<p>A finite volume method (FVM)-based phase-field framework is proposed to simulate hydraulic fracturing in brittle poroelastic media. The porous medium is modeled using classical Biot’s poroelastic theory, while fracture behavior is described using the phase-field method. The governing multi-field coupled equations are discretized with an implicit cell-centered FVM and solved using an iterative staggered scheme. Phase-field value-based linear indicator functions are adopted to facilitate a smooth transition between fracture and reservoir regions. To improve computational efficiency, adaptive mesh refinement (AMR) is employed, leveraging the cell-centered FVM’s ability to handle hanging nodes naturally. The framework is first validated through three benchmark examples with analytical and numerical solutions from the literature: Terzaghi’s 1D consolidation, pressure distribution in a single crack, and a 2D notched specimen subjected to increasing internal pressure. The accuracy and efficiency of the AMR technique are further demonstrated through the interaction between two perpendicular fractures, considering various crack spacings and injection configurations. Finally, the framework is applied to simulate the complex process of crack propagation and coalescence within a fracture network in saturated porous media. This framework proves to be an effective tool for simulating hydraulic fracturing, offering potential for optimizing designs in gas and oil extraction practices.</p>

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Phase-field modeling of hydraulic fracturing in porous media using the finite volume method with adaptive mesh refinement

  • X. L. Yang,
  • N. Guo,
  • Z. X. Yang,
  • T. Rabczuk

摘要

A finite volume method (FVM)-based phase-field framework is proposed to simulate hydraulic fracturing in brittle poroelastic media. The porous medium is modeled using classical Biot’s poroelastic theory, while fracture behavior is described using the phase-field method. The governing multi-field coupled equations are discretized with an implicit cell-centered FVM and solved using an iterative staggered scheme. Phase-field value-based linear indicator functions are adopted to facilitate a smooth transition between fracture and reservoir regions. To improve computational efficiency, adaptive mesh refinement (AMR) is employed, leveraging the cell-centered FVM’s ability to handle hanging nodes naturally. The framework is first validated through three benchmark examples with analytical and numerical solutions from the literature: Terzaghi’s 1D consolidation, pressure distribution in a single crack, and a 2D notched specimen subjected to increasing internal pressure. The accuracy and efficiency of the AMR technique are further demonstrated through the interaction between two perpendicular fractures, considering various crack spacings and injection configurations. Finally, the framework is applied to simulate the complex process of crack propagation and coalescence within a fracture network in saturated porous media. This framework proves to be an effective tool for simulating hydraulic fracturing, offering potential for optimizing designs in gas and oil extraction practices.