{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T00:18:32Z","timestamp":1779236312019,"version":"3.51.4"},"reference-count":52,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T00:00:00Z","timestamp":1707955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Lead recycling is very important for reducing environmental pollution risks and damages. Liquid lead is recovered from exhaust batteries inside stirred batch reactors; the process requires melting to be cleaned. Nevertheless, it is necessary to establish parameters for evaluating mixing to improve the efficiency of the industrial practices. Computational fluid dynamics (CFD) has become a powerful tool to analyze industrial processes for reducing operating costs, avoiding potential damages, and improving the equipment\u2019s performance. Thus, the present work is focused on simulating the fluid hydrodynamics inside a lead-stirred reactor monitoring the distribution of an injected tracer in order to find the best injection point. Then, different injected points are placed on a control plane for evaluation; these are evaluated one by one by monitoring the tracer concentration at a group of points inside the batch. The analyzed reactor is a symmetrical, vertical batch reactor with two geometrical sections: one cylindrical body and a semi-spherical bottom. Here, one impeller with four flat blades in a shaft is used for lead stirring. The tracer concentration on the monitoring points is measured and averaged for evaluating the efficiency inside the tank reactor. Hydrodynamics theory and a comparison between the concentration profiles and distribution of tracer curves are used to demonstrate both methods\u2019 similarities. Then, the invariability of the tracer concentration on the monitoring points is adopted as the main parameter to evaluate the mixing, and the best injection point is found as a function of the shortest mixing time. Additionally, the influence of the impeller rotation speed is analyzed as an additional control parameter to improve industrial practices.<\/jats:p>","DOI":"10.3390\/sym16020237","type":"journal-article","created":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T05:55:59Z","timestamp":1707976559000},"page":"237","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Analysis of Mixing Efficiency in a Stirred Reactor Using Computational Fluid Dynamics"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7678-4572","authenticated-orcid":false,"given":"Adan","family":"Ram\u00edrez-L\u00f3pez","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering, Technological and Autonomous Institute of M\u00e9xico (ITAM), Rio Hondo #1 col. Progreso Tizapan, M\u00e9xico City 01080, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.rser.2016.03.046","article-title":"A critical review on secondary lead recycling technology and its prospect","volume":"61","author":"Zhang","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.jclepro.2019.01.197","article-title":"Novel recycling process for lead-acid battery paste without SO2 generation\u2014Reaction mechanism and industrial pilot campaign","volume":"217","author":"Li","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/j.wasman.2017.03.007","article-title":"Spent lead-acid battery recycling in China\u2014A review and sustainable analyses on mass flow of lead","volume":"64","author":"Sun","year":"2017","journal-title":"Waste Manag."},{"key":"ref_4","unstructured":"Prengaman, R.D., and Mirza, A.H. (2017). Lead-Acid Batteries for Future Automobiles, Elsevier."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Moseley, P.T., Rand, D.A.J., and Garche, J. (2017). Lead-Acid Batteries for Future Automobiles, Elsevier.","DOI":"10.1016\/B978-0-444-63700-0.00021-0"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.resconrec.2014.10.008","article-title":"Management of used lead acid battery in China: Secondary lead industry progress, policies and problems","volume":"93","author":"Tian","year":"2014","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_7","unstructured":"Sloop, S.E., Kotaich, K., Ellis, T.W., and Clarke, R. (2021). RECYCLING|Lead\u2013Acid Batteries: Electrochemical, Reference Module in Chemistry, Molecular Sciences and Chemical Engineering."},{"key":"ref_8","unstructured":"Garche, J., Dyer, C.K., Moseley, P.T., Ogumi, Z., Rand, D.A., and Scrosati, B. (2009). Encyclopedia of Electrochemical Power Sources, Elsevier."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6548","DOI":"10.1021\/ie0308240","article-title":"Ring, Residence Time Distributions in a Stirred Tank:\u2009 Comparison of CFD Predictions with Experiment","volume":"43","author":"Choi","year":"2004","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6143","DOI":"10.1016\/j.ces.2007.06.033","article-title":"Flow field of suspended solids in a stirred tank reactor by Lagrangian tracking","volume":"62","author":"Guha","year":"2007","journal-title":"Chem. Eng. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7535","DOI":"10.1016\/j.ces.2006.08.046","article-title":"Measurement of phase holdups in liquid\u2013liquid\u2013solid three-phase stirred tanks and CFD simulation","volume":"61","author":"Wang","year":"2006","journal-title":"Chem. Eng. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3025","DOI":"10.1016\/j.ces.2005.10.058","article-title":"Numerical simulation of a dissolution process in a stirred tank reactor","volume":"61","author":"Hartmann","year":"2006","journal-title":"Chem. Eng. Sci."