A modified drag coefficient model for calculating the terminal settling velocity and horizontal diffusion distance of irregular plume particles in deep-sea mining

Deep-sea mining inevitably produces plumes, which will pose a serious threat to the marine environment with the continuous movement and diffusion of plumes along with ocean currents. The terminal settling velocity ( w t ) of irregular particles is one of the crucial factors for determining the plumes’ diffusion range. It is generally calculated by drag coefficient ( C D ), while most existing C D models only consider single shape characteristic parameter or have a smaller range of Reynolds number ( Re ). In this study, a new shape factor (γ) of irregular particles is proposed by considering the thickness (one-dimension), the projected area (two-dimension), and the surface area (three-dimension) of irregular particles as well as their coupling effect to establish a modified C D model for calculating the w t . A modified Gaussian plume model is proposed to predict the horizontal diffusion distance of the plume particles by considering the settling velocity and diffusion effect of irregular particles. Research results show that the w t increases nearly linearly, with a gradually decreased slope and slightly then greatly with the increasing of γ, d p (diameter) and ρ p (density), respectively. The modified C D model is verified to be more valid with a wider application range ( Re < 3×10 5 ) than five existing C D models by the test results. The larger the ρ p or d p , the larger the w t and thus the smaller the S h . This study could provide a theoretical basis for calculating the plume diffusion range to further study the impact of deep-sea mining on the ocean environment.