CFD model simulation of bubble surface area flux in flotation column reactor in presence of minerals
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摘要
Bubble surface area flux(S_b) is one of the main design parameter in flotation column that typically employed to describe the gas dispersion properties, and it has a strong correlation with the flotation rate constant. There is a limited information available in the literature regarding the effect of particle type,density, wettability and concentration on Sb. In this paper, computational fluid dynamics(CFD) simulations are performed to study the gas–liquid–solid three-phase flow dynamics in flotation column by employing the Eulerian–Eulerian formulation with k-e turbulence model. The model is developed by writing Fortran subroutine and incorporating then into the commercial CFD code AVL FIRE, v.2014.This paper studies the effects of superficial gas velocities and particle type, density, wettability and concentration on Sband bubble concentration in the flotation column. The model has been validated against published experimental data. It was found that the CFD model was able to predict, where the response variable as indicated by R-Square value of 0.98. These results suggest that the developed CFD model is reasonable to describe the flotation column reactor. From the CFD results, it is also found that Sb decreased with increasing solid concentration and hydrophobicity, but increased with increasing superficial gas velocity. For example, approximately 28% reduction in the surface area flux is observed when coal concentration is increased from 0 to 10%, by volume. While for the same solid concentration and gas flow rate, the bubble surface area flux is approximately increased by 7% in the presences of sphalerite.A possible explanation for this might be that increasing solid concentration and hydrophobicity promotes the bubble coalescence rate leading to the increase in bubble size. Also, it was found that the bubble concentration would decrease with addition of hydrophobic particle(i.e., coal). For instance, under the same operating conditions, approximately 23% reduction in the bubble concentration is predicted when the system was working with hydrophobic particles. The results presented are useful for understanding flow dynamics of three-phase system and provide a basis for further development of CFD model for flotation column.
Bubble surface area flux(S_b) is one of the main design parameter in flotation column that typically employed to describe the gas dispersion properties, and it has a strong correlation with the flotation rate constant. There is a limited information available in the literature regarding the effect of particle type,density, wettability and concentration on Sb. In this paper, computational fluid dynamics(CFD) simulations are performed to study the gas–liquid–solid three-phase flow dynamics in flotation column by employing the Eulerian–Eulerian formulation with k-e turbulence model. The model is developed by writing Fortran subroutine and incorporating then into the commercial CFD code AVL FIRE, v.2014.This paper studies the effects of superficial gas velocities and particle type, density, wettability and concentration on Sband bubble concentration in the flotation column. The model has been validated against published experimental data. It was found that the CFD model was able to predict, where the response variable as indicated by R-Square value of 0.98. These results suggest that the developed CFD model is reasonable to describe the flotation column reactor. From the CFD results, it is also found that Sb decreased with increasing solid concentration and hydrophobicity, but increased with increasing superficial gas velocity. For example, approximately 28% reduction in the surface area flux is observed when coal concentration is increased from 0 to 10%, by volume. While for the same solid concentration and gas flow rate, the bubble surface area flux is approximately increased by 7% in the presences of sphalerite.A possible explanation for this might be that increasing solid concentration and hydrophobicity promotes the bubble coalescence rate leading to the increase in bubble size. Also, it was found that the bubble concentration would decrease with addition of hydrophobic particle(i.e., coal). For instance, under the same operating conditions, approximately 23% reduction in the bubble concentration is predicted when the system was working with hydrophobic particles. The results presented are useful for understanding flow dynamics of three-phase system and provide a basis for further development of CFD model for flotation column.
