Extending the EMMS/bubbling model to fluidization of binary particle mixture: Formulation and steady-state validation
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摘要
The EMMS/bubbling model originally proposed for fluidization of monodisperse particles is extended to fluidization of binary particle mixture in this study.The dense and dilute phases are considered to comprise of two types of particles differing in size and/or density.Governing equations and the stability condition are then formulated and solved by using an optimization numerical scheme.The effects of bubble diameter are first investigated and a suitable bubble diameter correlation is chosen.Preliminary validation for steady state behavior shows the extended model can fairly capture the overall hydrodynamic behaviors in terms of volume fraction of bubbles and average bed voidage for both monodisperse and binary particle systems.This encourages us to integrate this model with CFD for more validations in the future.
The EMMS/bubbling model originally proposed for fluidization of monodisperse particles is extended to fluidization of binary particle mixture in this study.The dense and dilute phases are considered to comprise of two types of particles differing in size and/or density.Governing equations and the stability condition are then formulated and solved by using an optimization numerical scheme.The effects of bubble diameter are first investigated and a suitable bubble diameter correlation is chosen.Preliminary validation for steady state behavior shows the extended model can fairly capture the overall hydrodynamic behaviors in terms of volume fraction of bubbles and average bed voidage for both monodisperse and binary particle systems.This encourages us to integrate this model with CFD for more validations in the future.
The EMMS/bubbling model originally proposed for fluidization of monodisperse particles is extended to fluidization of binary particle mixture in this study.The dense and dilute phases are considered to comprise of two types of particles differing in size and/or density.Governing equations and the stability condition are then formulated and solved by using an optimization numerical scheme.The effects of bubble diameter are first investigated and a suitable bubble diameter correlation is chosen.Preliminary validation for steady state behavior shows the extended model can fairly capture the overall hydrodynamic behaviors in terms of volume fraction of bubbles and average bed voidage for both monodisperse and binary particle systems.This encourages us to integrate this model with CFD for more validations in the future.
引文
[1]J.Li,M.Kwauk,Particle-fluid Two-phase Flow:The Energy-minimization Multiscale Method,Metallurgical Industry Press,Beijing,1994(in Chinese).
[2]S.Sundaresan,Modeling the hydrodynamics of multiphase flow reactors:Current status and challenges,AICHE J.46(2000)1102-1105.
[3]J.Li,M.Kwauk,Exploring complex systems in chemical engineering-The multi-scale methodology,Chem.Eng.Sci.58(2003)521-535.
[4]J.R.Grace,R.Clift,On the two-phase theory of fluidization,Chem.Eng.Sci.29(1974)327-334.
[5]R.J.Best,J.G.Yates,The expansion characteristics of a bubbling fluidized bed,Powder Technol.16(1977)285-288.
[6]D.Kunii,O.Levenspiel,Fluidization Engineering,Second ed.Butterworth-Heinemann,Boston,1991 137-164.
[7]J.Li,A.Chen,Z.Yan,G.Xu,X.Zhang,Particle-fluid Contacting in Circulating Fluidized Beds,Preprint Volume for Circulating Fluidized Beds IV,AIChE,Somerset,1993.
[8]T.J.O.Brien,M.Syamlal,Particle Cluster Effects in the Numerical Simulation of a Circulating Fluidized Bed,Preprint Volume for Circulating Fluidized Beds IV,AIChE,Somerset,1993.
[9]J.Li,L.Wen,W.Ge,H.Cui,J.Ren,Dissipative structure in concurrent-up gas-solid flow,Chem.Eng.Sci.53(1998)3367-3379.
[10]N.Yang,W.Wang,W.Ge,J.Li,Choosing structure-dependent drag coefficient in modeling gas-solid two-phase flow,China Particuology 1(2003)38-41.
[11]B.Lu,W.Wang,J.Li,X.Wang,S.Gao,W.Lu,Y.Xu,J.Long,Multi-scale CFD simulation of gas-solid flow in MIP reactors with a structure-dependent drag model,Chem.Eng.Sci.62(2007)5487-5494.
