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This paper presents an immersed phase field model designed to predict the fracture-induced 6 flow due to brittle fracture in vuggy porous media. Due to the multiscale nature of pores in vuggy porous 7 material, crack growth may connect previously isolated pores which lead to flow conduits. This mecha8 nism has important implications for many applications such as disposal of carbon dioxide and radioactive 9 materials, hydraulic fracture and mining. To understand the detailed microporomechanics that causes the 10 fracture-induced flow, we introduce a new phase field fracture framework where the phase field is not only 11 used as an indicator function for damage of the solid skeleton, but also as an indicator of the pore space. 12 By coupling the Stokes equation that governs the fluid transport in the voids, cavities and cracks, and the 13 Darcy’s flow in the deformable porous media, our proposed model enables us to capture the fluid-solid 14 interaction of the pore fluid and solid constituents during the crack growth. Numerical experiments are 15 conducted to analyze how presence of cavities affects the accuracy of the predictions based on homoge16 nized effective medium during crack growth. 17

An immersed phase field fracture model for microporomechanics with Darcy–Stokes flow