# CFD-DEM Simulation of the Transport of Manganese Nodules in a Vertical Pipe
## 1 Introduction  
Abundant mineral resources have been identified in deep sea, which has motivated worldwide efforts to develop deep-sea mining systems. The hydraulic mineral lifting system proves effective for deep-sea mining. This system is mainly composed of the mineral collection vehicle, pipes, the slurry pump, and the production support vessel [1]. Mineral particles and seawater are mixed into a two-phase fluid, which is transported through the lifting system. The drive comes from the delivery pump. Manganese nodules have been found in the seabed with ranges of depth of 3000 m to 6000 m. Accordingly, the exploitation of manganese nodules necessitates rather long pipes. Essentially, the two-phase flows in the pipes are critical for the operational stability of the lifting system. General solid-liquid two-phase flows encountered in the chemical and mining industries involve small particles, measuring 0.3 mm to 5.0 mm in mean diameter. In contrast, the most economical diameter of the deep-sea manganese nodules is about 30.0 mm, whereas the maximum can reach 50.0 mm. For the transport of small particles with a mean diameter of approximately 4.0 mm, both operating parameters and flow characteristics have been well interpreted [2]. Overall particle velocity is proportional to the average velocity of the mixture. The pressure drop first increases and then decreases as the solid volume fraction (SVF) increases [3]. For the cases with small particles, measuring performance parameters such as the pressure drop is convenient [4]. For large solid particles, [PERSON] et al. [5] studied particles with a mean diameter of 15.0 mm in a vertical pipe, and proposed some relationships to calculate the settling velocity, slip velocity, and pressure drop. The transportof solid particles with a mean diameter of 20.0 mm has been discussed by [PERSON] et al. [6]. They demonstrated the pressure drop varied inversely with the flow velocity. Apart from particle size, the effect of the inclination angle of the pipe on the solid-liquid two-phase flow was investigated by [PERSON] et al. [7,8]. It was evidenced that large inclination angles are responsible for high pressure drop. In the study of solid-liquid two-phase flows, both experimental and numerical methods have been exercised. For experimental work, the relationship between pressure drop and particle size has been focused on for various flow regimes [9,10]. However, visualization of the solid-liquid two-phase flows is not an easy task. High-speed photography and particle image velocimetry (PIV) techniques exhibit apparent shortages in the presence of non-transparent solid particles. [PERSON] et al. [11] measured solid-liquid flows using PIV and the technique of particle tracking velocimetry (PTV) at a high Reynolds number of 320,000. They concluded that solid particles with diameters of 0.5, 1.0, and 2.0 mm have an insignificant effect on the turbulence of the liquid phase. The computational fluid dynamics (CFD) method has lent its support to the understanding of the solid-liquid two-phase flow. There are two major numerical models, the two-fluid model and the discrete particle model, that have been used in the simulation for solid-liquid two-phase flows. For the two-fluid model, the solid phase is specified as a continuum. However, as the solid phase concentration is high and the distribution of solid particles is non-uniform, the feasibility of the two-fluid model is questionable [12]. The discrete particle model enables a one-way coupling between the flow and solid particles, and the effect of the flow on solid particles is considered. Because the interaction between solid particles is neglected, the model is not suitable for two-phase flows with a high solid volume fraction (SVF). Meanwhile, the two-flow model cannot be used to depict the particle trajectories [13]. The combination of the CFD technique and the discrete element method (DEM) has been introduced and developed in recent years.