency is 12MHz, echo interval is 0.2ms, echo number is 12000, accumulation number is 64, and waiting time is 3000ms;

[0062] In step 3, before acquiring the MRI image by the nuclear magnetic resonance imaging module, the nuclear magnetic resonance imaging module needs to be parameterized, specifically, selecting SE sequence for imaging, setting the parameters as follows: repetition waiting time is 3000 ms, accumulation number is 64, taking rock axial direction as the imaging direction, setting the slice thickness as 5 mm and the slice interval as 5 mm, dividing the rock into 9 slices for imaging experiment, the slice positions of the 4 sandstone samples are as shown in Figure 4 , wherein the pore distribution of different slices of sandstone sample 1 is as shown in Figure 5 .

[0063] In step 3, before calculating the fractal dimension of the rock pore distribution, the MRI image is preprocessed, including image splicing, filtering and denoising processing of the image by ImageJ software, threshold determination and binary processing by Matlab program, etc. The slice image after preprocessing is as shown in Figure 6 .

[0064] In step 3, the box-counting method is used to determine the fractal dimension D f of the pore distribution. Different size boxes are respectively covered on the surface of the MRI image, the number N(d) of boxes containing pores (i.e. containing pore pixels) is counted, then the size d of the box is continuously reduced until the smallest box size reaches the pixel, according to the scaling relationship of fractal ln[N(d)] = -D f ln d, the linear fitting of different size boxes and the number of boxes containing pores in the logarithmic coordinate system is established, and the slope k of the fitting straight line is the fractal dimension representing the pore structure distribution. The fitting result is as shown in Figure 7 , and the fractal dimensions of the pore distribution of the 4 sandstone samples are 1.3405, 1.3318, 1.3592 and 1.3262 respectively.

[0065] In step 4, the specific method for determining the number of capillaries under different tortuosity is as follows:

[0066] The number of capillaries under the capillary volume V i of a specific pore size r i , the relationship is as follows:

[0067]

[0068] , wherein V is the volume of a single capillary of a specific pore size r i , V i is the total volume of capillaries of a specific pore size r i .

[0069] The volume of the capillary is calculated as follows:

[0070] V = πr 2L t (r) (2)

[0071] wherein, r represents capillary radius, L t (r) represents tortuous capillary length.

[0072]

[0073] wherein, D t is tortuosity fractal dimension, which varies from 1-2 in two-dimensional space, L0is characteristic length of capillary, (2r) 1-Dt represents (1-D t ) power of 2r.

[0074] Substituting equation (2) and equation (3) into equation (1), the number of capillaries N i with capillary volume V i of specific pore size r i can be expressed as:

[0075]

[0076] The number of capillaries with radius greater than r i can be expressed as:

[0077]

[0078] wherein, n represents the number of capillaries with pore size r i ;

[0079] The specific content of step 5 is:

[0080] According to fractal theory, the number of capillaries with size greater than r and the pore size r have the following power function relationship:

[0081]

[0082] wherein, D f is fractal dimension of pore distribution, r max is maximum capillary size.

[0083] According to the principle of nuclear magnetic resonance, each transverse relaxation time T2 of nuclear magnetic resonance represents a specific capillary radius r, and the signal amplitude represents the capillary volume V i with capillary radius r i . The transverse relaxation time T2 and the pore size have the following relationship:

[0084]

[0085] wherein, ρ is relaxation rate, r is pore radius, F SFor the geometric shape factor, F S Take 2.

[0086] In combination with the above relationship, we can get:

[0087]

[0088] Where, T 2i Indicates that the capillary radius is r i The corresponding transverse relaxation time;

[0089] Taking the logarithm of both sides of equation (8) has:

[0090]

[0091] Take different tortuosity fractal dimensions into equation (9) for iterative calculation until the pore distribution fractal dimension and the fractal dimension calculated by the box counting method are the same, at this time the tortuosity fractal dimension is the representation parameter of the capillary tortuosity. The iterative calculation result is shown in Table 1. Wherein, the tortuosity fractal dimensions of the four sandstone samples are 1.5271, 1.5215, 1.4719 and 1.5406 respectively. The pore structure characteristic data of the sandstone samples calculated by the embodiment are shown in Table 1: Figure 8

[0092] Table 1 Pore structure characteristics of sandstone samples

[0093]

[0094] Figure 9 The comparison diagram of the tortuosity fractal dimensions obtained by the present application and other scholars based on the average tortuosity is shown in the following table.

