A method for calculating fractal dimension of shale pores

Abstract

The invention discloses a method for calculating the fractal dimension of shale pores. Firstly, several parallel samples are selected on the same core, and a carbon dioxide adsorption experiment, a nitrogen adsorption experiment and a high-pressure mercury injection experiment are respectively carried out; experimental data of an aperture segment with an aperture between 0-2nm in the carbon dioxide adsorption experiment, experimental data of an aperture segment with an aperture between 2-50m in the nitrogen adsorption experiment, and experimental data of an aperture segment with an aperture greater than 50nm in the high-pressure mercury injection experiment are respectively selected; several secondary aperture segments are taken in each aperture segment, the average aperture of each secondary aperture segment is calculated, and the fractal dimension of the pores of each secondary aperture segment is calculated; a fractal dimension-average aperture curve graph is drawn with the average aperture as the abscissa and the fractal dimension as the ordinate, and a functional relationship between the average aperture and the fractal dimension of the corresponding aperture segment is obtained by fitting; the fractal dimension of any aperture segment is obtained according to the functional relationship obtained by fitting, and the fractal dimension of the full aperture segment of the shale is characterized.

Description

Technical Field

[0001] The invention relates to the technical field of shale oil and gas resource exploitation, in particular to a method for calculating the fractal dimension of shale pores. Background Art

[0002] Shale oil and gas resources are an important part of the energy strategy. The abundant micro-nano pores in its reservoirs play a decisive role in the adsorption, seepage and migration of oil and gas. As a key quantitative indicator for studying shale reservoirs, the pore fractal dimension can reveal the heterogeneity and complexity of the pore structure, effectively evaluate the permeability of the reservoir, and comprehensively reflect the pore structure characteristics. It can evaluate the reservoir development effect and provide a scientific basis for shale oil and gas exploration and development. Existing studies have shown that the pore fractal dimension of shale is between 2 and 3. For the same shale, the smaller the pore size, the more complex its pore structure and microscopic state, and the closer the fractal dimension is to 3; the larger the pore size, the more regular the pore shape and distribution, and the closer the fractal dimension is to 2. In general, with the increase of pore size, the fractal dimension of shale pores tends to decrease gradually, and the fractal dimension is negatively correlated with the pore size.

[0003] At present, the main methods for obtaining pore fractal dimensions are: ① Carbon dioxide adsorption experiment, nitrogen adsorption experiment and mercury injection experiment. These three methods can obtain the fractal dimension of pore size distribution and pore structure by measuring the adsorption amount of carbon dioxide, nitrogen and mercury in shale pores at different pressures. However, the carbon dioxide adsorption experiment is only applicable to micropores with pore diameters between 0 and 3 nm, the nitrogen adsorption experiment is only applicable to mesopores with pore diameters between 3 and 50 nm, and the mercury injection experiment is only applicable to macropores with pore diameters greater than 50 nm. They cannot characterize the fractal dimension within any pore diameter range, have poor continuity and low resolution. ② Small-angle neutron scattering (SAXS): Use synchrotron radiation or laboratory X-ray sources to irradiate the sample and collect scattering data within a small angle range (usually less than 5°). The collected SAXS data needs to undergo preprocessing steps such as background noise subtraction and scattering intensity normalization to obtain a clear scattering curve. The fractal dimension is calculated by analyzing the SAXS curve, especially its behavior in the low-angle region. This method has high requirements on the shape and size of the experimental samples, and detects structures at the nanometer to micrometer scale. For smaller or larger structural features, other techniques such as TEM or SEM may be needed to supplement them. Summary of the invention

[0004] In view of the above-mentioned shortcomings of the current method for obtaining pore fractal dimension, the present invention provides a method for calculating the shale pore fractal dimension.

[0005] The method for calculating the fractal dimension of shale pores provided by the present invention comprises the following steps:

[0006] S1. Select several parallel samples from the same core and conduct carbon dioxide adsorption experiment, nitrogen adsorption experiment and high-pressure mercury injection experiment respectively.

[0007] S2. Select the experimental data with pore size between 0-2nm in the carbon dioxide adsorption experiment, take several secondary pore size segments within the pore size segment, calculate the average pore size of each secondary pore size segment, and use the fractal theory of microporous media to calculate the fractal dimension of the pores in each secondary pore size segment.

[0008] S3. Select the experimental data with pore size between 2-50 μm in the nitrogen adsorption experiment, take several secondary pore size segments in the pore size segment, calculate the average pore size of each secondary pore size segment, and use the FHH fractal model to calculate the fractal dimension of the pores in each secondary pore size segment.

