Abstract Accurate simulation of multiphase flow in subsurface formations is challenging, as the formations span large length scales (km) with high-resolution heterogeneous properties. To deal with this challenge, different multiscale methods have been developed. Such methods construct coarse-scale systems, based on a given high-resolution fine-scale system. Furthermore, they are amenable to parallel computing and allow for a-posteriori error control. The multiscale methods differ from each other in the way the transition between the different scales is made. Multiscale (finite element and finite volume) methods compute local basis functions to map the solutions (e.g. pressure) between coarse and fine scales. Instead, homogenization methods solve local periodic problems to determine effective models and parameters (e.g. permeability) at a coarser scale. It is yet unknown how these two methods compare with each other, especially when applied to complex geological formations, with no clear scale separation in the property fields. This paper develops the first comparison benchmark study of these two methods and extends their applicability to fully implicit simulations using the algebraic dynamic multilevel (ADM) method. At each time step, on the given fine-scale mesh and based on an error analysis, the fully implicit system is solved on a dynamic multilevel grid. The entries of this system are obtained by using multiscale local basis functions (ADM-MS), and, respectively, by homogenization over local domains (ADM-HO). Both sets of local basis functions (ADM-MS) and local effective parameters (ADM-HO) are computed at the beginning of the simulation, with no further updates during the multiphase flow simulation. The two methods are extended and implemented in the same open-source DARSim2 simulator (https://gitlab.com/darsim2simulator), to provide fair quality comparisons. The results reveal insightful understanding of the two approaches, and qualitatively benchmark their performance. It is re-emphasized that the test cases considered here include permeability fields with no clear scale separation. The development of this paper sheds new lights on advanced multiscale methods for simulation of coupled processes in porous media.

中文翻译：

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用于全隐式多相流模拟的多尺度和均质化方法的基准研究

摘要 地下地层中多相流的准确模拟具有挑战性，因为地层跨越大长度尺度 (km) 并具有高分辨率的非均质特性。为了应对这一挑战，已经开发了不同的多尺度方法。这些方法基于给定的高分辨率精细尺度系统构建粗尺度系统。此外，它们适合并行计算并允许后验错误控制。多尺度方法的不同之处在于不同尺度之间的转换方式。多尺度（有限元和有限体积）方法计算局部基函数以映射粗尺度和细尺度之间的解（例如压力）。相反，均质化方法解决局部周期性问题以确定有效的模型和参数（例如 渗透率）更粗略的尺度。目前尚不清楚这两种方法如何相互比较，特别是应用于复杂的地质地层时，在属性领域没有明显的尺度分离。本文开发了这两种方法的第一个比较基准研究，并将它们的适用性扩展到使用代数动态多级 (ADM) 方法的全隐式模拟。在每个时间步长，在给定的细尺度网格上并基于误差分析，在动态多级网格上求解全隐式系统。该系统的条目分别通过使用多尺度局部基函数 (ADM-MS) 和局部域上的同质化 (ADM-HO) 获得。在模拟开始时计算两组局部基函数 (ADM-MS) 和局部有效参数 (ADM-HO)，在多相流模拟期间没有进一步更新。这两种方法在同一个开源 DARSim2 模拟器 (https://gitlab.com/darsim2simulator) 中扩展和实现，以提供公平的质量比较。结果揭示了对这两种方法的深刻理解，并对它们的性能进行了定性基准测试。再次强调，这里考虑的测试案例包括没有明显尺度分离的渗透场。本文的发展为模拟多孔介质中耦合过程的先进多尺度方法提供了新的思路。结果揭示了对这两种方法的深刻理解，并对它们的性能进行了定性基准测试。再次强调，这里考虑的测试案例包括没有明显尺度分离的渗透场。本文的发展为模拟多孔介质中耦合过程的先进多尺度方法提供了新的思路。结果揭示了对这两种方法的深刻理解，并对它们的性能进行了定性基准测试。再次强调，这里考虑的测试案例包括没有明显尺度分离的渗透场。本文的发展为模拟多孔介质中耦合过程的先进多尺度方法提供了新的思路。