In this study, two classes of advanced finite volume schemes, including Multi-Point Flux Approximation (MPFA) and Dual Discrete Finite Volume (DDFV) method, have been employed in conjunction with the finite element (FE) geomechanics simulator to model the coupled fluid-solid system. Fully saturated porous media with poroelastic behavior, random field permeability and elastic modulus are considered as parameters. The performance of the proposed hydro-mechanical models, including MPFA O-FEM and DDFV-FEM, is examined through different test cases. First, the models are validated and compared with the closed-form solutions in the homogeneous domain. Second, the methods' stability and convergence properties are analyzed in highly heterogeneous porous media with different permeability and elastic modulus realizations. Finally, implementing the models in a large-size realistic problem of a synthetic reservoir accomplishes this comprehensive study. Although both methods agree well with the analytical solutions in homogeneous porous media, the DDFV-FEM yields higher accuracy. In the cases where the random field of permeability varies over several orders of magnitude (4th and more), the MPFA O-FEM suffers from significant oscillations and even instability. The analysis illustrates that MPFA O-FEM exhibits oscillation in the cases with high anisotropy ratio, while the DDFV-FEM demonstrates superior performance for handling anisotropy and heterogeneity.

在这项研究中，两类先进的有限体积方案，包括多点通量近似（MPFA）和双重离散有限体积（DDFV）方法，已与有限元（FE）地质力学模拟器一起使用，以对耦合流体进行建模-固体系统。具有孔隙弹性行为，随机场渗透率和弹性模量的完全饱和多孔介质被视为参数。通过不同的测试案例来检验所提出的液压力学模型（包括MPFA O-FEM和DDFV-FEM）的性能。首先，对模型进行验证，并将其与齐次域中的闭式解进行比较。其次，在具有不同渗透率和弹性模量实现的高度非均质多孔介质中分析了方法的稳定性和收敛性。最后，在合成油藏的大型现实问题中实施模型可以完成这项全面的研究。尽管这两种方法都与均质多孔介质中的分析解决方案非常吻合，但DDFV-FEM可以产生更高的精度。在渗透率的随机场变化几个数量级（第4个或更多）的情况下，MPFA O-FEM会遭受明显的振荡甚至不稳定。分析表明，MPFA O-FEM在各向异性高的情况下会发生振荡，而DDFV-FEM在处理各向异性和异质性方面表现出优异的性能。在渗透率的随机场变化几个数量级（第4个或更多）的情况下，MPFA O-FEM会遭受明显的振荡甚至不稳定。分析表明，MPFA O-FEM在各向异性高的情况下会出现振荡，而DDFV-FEM在处理各向异性和异质性方面表现出优异的性能。在渗透率的随机场变化几个数量级（第4个或更多）的情况下，MPFA O-FEM会遭受明显的振荡甚至不稳定。分析表明，MPFA O-FEM在各向异性高的情况下会出现振荡，而DDFV-FEM在处理各向异性和异质性方面表现出优异的性能。