The mechanical behavior of fractures in solids, such as rocks, has strong implications for reservoir engineering applications. Deformations, and the corresponding change in solid contact area and aperture field, impact rock fracture stiffness and permeability thus altering the reservoir properties significantly. Simulating contact between fractures is numerically difficult as the non-penetration constraints lead to a nonlinear problem and the surface meshes of the solid bodies on the opposing fracture sides may be non-matching. Furthermore, the challenging geometry of the arising constraints requires to solve the problem in several iterations, adjusting the constraints in each one. Here we present a novel discrete implementation of a dual mortar method and a non-smooth SQP solver, suitable for parallel computing, and apply it to a two body contact problem consisting of realistic rock fracture geometries from the Grimsel underground laboratory in Switzerland. The contributions of this article are: 1) a novel, parallel implementation of a dual mortar method and non-smooth SQP method, 2) realistic rock geometries with rough surfaces, and 3) numerical examples, which prove that the dual mortar method is capable of replicating the nonlinear closure behavior of fractures, observed in laboratory experiments.

中文翻译：

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使用双砂浆方法在粗糙岩石表面之间接触

固体（如岩石）中裂缝的力学行为对油藏工程应用具有重要意义。变形以及固体接触面积和孔径场的相应变化会影响岩石裂缝刚度和渗透率，从而显着改变储层性质。模拟裂缝之间的接触在数值上是困难的，因为非渗透约束会导致非线性问题，并且相对裂缝两侧的实体的表面网格可能不匹配。此外，产生约束的具有挑战性的几何形状需要在多次迭代中解决问题，调整每个迭代中的约束。在这里，我们提出了一种适用于并行计算的双砂浆方法和非光滑 SQP 求解器的新颖离散实现，并将其应用于由来自瑞士 Grimsel 地下实验室的真实岩石断裂几何结构组成的两体接触问题。本文的贡献是：1) 双砂浆方法和非光滑 SQP 方法的新颖并行实现，2) 具有粗糙表面的真实岩石几何形状，以及 3) 数值例子，证明双砂浆方法是有能力的复制在实验室实验中观察到的裂缝的非线性闭合行为。