We develop a new computational model to describe hydro-mechanical coupling in fractured rocks composed of a linear poroelastic Biot medium and nonlinear elastic joints with constitutive response governed by the Barton–Bandis (BB) law. The model aims at capturing increase in stiffness induced by fracture closure during fluid withdrawal. The nonlinear hydro-mechanical formulation is constructed within the framework of the Discrete Fracture Model, with flow and geomechanical sub-systems coupled through a sequential iterative algorithm. The internal contact constraint arising from non-overlapping between opposite fracture faces is enforced through the weak fulfillment of the BB-law. Such a constraint is captured within the framework of the Augmented Lagrangian formulation, where the non-linear mechanical interaction is enforced adopting successive approximations of the Lagrange multiplier, interpreted as the contact pressure in the joint, supplemented by a penalty component associated with the rock stiffness. Furthermore, adopting a traditional flow based upscaling method, macroscopic permeabilities are numerically reconstructed with magnitude strongly dependent on the local stress state. Such a mechanical dependence of the homogenized properties is represented in a discrete manner through pseudo-coupling tables, with enormous potential to be explored within a preprocessing stage in reservoir simulators to compute multipliers relative to a chosen pre-stressed reference state, where input data is available. Numerical simulations are performed for some fracture arrangements illustrating the potential of the formulation proposed herein in bridging hydromechanical coupling at different scales in jointed rocks.

我们开发了一种新的计算模型来描述由线性多孔弹性Biot介质和非线性弹性缝组成的裂隙岩中的水力耦合，其本构响应受Barton-Bandis（BB）定律控制。该模型的目的是捕获在流体抽出过程中裂缝闭合引起的刚度增加。非线性水力力学公式是在离散断裂模型的框架内构造的，流动和岩土力学子系统通过顺序迭代算法耦合。相对断裂面之间不重叠引起的内部接触约束是通过BB律的弱实现而强制执行的。这种约束是在增强拉格朗日公式的框架内捕获的，其中采用拉格朗日乘数的逐次逼近来强制进行非线性机械相互作用，这被解释为节中的接触压力，并辅以与岩石刚度相关的罚分。此外，采用传统的基于流的放大方法，通过数值重建宏观渗透率，其幅度强烈依赖于局部应力状态。均质特性的这种机械依赖性通过伪耦合表以离散方式表示，在油藏模拟器的预处理阶段内有巨大的潜力可以探索，以计算相对于所选预应力参考状态的乘数，其中输入数据为可用。