[12]W.Wang,J.Li,Simulation of gas-solid two-phase flow by a multi-scale CFDapproach-Extension of the EMMS model to the sub-grid level,Chem.Eng.Sci.62(2007)208-231.
[13]B.Lu,W.Wang,J.Li,Searching for a mesh-independent sub-grid model for CFDsimulation of gas-solid riser flows,Chem.Eng.Sci.64(2009)3437-3447.
[14]B.Lu,W.Wang,J.Li,Eulerian simulation of gas-solid flows with particles of Geldart groups A,B and D using EMMS-based meso-scale model,Chem.Eng.Sci.66(2011)4624-4635.
[15]Y.Mei,M.Zhao,B.Lu,S.Chen,W.Wang,Numerical comparison of two modes of gas-solid riser operation:Fluid catalytic cracking vs CFB combustor,Particuology31(2017)42-48.
[16]Z.Shi,W.Wang,J.Li,A bubble-based EMMS model for gas-solid bubbling fluidization,Chem.Eng.Sci.66(2011)5541-5555.
[17]K.Hong,Z.Shi,W.Wang,J.Li,A structure-dependent multi-fluid model(SFM)for heterogeneous gas-solid flow,Chem.Eng.Sci.99(2013)191-202.
[18]K.Hong,Z.Shi,A.Ullah,W.Wang,Extending the bubble-based EMMS model to CFBriser simulations,Powder Technol.266(2014)424-432.
[19]O.Owoyemi,L.Mazzei,P.Lettieri,CFD modeling of binary-fluidized suspensions and investigation of role of particle-particle drag on mixing and segregation,AICHE J.53(2007)1924-1940.
[20]V.Mizonov,H.Berthiaux,C.Gatumel,Theoretical search for solutions to minimize negative influence of segregation in mixing of particulate solids,Particuology 25(2016)36-41.
[21]M.Kiani,M.R.Rahimi,S.H.Hosseini,G.Ahmadi,Mixing and segregation of solid particles in a conical spouted bed:Effect of particle size and density,Particuology32(2017)132-140.
[22]M.P.Babu,P.S.T.Sai,K.Krishnaiah,Continuous segregation of binary heterogeneous solids in a fast-fluidized bed,Particulogy 35(2017)93-100.
[23]M.Wormsbecker,A.Adams,T.Pugsley,C.Winters,Segregation by size difference in a conical fluidized bed of pharmaceutical granulate,Powder Technol.153(2005)72-80.
[24]J.R.Grace,G.Sun,Influence of particle size distribution on the performance of fluidized bed reactors,Can.J.Chem.Eng.69(1991)1126-1134.
[25]X.Z.Chen,Z.H.Luo,W.C.Yan,Y.H.Lu,I.S.Ng,Three-dimensional CFD-PBM coupled model of the temperature fields in fluidized-bed polymerization reactors,AICHE J.57(2011)3351-3366.
[26]L.T.Zhu,H.Pan,Y.H.Su,Z.H.Luo,Effect of particle polydispersity on flow and reaction behaviors of methanol-to-olefins fluidized bed reactors,Ind.Eng.Chem.Res.56(2017)1090-1102.
[27]P.N.Rowe,A.W.Nienow,Particle mixing and segregation in gas fluidised beds.Areview,Powder Technol.15(1976)141-147.
[28]J.W.Chew,R.Hays,J.G.Findlay,T.M.Knowlton,S.B.R.Karri,R.A.Cocco,C.M.Hrenya,Cluster characteristics of Geldart group B particles in a pilot-scale CFB riser.II.Polydisperse systems,Chem.Eng.Sci.68(2012)82-93.
[29]B.Lu,N.Zhang,W.Wang,J.Li,J.H.Chiu,S.G.Kang,3-D full-loop simulation of an industrial-scale circulating fluidized-bed boiler,AICHE J.59(2013)1108-1117.
