Many reservoirs consist of fully saturated rock masses containing a very complex natural fracture network. In such cases a decrease in the fracture fluid pressure reduces its aperture due to an increase in the effective stresses. In order to tackle the influence of fracture permeability on the pressure field and fluid flow, this paper proposes a Discrete Fracture-Matrix (DFM) model based on the finite elements to simulate coupled flow and geomechanics in porous media containing fractures with known position and properties (e.g. DFN realizations and fracture networks interpreted from outcrops). The proposed model is based on the use of triangular finite elements with high aspect ratio (HAR) to explicitly represent the fractures. These HAR elements have been successfully used to deal with cracks in concrete structures, desiccation cracks in soils and hydraulic fracturing in geo-reservoirs. This work demonstrate that these HAR elements equipped with a simple continuum (stress-strain) constitutive contact model that mimics the discrete (stress-displacement) Barton-Bandis joint model are able to properly describe the closure behavior associated with natural fractures. The constitutive model is integrated by means of the IMPL-EX scheme, which is a robust and stable technique used to achieve faster convergence. Darcy's law establishes the relationship between the fluid flow and the pressure field, and a fully coupled hydro-mechanical formulation comprises the mathematical framework. The proposed approach is based on continuous mechanics concepts and the implementation is made at constitutive level, and therefore it is simple and easy to be included in any existing FE program. To show the efficiency and accuracy of the proposed model, three numerical examples are conducted in this work: (i) benchmarks involving a medium with a single natural fracture, (ii) three reservoirs with different discrete fracture networks, and (iii) a transient analysis of a reservoir under different fracture conditions, such that the behavior of a intact reservoir, a reservoir containing fractures with constant aperture, and a reservoir in which the fractures aperture depends on the stress state are compared in terms of pore pressure, displacement field and fluid loss. In the first example, the results obtained with the proposed methodology are validated against the Barton-Bandis model. The agreement between the results is very satisfactory. The analysis of the latter two cases show the Barton-Bandis contact model is able to reproduce the effects of fracture permeability on pressure field in the reservoir, showing the capacity of the model to reproduce the main trends associated with the closure of natural fractures.

许多储层由完全饱和的岩体组成，其中包含非常复杂的天然裂缝网络。在这种情况下，由于有效应力的增加，压裂液压力的减小会减小其孔径。为了解决裂缝渗透率对压力场和流体流动的影响，本文提出了一种基于有限元的离散裂缝矩阵（DFM）模型，以模拟具有已知位置和性质的裂缝的多孔介质中的渗流与地质力学耦合。 （例如，DFN实现和从露头解释的裂缝网络）。所提出的模型基于使用具有高长宽比（HAR）的三角形有限元来明确表示裂缝。这些HAR元件已成功用于处理混凝土结构中的裂缝，土壤干燥裂缝和地质储层的水力压裂。这项工作表明，这些具有简单连续体（应力-应变）本构接触模型的HAR元件能够模拟离散（应力-位移）Barton-Bandis接头模型，能够正确描述与自然裂缝相关的闭合行为。本构模型是通过IMPL-EX方案进行集成的，该方案是用于实现更快收敛的可靠且稳定的技术。达西定律建立了流体流动与压力场之间的关系，并且完全耦合的水力-机械公式包括数学框架。所提出的方法基于连续力学概念，并且在本构层次上进行了实现，因此，它很容易被包含在任何现有的有限元程序中。为了显示所提出模型的效率和准确性，在此工作中进行了三个数值示例：（i）涉及具有单一天然裂缝的介质的基准；（ii）具有不同离散裂缝网络的三个油藏；以及（iii）瞬变对不同裂缝条件下的储层进行了分析，从而比较了完整储层，包含恒定孔径裂缝的储层的行为以及裂缝孔径取决于应力状态的储层的孔隙压力，位移场和液体流失。在第一个示例中，针对Barton-Bandis模型验证了使用所提出的方法获得的结果。结果之间的一致性非常令人满意。