The sequential fully implicit (SFI) scheme was introduced (Jenny et al. J. Comput. Phys. 217(2), 627–641 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, Comput. Methods Appl. Mech. Eng. 352, 246–275, 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.

引入了顺序完全隐式 (SFI) 方案（Jenny et al. J. Comput. Phys. 217 (2), 627–641 2006）来解决耦合流动和运输问题。SFI 的每个时间步长都包含一个外部循环，其中有内部牛顿循环来隐式和顺序地解决压力和传输子问题。在标准 SFI 中，子问题通常在每次外部迭代时以严格的容差解决。这可能会导致计算浪费，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 收敛速度的同时最小化内部求解器的成本。我们首先扩展了一个非线性加速 (NA) 框架（Jiang 和 Tchelepi，Comput. Methods Appl. Mech. Eng. 352, 246–275, 2019) 到多分量组合模型，以确保稳健的外环收敛。然后我们开发了不精确类型的方法来缓解“过度求解”。发现一个子问题不需要追求完美，而耦合（外）残差由于另一个子问题而保持高位。新的 SFI 求解器使用几种复杂的情况进行了测试。这些问题涉及多相和基于 EoS 的成分流体系统。我们比较了不同的策略，例如内部求解器的绝对和相对容差的固定松弛，以及自适应方法。结果表明，基本的 SFI 方法效率很低。远离耦合解决方案，在内部求解器中实现的额外精度被浪费，导致很少或根本没有减少整体外部残差。通过对比，自适应不精确方法为子问题的当前收敛状态提供了足够的相对容差。我们在广泛的流动条件下表明，新的求解器可以有效地解决过度求解问题，从而大大提高整体效率。