Research on the equivalence between digital core and rock physics models

Abstract

In this paper, we calculate the elastic modulus of 3D digital cores using the finite element method, systematically study the equivalence between the digital core model and various rock physics models, and carefully analyze the conditions of the equivalence relationships. The influences of the pore aspect ratio and consolidation coefficient on the equivalence relationships are also further refined. Theoretical analysis indicates that the finite element simulation based on the digital core is equivalent to the boundary theory and Gassmann model. For pure sandstones, effective medium theory models (SCA and DEM) and the digital core models are equivalent in cases when the pore aspect ratio is within a certain range, and dry frame models (Nur and Pride model) and the digital core model are equivalent in cases when the consolidation coefficient is a specific value. According to the equivalence relationships, the comparison of the elastic modulus results of the effective medium theory and digital rock physics is an effective approach for predicting the pore aspect ratio. Furthermore, the traditional digital core models with two components (pores and matrix) are extended to multiple minerals to more precisely characterize the features and mineral compositions of rocks in underground reservoirs. This paper studies the effects of shale content on the elastic modulus in shaly sandstones. When structural shale is present in the sandstone, the elastic modulus of the digital cores are in a reasonable agreement with the DEM model. However, when dispersed shale is present in the sandstone, the Hill model cannot describe the changes in the stiffness of the pore space precisely. Digital rock physics describes the rock features such as pore aspect ratio, consolidation coefficient and rock stiffness. Therefore, digital core technology can, to some extent, replace the theoretical rock physics models because the results are more accurate than those of the theoretical models.