We critically assess diffuse interface models for fluid transport in fractured porous media. Such models, often called fracture phase field models, are commonly used to simulate hydraulic stimulation or hydraulic fracturing of fluid-saturated porous rock. In this paper, we focus on the less complex case of fluid transport in stationary fracture networks that is triggered by a hydro-mechanical interaction of the fluid in the fractures with a surrounding poroelastic matrix material. In other words, fracture propagation is not taken into account. This allows us to validate the diffuse interface model quantitatively and to benchmark it against solutions obtained from sharp interface formulations and analytical solutions.

We introduce the relevant equations for the sharp and diffuse, i.e. fracture phase field, interface formulations. Moreover, we derive the scale-transition rules for upscaling the fluid-transport problem towards a viscoelastic substitute model via Variationally Consistent Computational Homogenization. This allows us to measure the attenuation associated with fluid transport on the sub-scale.

From the numerical investigations we conclude that the conventional diffuse interface formulation fails in predicting the fluid-transport behavior appropriately. The results even tend to be non-physical under certain conditions. We, therefore, propose a modification of the interpolation functions used in the diffuse interface model that leads to reasonable results and to a good approximation of the reference solutions.

我们严格评估在多孔介质中流体传输的扩散界面模型。这种模型通常称为裂缝相场模型，通常用于模拟流体饱和的多孔岩的水力增产或水力压裂。在本文中，我们关注于固定裂缝网络中较不复杂的流体运移情况，这是由裂缝中的流体与周围的多孔弹性基质材料的水力相互作用引起的。换句话说，不考虑裂缝扩展。这使我们能够定量验证扩散界面模型，并根据从清晰的界面公式和分析解决方案中获得的解决方案对其进行基准测试。

我们介绍了有关尖锐和弥散的相关方程，即断裂相场界面公式。此外，我们通过变分一致计算均质化推导了将流体传输问题向粘弹性替代模型扩展的尺度转换规则。这使我们能够在子尺度上测量与流体传输相关的衰减。

从数值研究中我们得出结论，传统的扩散界面公式无法正确预测流体的传输行为。在某些条件下，结果甚至往往是非物理的。因此，我们提出对在扩散界面模型中使用的插值函数的修改，以得出合理的结果并很好地逼近参考解。