Abstract
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 (wt) of irregular particles is one of the crucial factors for determining the plumes’ diffusion range. It is generally calculated by drag coefficient (CD), while most existing CD 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 CD model for calculating the wt. 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 wt increases nearly linearly, with a gradually decreased slope and slightly then greatly with the increasing of γ, dp (diameter) and ρp (density), respectively. The modified CD model is verified to be more valid with a wider application range (Re < 3×105) than five existing CD models by the test results. The larger the ρp or dp, the larger the wt and thus the smaller the Sh. 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Data will be made available on request.
References
Aleynik D, Inall ME, Dale A, Vink A (2017) Impact of remotely generated eddies on plume dispersion at abyssal mining sites in the Pacific. Sci Rep 7:16959. https://doi.org/10.1038/s41598-017-16912-2
Arystanbekova NK (2004) Application of Gaussian plume models for air pollution simulation at instantaneous emissions. Math Comput Simul 67:451–458. https://doi.org/10.1016/j.matcom.2004.06.023
Baba J, Komar PD (1981) Settling velocities of irregular grains at low Reynolds numbers. J Sediment Res 51:121–128. https://doi.org/10.1306/212F7C25-2B24-11D7-8648000102C1865D
Bagheri G, Bonadonna C (2016) On the drag of freely falling non-spherical particles. Powder Technol 301:526–544. https://doi.org/10.1016/j.powtec.2016.06.015
Briggs LI, McCulloch DS, Moser F (1962) The hydraulic shape of sand particles. J Sediment Res 32:645–656. https://doi.org/10.1306/74D70D44-2B21-11D7-8648000102C1865D
Camenen B (2007) Simple and general formula for the settling velocity of particles. J Hydraul Eng ASCE 133:229–233. https://doi.org/10.1061/(asce)0733-9429(2007)133:2(229)
Chambert S, James CS (2009) Sorting of seeds by hydrochory. River Res Appl 25:48–61. https://doi.org/10.1002/rra.1093
Chien S-F (1994) Settling velocity of irregularly shaped particles. SPE Drill Complet 9:281–289. https://doi.org/10.2118/26121-PA
Christiansen EB, Barker DH (1965) The effect of shape and density on the free settling of particles at high Reynolds numbers. AlChE J 11:145–151. https://doi.org/10.1002/aic.690110130
Clift R, Gauvin WH (1971) Motion of entrained particles in gas streams. Can J Chem Eng 49:439–448. https://doi.org/10.1002/cjce.5450490403
Dellino P, Mele D, Bonasia R, Braia G, La Volpe L, Sulpizio R (2005) The analysis of the influence of pumice shape on its terminal velocity. Geophys Res Lett 32:L21306. https://doi.org/10.1029/2005GL023954
Dioguardi F, Mele D (2015) A new shape dependent drag correlation formula for non-spherical rough particles. Experiments and results. Powder Technol 277:222–230. https://doi.org/10.1016/j.powtec.2015.02.062
Dioguardi F, Mele D, Dellino P (2018) A new one-equation model of fluid drag for irregularly shaped particles valid over a wide range of Reynolds number. J Geophys Res Solid Earth 123:144–156. https://doi.org/10.1002/2017jb014926
Francalanci S, Paris E, Solari L (2021) On the prediction of settling velocity for plastic particles of different shapes. Environ Pollut 290:118068. https://doi.org/10.1016/j.envpol.2021.118068
Ganser GH (1993) A rational approach to drag prediction of spherical and nonspherical particles. Powder Technol 77:143–152. https://doi.org/10.1016/0032-5910(93)80051-B
Gogus M, Ipekci ON, Kokpinar MA (2001) Effect of particle shape on fall velocity of angular particles. J Hydraul Eng 127:860–869
Goral KD, Guler HG, Larsen BE, Carstensen S, Christensen ED, Kerpen NB, Schlurmann T, Fuhrman DR (2023) Settling velocity of microplastic particles having regular and irregular shapes. Environ Res 228:115783. https://doi.org/10.1016/j.envres.2023.115783
Haider A, Levenspiel O (1989) Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol 58:63–70. https://doi.org/10.1016/0032-5910(89)80008-7
Koch EW, Ailstock MS, Booth DM, Shafer DJ, Magoun AD (2010) The role of currents and waves in the dispersal of submersed angiosperm seeds and seedlings. Restor Ecol 18:584–595. https://doi.org/10.1111/j.1526-100X.2010.00698.x