[0009] S4. Select the experimental data of pores larger than 50 nm in the high-pressure mercury injection experiment, take several secondary pore segments within the pore segment, calculate the average pore size of each secondary pore segment, and use the Menger sponge model to calculate the fractal dimension of the pores in each secondary pore segment.

[0010] S5. Draw a fractal dimension-average aperture curve graph with all the average apertures obtained in steps S2, S3, and S4 as the horizontal coordinates and the fractal dimension as the vertical coordinate. According to the different slope characteristics of the curve, different function expressions are selected, and the parameters in the function expressions are obtained to obtain the functional relationship between the average aperture and the fractal dimension of the corresponding aperture segment by fitting.

[0011] According to the different characteristics of the slope of the curve, different function expressions are selected. The specific methods are as follows:

[0012] (1) Type 1: When the slope of the curve shows an overall trend of increasing from small to large, the function expression is as follows:

[0013] y=px+q

[0014] Where y represents the fractal dimension, x represents the average pore size, nm; p and q are the coefficients to be solved.

[0015] The coefficients p and q are solved as follows:

[0016] Step (1): Find the average of the two variables x and y and

[0017] Step (2): Calculate the covariance of the variables:

[0018]

[0019]

[0020] In the formula, yi represents each fractal dimension, x i represents each average pore size;

[0021] Step (3): Calculate the coefficients p and q:

[0022]

[0023]

[0024] Substitute the obtained coefficients p and q into the formula y=px+q to obtain the specific functional relationship between y and x.

[0025] (2) The second type: When the slope of the curve shows a trend of decreasing as a whole, the function expression is as follows:

[0026] y=ux v

[0027] Where y represents the fractal dimension, x represents the average pore size, nm; u and v are the coefficients to be solved.

[0028] The coefficients u and v are solved as follows:

[0029] Step (1): For the formula y=ux v Taking the logarithm of both sides converts to:

[0030] lny=vlnx+lnu

[0031] Let lny=α,lnx=β,lnu=γ, then it is transformed into:

[0032] α=vβ+γ

[0033] Step (2): Calculate the average value of the two variables α and β and

[0034] Step (3): Calculate the covariance of the variables:

[0035]

[0036]

[0037] In the formula, α i and β i Each fractal dimension y is i , each average pore size x i Calculated;

[0038] Step (4): Calculate the coefficients v and γ:

[0039]

[0040]

[0041] Step (5): Calculate u based on the coefficient γ.

[0042] Substitute the coefficients u and v obtained into the formula y = ux v In the equation, we can get the specific functional relationship between y and x.

[0043] (3) The third type: When the slope of the curve belongs to other trends other than the above two trends (1) and (2), the function expression is as follows:

[0044] y=alnx+b

[0045] Where y represents the fractal dimension, x represents the average pore size, nm; a and b are the coefficients to be solved.

[0046] The coefficients a and b are solved as follows:

[0047] Step (1): In the formula y=alnx+b, let lnx=t, then it is converted to: y=at+b,

[0048] Step (2): Find the average value of the two variables t and y and

[0049]

[0050]

[0051] Step (3): Calculate the covariance of the variables:

[0052]

[0053]

[0054] Where, t i Each average pore size x i Calculated, y i represents each fractal dimension;

[0055] Step (4) Calculate coefficients a and b:

[0056]

[0057]

[0058] Substitute the obtained coefficients a and b into the formula y=alnx+b to obtain the specific functional relationship between y and x.

[0059] S6. According to the functional relationship obtained by fitting in step S5, the fractal dimension of any aperture segment is obtained, and the fractal dimension of the full aperture segment of the shale is characterized.

[0060] Compared with the prior art, the present invention is beneficial in that:

[0061] The present invention can obtain the functional relationship between the fractal dimension and the pore size, and can not only continuously calculate the fractal dimension of the entire pore size range, but also calculate the fractal dimension of any pore size range, thereby improving the resolution of the pore fractal dimension representation.

[0062] Other advantages, objectives and features of the present invention will be embodied in part through the following description, and in part will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a fractal dimension-average pore size curve for different pore size segments of Example 1.

[0064] Figure 2 This is a fractal dimension-average pore size curve for different pore size segments of Example 2.

[0065] Figure 3 This is a fractal dimension-average pore size curve for different pore size segments of Example 3. DETAILED DESCRIPTION

[0066] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0067] Example 1

[0068] Taking a target layer in Block X of the S Basin as an example, the calculation method of the shale pore fractal dimension of the present invention is described in detail. The specific method steps are as follows:

[0069] S1. Obtaining experimental data. Each target core sample is divided into three equal parts as parallel samples, and the carbon dioxide adsorption experiment, nitrogen adsorption experiment and high-pressure mercury injection experiment are carried out respectively.

