This work studies the performance of a novel preconditioner, designed for thermal reservoir simulation cases and recently introduced in Roy et al. (2020) and Cremon et al. (2020), on large-scale thermal CO2 injection cases. For Carbon Capture and Sequestration (CCS) projects, injecting CO2 under supercritical conditions is typically tens of degrees colder than the reservoir temperature. Thermal effects can have a significant impact on the simulation results, but they also add many challenges for the solvers. More specifically, the usual combination of an iterative linear solver (such as GMRES) and the Constrained Pressure Residual (CPR) physics-based block-preconditioner is known to perform rather poorly or fail to converge when thermal effects play a significant role. The Constrained Pressure-Temperature Residual (CPTR) preconditioner retains the 2x2 block structure (elliptic/hyperbolic) of CPR but includes the temperature in the elliptic subsystem. The elliptic subsystem is now formed by two equations, and is dealt with by the system-solver of BoomerAMG (from the HYPRE library). Then a global smoother, ILU(0), is applied to the full system to handle the local, hyperbolic temperature fronts. We implemented CPTR in the multi-physics solver GEOS and present results on various large-scale thermal CCS simulation cases, including both Cartesian and fully unstructured meshes, up to tens of millions of degrees of freedom. The CPTR preconditioner severely reduces the number of GMRES iterations and the runtime, with cases timing out in 24h with CPR now requiring a few hours with CPTR. We present strong scaling results using hundreds of CPU cores for multiple cases, and show close to linear scaling. CPTR is also virtually insensitive to the thermal Peclet number (which compares advection and diffusion effects) and is suitable to any thermal regime.

翻译：本研究评估了一种针对热油藏模拟案例设计的新型预条件子在大规模热CO₂注入问题中的性能。该预条件子最近由Roy等人（2020年）和Cremon等人（2020年）提出。在碳捕集与封存（CCS）项目中，注入的超临界CO₂通常比油藏温度低数十度。热效应会对模拟结果产生显著影响，但也给求解器带来诸多挑战。具体而言，当热效应起主导作用时，常用组合方案——如迭代线性求解器（如GMRES）与基于物理过程的约束压力残差（CPR）块预条件子——往往表现不佳或无法收敛。约束压力-温度残差（CPTR）预条件子保留了CPR的2×2块结构（椭圆型/双曲型），但将温度纳入椭圆子系统。该椭圆子系统现由两个方程构成，并通过BoomerAMG（来自HYPRE库）的系统求解器处理。随后，对全局系统应用全局光滑算子ILU(0)以处理局部的双曲型温度锋面。我们在多物理场求解器GEOS中实现了CPTR，并展示了多种大规模热CCS模拟案例的结果，这些案例涵盖笛卡尔网格和完全非结构化网格，自由度规模达数千万。CPTR预条件子大幅减少了GMRES迭代次数和运行时间：原本在CPR方案下需24小时超时算例，现仅需数小时即可完成。我们通过数百个CPU核心对多个案例进行了强扩展性测试，结果显示其接近线性扩展。此外，CPTR几乎不受热佩克莱数（用于比较对流与扩散效应）的影响，适用于任何热力学工况。