In this paper, the effect of random permeability is considered for the real fracture reservoir, hence a stochastic dual-porosity-Navier-Stokes model with random permeability is proposed to simulate shale oil problem based on superhydrophobic material modification. Finite element method and Monte Carlo method are used to deal with discrete physical space and probability space, respectively. The decoupled finite element method with backward-Euler temporal discretization is presented, which allows the coupling problem to be divided into three subproblems in a non-iterative manner. Furthermore, the stability analysis and error estimation of the corresponding partition scheme are given. 2D/3D numerical experiments verify the validity of the theoretical analysis and prove the reliability and applicability of the scheme.

中文翻译：

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基于超疏水材料改性的非平稳随机页岩油模型解耦稳定有限元方法


本文针对实际裂缝油藏考虑了随机渗透率的影响，提出了基于超疏水材料改性的随机渗透率随机双孔隙-Navier-Stokes模型来模拟页岩油问题。有限元法和蒙特卡罗法分别用于处理离散物理空间和概率空间。提出了后向欧拉时间离散的解耦有限元方法，该方法允许耦合问题以非迭代方式分为三个子问题。此外，还给出了相应划分方案的稳定性分析和误差估计。 2D/3D数值实验验证了理论分析的有效性，证明了方案的可靠性和适用性。