Research On Markov Monte Carlo Anisotropic Digital Core Reconstruction Method And Electrical Properties Calculation

The electrical parameters of rock are important indicators in the field of petrophysics,which are of great significance for lithology and gas bearing judgment.The digital core technology is widely used in the calculation of core electrical parameters due to limited laboratory samples.The traditional Markov Chain-Monte Carlo(MCMC)method uses the Markov property to obtain the known information about the image and obtain the conditional probability according to the statistical law.The state value of unknown pixels is predicted by combining with the Monte Carlo method.However,the reconstruction accuracy of core images with severe anisotropy cannot meet the demand.To solve the above problems,this paper analyzes the results of image reconstruction according to the characteristics of row and row distribution,the direction of the reconstruction path,and different neighborhood systems.Considering the role of the degree of anisotropy in the selection of neighborhood and path,a reconstruction method suitable for different degrees of anisotropy is proposed.The main work is as follows:After comparing the influences of different reconstruction directions and different neighborhood systems on the reconstruction effect,a reconstruction algorithm combining MCMC and potential function was designed and implemented.The reconstruction effect of a two-dimensional rock image was compared and analyzed by means of various function and principal component analysis method.It is proved that the reconstruction algorithm proposed in this paper has obvious advantages in reconstruction accuracy for rock images with different anisotropy degree characteristics.The linear path function is used to analyze the column and row distribution characteristics of rock images,and the parameters representing the column and row distribution differences are constructed,and the column and row distribution differences are further reflected in the reconstruction algorithm by the potential function.Experiments show that the algorithm has good applicability in core image reconstruction with different degrees of column and row distribution.With the core 3D scanning image as the initial condition,the 3D core reconstruction algorithm combined with the designed MCMC and potential function is used to reconstruct the core,and the digital core with porosity and variation function curve fitting the original model is constructed.The 3D-FDM(Finite Difference Method,FDM)was used to calculate the equivalent dielectric constant.The experimental results show that the reconstructed models with different sizes and different rock samples are in good agreement with the equivalent dielectric constant values of the original core model,which verifies the effectiveness of the three-dimensional core reconstruction algorithm designed in this paper.The modeling algorithm of potential function combined with MCMC proposed in this paper is suitable for rock images with different anisotropy degree characteristics and has high engineering practical value.