[30]S.Benyahia,Analysis of model parameters affecting the pressure profile in a circulating fluidized bed,AICHE J.58(2012)427-439.
[31]M.Lungu,Y.Zhou,J.Wang,Y.Yang,A CFD study of a bi-disperse gas-solid fluidized bed:Effect of the EMMS sub grid drag correction,Powder Technol.280(2015)154-172.
[32]Q.Zhou,J.Wang,CFD study of mixing and segregation in CFB risers:Extension of EMMS drag model to binary gas-solid flow,Chem.Eng.Sci.122(2015)637-651.
[33]J.Wang,W.Ge,J.Li,Eulerian simulation of heterogeneous gas-solid flows in CFBrisers:EMMS-based sub-grid scale model with a revised cluster description,Chem.Eng.Sci.63(2008)1553-1571.
[34]Y.Zhao,H.Li,M.Ye,Z.Liu,3D numerical simulation of a large scale MTO fluidized bed reactor,Ind.Eng.Chem.Res.52(2013)11354-11364.
[35]K.Hong,S.Chen,W.Wang,J.Li,Fine-grid two-fluid modeling of fluidization of Geldart A particles,Powder Technol.296(2016)2-16.
[36]B.Lu,H.Luo,H.Li,W.Wang,M.Ye,Z.Liu,J.Li,Speeding up CFD simulation of fluidized bed reactor for MTO by coupling CRE model,Chem.Eng.Sci.143(2016)341-350.
[37]B.Lu,J.Zhang,H.Luo,W.Wang,H.Li,M.Ye,Z.Liu,J.Li,Numerical simulation of scale-up effects of methanol-to-olefins fluidized bed reactors,Chem.Eng.Sci.171(2017)244-255.
[38]H.Luo,B.Lu,J.Zhang,H.Wu,W.Wang,A grid-independent EMMS/bubbling drag model for bubbling and turbulent fluidization,Chem.Eng.J.326(2017)47-57.
[39]Y.Tian,J.Geng,W.Wang,Structure-dependent analysis of energy dissipation in gas-solid flows:Beyond nonequilibrium thermodynamics,Chem.Eng.Sci.171(2017)271-281.
[40]S.Mori,C.Y.Wen,Estimation of bubble diameter in gaseous fluidized beds,AICHE J.21(1975)109-115.
[41]S.Karimipour,T.Pugsley,A critical evaluation of literature correlations for predicting bubble size and velocity in gas-solid fluidized beds,Powder Technol.205(2011)1-14.
[42]J.B.Romero,L.N.Johanson,Factors affecting fluidized bed quality,Chem.Eng.Prog.Symp.Ser.58(1962)28-37.
[43]A.Whitehead,A.Young,Fluidization performance in large scale equipment,Proceedings of the International Symposium on Fluidization 1967,pp.284-293.
[44]D.Geldart,The effect of particle size and size distribution on the behaviour of gasfluidised beds,Powder Technol.6(1972)201-215.
[45]C.Fryer,O.E.Potter,Experimental investigation of models for fluidized bed catalytic reactors,AICHE J.22(1976)38-47.
[46]C.X.Yacono,An X-ray study of bubbbles in gas-fluidised beds of small particles,Ph.D.Dissertation,University of London,1975.
[47]J.Werther,Hydrodynamics and mass transfer between the bubble and emulsion phases in fluidized beds of sand and cracking catalyst,in:R.Toei(Ed.),Fluidization,New York Engineering Foundation,1983.
[48]P.Cai,M.Schiavetti,G.De Michele,G.C.Grazzini,M.Miccio,Quantitative estimation of bubble size in PFBC,Powder Technol.80(1994)99-109.
[49]M.Horio,A.Nonaka,A generalized bubble diameter correlation for gas-solid fluidized beds,AICHE J.33(1987)1865-1872.
[50]R.Krishna,J.M.van Baten,Using CFD for scaling up gas-solid bubbling fluidised bed reactors with Geldart A powders,Chem.Eng.J.82(2001)247-257.
