Reconstruction of digital rock considering micro-fracture based on multi-point statistics

Abstract

The macroscopic transport properties of shale are determined by microscopic pore structure, which displays typical multi- scale characteristic with pore size ranging from nanometers to microns and well development of natural micro cracks. The physical experimental method is limited by the contradiction between the selected resolution and imaging sample size. Therefore it is significant to obtain the representative elementary volume to simultaneously incorporate nano-micro pore information and micro-fracture characteristics. To deal with this, numerical reconstruction algorithms are commonly applied to reconstruct pore structure based on easily obtained 2D images and in recent years are applied to reconstruct multi-scale shale porous media. The reconstruction algorithms mainly include the truncated Gaussian random field, simulated annealing, Markov chain Monte Carlo sequential indicator simulation, multiple-point statistics, phase-recovery algorithm and process-based method. In this study, a pattern based on multipoint statistics (MPS) method is proposed to account for multi-scale pore structure characteristics in shale. MPS comes from a statistical method to reconstruct large-scale patterns using pixel-based representations and can characterize the correlation between multiple points compared with traditional two-point statistics. First, different pore types and fractures are identified based on the gray scale shale image. Second, multi-scale shale images are constructed by containing formation of cracks with different properties as well as randomly pore-fracture distribution pattern and then treated as the basic training images. Next, the search tree is used to store and classify occurrences of all pore-fracture distribution patterns that are obtained after the multiple data template scanning the training image. Data template capturing pattern library and conditional probability functions are both stored in the search tree to reflect the long-range connectivity. Accordingly, a random path is defined to visit all unsampled voxels. For every new voxel, the data event is obtained by using the previous template and the conditional probability distribution function (CPDF) of this voxel is established from the search tree. The state value is taken stochastically and put into conditional events for the future voxel simulation. The following voxels are simulated on the random path until a new 2D image is produced. Finally, the type-method interpolation approach is employed to construct the potential simulation space. In order to evaluate the consequence of reconstruction, the constructed images are compared with the training image in terms of autocorrelation function, pore morphology, topology structure and permeability value. Different fracture distribution patterns including orthogonal fractures, dipping fractures and fractal rough fractures are generated. The structure and transport properties of generated pore-fracture models are compared with those of the training images to test the robustness of the proposed reconstruction algorithm. The results show that the constructed images display similar characteristics as training images and their property values are identical with each other under the conditions of adding different types of cracks, which verifies the rationality of proposed method.