[0095] In combination with the above, the present application provides a sandstone pore tortuosity fractal dimension prediction method based on the nuclear magnetic resonance imaging technology, which considers the relationship between the number of capillaries and the pore distribution under different tortuosity, and establishes a new method for determining the sandstone pore tortuosity fractal dimension based on the nuclear magnetic resonance imaging technology, which includes the following steps: obtaining the rock pore size distribution curve and the lamella image by nuclear magnetic resonance technology; pre-processing the nuclear magnetic image, and obtaining the pore distribution fractal dimension by the box counting method; then taking the pore distribution fractal dimension as the target parameter, combining the fractal scalar relationship between the number of capillaries and the pore size under different tortuosity, and iteratively obtaining the sandstone tortuosity fractal dimension. The fractal dimension obtained by the present application can describe the difference in tortuosity caused by different pore arrangement modes in the rock, and provides a basis for quantitatively describing the pore structure and permeability characteristics of the rock.

[0096] ​The above examples only illustrate the technical idea of the present application, and cannot be used to limit the protection scope of the present application. Any modification made according to the technical idea of the present application on the basis of the technical scheme falls within the protection scope of the present application.

Claims

1. A method for predicting the fractal dimension of rock porosity tortuosity based on nuclear magnetic resonance images, characterized in that... Includes the following steps: Step 1: Pre-treat the rock sample; Step 2: Perform T2 spectrum testing on the rock sample and invert the pore size distribution curve to obtain the pore size distribution curve; Step 3: Obtain MRI images of the rock sample using a nuclear magnetic resonance imaging module, and calculate the fractal dimension of the rock pore distribution based on the images; Step 4: Simplify the rock pore space into capillaries with different pore sizes and tortuosity, and determine the number of capillaries with different tortuosity. Step 5: Based on the scaling relationship between pore distribution and capillary number, establish the mathematical relationship between the tortuosity fractal dimension and the pore distribution fractal dimension, and solve for the tortuosity fractal dimension. In step 3, the fractal dimension D of the pore distribution is calculated using the box-counting dimension method. f Boxes of different side lengths were placed over the surface of the MRI image, and the number of boxes containing pores, N(d), was counted. Then, the side length d of the boxes was continuously decreased until the smallest box had a side length that was a pixel. The scaling relationship of fractals was then applied. A linear fit was established between boxes of different sizes and the number of boxes containing pores in a logarithmic coordinate system, and the slope k of the fitted line was the fractal dimension characterizing the distribution of the pore structure. The specific process of step 4 is as follows: Calculate the specific aperture r according to the following formula. i capillary volume V i Number of capillaries below: （1） Where V is a single specific aperture r i The volume of the capillary, V i For a specific aperture r i The total volume of the capillary; The volume of the capillary can be calculated using the following formula: （2） Where r represents the capillary radius, L t (r) represents the length of the tortuous capillary; （3） Among them, D t It is the tortuosity fractal dimension, which varies from 1 to 2 in two-dimensional space, and L0 is the characteristic length of the capillary, (2r). 1-Dt Represents 2r of (1-D) t ) to the power of; Substituting equations (2) and (3) into equation (1), we get the specific aperture r. i capillary volume V i The number of capillaries N i Represented as: （4） Then the radius is greater than r i The number of capillaries is expressed as: （5） Where n represents the aperture of r i The number of capillaries; The specific content of step 5 is as follows: According to fractal theory, the number of capillaries with a capillary size greater than r and the diameter r have the following power function relationship: （6） Among them, D f It is the fractal dimension of the pore distribution, r max It is the maximum value of the capillary tube diameter; Based on the principles of nuclear magnetic resonance (NMR), each NMR transverse relaxation time T2 represents a specific capillary radius r, and its signal amplitude represents the capillary radius r. i capillary volume V i The transverse relaxation time T2 is related to the aperture as follows: （7） Where ρ is the relaxation rate, r is the pore radius, and F S For capillaries with tortuosity, F is the geometric shape factor. S =2; Combining the above relationships, we get: （8） Among them, T 2i The capillary radius is r i The corresponding lateral relaxation time; Taking the logarithm of both sides of equation (8) gives: （9） Substitute different tortuosity fractal dimensions into equation (9) for iterative calculation until the pore distribution fractal dimension is the same as the fractal dimension calculated by the box-counting method. At this time, the tortuosity fractal dimension is the characterization parameter of capillary tortuosity.

2. The method as described in claim 1, characterized in that: The specific content of step 1 is to process the rock sample into a cylinder that conforms to the standards of the International Union of Theoretical and Applied Mechanics, and then saturate it under pressure after vacuum treatment.

3. The method as described in claim 1, characterized in that: In step 2, the measurement system is used to perform T2 spectrum testing on the rock sample. Before the test, the measurement system is debugged. The FID sequence is selected to automatically find the center frequency and hard pulse width for initial system debugging. The CPMG sequence is selected to perform T2 spectrum testing on the rock sample.

4. The method as described in claim 1, characterized in that: In step 3, before acquiring MRI images using the MRI module, the parameters of the MRI module are first adjusted, the SE sequence is selected for imaging, and the parameters are set.

5. The method as described in claim 1, characterized in that: In step 3, before calculating the fractal dimension of rock pore distribution, the MRI image is preprocessed, including image stitching, image filtering and noise reduction using ImageJ software, and threshold determination and binarization using Matlab program.

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