面向油藏网格的虚拟元方法
Virtual Element Method for geomechanics on reservoir grids
AI总结：
本文研究虚拟元方法在油藏模拟中的应用，探讨其在处理复杂几何结构时的鲁棒性及曲面三角化对稳定性的影响，提出更稳定的正则化项。
摘要：
本文研究了虚拟元方法在地质力学中的应用，重点探讨其在油藏模拟中的局限性。首先，证明在处理高度拉长的单元时需谨慎，以确保方法的鲁棒性，并展示在拉长变形单元中计算边界上的应力的重要性。其次，研究了曲面三角化对地下模型的影响，并展示了如何为油藏应用推导更稳定的正则化项。
英文摘要：
In this paper we study the use of Virtual Element method for geomechanics. Our emphasis is on applications to reservoir simulations. The physical processes that form the reservoirs, such as sedimentation, erosion and faulting, lead to complex geometrical structures. A minimal representation, with respect to the physical parameters of the system, then naturally leads to general polyhedral grids. Numerical methods which can directly handle this representation will be highly favorable, in particular in the setting of advanced work-flows. The Virtual Element method is a promising candidate to solve the linear elasticity equations on such models. In this paper, we investigate some of the limits of the VEM method when used on reservoir models. First, we demonstrate that care must be taken to make the method robust for highly elongated cells, which is common in these applications, and show the importance of calculating forces in terms of traction on the boundary of the elements for elongated distorted cells. Second, we study the effect of triangulations on the surfaces of curved faces, which also naturally occur in subsurface models. We also demonstrate how a more stable regularization term for reservoir application can be derived.
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