Bubble surface area flux(S_b) is one of the main design parameter in flotation column that typically employed to describe the gas dispersion properties, and it has a strong correlation with the flotation rate constant. There is a limited information available in the literature regarding the effect of particle type,density, wettability and concentration on Sb. In this paper, computational fluid dynamics(CFD) simulations are performed to study the gas–liquid–solid three-phase flow dynamics in flotation column by employing the Eulerian–Eulerian formulation with k-e turbulence model. The model is developed by writing Fortran subroutine and incorporating then into the commercial CFD code AVL FIRE, v.2014.This paper studies the effects of superficial gas velocities and particle type, density, wettability and concentration on Sband bubble concentration in the flotation column. The model has been validated against published experimental data. It was found that the CFD model was able to predict, where the response variable as indicated by R-Square value of 0.98. These results suggest that the developed CFD model is reasonable to describe the flotation column reactor. From the CFD results, it is also found that Sb decreased with increasing solid concentration and hydrophobicity, but increased with increasing superficial gas velocity. For example, approximately 28% reduction in the surface area flux is observed when coal concentration is increased from 0 to 10%, by volume. While for the same solid concentration and gas flow rate, the bubble surface area flux is approximately increased by 7% in the presences of sphalerite.A possible explanation for this might be that increasing solid concentration and hydrophobicity promotes the bubble coalescence rate leading to the increase in bubble size. Also, it was found that the bubble concentration would decrease with addition of hydrophobic particle(i.e., coal). For instance, under the same operating conditions, approximately 23% reduction in the bubble concentration is predicted when the system was working with hydrophobic particles. The results presented are useful for understanding flow dynamics of three-phase system and provide a basis for further development of CFD model for flotation column.
引文
[1]Fan MM,Tao D,Zhao YM,Honaker R.Effect of nanobubbles on the flotation of different sizes of coal particle.Miner Metall Proc 2013;30(3):157-61.
[2]Bhunia K,Kundu G,Mukherjee D.Statistical model for gas holdup in flotation column in presence of minerals.Can Metall Q 2015;54(2):235-46.
[3]Ahmadi R,Khodadadi DA,Abdollahy M,Fan M.Nano-microbubble flotation of fine and ultrafine chalcopyrite particles.Int J Min Sci Technol 2014;24(4):559-66.
[4]Fan M,Tao D,Honaker R,Luo Z.Nanobubble generation and its applications in froth flotation(part IV):mechanical cells and specially designed column flotation of coal.Min Sci Technol(China)2010;20(5):641-71.
[5]Ran JC,Liu JT,Zhang CJ,Wang DY,Li XB.Experimental investigation and modeling of flotation column for treatment of oily wastewater.Int J Min Sci Technol 2013;23(5):665-8.
[6]Shahbazi B,Rezai B,Chelgani SC,Koleini SMJ,Noaparast M.Estimation of diameter and surface area flux of bubbles based on operational gas dispersion parameters by using regression and ANFIS.Int J Min Sci Technol 2013;23(3):343-8.
[7]Sarhan AR,Naser J,Brooks G.CFD simulation on influence of suspended solid particles on bubbles’coalescence rate in flotation cell.Int J Miner Process2016;146:54-64.
[8]Rahman RM,Ata S,Jameson GJ.The effect of flotation variables on the recovery of different particle size fractions in the froth and the pulp.Int J Miner Process2012;106:70-7.
[9]Bhunia K,Kundu G,Mukherjee D.Application of statistical analysis on the bubble surface area flux in a column flotation cell.Sep Sci Technol 2015;50(8):1230-8.
[10]Mirgaux O,Ablitzer D,Waz E,Bellot JP.Mathematical modeling and computer simulation of molten aluminum purification by flotation in stirred reactor.Metall Mater Trans B 2009;40(3):363-75.
[11]Bloom F,Heindel TJ.An approximate analytical expression for the probability of attachment by sliding.J Colloid Interface Sci 1999;218(2):564-77.
[12]Khan MJH,Hussain MA,Mansourpour Z,Mostoufi N,Ghasem NM,Abdullah EC.CFD simulation of fluidized bed reactors for polyolefin production-a review.JInd Eng Chem 2014;20(6):3919-46.
[13]Sha J,Xie G,Wang H,Liu J,Tang L.Effect of the column height on the performance of liquid-solid fluidized bed for the separation of coarse slime.Int J Min Sci Technol 2012;22(4):585-8.
[14]Finch JA,Dobby GS.Column flotation;1990.
[15]Gallegos-Acevedo PM,Perez-Garibay R,Uribe-Salas A,Nava-Alonso F.Bubble load estimation in the froth zone to predict the concentrate mass flow rate of solids in column flotation.Miner Eng 2007;20(13):1210-7.
[16]Finch JA,Xiao J,Hardie C,Gomez CO.Gas dispersion properties:bubble surface area flux and gas holdup.Miner Eng 2000;13(4):365-72.
