There is strong interest to design sequential fully implicit (SFI) methods for compositional flow simulations with convergence properties that are comparable to fully implicit (FI) methods. SFI methods decompose the fully coupled system into a pressure equation and a transport system of the components. During the pressure update, the compositions are frozen, and during the transport calculations, both the pressure and total velocity are kept constant. The two systems are solved sequentially, and the solution, which is a fully implicit one, is obtained by controlling the splitting errors due to the decoupling. Having an SFI scheme that enjoys a convergence rate similar to FI makes it possible to design specialized numerical methods optimized for the different parabolic and the hyperbolic operators, as well as the use of high-order spatial and temporal discretization schemes. Here, we use the multiscale restriction-smoothed basis (MsRSB) method for the parabolic operator. We also show that phase-potential upwinding is incompatible with the total velocity formulation of the fluxes, which is common in SFI schemes. We observe that in cases with strong gravity or capillary pressure, it is possible to have flow reversals. These reversals can strongly affect the convergence rate of SFI methods. In this work, we employ phase upwinding (PU) as well as implicit hybrid upwinding (IHU) with a SFI method. IHU determines the upwinding direction differently for the viscous, buoyancy, and capillary pressure terms in the phase velocity expressions. The use of IHU leads to a consistent SFI scheme in terms of both pressure and compositions, and it improves the SFI convergence significantly in settings with strong buoyancy or capillarity. We demonstrate the robustness of the IHU-based SFI algorithm across a wide parameter range. Realistic compositional models with gas and water injection are presented and discussed.

中文翻译：

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连续向上隐式连续完全隐式多尺度合成模拟

设计用于合成流模拟的顺序完全隐式（SFI）方法具有与完全隐式（FI）方法相当的收敛特性，引起了人们极大的兴趣。SFI方法将完全耦合的系统分解为组件的压力方程和传输系统。在压力更新过程中，冷冻成分，在运输计算过程中，压力和总速度均保持恒定。依次求解这两个系统，并通过控制由于解耦引起的分裂误差来获得完全隐式的解决方案。SFI方案的收敛速度与FI相似，因此可以设计出专门针对不同抛物线和双曲线算符进行优化的数值方法，以及使用高阶空间和时间离散化方案。在这里，我们对抛物线算子使用多尺度限制平滑基（MsRSB）方法。我们还表明，相势上风与通量的总速度公式不兼容，这在SFI方案中很常见。我们观察到，在重力或毛细管压力较大的情况下，可能会发生逆流。这些逆转会严重影响SFI方法的收敛速度。在这项工作中，我们采用SFI方法采用相位上风（PU）以及隐式混合上风（IHU）。IHU在相速度表达式中针对粘性，浮力和毛细管压力项来确定上风方向。使用IHU可以在压力和成分方面实现一致的SFI方案，在浮力或毛细作用强烈的环境中，它可以显着改善SFI收敛。我们证明了在广泛的参数范围内基于IHU的SFI算法的鲁棒性。提出并讨论了带有注气和注水的实际组成模型。