[51]F.Johnsson,S.Andersson,B.Leckner,Expansion of a freely bubbling fluidized bed,Powder Technol.68(1991)117-123.
[52]D.Geldart,The size and frequency of bubbles in two-and three-dimensional gasfluidised beds,Powder Technol.4(1970)41-55.
[53]G.Yasui,L.N.Johanson,Characteristics of gas pockets in fluidised beds,AICHE J.4(1958)445-452.
[54]W.H.Park,W.K.Kang,C.E.Capes,G.L.Osberg,The properties of bubbles in fluidised beds of conducting particles as measured by an electroresistivity probe,Chem.Eng.Sci.24(1969)851-865.
[55]A.R.Abrahamsen,D.Geldart,Behaviour of gas-fluidized beds of fine powders part II.Voidage of the dense phase in bubbling beds,Powder Technol.26(1980)47-55.
[56]H.Cui,N.Mostoufi,J.Chaouki,Gas and solids between dynamic bubble and emulsion in gas-fluidized beds,Powder Technol.120(2001)12-20.
[57]K.Hilligardt,J.Werther,Influence of temperature and properties of solids on the size and growth of bubbles in gas fluidized beds,Chem.Eng.Technol.10(1987)272-280.
[58]S.Chiba,T.Chiba,A.W.Nienow,H.Kobayashi,The minimum fluidisation velocity,bed expansion and pressure-drop profile of binary particle mixtures,Powder Technol.22(1979)255-269.
[59]B.Formisani,G.D.Cristofaro,R.Girimonte,A fundamental approach to the phenomenology of fluidization of size segregating binary mixtures of solids,Chem.Eng.Sci.56(2001)109-119.
[2]S.Sundaresan,Modeling the hydrodynamics of multiphase flow reactors:Current status and challenges,AICHE J.46(2000)1102-1105.
[3]J.Li,M.Kwauk,Exploring complex systems in chemical engineering-The multi-scale methodology,Chem.Eng.Sci.58(2003)521-535.
[4]J.R.Grace,R.Clift,On the two-phase theory of fluidization,Chem.Eng.Sci.29(1974)327-334.
[5]R.J.Best,J.G.Yates,The expansion characteristics of a bubbling fluidized bed,Powder Technol.16(1977)285-288.
[6]D.Kunii,O.Levenspiel,Fluidization Engineering,Second ed.Butterworth-Heinemann,Boston,1991 137-164.
[7]J.Li,A.Chen,Z.Yan,G.Xu,X.Zhang,Particle-fluid Contacting in Circulating Fluidized Beds,Preprint Volume for Circulating Fluidized Beds IV,AIChE,Somerset,1993.
[8]T.J.O.Brien,M.Syamlal,Particle Cluster Effects in the Numerical Simulation of a Circulating Fluidized Bed,Preprint Volume for Circulating Fluidized Beds IV,AIChE,Somerset,1993.
[9]J.Li,L.Wen,W.Ge,H.Cui,J.Ren,Dissipative structure in concurrent-up gas-solid flow,Chem.Eng.Sci.53(1998)3367-3379.
[10]N.Yang,W.Wang,W.Ge,J.Li,Choosing structure-dependent drag coefficient in modeling gas-solid two-phase flow,China Particuology 1(2003)38-41.
[11]B.Lu,W.Wang,J.Li,X.Wang,S.Gao,W.Lu,Y.Xu,J.Long,Multi-scale CFD simulation of gas-solid flow in MIP reactors with a structure-dependent drag model,Chem.Eng.Sci.62(2007)5487-5494.
[12]W.Wang,J.Li,Simulation of gas-solid two-phase flow by a multi-scale CFDapproach-Extension of the EMMS model to the sub-grid level,Chem.Eng.Sci.62(2007)208-231.
[13]B.Lu,W.Wang,J.Li,Searching for a mesh-independent sub-grid model for CFDsimulation of gas-solid riser flows,Chem.Eng.Sci.64(2009)3437-3447.