[0070] S2. Select the experimental data of the micropore segment with a pore size between 0-2nm in the carbon dioxide adsorption experiment, select four secondary pore size segments of 0-0.5, 0.6-1, 1.2-1.6, and 1.7-2nm in this pore size segment, calculate the average pore size of each secondary pore size segment, and use the fractal theory of microporous media to calculate the fractal dimension of the pores in each secondary pore size segment.

[0071] S3. Select the experimental data of the mesopore segment with a pore size between 2-50 nm in the nitrogen adsorption experiment, select six secondary pore size segments of 2.5-3, 4-10, 12-21, 24-35, 36-43, and 45-50 nm in this pore size segment, calculate the average pore size of each secondary pore size segment, and use the fractal theory of microporous media to calculate the fractal dimension of the pores in each secondary pore size segment.

[0072] S4. Select the experimental data of the macropore segment with a pore size greater than 50 nm in the high-pressure mercury injection experiment, select five secondary pore size segments of 50-100, 110-500, 650-1000, 1000-2000, and 2000-5000 in the pore size segment, calculate the average pore size of each secondary pore size segment, and use the microporous medium fractal theory to calculate the fractal dimension of the pores in each secondary pore size segment. The calculation results are shown in Table 1.

[0073] Table 1. Experimental data of average pore size and fractal dimension of different pore size segments

[0074]

[0075] S5. Collect and organize the above experimental data, draw a fractal dimension-average pore size curve in a plane rectangular coordinate system, with the average pore size as the horizontal coordinate x and the fractal dimension as the vertical coordinate y, and observe the shape of the curve. Figure 1 As shown, the overall slope of the curve does not have an obvious uniform trend of changing from small to large or from large to small, that is, the slope of the curve belongs to the third type described in the present invention. At this time, assume:

[0076] y=alnx+b(Formula 1)

[0077] Let lnx = t, then equation 1 is transformed into:

[0078] y=at+b(Formula 2)

[0079] Solving a and b in equation 2 includes the following steps:

[0080] ① Find the average value of two variables t and y:

[0081]

[0082]

[0083] ② Obtain the covariance of the variables:

[0084]

[0085]

[0086] ③ Calculate coefficients a and b:

[0087]

[0088]

[0089] ④ Substitute the coefficients a, b and t=lnx back into equation 1 to obtain the specific functional relationship between y and x:

[0090] y=-0.08031nx+2.834.

[0091] Example 2

[0092] Taking a target layer in the Y block of the S basin as an example, the calculation method of the shale pore fractal dimension of the present invention is described in detail. Steps S1-S4 are the same as in Example 1. The selection method of the secondary aperture segment of each aperture segment and the calculation results in step S4 are shown in Table 2.

[0093] Table 2. Experimental data of average pore size and fractal dimension of different pore size segments

[0094]

[0095] S5. Collect and organize the above experimental data, draw a fractal dimension-average pore size curve in a plane rectangular coordinate system, with the average pore size as the horizontal coordinate x and the fractal dimension as the vertical coordinate y, and observe the shape of the curve. Figure 2 As shown, the slope of the curve shows a trend of changing from small to large as a whole, that is, the slope of the curve belongs to the first type described in the present invention. At this time, it is assumed that:

[0096] y=px+q (Formula 3)

[0097] Solving for p and q in equation 3 includes the following steps:

[0098] ① Find the average value of two variables x and y:

[0099]

[0100]

[0101] ② Obtain the covariance of the variables:

[0102]

[0103]

[0104] ③ Calculate the coefficients p and q:

[0105]

[0106]

[0107] ④ Substitute the values ​​of coefficients p and q into equation 3 to obtain the specific functional relationship between y and x:

[0108] y=-0.00003x+2.8838.

[0109] Example 3

[0110] Taking a target layer in a certain basin block M as an example, the calculation method of the shale pore fractal dimension of the present invention is described in detail. Steps S1-S4 are the same as in Example 1. The selection method of the graded aperture segments of each aperture segment in step S4 and the calculation results are shown in Table 3.

[0111] Table 3. Experimental data of average pore size and fractal dimension of different pore size segments

[0112]

[0113]

[0114] S5. Collect and organize the above experimental data, draw a fractal dimension-average pore size curve in a plane rectangular coordinate system, with the average pore size as the horizontal coordinate x and the fractal dimension as the vertical coordinate y, and observe the shape of the curve. Figure 3 As shown, the slope of the curve shows a trend of decreasing from large to small as a whole, that is, the slope of the curve belongs to the second type described in the present invention. At this time, it is assumed that:

[0115] y=ux v (Formula 4)

[0116] Taking the logarithm of both sides converts to:

[0117] lny=vlnx+lnu (Formula 5)

[0118] Let lny=α,lnx=β,lnu=γ, then equation 5 is transformed into:

[0119] α=vβ+γ(Formula 6)

[0120] Solving u and γ in equation 6 includes the following steps:

[0121] ① Find the average value of the two variables α and β:

[0122]

[0123]

[0124] ② Obtain the covariance of the variables:

[0125]

[0126]

[0127] ③ Calculate the coefficients v and γ:

[0128]

[0129]

[0130] ④ Calculate the coefficient u based on the coefficient γ, substitute the values ​​of the coefficients v and u back into formula 4, and get the specific functional relationship between y and x:

[0131] y=22.781x -0.009 .

