Summary The Reservoir GeoMechanics Simulator (RGMS or RGM simulator), a geomechanics simulator based on the finite element method (FEM) and parallelized using the Message Passing Interface (MPI), is developed in this work to model the stresses and deformations in subsurface systems. RGMS can be used standalone or coupled with flow and transport models. pTOUGH+ HYDRATE (pT+H) V1.5, a parallel MPI-based version of the serial TOUGH+HYDRATE (T+H) V1.5 code that describes mass and heat flow in hydrate-bearing porous media, is also developed. Using the fixed-stress split iterative scheme, RGMS is coupled with the pT+H V1.5 codes to investigate the geomechanical responses associated with gas production from hydrate accumulations. In the first paper of this series, we discuss the governing equations underlying physics and their mathematical representation in the modeling of the geomechanics, methane hydrate, and coupled problems as well as the numerical methods and the parallelization processes (involving a domain decomposition method based on the MPI approach) used for the parallel simulators. Two 2D problems (in Cartesian and radial-cylindrical coordinates) and a 3D Cartesian coordinate problem are created to validate the FEM and the parallelization method in RGMS. The displacements and the maximum principal effective stresses obtained from the RGMS solution of these three problems are compared to those from the commercial software Ansys Mechanical and are shown to practically coincide. The parallelization of pT+H V1.5 is validated by comparing its results to those from the serial T+H V1.5 code in a study that involved (a) fluid production from a large-scale 2D cylindrical system describing a real-life oceanic hydrate deposit and (b) a simplified geomechanical model based on hydrate-dependent pore compressibility. The coupling method is validated by comparing the numerical results to the analytical solutions of the Terzaghi and the McNamee-Gibson problems. The parallelization validation of the coupled simulator is achieved by comparing the results obtained for different numbers of processes in the solution of the problems used for the pT+H V1.5 parallelization validation with the full geomechanical model. The results clearly demonstrate the validity and reliability of the parallel codes (a) RGMS, (b) pT+H V1.5, and the (c) coupled pT+H V1.5 and RGM simulators, which can be used to solve the large-scale physics of complex problems.

中文翻译：

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迭代耦合流体流动和地质力学代码的消息传递接口 (MPI) 并行化，用于模拟含水合物地质介质中的系统行为。第 1 部分：方法和验证

总结 油藏地质力学模拟器（RGMS 或 RGM 模拟器）是一种基于有限元法 (FEM) 并使用消息传递接口 (MPI) 并行化的地质力学模拟器，用于模拟地下系统中的应力和变形。RGMS 可以单独使用，也可以与流量和传输模型结合使用。pTOUGH+ HYDRATE (pT+H) V1.5 是串行 TOUGH+HYDRATE (T+H) V1.5 代码的并行基于 MPI 的版本，用于描述含水合物多孔介质中的质量和热流。使用固定应力拆分迭代方案，RGMS 与 pT+H V1.5 代码相结合，以研究与水合物聚集体产气相关的地质力学响应。在本系列的第一篇论文中，我们讨论了物理基础的控制方程及其在地质力学、甲烷水合物和耦合问题建模中的数学表示，以及用于并行计算的数值方法和并行化过程（涉及基于 MPI 方法的域分解方法）模拟器。创建了两个 2D 问题（笛卡尔坐标和径向圆柱坐标）和一个 3D 笛卡尔坐标问题，以验证 RGMS 中的 FEM 和并行化方法。从这三个问题的 RGMS 解决方案中获得的位移和最大主有效应力与从商业软件 Ansys Mechanical 中获得的位移和最大主有效应力进行了比较，结果表明它们实际上是一致的。pT+H V1.5 的并行化通过将其结果与串行 T+H V1 的结果进行比较来验证。5 代码在一项研究中涉及（a）从描述真实海洋水合物沉积物的大型二维圆柱系统中生产流体和（b）基于水合物相关孔隙可压缩性的简化地质力学模型。通过将数值结果与 Terzaghi 和 McNamee-Gibson 问题的解析解进行比较来验证耦合方法。耦合模拟器的并行化验证是通过将 pT+H V1.5 并行化验证与完整地质力学模型所用问题的解决方案中不同数量的过程获得的结果进行比较来实现的。结果清楚地证明了并行代码 (a) RGMS、(b) pT+H V1.5 和 (c) 耦合的 pT+H V1.5 和 RGM 模拟器的有效性和可靠性，可用于解决复杂问题的大规模物理。