论文标题
顺序完全隐式（SFI）储层模拟的不精确方法
Inexact Methods for Sequential Fully Implicit (SFI) Reservoir Simulation
论文作者
论文摘要
引入了顺序完全隐式（SFI）方案（Jenny等，2006），以解决耦合流和传输问题。 SFI的每个时间步骤都由一个外循环组成，其中牛顿内部循环具有隐式和顺序地求解压力和运输子问题。在标准SFI中，通常在每次外迭代时都以紧密的公差来解决子问题。这可能会导致浪费的计算，从而对耦合解决方案几乎没有进展。这个问题被称为“过度解决”。我们的目标是在保持SFI的收敛速度的同时最大程度地降低内求解器的成本。我们首先将非线性加速器（NA）框架（Jiang and Tchelepi 2019）扩展到多组分组成模型，以确保强大的外环收敛。然后，我们开发了减轻“过度解决”的不精确方法。发现不需要一个子问题即可努力完美，而由于另一个子问题，耦合（外部）残留物保持很高。使用几个复杂情况测试了新的SFI求解器。这些问题涉及多相和基于EOS的组成流体系统。我们比较了不同策略，例如对内求解器的绝对和相对公差的固定放松以及一种自适应方法。结果表明，基本的SFI方法效率很低。远离耦合溶液，浪费了内部求解器中获得的额外准确性，从而几乎没有或根本没有减少整体外部残留物。相比之下，自适应不进行的方法为亚问题的当前收敛状态提供了足够的相对公差。我们在各种流量条件下显示，新求解器可以有效地解决过度解决的问题，从而大大提高了整体效率。
The sequential fully implicit (SFI) scheme was introduced (Jenny et al. 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and sequentially solve the pressure and transport sub-problems. In standard SFI, the sub-problems are usually solved with tight tolerances at every outer iteration. This can result in wasted computations that contribute little progress towards the coupled solution. The issue is known as `over-solving'. Our objective is to minimize the cost of inner solvers while maintaining the convergence rate of SFI. We first extended a nonlinear-acceleration (NA) framework (Jiang and Tchelepi 2019) to multi-component compositional models, for ensuring robust outer-loop convergence. We then developed inexact-type methods that alleviate `over-solving'. It is found that there is no need for one sub-problem to strive for perfection, while the coupled (outer) residual remains high due to the other sub-problem. The new SFI solver was tested using several complex cases. The problems involve multi-phase and EoS-based compositional fluid systems. We compared different strategies such as fixed relaxations on absolute and relative tolerances for the inner solvers, as well as an adaptive approach. The results show that the basic SFI method is quite inefficient. Away from a coupled solution, additional accuracy achieved in inner solvers is wasted, contributing to little or no reduction of the overall outer residual. By comparison, the adaptive inexact method provides relative tolerances adequate for the current convergence state of the sub-problems. We show across a wide range of flow conditions that the new solver can effectively resolve the over-solving issue, and thus greatly improve the overall efficiency.
