Hydraulic gradient analysis in vertical hydraulic transport for coarse particles

This paper investigates the hydraulic gradient in vertical hydraulic transport (VHT) for coarse particles using a one-dimensional (1D) quasi-fluid model developed in previous work. The hydraulic gradient is divided into three key mechanisms—transport medium, mixture gravity, and particle–wall collisions—each of which is thoroughly analyzed in terms of its contribution to the overall pressure drop. The model's accuracy is validated through comparison with experimental data, yielding a mean absolute percentage error of 13.38%, indicating strong agreement. The study systematically investigates the impact of feed concentration, particle diameter, and mixture velocity on both the values of the individual hydraulic gradient components and their proportions within the total hydraulic gradient. The changes in total pressure drop predicted by the 1D model are also examined across various initial conditions, showing that the total pressure drop increases with higher feed concentration and greater mixture velocity, respectively. Additionally, the total pressure drop is insensitive to the change of particle diameter. This detailed analysis provides key insights into how each mechanism influences pressure loss in VHT systems, offering practical recommendations for enhancing the efficiency and accuracy of hydraulic transport processes in engineering applications.