},{"key":"ref_13","unstructured":"Hildebrandt, T., Osada, A., Peng, S., and Moyer, T.J. (2017). Lead-Acid Batteries for Future Automobiles, Elsevier."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Blanpain, B., Arnout, S., Chintinne, M., and Swinbourne, D.R. (2014). Handbook of Recycling: State-of-the-Art for Practitioners, Analysts, and Scientists, Elsevier.","DOI":"10.1016\/B978-0-12-396459-5.00008-8"},{"key":"ref_15","unstructured":"Bailey, C., Kumar, S., Patel, M., Piper, A.W., Fosdick, R.A., and Hance, S. (1999, January 6\u20138). Comparison between CFD and measured data for the mixing of lead bullion. Proceedings of the Second International Conference on CFD in Minerals and Process Industries CSIRO, Melbourne, Australia."},{"key":"ref_16","first-page":"A38","article-title":"Numerical Analysis of a Two-Phase Flow and Mixing Process in a Stirred Tank","volume":"6","author":"Huang","year":"2008","journal-title":"Int. J. Chem. React. Eng."},{"key":"ref_17","unstructured":"Koh, P.T.L., and Xantidis, F. (1999, January 6\u20138). CFD Modelling in the scale-up of a stirred reactor for resin beads. Proceedings of the Second International Conference on CFD in Minerals and Process Industries CSIRO, Melbourne, Australia."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3839","DOI":"10.1016\/j.ces.2007.03.043","article-title":"Hollow self-inducing impellers: Flow visualization and CFD simulation","volume":"62","author":"Murthy","year":"2007","journal-title":"Chem. Eng. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.chaos.2006.06.024","article-title":"Liquid mixing enhancement by chaotic perturbations in stirred tanks","volume":"36","author":"Zhang","year":"2008","journal-title":"Chaos Solitons Fractals"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1016\/j.compchemeng.2006.07.009","article-title":"CFD study on mixing by coupled jet-impeller mixers in a large crude oil storage tank","volume":"31","author":"Rahimi","year":"2007","journal-title":"Comput. Chem. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.cep.2015.04.009","article-title":"Computational simulation of mixing flow of shear thinning non-Newtonian fluids with various impellers in a stirred tank","volume":"93","author":"Taghipour","year":"2015","journal-title":"Chem. Eng. Process. Process Intensif."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"430","DOI":"10.1016\/j.jhazmat.2006.02.055","article-title":"Reactivity of waste generated during lead recycling: An integrated study","volume":"139","author":"Lassin","year":"2007","journal-title":"J. Hazard. Mater."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1670","DOI":"10.1016\/j.chemosphere.2007.06.005","article-title":"Evidence of recycling of lead battery waste into highly leaded jewelry","volume":"69","author":"Weidenhamer","year":"2007","journal-title":"Chemosphere"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4920","DOI":"10.1016\/j.ces.2006.12.036","article-title":"CFD simulation of accidents in industrial batch stirred tank reactors","volume":"62","author":"Milewska","year":"2007","journal-title":"Chem. Eng. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.1016\/j.ces.2004.11.018","article-title":"Stirring of a liquid in a stirred tank with an eccentrically located impeller","volume":"60","author":"Karcz","year":"2005","journal-title":"Chem. Eng. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3793","DOI":"10.1016\/j.ces.2003.12.033","article-title":"Mixing analysis in a tank stirred with Ekato Intermig\u00ae impellers","volume":"59","author":"Szalai","year":"2004","journal-title":"Chem. Eng. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3287","DOI":"10.1016\/S0009-2509(99)00570-9","article-title":"Turbulent flow in stirred vessels agitated by a single, low-clearance hyperboloid impeller","volume":"55","author":"Pinho","year":"2000","journal-title":"Chem. Eng. Sci."},{"key":"ref_28","first-page":"25","article-title":"Improving of Mixing Efficiency in a Stirred Reactor for Lead Recycling Using Computer Simulation","volume":"16","year":"2014","journal-title":"Inz. Miner."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.compchemeng.2013.09.005","article-title":"Optimization of reagents injection in a stirred batch reactor by numerical simulation","volume":"60","year":"2014","journal-title":"Comput. Chem. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2000022","DOI":"10.1002\/srin.202000022","article-title":"Numerical Simulation of Tracers Transport Process in Water Model of a Vacuum Refining Unit: Single Snorkel Refining Furnace","volume":"91","author":"Zhang","year":"2020","journal-title":"Steel Res. Int."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Wang, S., Li, Z., He, C., Liu, D., and Zou, G. (2021). An Integrated Method for Modular Design Based on Auto-Generated Multi-Attribute DSM and Improved Genetic Algorithm. Symmetry, 14.","DOI":"10.3390\/sym14010048"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Theyab, S.D., Atshan, W.G., Lupa\u0219, A.A., and Abdullah, H.K. (2022). New Results on Higher-Order Differential Subordination and Superordination for Univalent Analytic Functions Using a New Operator. Symmetry, 14.","DOI":"10.3390\/sym14081576"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1007\/s11696-017-0128-5","article-title":"CFD simulation of floating particles suspension in a stirred tank","volume":"71","author":"Li","year":"2017","journal-title":"Chem. Pap."