[17]Gomez CO,Finch JA.Gas dispersion measurements in flotation cells.Int J Miner Process 2007;84(1-4):51-8.
[18]Gorain BK,Franzidis JP,Manlapig EV.The empirical prediction of bubble surface area flux in mechanical flotation cells from cell design and operating data.Miner Eng 1999;12(3):309-22.
[19]Hernandez H,Gomez CO,Finch JA.Gas dispersion and de-inking in a flotation column.Miner Eng 2003;16(8):739-44.
[20]Schwarz S,Alexander D.Gas dispersion measurements in industrial flotation cells.Miner Eng 2006;19(6-8):554-60.
[21]Jameson GJ,Nam S,Young MM.Physical factors affecting recovery rates in flotation.Miner Sci Eng 1977;9(3):103-18.
[22]Gorain BK,Franzidis JP,Manlapig EV.Studies on impeller type,impeller speed and air flow rate in an industrial scale flotation cell.Part 4:Effect of bubble surface area flux on flotation performance.Miner Eng 1997;10(4):367-79.
[23]Hernandez-Aguilar JR,Rao SR,Finch JA.Testing the k-S-b relationship at the microscale.Miner Eng 2005;18(6):591-8.
[24]Leiva J,Vinnett L,Contreras F,Yianatos J.Estimation of the actual bubble surface area flux in flotation.Miner Eng 2010;23(11-13):888-94.
[25]Deglon DA,Sawyerr F,O’Connor CT.A model to relate the flotation rate constant and the bubble surface area flux in mechanical flotation cells.Miner Eng 1999;12(6):599-608.
[26]AVL-FIRE,AVL advanced simulation technologies software documentation;2014.
[27]Li WL,Zhong WQ.CFD simulation of hydrodynamics of gas-liquid-solid threephase bubble column.Powder Technol 2015;286:766-88.
[28]Tomiyama A,Kataoka I,Zun I,Sakaguchi T.Drag coefficients of single bubbles under normal and micro gravity conditions.JSME Int J B-Fluid T 1998;41(2):472-9.
[29]Sattar MA,Naser J,Brooks G.Numerical simulation of two-phase flow with bubble break-up and coalescence coupled with population balance modeling.Chem Eng Process 2013;70:66-76.
[30]Koh PTL,Schwarz MP.CFD model of a self-aerating flotation cell.Int J Miner Process 2007;85(1-3):16-24.
[31]Koh PTL,Schwarz MP.CFD modelling of bubble-particle attachments in flotation cells.Miner Eng 2006;19(6-8):619-26.
[32]Huang K,Lin S,Wang JJ,Luo ZH.Numerical evaluation on the intraparticle transfer in butylene oxidative dehydrogenation fixed-bed reactor over ferrite catalysts.J Ind Eng Chem 2015;29:172-84.
[33]Hosseini SH,Shojaee S,Ahmadi G,Zivdar M.Computational fluid dynamics studies of dry and wet pressure drops in structured packings.J Ind Eng Chem2012;18(4):1465-73.
[34]Akhtar MA,Tade MO,Pareek VK.Two-fluid Eulerian simulation of bubble column reactors with distributors.J Chem Eng Jpn 2006;39(8):831-41.
[35]Prakash A,Margaritis A,Li H,Bergougnou MA.Hydrodynamics and local heat transfer measurements in a bubble column with suspension of yeast.Biochem Eng J 2001;9(2):155-63.
[36]Zhang W,Finch JA.Effect of solids on pulp and froth properties in flotation.JCent South Univ 2014;21(4):1461-9.
[37]Ojima S,Hayashi K,Tomiyama A.Effects of hydrophilic particles on bubbly flow in slurry bubble column.Int J Multiph Flow 2014;58:154-67.
[38]Banisi S,Finch JA,Laplante AR,Weber ME.Effect of solid particles on gas holdup in flotation columns-I.Measurement.Chem Eng Sci 1995;50(14):2329-34.
[39]Tavera FJ,Escudero R.Effect of solids on gas dispersion characteristics:addition of hydrophobic and hydrophilic solids.J Mex Chem Soc 2012;56(2):217-21.
