Estimation of Rate Constants and Mixing Characteristics in Flotation Columns

The effect of mixing in a flotation column has long been recognized as an important factor in determining the performance of flotation. The paper presents the effects of mixing on the rate constant in a flotation column, and the establishment of relationships based on vessel dispersion numbers (<...

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Autor principal:	Chul-Hyun Park
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	column flotation axial mixing collection rate constant vessel dispersion number Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/b3435c3916b944e4814a7185258ce294
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spelling	oai:doaj.org-article:b3435c3916b944e4814a7185258ce2942021-11-11T15:09:12ZEstimation of Rate Constants and Mixing Characteristics in Flotation Columns10.3390/app1121100842076-3417https://doaj.org/article/b3435c3916b944e4814a7185258ce2942021-10-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/10084https://doaj.org/toc/2076-3417The effect of mixing in a flotation column has long been recognized as an important factor in determining the performance of flotation. The paper presents the effects of mixing on the rate constant in a flotation column, and the establishment of relationships based on vessel dispersion numbers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mi>d</mi></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> that can describe axial dispersion. The rate constants were evaluated using models of plug flow, fully mixed tanks, and axial mixing for a coal cleaning operation. Results showed that fine particles are similar between each model; however, for coarse particles, the deviation is large in the case of perfect mixing, while axial mixing is suitable. It reveals the suitability of using an axial dispersion model for estimating the rate constants, particularly for coarser particles. A regression equation to determine the flotation rate constant was also developed with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mi>d</mi></msub></mrow></semantics></math></inline-formula> values between 0.2 to 0.5. The ratio of particles to liquid the residence times time (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>τ</mi><mi>p</mi></msub><mo>/</mo><msub><mi>τ</mi><mi>L</mi></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> decreases with particle size from small sizes to coarser sizes. Axial dispersion is increased by the superficial gas velocity while is suppressed by the wash water. The relationship between calculated and observed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mi>d</mi></msub></mrow></semantics></math></inline-formula> can be used with a 94% accuracy for the coal cleaning application within the range of operating conditions of superficial gas velocity (0.7–1.6 cm/s), superficial wash water velocity (0.1–0.4 cm/s), and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mi>c</mi></msub><mo>/</mo><msub><mi>d</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula> (26.8–32.7). The empirical relationship of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mi>d</mi></msub></mrow></semantics></math></inline-formula> with significant variables along with the aspect ratio of the column was found to be applicable for coal beneficiation. It may be useful in terms of design and scale up of the columns.Chul-Hyun ParkMDPI AGarticlecolumn flotationaxial mixingcollection rate constantvessel dispersion numberTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10084, p 10084 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	column flotation axial mixing collection rate constant vessel dispersion number Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	column flotation axial mixing collection rate constant vessel dispersion number Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Chul-Hyun Park Estimation of Rate Constants and Mixing Characteristics in Flotation Columns
description	The effect of mixing in a flotation column has long been recognized as an important factor in determining the performance of flotation. The paper presents the effects of mixing on the rate constant in a flotation column, and the establishment of relationships based on vessel dispersion numbers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mi>d</mi></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> that can describe axial dispersion. The rate constants were evaluated using models of plug flow, fully mixed tanks, and axial mixing for a coal cleaning operation. Results showed that fine particles are similar between each model; however, for coarse particles, the deviation is large in the case of perfect mixing, while axial mixing is suitable. It reveals the suitability of using an axial dispersion model for estimating the rate constants, particularly for coarser particles. A regression equation to determine the flotation rate constant was also developed with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mi>d</mi></msub></mrow></semantics></math></inline-formula> values between 0.2 to 0.5. The ratio of particles to liquid the residence times time (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>τ</mi><mi>p</mi></msub><mo>/</mo><msub><mi>τ</mi><mi>L</mi></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> decreases with particle size from small sizes to coarser sizes. Axial dispersion is increased by the superficial gas velocity while is suppressed by the wash water. The relationship between calculated and observed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mi>d</mi></msub></mrow></semantics></math></inline-formula> can be used with a 94% accuracy for the coal cleaning application within the range of operating conditions of superficial gas velocity (0.7–1.6 cm/s), superficial wash water velocity (0.1–0.4 cm/s), and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mi>c</mi></msub><mo>/</mo><msub><mi>d</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula> (26.8–32.7). The empirical relationship of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>N</mi><mi>d</mi></msub></mrow></semantics></math></inline-formula> with significant variables along with the aspect ratio of the column was found to be applicable for coal beneficiation. It may be useful in terms of design and scale up of the columns.
format	article
author	Chul-Hyun Park
author_facet	Chul-Hyun Park
author_sort	Chul-Hyun Park
title	Estimation of Rate Constants and Mixing Characteristics in Flotation Columns
title_short	Estimation of Rate Constants and Mixing Characteristics in Flotation Columns
title_full	Estimation of Rate Constants and Mixing Characteristics in Flotation Columns
title_fullStr	Estimation of Rate Constants and Mixing Characteristics in Flotation Columns
title_full_unstemmed	Estimation of Rate Constants and Mixing Characteristics in Flotation Columns
title_sort	estimation of rate constants and mixing characteristics in flotation columns
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/b3435c3916b944e4814a7185258ce294
work_keys_str_mv	AT chulhyunpark estimationofrateconstantsandmixingcharacteristicsinflotationcolumns
_version_	1718437168402137088

Estimation of Rate Constants and Mixing Characteristics in Flotation Columns

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