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.resconrec.2018.09.012","article-title":"Sustainability evaluation of secondary lead production from spent lead acid batteries recycling","volume":"140","author":"Pan","year":"2019","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2771","DOI":"10.1016\/j.ces.2005.09.022","article-title":"Analysis of turbulence anisotropy in a mixing tank","volume":"61","year":"2006","journal-title":"Chem. Eng. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"7312","DOI":"10.1016\/j.electacta.2011.06.047","article-title":"Evaluation of the hydrodynamic behavior of turbulence promoters in parallel plate electrochemical reactors by means of the dispersion model","volume":"56","author":"Colli","year":"2011","journal-title":"Electrochim. Acta"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2650","DOI":"10.1016\/S1003-6326(14)63395-1","article-title":"Experimental and CFD studies of solid\u2013liquid slurry tank stirred with an improved Intermig impeller","volume":"24","author":"Zhao","year":"2014","journal-title":"Trans. Nonferrous Met. Soc. China"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.wasman.2015.09.004","article-title":"Recent development of recycling lead from scrap CRTs: A technological review","volume":"57","author":"Gong","year":"2016","journal-title":"Waste Manag."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1016\/j.cherd.2013.10.020","article-title":"Influence of drag and turbulence modelling on CFD predictions of solid liquid suspensions in stirred vessels","volume":"92","author":"Tamburini","year":"2014","journal-title":"Chem. Eng. Res. Des."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1224","DOI":"10.2355\/isijinternational.ISIJINT-2018-797","article-title":"Demystifying Underlying Fluid Mechanics of Gas Stirred Ladle Systems with Top Slag Layer Using Physical Modeling and Mathematical Modeling","volume":"59","author":"Morales","year":"2019","journal-title":"ISIJ Int."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1007\/s00170-017-0556-y","article-title":"Heat removal analysis on steel billets and slabs produced by continuous casting using numerical simulation","volume":"93","year":"2017","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Ouyang, X., Lin, W., Luo, Y., Zhang, Y., Fan, J., Chen, C., and Cheng, G. (2022). Effect of Salt Tracer Dosages on the Mixing Process in the Water Model of a Single Snorkel Refining Furnace. Metals, 12.","DOI":"10.3390\/met12111948"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.partic.2016.01.012","article-title":"CFD simulation of solid\u2013liquid stirred tanks for low to dense solid loading systems","volume":"29","author":"Wadnerkar","year":"2016","journal-title":"Particuology"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/j.apt.2012.03.007","article-title":"CFD simulation of solid\u2013liquid stirred tanks","volume":"23","author":"Wadnerkar","year":"2012","journal-title":"Adv. Powder Technol."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.ces.2017.11.017","article-title":"Modeling and simulation of the influences of particle-particle interactions on dense solid\u2013liquid suspensions in stirred vessels","volume":"176","author":"Xie","year":"2018","journal-title":"Chem. Eng. Sci."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2723","DOI":"10.1016\/j.apt.2017.07.025","article-title":"Numerical simulation of solid-liquid suspension in a stirred tank with a dual punched rigid-flexible impeller","volume":"28","author":"Gu","year":"2017","journal-title":"Adv. Powder Technol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1016\/j.cej.2013.03.048","article-title":"CFD simulations of dense solid\u2013liquid suspensions in baffled stirred tanks: Prediction of solid particle distribution","volume":"223","author":"Tamburini","year":"2013","journal-title":"Chem. Eng. J."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.cej.2012.04.044","article-title":"CFD simulations of dense solid\u2013liquid suspensions in baffled stirred tanks: Prediction of the minimum impeller speed for complete suspension","volume":"193\u2013194","author":"Tamburini","year":"2012","journal-title":"Chem. Eng. J."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.cherd.2008.08.012","article-title":"Modeling flow and residence time distribution in an industrial-scale reactor with a plunging jet inlet and optional agitation","volume":"86","author":"Bai","year":"2008","journal-title":"Chem. Eng. Res. Des."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1021\/ie0496683","article-title":"Mixing in Liquid Jet-Agitated Tanks: Effects of Jet Asymmetry","volume":"44","author":"Zughbi","year":"2005","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1939","DOI":"10.1021\/acs.iecr.0c06287","article-title":"Study on the Numerical Model of Dense Solid Suspension Driven by a Coaxial Mixer","volume":"60","author":"Xu","year":"2021","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1252\/jcej.18we236","article-title":"Mixing Process in a Tank Stirred with Improved Double Intermig Impellers","volume":"52","author":"Zhou","year":"2019","journal-title":"J. Chem. Eng. Jpn."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/2\/237\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:00:06Z","timestamp":1760104806000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/2\/237"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,15]]},"references-count":52,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,2]]}},"alternative-id":["sym16020237"],"URL":"https:\/\/doi.org\/10.3390\/sym16020237","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,15]]}}}