Abstract
This study presents a phase field model for brittle fracture in fluid-infiltrating vuggy porous media. While the state-of-the-art in hydraulic phase field fracture considers Darcian fracture flow with enhanced permeability along the crack, in this study, the phase field not only acts as a damage variable that provides diffuse representation of cracks or cavities, but also acts as an indicator function that separates the domain into two regions where fluid flows are governed by Stokes and Darcy equations, respectively. Since the phase field and its gradient can be respectively regarded as smooth approximations of the Heaviside function and Dirac delta function, our new approach is capable of imposing interfacial transmissibility conditions without explicit interface parametrizations. In addition, the interaction between solid and fluid constituents is modeled by adopting the concept of mixture theory, where the fluid velocities in Stokes and Darcy regions are considered as relative measures compared to the solid motion. This model is particularly attractive for coupled flow analysis in geological materials with complex microstructures undergoing brittle fracture often encountered in energy geotechnics problems, since it completely eliminates the needs to generate specific enrichment function, integration scheme, or meshing algorithm tailored for complex geological features.
Highlights
Defects, such as cracks, joints, vuggy pores and cavities and impurities are important for the hydro-mechanical coupling encountered in porous media in energy geotechnics problems like enhanced oil recovery or the development of enhanced geothermal energy reservoirs
It is essential to employ a proper representation for the defects either explicitly or implicitly. While both approaches have achieved a level of success in the past decades for solid mechanics problems, the modeling effort of the hydraulic responses of defects are often limited to cubic law models that relates hydraulic aperture to hydraulic conductivity [18, 21]
By leveraging the phase field as an indicator function for the location of cracks and other defects such as cavities and large or geometrically complicated voids that does not fit for computational homogenization, we introduce a phase field framework that may efficiently couple the Stokes flow in the defect regions that interact with the pore fluid infiltrating in the intact porous matrix while the Stokes and Darcy regions are evolving due to the crack growth
Summary
Defects, such as cracks, joints, vuggy pores and cavities and impurities are important for the hydro-mechanical coupling encountered in porous media in energy geotechnics problems like enhanced oil recovery or the development of enhanced geothermal energy reservoirs. One possible modeling choice is to not explicitly model each defect and imperfects but instead incorporate the influences of these defects in the constitutive laws of an imaginary effective medium at a scale where a representative elementary volume exists In this case, defects may be treated as a different pore system that may interact with the prime pore space through fluid mass exchanges, as shown in the multi-porosity and multipermeability models in the literature [6, 11, 12, 33]. Numerical examples are provided to showcase the potential applications of this proposed models
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