| CPC G01N 23/20 (2013.01) [G01N 33/24 (2013.01); G01N 2223/616 (2013.01)] | 6 Claims |
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1. A calculation method for fractal dimensions of shale pores, the calculation method comprising:
S1: obtaining multiple shale samples from a target stratum of a study area, obtaining parameter values of geological parameters of each of the multiple shale samples, and dividing the multiple shale samples into target shale samples and experimental shale samples, wherein the geological parameters comprise a mineral composition, a total organic carbon (TOC) content, a porosity, a permeability, and an average pore size;
S2: performing principal component analysis (PCA) on the parameter values of the geological parameters of the experimental shale samples to obtain principal components representing a variation of the geological parameters of the experimental shale samples, and calculating fractal dimensions of the experimental shale samples by using an existing fractal dimension calculation method;
wherein the performing PCA on the parameter values of the geological parameters of the experimental shale samples to obtain principal components representing a variation of the parameter values of the geological parameters of the experimental shale samples comprises:
S21: standardizing parameter values of the geological parameters of the experimental shale samples using formulas (1)-(3) as follows to obtain standardized parameter values of the geological parameters of the experimental shale samples:
 where Zxij represents a standardized parameter value of a j-th geological parameter of an i-th sample of the experimental shale samples; xij represents a parameter value of the j-th geological parameter of the i-th sample of the experimental shale samples; xj represents a sample mean of the j-th geological parameter of the experimental shale samples; Sj represents a sample standard deviation of the j-th geological parameter of the experimental shale samples; n represents a number of the experimental shale samples; and m represents a number of the geological parameters of the experimental shale samples;
S22: establishing a correlation coefficient matrix between the geological parameters of the experimental shale samples based on the standardized parameter values of the geological parameters of the experimental shale samples, wherein the correlation coefficient matrix is expressed by formulas (4)-(8) as follows:
 where R represents the correlation coefficient matrix; rAB represents a correlation coefficient between a geological parameter A and a geological parameter B; Cov(A, B) represents a covariance between the geological parameter A and the geological parameter B; σA represents a standard deviation of the geological parameter A, σB represents a standard deviation of the geological parameter B, Ai and Bi represent values of the i-th sample of the geological parameter A and the geological parameter B, respectively; Ā represents a sample mean of the geological parameter A of the experimental shale samples; and B represents a sample mean of the geological parameter B of the experimental shale samples;
S23: calculating eigenvalues, contribution rates, and cumulative contribution rates of the correlation coefficient matrix;
where when the eigenvalues of the correlation coefficient matrix are calculated, a characteristic equation (9) of the correlation coefficient matrix is as follows:
|R−λE|=0 (9)
where λ represents one of the eigenvalues of the correlation coefficient matrix, and E represents an identity matrix; and
where each of the contribution rates is calculated using a formula (10) as follows:
 where D represents the contribution rate, and λk represents a k-th eigenvalue of the eigenvalues of the correlation coefficient matrix;
S24: determining a number of the principal components representing the variation of the parameters values of the geological parameters of the experimental shale samples and eigenvalues of the principal components based on the cumulative contribution rates;
S25: calculating eigenvectors of the correlation coefficient matrix based on the eigenvalues of the principal components determined in step S24; and
S26: obtaining a mathematical expression (11) of the principal components based on the eigenvectors, wherein the mathematical expression (11) is expressed as follows:
 where Fik represents a k-th principal component of the i-th sample of the experimental shale samples; and ukj represents a j-th element in a k-th eigenvector of the eigenvectors;
S3: performing regression analysis using the principal components as independent variables and the fractal dimensions of the experimental shale samples as dependent variables to obtain a quantitative calculation model for fractal dimensions based on geological parameters;
S4: calculating fractal dimensions of the target shale samples according to the parameter values of the geological parameters of the target shale samples and the quantitative calculation model for fractal dimension based on geological parameters; and
S5: evaluating, based on the fractal dimensions of the target shale samples, a strength of heterogeneity in pore structure of the target stratum of the study area; determining whether the strength of heterogeneity is smaller than a target strength of heterogeneity; and in response to the strength of heterogeneity being smaller than the target strength of heterogeneity, exploring shale oil and gas on the target stratum of the study area.
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