Numerical simulation of water exchange between the karst matrix and the adjacent conduit at the micro-scale

At the micro-scale, the water exchange in karst water-bearing media remains unclear. This study applies the Stokes-Brinkman equation to couple the seepage within the karst matrix and the free flow within the karst conduit. The digital core technology is employed to characterize the micro-heterogeneous structure of the matrix and quantify its hydraulic properties, establishing a numerical model of water exchange between the matrix and the adjacent conduit at the micro-scale. The results reveal significant differences in the hydraulic properties of distinct matrix samples, highlighting their key role in the water exchange process. Visualizations of flow velocity distribution and pressure gradients provide insights into the characteristics of the water exchange interface. A linear positive correlation between the exchange flow and the flow velocity of the conduit inlet is investigated, which can be attributed to the hydraulic head difference between the matrix and conduit. Additionally, the study demonstrates that the micro-heterogeneous structure of the matrix notably influences the water exchange compared to the homogeneous model. This research offers a new perspective on water exchange in karst water-bearing media at the micro-scale, providing valuable insights for optimizing the prediction and management of karst systems by understanding the multi-scale mechanisms of water exchange.