[0132] S6. According to the functional relationship obtained by fitting in step S5, the average pore size of a shale full-pore segment is substituted to obtain the fractal dimension of the full-pore segment.

[0133] In summary, by obtaining the functional relationship between the fractal dimension and the pore size, the method of the present invention can not only continuously calculate the fractal dimension of the entire pore size range, but also calculate the fractal dimension within any pore size range, thereby improving the resolution of the pore fractal dimension characterization.

[0134] The above description is only a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of the technical solution of the present invention.

Claims

1. A method for calculating the fractal dimension of shale pores, characterized in that: Here are the steps: S1. Select several parallel samples from the same core and conduct carbon dioxide adsorption experiment, nitrogen adsorption experiment and high-pressure mercury injection experiment respectively; S2. Select the experimental data of the pore size segment with a pore size between 0-2 nm in the carbon dioxide adsorption experiment, select a number of secondary pore size segments in the pore size segment, calculate the average pore size of each secondary pore size segment, and calculate the fractal dimension of the pores of each secondary pore size segment using the microporous medium fractal theory; S3, selecting the experimental data of the aperture segment with an aperture of 2-50 μm in the nitrogen adsorption experiment, taking a number of secondary aperture segments in the aperture segment, calculating the average aperture of each secondary aperture segment, and calculating the fractal dimension of the pores of each secondary aperture segment using the FHH fractal model; S4, selecting the experimental data of the pore size segment with a pore size greater than 50 nm in the high-pressure mercury injection experiment, taking a number of secondary pore size segments in the pore size segment, calculating the average pore size of each secondary pore size segment, and using the Menger sponge model to calculate the fractal dimension of the pores of each secondary pore size segment; S5, using all the average pore sizes obtained in steps S2, S3, and S4 as the abscissa and the fractal dimension as the ordinate to draw a fractal dimension-average pore size curve, selecting different function expressions according to different slope characteristics of the curve, obtaining parameters in the function expressions, and fitting to obtain a functional relationship between the average pore size and the fractal dimension of the corresponding pore size segment; Select different function expressions according to the different slope characteristics of the curve. The specific methods are as follows: (1) When the slope of the curve shows a trend of increasing from small to large, the function expression is as follows: y=px+q In the formula, y represents the fractal dimension, x represents the average pore size, nm; p and q are the coefficients to be solved; The coefficients p and q are solved as follows: Step (1): Find the average of the two variables x and y and Step (2): Calculate the covariance of the variables: In the formula, y i represents each fractal dimension, x i represents each average pore size; Step (3): Calculate the coefficients p and q: (2) When the slope of the curve shows a trend of decreasing as a whole, the function expression is selected as follows: y=ux v In the formula, y represents the fractal dimension, x represents the average pore size, nm; u and v are the coefficients to be solved; The coefficients u and v are solved as follows: Step (1): For the formula y=ux v Taking the logarithm of both sides converts to: lny=vlnx+lnu Let lny=α,lnx=β,lnu=γ, then it is transformed into: α=vβ+γ Step (2): Calculate the average value of the two variables α and β and Step (3): Calculate the covariance of the variables: In the formula, α i and β i Each fractal dimension y is i , each average pore size x i Calculated; Step (4): Calculate the coefficients v and γ: Step (5): Calculate u based on the coefficient γ; (3) When the slope of the curve belongs to other trends other than the above two trends (1) and (2), the selection function expression is as follows: y=alnx+b Where y represents the fractal dimension, x represents the average pore size, nm; a and b are the coefficients to be solved. The coefficients a and b are solved as follows: Step (1): In the formula y=alnx+b, let lnx=t, then it is transformed into: y=at+b; Step (2): Find the average value of the two variables t and y and Step (3): Calculate the covariance of the variables: Where, t i Each average pore size x i Calculated, y i represents each fractal dimension; Step (4) Calculate coefficients a and b: S6. According to the functional relationship obtained by fitting in step S5, the fractal dimension of any aperture segment is obtained, and the fractal dimension of the full aperture segment of the shale is characterized.

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