[40]Grevskott S,Sann?s BH,Dudukovic′MP,Hjarbo KW,Svendsen HF.Liquid circulation,bubble size distributions,and solids movement in two-and threephase bubble columns.Chem Eng Sci 1996;51(10):1703-13.
[41]Banisi S,Finch JA,Laplante AR,Weber ME.Effect of solid particles on gas holdup in flotation columns-II.Investigation of mechanisms of gas holdup reduction in presence of solids.Chem Eng Sci 1995;50(14):2335-42.
[42]Sarhan AR,Naser J,Brooks G.CFD analysis of solid particles properties effect in three-phase flotation column.Sep Purif Technol 2017;185:1-9.
[2]Bhunia K,Kundu G,Mukherjee D.Statistical model for gas holdup in flotation column in presence of minerals.Can Metall Q 2015;54(2):235-46.
[3]Ahmadi R,Khodadadi DA,Abdollahy M,Fan M.Nano-microbubble flotation of fine and ultrafine chalcopyrite particles.Int J Min Sci Technol 2014;24(4):559-66.
[4]Fan M,Tao D,Honaker R,Luo Z.Nanobubble generation and its applications in froth flotation(part IV):mechanical cells and specially designed column flotation of coal.Min Sci Technol(China)2010;20(5):641-71.
[5]Ran JC,Liu JT,Zhang CJ,Wang DY,Li XB.Experimental investigation and modeling of flotation column for treatment of oily wastewater.Int J Min Sci Technol 2013;23(5):665-8.
[6]Shahbazi B,Rezai B,Chelgani SC,Koleini SMJ,Noaparast M.Estimation of diameter and surface area flux of bubbles based on operational gas dispersion parameters by using regression and ANFIS.Int J Min Sci Technol 2013;23(3):343-8.
[7]Sarhan AR,Naser J,Brooks G.CFD simulation on influence of suspended solid particles on bubbles’coalescence rate in flotation cell.Int J Miner Process2016;146:54-64.
[8]Rahman RM,Ata S,Jameson GJ.The effect of flotation variables on the recovery of different particle size fractions in the froth and the pulp.Int J Miner Process2012;106:70-7.
[9]Bhunia K,Kundu G,Mukherjee D.Application of statistical analysis on the bubble surface area flux in a column flotation cell.Sep Sci Technol 2015;50(8):1230-8.
[10]Mirgaux O,Ablitzer D,Waz E,Bellot JP.Mathematical modeling and computer simulation of molten aluminum purification by flotation in stirred reactor.Metall Mater Trans B 2009;40(3):363-75.
[11]Bloom F,Heindel TJ.An approximate analytical expression for the probability of attachment by sliding.J Colloid Interface Sci 1999;218(2):564-77.
[12]Khan MJH,Hussain MA,Mansourpour Z,Mostoufi N,Ghasem NM,Abdullah EC.CFD simulation of fluidized bed reactors for polyolefin production-a review.JInd Eng Chem 2014;20(6):3919-46.
[13]Sha J,Xie G,Wang H,Liu J,Tang L.Effect of the column height on the performance of liquid-solid fluidized bed for the separation of coarse slime.Int J Min Sci Technol 2012;22(4):585-8.
[14]Finch JA,Dobby GS.Column flotation;1990.
[15]Gallegos-Acevedo PM,Perez-Garibay R,Uribe-Salas A,Nava-Alonso F.Bubble load estimation in the froth zone to predict the concentrate mass flow rate of solids in column flotation.Miner Eng 2007;20(13):1210-7.
[16]Finch JA,Xiao J,Hardie C,Gomez CO.Gas dispersion properties:bubble surface area flux and gas holdup.Miner Eng 2000;13(4):365-72.
[17]Gomez CO,Finch JA.Gas dispersion measurements in flotation cells.Int J Miner Process 2007;84(1-4):51-8.
[18]Gorain BK,Franzidis JP,Manlapig EV.The empirical prediction of bubble surface area flux in mechanical flotation cells from cell design and operating data.Miner Eng 1999;12(3):309-22.
[19]Hernandez H,Gomez CO,Finch JA.Gas dispersion and de-inking in a flotation column.Miner Eng 2003;16(8):739-44.
[20]Schwarz S,Alexander D.Gas dispersion measurements in industrial flotation cells.Miner Eng 2006;19(6-8):554-60.
