Mathematical modeling of the cyclical emptying and filling of water distribution system in a deep mine

This study presents a novel approach to analyzing complex water distribution system within deep mines, focusing on water supply through multiple shafts and the dynamic behavior of water flow. We begin with an initial analysis derived from experimental measurements of flow rates and pressures within the mine’s water distribution system. Observations revealed a cyclical pattern of system emptying and filling. To address the intricacies of such dynamic systems, we propose a one-dimensional mathematical model that integrates water hammer theory with volumetric water content transfer equations. This model accommodates the transient operation of shut-off and control devices, offering a comprehensive framework for simulating the mine’s water distribution system. The novelty of the model consists in the proposed method of calculating the water fraction in the pipelines, as well as in the introduced boundary condition on the pressure reducing valve. Through numerical simulations, we calibrated and validated the model against experimental data, successfully identifying critical periods and locations of system emptying and filling. The findings provide valuable insights into the management of water distribution system in deep mines, enhancing our understanding of their complex, non-stationary behavior.