In a literature review of the recent advancements in mathematical hydrologic models applied in fractured karstic formations, we highlight the necessary improvements in the fluid dynamic equations that are commonly applied to the flow in a discrete fracture network (DFN) via channel network models. Fluid flow and pollutant transport modeling in karst aquifers should consider the simultaneous occurrence of laminar, nonlaminar, and turbulent fluxes in the fractures rather than the laminar flow by the cubic law that has been widely applied in the scientific literature. Some simulations show overestimations up to 75% of the groundwater velocity when non-laminar flows are neglected. Moreover, further model development is needed to address the issues of tortuosity of preferential saturated fluid flow in fractures suggesting adjustments of the size of the mean aperture in DFN models. During the past decade, DFN mathematical models have been significantly developed aimed at relating the three-dimensional structure of interconnected fractures within rocky systems to the specific fracture properties measurable on the rock outcrops with the use of reliefs, tracer/pumping tests, and geotechnical field surveys. The capabilities and limitations of previous reported hydrological models together with specific research advancements and findings in modeling equations are described herein. New software is needed for creating three-dimensional contour maps in fractured aquifers corresponding to the outputs of particle tracking simulations. Existing software based on the equivalent continuum or multiple-interacting continua cannot delineate the spread of pollutant migrations affected by the tortuous preferential flow pathways that occur in DFNs.

中文翻译：

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岩溶和裂缝性水库中水流和污染物运移的水文地质模型

在对应用于裂缝性岩溶地层的数学水文模型的最新进展的文献综述中，我们强调了流体动力学方程的必要改进，这些方程通常通过通道网络模型应用于离散裂缝网络 (DFN) 中的流动。岩溶含水层中的流体流动和污染物输运建模应考虑裂缝中层流、非层流和湍流的同时发生，而不是科学文献中广泛应用的三次定律的层流。一些模拟显示，当忽略非层流时，地下水速度被高估了 75%。而且，需要进一步开发模型来解决裂缝中优先饱和流体流动的曲折问题，这表明在 DFN 模型中调整平均孔径的大小。在过去的十年中，DFN 数学模型得到了显着的发展，旨在将岩石系统内相互连接的裂缝的三维结构与岩石露头上可测量的特定裂缝特性相关联，使用地貌、示踪剂/泵送测试和岩土工程领域调查。本文描述了先前报告的水文模型的能力和局限性，以及建模方程中的具体研究进展和发现。需要新软件来创建对应于粒子跟踪模拟输出的裂缝含水层中的三维等值线图。