This paper presents the formulation of a robust integrated framework for the coupled multiphysics and multiple fracture growth analysis in porous media. The finite element-based thermo-hydro-mechanical method for fracture growth with frictional contact (THMf-g) simultaneously solves monolithically coupled equations, incorporating contact and frictional constraints from fracture sliding. It also implements an adaptive process to update fields and geometries during fracture growth, effectively modeling emerging new surfaces. The thermo-hydro-mechanical fields are derived from fundamental principles of mass, momentum, and energy conservation and discretized numerically using the finite element method. Fractures are represented as sub-dimensional surfaces embedded within the volume of the porous medium. The growth of multiple fracture is modeled based on stress intensity factors at fracture tips, with fracture aperture and permeability emerging as dynamic properties of the system. The main novelty of this work lies in extending the implicitly solved monolithic coupling to include frictional and growth modeling for multiple non-planar fractures of emerging geometry in three dimensions. This includes the direct incorporation of cubic terms in the fracture flow equations and convection terms in the heat transfer equations, adopting an incremental method to solve these coupled, nonlinear equations. To ensure energy conservation, the heat equations are resolved using an implicit scheme, establishing a velocity dependency on pressure fields and introducing quadratic terms into the heat equation. Furthermore, the heat transfer equation has been revised to account for the work done on the fluid, enhancing the accuracy of thermal modeling. A contact mechanics leader–follower strategy tracks a conformal mesh split at each fracture, accounting explicitly for permeability changes during deformation and growth, effectively reducing computational complexity and cost. The iterative process for applying these constraints and the solution of the coupled THMf-g with friction and growth is described. The method does not require calibrated material properties or artificial length scale parameters, and relies on laboratory-measured properties with direct physical interpretation. A detailed algorithm is presented, including the updating of apertures and handling of new surfaces during the simulation, accounting for the variability of fracture permeability and its interplay with contact and friction during the non-linear solution. Several validating numerical experiments are benchmarked against analytical solutions, demonstrating the accuracy and reliability of the proposed framework in capturing complex fracture behavior and multiphysics interactions in porous media.

中文翻译：

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一个强大的三维有限元框架，用于对多孔介质中摩擦接触的裂缝增长进行整体耦合热-水-力学分析


本文提出了一个稳健的集成框架，用于多孔介质中的耦合多物理场和多裂缝增长分析。基于有限元的热-水-机械方法用于摩擦接触的裂缝增长 （THMf-g） 同时求解整体耦合方程，并结合了裂缝滑动的接触和摩擦约束。它还实现了一个自适应过程，以在裂缝生长过程中更新场和几何结构，从而有效地对新出现的新表面进行建模。热-流体-机械场源自质量、动量和能量守恒的基本原理，并使用有限元方法进行数值离散化。裂缝表示为嵌入多孔介质体积内的亚维表面。多条裂缝的增长是根据裂缝尖端的应力强度因子建模的，裂缝孔径和渗透率成为系统的动态属性。这项工作的主要新颖之处在于扩展了隐式求解的整体耦合，包括三维新兴几何的多个非平面裂缝的摩擦和增长建模。这包括在裂缝流方程中直接加入三次项，在传热方程中直接加入对流项，采用增量方法来求解这些耦合的非线性方程。为了确保能量守恒，使用隐式方案求解热方程，建立对压力场的速度依赖性，并在热方程中引入二次项。此外，还修改了传热方程，以考虑对流体所做的工作，从而提高了热建模的准确性。 接触力学导从策略跟踪每个裂缝处的共形网格分割，明确考虑变形和生长过程中的磁导率变化，从而有效降低计算复杂性和成本。描述了应用这些约束的迭代过程以及 THMf-g 与摩擦和增长耦合的解。该方法不需要校准的材料特性或人工长度尺度参数，而是依赖于实验室测量的特性和直接的物理解释。提出了一个详细的算法，包括在仿真过程中更新孔径和处理新表面，考虑裂缝渗透率的变化及其在非线性求解过程中与接触和摩擦的相互作用。将几个验证数值实验与解析解进行基准测试，证明了所提出的框架在捕获多孔介质中复杂裂隙行为和多物理场相互作用方面的准确性和可靠性。