Implicit Space-Time Domain Decomposition Approach for Solving Multiphase Miscible Flow: Accuracy and Scalability
Implicit Space-Time Domain Decomposition Approach for Solving Multiphase Miscible Flow: Accuracy and Scalability
复制标题
求解多相混相流的隐式时空域分解方法：准确性和可扩展性
DOI：
10.2118/203989-pa
复制
发表时间：
2021
期刊：
影响因子：
3.6
通讯作者：
M. Wheeler
中科院分区：
文献类型：
--
作者：
Hanyu Li;M. Wheeler
本文提出了一种全隐式时空多尺度格式，以提高求解非线性多相渗流问题的计算效率。这里，误差估计器用于自适应地改变时空网格。将该算法应用于黑油模型，并与使用精细时间和空间网格的标准控制体方法进行了比较。
引入误差估计器来确定高非线性阻碍牛顿收敛的水库子域。然后对这些标记的区域应用局部精细时间步长，而其余区域保持粗略时间尺度。一旦确定了储集层不同部分的时间离散化，就对空间网格进行细化以处理饱和前沿。采用增强速度法对不同时间和空间尺度上的非匹配界面进行了解析，增强了通量的连续性。整个系统都得到了统一的解决。
文中描述了三相黑油模型的计算结果。将多尺度解与均匀精细的空间网格和精细的时间步长解进行比较，以确认精度。给出了高斯化渗透场和沟道化渗透场的解。在多尺度解中，我们观察到通过减小时间步长来保证牛顿收敛，对水和气饱和前沿进行了时间精化。我们还观察到，基于它们各自的非线性，细化的程度在两个饱和前沿之间是平衡的。对于高斯型渗透率场，该算法只在空间上处理饱和面，而对于沟道化渗透率场，该算法还考虑了地质特征。在特定的改进标准下，这三个阶段的生产概况在两个解决方案之间非常匹配。我们还研究了随着问题规模的增加，计算效率的提高以及算法的可扩展性。我们观察到求解线性系统的加速比约为10%，并且这种加速比随着问题规模的扩大而增加。
在油藏模拟中，随着物理过程变得更加复杂，试图解耦扩散和平流过程的方案变得不那么健壮。我们的方法专注于处理高度的非线性，可以完全隐式处理，并提供了模拟成本的降低。该方法也可用于模型降阶，以提供准确的快照解决方案。
注：本文是《2021年油藏模拟会议特刊》的一部分。
In this paper, we propose a fully implicit space-time multiscale scheme to improve computational efficiency in solving nonlinear multiphase flow in porous media. Here, error estimators are used for adaptively changing the spatial-temporal mesh. This algorithm applied to the black-oil model is compared to a standard control volume approach using a fine time and spatial mesh.
Error estimators are introduced to determine subdomains of the reservoir in which high nonlinearity hinders Newtonian convergence. This is followed by applying local fine timesteps to these marked regions, whereas the remaining regions retain the coarse time scale. Once a temporal discretization is determined for different parts of the reservoir, the spatial mesh is refined for treating saturation fronts. The nonmatching interfaces arising from different temporal and spatial scales are resolved by the enhanced velocity method, which enforces strongly the continuity of fluxes. This whole system is solved monolithically.
Results from a three-phaseblack-oil model are described. The multiscale solution is compared to a uniformly fine spatial mesh and fine timestepping solution to confirm accuracy. Solutions from both Gaussian and channelized permeability fields are presented. In the multiscale solution, we observe temporal refinements being applied to the water and gas saturation fronts by reducing the timestep size to guarantee Newtonian convergence. We also observe that the extent of refinements is balanced between the two saturation fronts based on their respective nonlinearity. For Gaussian permeability fields, the algorithm only treats saturation fronts spatially, whereas for channelized permeability fields, the geological features are also considered. Production profiles for the three phases match well between the two solutions under specific refinement criteria. We also investigate the improvement in computational efficiency, as well as the algorithm scalability in regard to increasing problem sizes. We observe a speedup of approximately 10 for solving the linear system, and such speedup increases as the problem size expands.
In reservoir simulation, schemes that attempt to decouple the diffusion and advection process become less robust as the physics becomes more complex. Our approach, which is focused on handling the high nonlinearities, can be treated fully implicitly and provide a reduction in simulation costs. This approach can also be applied to model order reduction in providing accurate snapshot solutions.
NOTE: This paper is published as part of the 2021 Reservoir Simulation Conference Special Issue.