Coupling-Strength Criteria for Sequential Implicit Formulations
Coupling-Strength Criteria for Sequential Implicit Formulations
复制标题
顺序隐式公式的耦合强度准则
DOI：
10.2118/203909-ms
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
H. Tchelepi
中科院分区：
文献类型：
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作者：
Jacques Franc;O. Møyner;H. Tchelepi
顺序完全隐式（SFI）方案已被提议作为完全隐式方法（FIM）的替代方案。 SFI 的一个显着优势是可以采用可扩展的策略来解决流量和传输问题。然而，与 FIM 相比，使用 SFI 的主要缺点是，将压力与饱和度分开的解耦算子引起的分裂误差可能会导致整个非线性问题的严重收敛困难。因此，以自适应方式量化空间和时间上的耦合强度非常重要。我们提出了定位压力和饱和度解紧密耦合的计算单元的标准。该方法使用 FIM 雅可比矩阵中的项，我们量化质量和体积平衡方程对压力和饱和度变化的敏感性。我们确定了三个标准来衡量方程和变量之间的耦合强度。标准 CFL 稳定性标准完全基于饱和方程，是新标准的子集。此处，使用代数多重网格 (AMG) 或多尺度求解器（例如多尺度受限平滑基 (MsRSB) 方法）求解压力方程。然后使用固定的总速度求解传输方程。这些“耦合强度”标准用于识别压力-饱和耦合较强的单元。使用几个测试用例测试了导出的耦合强度标准的适用性。第一个测试是在单位流度比和大密度差异下使用重力不混溶死油锁交换。对于这种情况，由于分裂误差较大，SFI算法无法收敛到全耦合解。在局部子域上引入完全耦合的求解阶段作为附加校正步骤可以恢复非线性收敛。对“耦合强度”标准的详细分析表明，与质量平衡对压力变化的敏感性和体积平衡对饱和度变化的敏感性相关的标准是最重要的满足条件。其他测试案例包括 SPE 10 测试案例顶层的交替气-水-气注入以及具有分层对数正态分布渗透率的三维储层中的注入-生产情景。我们提出了新的标准来估计压力和饱和度之间的耦合强度。这些类似 CFL 的数字用于识别非线性求解策略中需要完全隐式处理的单元。这些标准还可用于提高自适应隐式方法 (AIM) 的非线性收敛速度。
Sequential Fully Implicit (SFI) schemes have been proposed as an alternative to the Fully Implicit Method (FIM). A significant advantage of SFI is that one can employ scalable strategies to the flow and transport problems. However, the primary disadvantage of using SFI compared with FIM is the fact that the splitting errors induced by the decoupling operator, which separates the pressure from the saturation(s), can lead to serious convergence difficulties of the overall nonlinear problem. Thus, it is important to quantify the coupling strength in an adaptive manner in both space and time. We present criteria that localize the computational cells where the pressure and saturation solutions are tightly coupled. The approach is using terms in the FIM Jacobian matrix, we quantify the sensitivity of the mass and volume-balance equations to changes in the pressure and the saturations. We identify three criteria that provide a measure of the coupling strength across the equations and variables. The standard CFL stability criteria, which are based entirely on the saturation equations, are a subset of the new criteria. Here, the pressure equation is solved using Algebraic MultiGrid (AMG), or a multiscale solver, such as the Multiscale Restricted-Smooth Basis (MsRSB) approach. The transport equations are then solved using a fixed total-velocity. These ‘coupling strength’ criteria are used to identify the cells where the pressure-saturation coupling is strong. The applicability of the derived coupling-strength criteria is tested using several test cases. The first test is using a gravitational immiscible dead-oil lock-exchange under a unit mobility ratio and large differences in density. For this case, the SFI algorithm fails to converge to the fully coupled solution due to the large splitting errors. Introducing a fully coupled solution stage on the local subdomains as an additional correction step restores nonlinear convergence. Detailed analysis of the ‘coupling strength’ criteria indicates that the criteria related to the sensitivity of the mass balance to changes in the pressure and the sensitivity of the volume balance to changes in the saturations are the most important ones to satisfy. Other test cases include an alternate gas-water-gas injection in a top layer of the SPE 10 test case and an injection-production scenario in a three-dimensional reservoir with layered lognormally distributed permeability. We propose novel criteria to estimate the strength of coupling between pressure and saturation. These CFL-like numbers are used to identify the cells that require fully implicit treatment in the nonlinear solution strategy. These criteria can also be used to improve the nonlinear convergence rates of Adaptive Implicit Methods (AIM).