Komar PD (1980) Settling velocities of circular cylinders at low Reynolds numbers. J Geol 88:327–336. https://doi.org/10.1086/628510
Komar PD, Reimers CE (1978) Grain shape effects on settling rates. J Geol 86:193–209. https://doi.org/10.1086/649674
Le Roux JP (2004) A hydrodynamic classification of grain shapes. J Sediment Res 74:135–143. https://doi.org/10.1306/060603740135
Liu S, Yang J, Lu H, Sun P, Zhang B (2023) A numerical investigation of the dynamic interaction between the deep-sea mining vehicle and sediment plumes based on a small-scale analysis. J Mar Sci Eng 11:1458. https://doi.org/10.3390/jmse11071458
Liu X, Godbole A, Lu C, Michal G, Venton P (2015) Optimisation of dispersion parameters of Gaussian plume model for CO2 dispersion. Environ Sci Pollut Res 22:18288–18299. https://doi.org/10.1007/s11356-015-5404-8
Mestre NC, Rocha TL, Canals M, Cardoso C, Danovaro R, Dell’Anno A, Gambi C, Regoli F, Sanchez-Vidal A, Bebianno MJ (2017) Environmental hazard assessment of a marine mine tailings deposit site and potential implications for deep-sea mining. Environ Pollut 228:169–178. https://doi.org/10.1016/j.envpol.2017.05.027
Miller KA, Thompson KF, Johnston P, Santillo D (2018) An overview of seabed mining including the current state of development, environmental impacts, and knowledge gaps. Front Mar Sci 4:418. https://doi.org/10.3389/fmars.2017.00418
Miyake Y (1948) The measurement of the viscosity coefficient of sea water. J Mar Res 7:63–66
Munoz-Royo C, Ouillon R, El Mousadik S, Alford MH, Peacock T (2022) An in situ study of abyssal turbidity-current sediment plumes generated by a deep seabed polymetallic nodule mining preprototype collector vehicle. Sci Adv 8:eabn1219. https://doi.org/10.1126/sciadv.abn1219
Muñoz-Royo C, Peacock T, Alford MH, Smith JA, Le Boyer A, Kulkarni CS, Lermusiaux PFJ, Haley PJ, Mirabito C, Wang D, Adams EE, Ouillon R, Breugem A, Decrop B, Lanckriet T, Supekar RB, Rzeznik AJ, Gartman A, Ju S-J (2021) Extent of impact of deep-sea nodule mining midwater plumes is influenced by sediment loading, turbulence and thresholds. Commun Earth Environ 2:148. https://doi.org/10.1038/s43247-021-00213-8
Oebius HU, Becker HJ, Rolinski S, Jankowski JA (2001) Parametrization and evaluation of marine environmental impacts produced by deep-sea manganese nodule mining. Deep Sea Res Part II 48:3453–3467. https://doi.org/10.1016/S0967-0645(01)00052-2
Ouillon R, Muñoz-Royo C, Alford MH, Peacock T (2022) Advection–diffusion settling of deep-sea mining sediment plumes. Part 2. Collector plumes. Flow 2:E23. https://doi.org/10.1017/flo.2022.19
Palka I, Saniewska D, Bielecka L, Kobos J, Grzybowski W (2024) Uptake and trophic transfer of selenium into phytoplankton and zooplankton of the southern Baltic Sea. Sci Total Environ 909:168312. https://doi.org/10.1016/j.scitotenv.2023.168312
Peacock T, Ouillon R (2023) The fluid mechanics of deep-sea mining. Annu Rev Fluid Mech 55:403–430. https://doi.org/10.1146/annurev-fluid-031822-010257
Petersen S, Kraeschell A, Augustin N, Jamieson J, Hein JR, Hannington MD (2016) News from the seabed - geological characteristics and resource potential of deep-sea mineral resources. Mar Pol 70:175–187. https://doi.org/10.1016/j.marpol.2016.03.012
Qin B, Salipante PF, Hudson SD, Arratia PE (2019) Flow resistance and structures in viscoelastic channel flows at low Re. Phys Rev Lett 123:194501. https://doi.org/10.1103/PhysRevLett.123.194501
Riazi A, Türker U (2019) The drag coefficient and settling velocity of natural sediment particles. Comput Part Mech 6:427–437. https://doi.org/10.1007/s40571-019-00223-6
Roostaee A, Vaezi M (2022) Developing a standard platform to predict the drag coefficient of irregular shape particles. Powder Technol 395:314–337. https://doi.org/10.1016/j.powtec.2021.09.037
Rzeznik AJ, Flierl GR, Peacock T (2019) Model investigations of discharge plumes generated by deep-sea nodule mining operations. Ocean Eng 172:684–696. https://doi.org/10.1016/j.oceaneng.2018.12.012
Schulz EF, Wilde RH, Albertson ML (1954) Influence of shape on the fall velocity of sedimentary particles. Missouri River Division, Corps of Engineers, U. S. Army, through the Colorado A and M Research Foundation, Fort Collins, CO, Report No. CER56