[21]Jameson GJ,Nam S,Young MM.Physical factors affecting recovery rates in flotation.Miner Sci Eng 1977;9(3):103-18.
[22]Gorain BK,Franzidis JP,Manlapig EV.Studies on impeller type,impeller speed and air flow rate in an industrial scale flotation cell.Part 4:Effect of bubble surface area flux on flotation performance.Miner Eng 1997;10(4):367-79.
[23]Hernandez-Aguilar JR,Rao SR,Finch JA.Testing the k-S-b relationship at the microscale.Miner Eng 2005;18(6):591-8.
[24]Leiva J,Vinnett L,Contreras F,Yianatos J.Estimation of the actual bubble surface area flux in flotation.Miner Eng 2010;23(11-13):888-94.
[25]Deglon DA,Sawyerr F,O’Connor CT.A model to relate the flotation rate constant and the bubble surface area flux in mechanical flotation cells.Miner Eng 1999;12(6):599-608.
[26]AVL-FIRE,AVL advanced simulation technologies software documentation;2014.
[27]Li WL,Zhong WQ.CFD simulation of hydrodynamics of gas-liquid-solid threephase bubble column.Powder Technol 2015;286:766-88.
[28]Tomiyama A,Kataoka I,Zun I,Sakaguchi T.Drag coefficients of single bubbles under normal and micro gravity conditions.JSME Int J B-Fluid T 1998;41(2):472-9.
[29]Sattar MA,Naser J,Brooks G.Numerical simulation of two-phase flow with bubble break-up and coalescence coupled with population balance modeling.Chem Eng Process 2013;70:66-76.
[30]Koh PTL,Schwarz MP.CFD model of a self-aerating flotation cell.Int J Miner Process 2007;85(1-3):16-24.
[31]Koh PTL,Schwarz MP.CFD modelling of bubble-particle attachments in flotation cells.Miner Eng 2006;19(6-8):619-26.
[32]Huang K,Lin S,Wang JJ,Luo ZH.Numerical evaluation on the intraparticle transfer in butylene oxidative dehydrogenation fixed-bed reactor over ferrite catalysts.J Ind Eng Chem 2015;29:172-84.
[33]Hosseini SH,Shojaee S,Ahmadi G,Zivdar M.Computational fluid dynamics studies of dry and wet pressure drops in structured packings.J Ind Eng Chem2012;18(4):1465-73.
[34]Akhtar MA,Tade MO,Pareek VK.Two-fluid Eulerian simulation of bubble column reactors with distributors.J Chem Eng Jpn 2006;39(8):831-41.
[35]Prakash A,Margaritis A,Li H,Bergougnou MA.Hydrodynamics and local heat transfer measurements in a bubble column with suspension of yeast.Biochem Eng J 2001;9(2):155-63.
[36]Zhang W,Finch JA.Effect of solids on pulp and froth properties in flotation.JCent South Univ 2014;21(4):1461-9.
[37]Ojima S,Hayashi K,Tomiyama A.Effects of hydrophilic particles on bubbly flow in slurry bubble column.Int J Multiph Flow 2014;58:154-67.
[38]Banisi S,Finch JA,Laplante AR,Weber ME.Effect of solid particles on gas holdup in flotation columns-I.Measurement.Chem Eng Sci 1995;50(14):2329-34.
[39]Tavera FJ,Escudero R.Effect of solids on gas dispersion characteristics:addition of hydrophobic and hydrophilic solids.J Mex Chem Soc 2012;56(2):217-21.
[40]Grevskott S,Sann?s BH,Dudukovic′MP,Hjarbo KW,Svendsen HF.Liquid circulation,bubble size distributions,and solids movement in two-and threephase bubble columns.Chem Eng Sci 1996;51(10):1703-13.
[41]Banisi S,Finch JA,Laplante AR,Weber ME.Effect of solid particles on gas holdup in flotation columns-II.Investigation of mechanisms of gas holdup reduction in presence of solids.Chem Eng Sci 1995;50(14):2335-42.
[42]Sarhan AR,Naser J,Brooks G.CFD analysis of solid particles properties effect in three-phase flotation column.Sep Purif Technol 2017;185:1-9.
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