Abstract Dimensionally reduced models are effective approximations of flow and transport processes in structures containing thin layers. We propose and analyse such a model for flow in fractured porous media. The fractures can store and transport fluid and they are modelled as lower-dimensional entities in the surrounding porous medium. The flow system of interest in this work is single-phase, isothermal and non-compositional. The model consists of the full-dimensional Darcy’s law in the rock matrix coupled to the Stokes equations of co-dimension one in the fracture. The well-posedness of the reduced coupled problem is proved and the reduced model is validated against the full-dimensional model numerically. The simulation results demonstrate that the proposed model is indeed a cost effective alternative to full-dimensional models.

中文翻译：

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裂缝多孔介质中流体流动的降维斯托克斯-达西模型

摘要 降维模型是包含薄层结构中流动和输运过程的有效近似。我们提出并分析了这样一种用于裂缝多孔介质中流动的模型。裂缝可以储存和运输流体，它们被建模为周围多孔介质中的低维实体。这项工作中感兴趣的流动系统是单相、等温和非组成的。该模型由岩石基质中的全维达西定律与裂缝中一维的斯托克斯方程耦合组成。证明了简化耦合问题的适定性，并针对全维模型对简化模型进行了数值验证。仿真结果表明，所提出的模型确实是全维模型的一种具有成本效益的替代方案。