Song X, Xu Z, Li G, Pang Z, Zhu Z (2017) A new model for predicting drag coefficient and settling velocity of spherical and non-spherical particle in Newtonian fluid. Powder Technol 321:242–250. https://doi.org/10.1016/j.powtec.2017.08.017
Spearman J, Taylor J, Crossouard N, Cooper A, Turnbull M, Manning A, Lee M, Murton B (2020) Measurement and modelling of deep sea sediment plumes and implications for deep sea mining. Sci Rep 10:5075. https://doi.org/10.1038/s41598-020-61837-y
Sun P, Lu H, Yang J, Liu M, Li S, Zhang B (2022) Numerical study on shear interaction between the track plate of deep-sea mining vehicle and the seafloor sediment based on CEL method. Ocean Eng 266:112785. https://doi.org/10.1016/j.oceaneng.2022.112785
Swamee PK, Ojha CSP (1991) Drag coefficient and fall velocity of nonspherical particles. J Hydraul Eng ASCE 117:660–667. https://doi.org/10.1061/(ASCE)0733-9429(1991)117:5(660
Tran-Cong S, Gay M, Michaelides EE (2004) Drag coefficients of irregularly shaped particles. Powder Technol 139:21–32. https://doi.org/10.1016/j.powtec.2003.10.002
Van Melkebeke M, Janssen C, De Meester S (2020) Characteristics and sinking behavior of typical microplastics including the potential effect of biofouling: implications for remediation. Environ Sci Technol 54:8668–8680. https://doi.org/10.1021/acs.est.9b07378
Wadell H (1932) Volume, shape, and roundness of rock particles. J Geol 40:443–451. https://doi.org/10.1086/623964
Wang J, Qi H, Zhu J (2011) Experimental study of settling and drag on cuboids with square base. Particuology 9:298–305. https://doi.org/10.1016/j.partic.2010.11.002
Wang Y, Zhou L, Wu Y, Yang Q (2018) New simple correlation formula for the drag coefficient of calcareous sand particles of highly irregular shape. Powder Technol 326:379–392. https://doi.org/10.1016/j.powtec.2017.12.004
Weaver PPE, Aguzzi J, Boschen-Rose RE, Colaco A, de Stigter H, Gollner S, Haeckel M, Hauton C, Helmons R, Jones DOB, Lily H, Mestre NC, Mohn C, Thomsen L (2022) Assessing plume impacts caused by polymetallic nodule mining vehicles. Mar Pol 139:105011. https://doi.org/10.1016/j.marpol.2022.105011
Wilson L, Huang TC (1979) The influence of shape on the atmospheric settling velocity of volcanic ash particles. Earth Planet Sci Lett 44:311–324. https://doi.org/10.1016/0012-821X(79)90179-1
Wu WM, Wang SSY (2006) Formulas for sediment porosity and settling velocity. J Hydraul Eng 132:858–862. https://doi.org/10.1061/(asce)0733-9429(2006)132:8(858)
Yow HN, Pitt MJ, Salman AD (2005) Drag correlations for particles of regular shape. Adv Powder Technol 16:363–372. https://doi.org/10.1163/1568552054194221
Zhu X, Zeng YH, Huai WX (2017) Settling velocity of non-spherical hydrochorous seeds. Adv Water Resour 103:99–107. https://doi.org/10.1016/j.advwatres.2017.03.001
Acknowledgements
We are grateful to thanks the reviewers who provided valuable comments and suggestions. We also thank the people who provided valuable test data.
Funding
This work was supported by the Major project of Hunan Natural Science Foundation (No. 2021JC0010) and the Fundamental Research Funds for the Central Universities of Central South University (2022zzts0036).
Author information
Authors and Affiliations
Contributions
Zelin Liu: conceptualization, investigation, data curation, visualization, writing—review and editing. Qiuhua Rao: conceptualization, investigation, visualization, writing—review and editing. Wei Yi: investigation, visualization. Wei Huang: investigation.
Corresponding author
Ethics declarations
Ethical approval
Not applicable
Consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare no competing interests.
Additional information
Responsible Editor: Philippe Garrigues
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
ESM 1
(XLSX 1158 kb)
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Liu, Zl., Rao, Qh., Yi, W. et al. A modified drag coefficient model for calculating the terminal settling velocity and horizontal diffusion distance of irregular plume particles in deep-sea mining. Environ Sci Pollut Res 31, 33848–33866 (2024). https://doi.org/10.1007/s11356-024-33422-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11356-024-33422-7