Dimensional reduction strategy is an effective approach to derive reliable conceptual models to describe flow in fractured porous media. The fracture aperture is several orders of magnitude smaller than the characteristic size (e.g., the length of the fracture) of the physical problem. We identify the aperture to length ratio as the small parameter 𝜖 with the fracture permeability scaled as an exponent of 𝜖. We consider a non-Newtonian fluid described by the Carreau model type where the viscosity is dependent on the fluid velocity. Using formal asymptotic approach, we derive a catalogue of reduced models at the vanishing limit of 𝜖. Our derivation provides new models in a hybrid-dimensional setting as well as models which exhibit two-scale behaviour. Several numerical examples confirm the theoretical derivations of the upscaled models. Moreover, we have also studied the sensitivity of the upscaled models when a particular upscaled model is used beyond its range of validity to provide additional insight.

降维策略是一种有效的方法，可以导出可靠的概念模型来描述裂缝性多孔介质中的流动。裂缝孔径比物理问题的特征尺寸（例如裂缝的长度）小几个数量级。我们将孔径与长度比确定为小参数𝜖，裂缝渗透率作为𝜖的指数。我们考虑由 Carreau 模型类型描述的非牛顿流体，其中粘度取决于流体速度。使用形式渐近方法，我们推导出一个在𝜖的消失极限处的简化模型目录. 我们的推导提供了混合维设置中的新模型以及表现出二维行为的模型。几个数值例子证实了放大模型的理论推导。此外，我们还研究了当使用特定放大模型超出其有效性范围时放大模型的敏感性，以提供额外的洞察力。