One-dimensional model for vertical hydraulic transport of high-concentration mineral particles

A novel model is proposed for analyzing high-concentration granular flow systems comprising equally sized spherical particles within vertical, long straight pipelines. This model is specifically tailored for simulating the vertical hydraulic transport of ore particles in marine mining projects. The proposed model treats the granular system akin to a pseudo-fluid and operates through three mechanisms. First, fluid characteristics of the granular system are derived from particle–particle collisions. Second, the resistance exerted by the pipe wall on the granular system is calculated based on the momentum loss of particles during particle–wall collisions. Third, the interaction between individual particles and the surrounding fluid is transformed into an interaction between the carrier fluid and the pseudo-fluid. Additionally, the present work develops a dedicated numerical format and iterative method for solving the one-dimensional two-fluid governing equations. The one-dimensional (1D) model notably enhances computational efficiency and facilitates accurate tracking of high-concentration particles over extended distances within straight pipelines. Notably, the proposed 1D model demonstrates a high degree of predictive accuracy when compared against experimental data as well as results from computational fluid dynamics and discrete element method simulations.