An extended multiphase drift-flux model with a discretized form of population balance equations for flocculation and settling process of cohesive sediment in deep-sea mining plumes

Abstract

To meet energy demand towards a low-carbon future, the global market demand is growing for metals such as cobalt and nickel which are major elements in batteries. Polymetallic nodules, which are formed on abyssal plains at depths ranging from 4 to 6 kilometres and are distributed in high abundance on the top of the seabed, contains several times more cobalt and nickel than the entire global terrestrial reserves. This has raised the interest to exploit these resources from the deep ocean. The seafloor mining tool (SMT) can move along the soft sea bottom and can collect polymetallic nodules. While doing so, it will also entrain sediments and water. The excess of water and sediment entrained is discharged at the back of the SMT, forming a sediment plume. The sediment plume dispersion has strong adverse impacts on deep-sea environment.Thus, it is essential to study the sediment plume behavior in order to limit plume dispersion and thus to reduce its environmental impact.
Experimental research is a powerful technique to study the plume behaviour. However, experiments sometimes take a long time due to complex set-up. In comparision, numerical analysis can save time and costs when solving complex problems. Furthermore, numerical modelling can provide deeper understanding and flexibility for boundary conditions and sediment types, which is applicable on both model and prototype scale. Previous numerical studies have noted the significant role of flocculation in limiting plume dispersion, but flocculation process has not been modelled explicitly. This study aims to establish a numerical model to study flocculation process and its effect on sediment transport.
Previous flocculation-fluid dynamics modelling has applied a Euler-Euler method with additional population balance equations. The disadvantage is that many equations need to be solved. To avoid excessive computational costs, the sediment transport is described by a multiphase drift-flux model in this study. The flocculation process is modelled by a discretized form of population balance equations. The author has found that, by multiplying the particle volume, the population balance can be efficiently incorporated in the phase continuity equations in the drift-flux model. The population dynamics of particle aggregation and breakup can thus be characterized by the phase transition terms in the phase continuity equations. Hence, no additional equation needs to be introduced and solved.
Verification is carried out to check conservation relationships and iterative convergence of numerical results. Then, an initial numerical investigation has shown the results can qualitatively show the three settling stages (i.e., flocculent settling, hindered settling and compression settling) found in the experimental studies. Afterwards, the collision efficiency is calibrated using the settling column tests conducted by Enthoven (2021). The results of calibration show a good fit to the experimental data. Another advantage is that numerical simulations can provide the particle size distribution over time, which is not measured in the experiments.
The major novelty of this study is the coupling of the drift-flux model and the population balance equations, which inherits both the characteristics of population balance and the merits of drift-flux model in reducing computational costs. The flocculation modeling technique as proposed in this study can be incorporated as a module into an extended drift-flux model to predict the dispersion of deep-sea mining plumes.