Hydromechanical behavior analysis of fractured vuggy carbonate rocks based on homogenization theory

Fractured vuggy carbonate rocks are important for underground water and geo-energy reservoirs due to their significant contribution on water and hydrocarbon reserves and production. A vug is a small cavity in a carbonate rock, which is relatively larger than the intergranular pore space. The presence of multiscale fractures and vugs makes the hydromechanical behavior of rocks different from that of most geological materials. The objective of this work is to develop an upscaling method to analyze the hydromechanical behavior of fractured vuggy carbonate rocks based on homogenization theory. To this end, at first a novel conceptual model named discrete fracture-vug network (DFVN) model was proposed to describe the hydromechanical behavior on the fine scale. The matrix and fractures are poroelastic domains in which Biot equations are applied. The vugs are free fluid domains governed by Stokes equations. Two domains are coupled with extended Beavers–Joseph–Saffman interface conditions. Then, an upscaled hydromechanical model was developed via two-scale asymptotic homogenization. The model consistent with classical Biot equations, but the model coefficients possess explicit formulations which can be determined by three periodicity cell problems. Subsequently, efficient numerical solutions of cell problems are provided using finite element methods. Herein, the discrete fractures are modeled as lower-dimensional interfaces between matrix elements. The proposed model and method are verified through several numerical examples and experimental data. The results show that the storage coefficient and Biot coefficient increase with the presence of fractures and vugs. The equivalent elastic stiffness of a fractured vuggy rock is majorly affected by the vugs' volume ratio. The connectivity of DFVN has an important impact on the equivalent permeability.