[14]B.Lu,W.Wang,J.Li,Eulerian simulation of gas-solid flows with particles of Geldart groups A,B and D using EMMS-based meso-scale model,Chem.Eng.Sci.66(2011)4624-4635.
[15]Y.Mei,M.Zhao,B.Lu,S.Chen,W.Wang,Numerical comparison of two modes of gas-solid riser operation:Fluid catalytic cracking vs CFB combustor,Particuology31(2017)42-48.
[16]Z.Shi,W.Wang,J.Li,A bubble-based EMMS model for gas-solid bubbling fluidization,Chem.Eng.Sci.66(2011)5541-5555.
[17]K.Hong,Z.Shi,W.Wang,J.Li,A structure-dependent multi-fluid model(SFM)for heterogeneous gas-solid flow,Chem.Eng.Sci.99(2013)191-202.
[18]K.Hong,Z.Shi,A.Ullah,W.Wang,Extending the bubble-based EMMS model to CFBriser simulations,Powder Technol.266(2014)424-432.
[19]O.Owoyemi,L.Mazzei,P.Lettieri,CFD modeling of binary-fluidized suspensions and investigation of role of particle-particle drag on mixing and segregation,AICHE J.53(2007)1924-1940.
[20]V.Mizonov,H.Berthiaux,C.Gatumel,Theoretical search for solutions to minimize negative influence of segregation in mixing of particulate solids,Particuology 25(2016)36-41.
[21]M.Kiani,M.R.Rahimi,S.H.Hosseini,G.Ahmadi,Mixing and segregation of solid particles in a conical spouted bed:Effect of particle size and density,Particuology32(2017)132-140.
[22]M.P.Babu,P.S.T.Sai,K.Krishnaiah,Continuous segregation of binary heterogeneous solids in a fast-fluidized bed,Particulogy 35(2017)93-100.
[23]M.Wormsbecker,A.Adams,T.Pugsley,C.Winters,Segregation by size difference in a conical fluidized bed of pharmaceutical granulate,Powder Technol.153(2005)72-80.
[24]J.R.Grace,G.Sun,Influence of particle size distribution on the performance of fluidized bed reactors,Can.J.Chem.Eng.69(1991)1126-1134.
[25]X.Z.Chen,Z.H.Luo,W.C.Yan,Y.H.Lu,I.S.Ng,Three-dimensional CFD-PBM coupled model of the temperature fields in fluidized-bed polymerization reactors,AICHE J.57(2011)3351-3366.
[26]L.T.Zhu,H.Pan,Y.H.Su,Z.H.Luo,Effect of particle polydispersity on flow and reaction behaviors of methanol-to-olefins fluidized bed reactors,Ind.Eng.Chem.Res.56(2017)1090-1102.
[27]P.N.Rowe,A.W.Nienow,Particle mixing and segregation in gas fluidised beds.Areview,Powder Technol.15(1976)141-147.
[28]J.W.Chew,R.Hays,J.G.Findlay,T.M.Knowlton,S.B.R.Karri,R.A.Cocco,C.M.Hrenya,Cluster characteristics of Geldart group B particles in a pilot-scale CFB riser.II.Polydisperse systems,Chem.Eng.Sci.68(2012)82-93.
[29]B.Lu,N.Zhang,W.Wang,J.Li,J.H.Chiu,S.G.Kang,3-D full-loop simulation of an industrial-scale circulating fluidized-bed boiler,AICHE J.59(2013)1108-1117.
[30]S.Benyahia,Analysis of model parameters affecting the pressure profile in a circulating fluidized bed,AICHE J.58(2012)427-439.
[31]M.Lungu,Y.Zhou,J.Wang,Y.Yang,A CFD study of a bi-disperse gas-solid fluidized bed:Effect of the EMMS sub grid drag correction,Powder Technol.280(2015)154-172.
[32]Q.Zhou,J.Wang,CFD study of mixing and segregation in CFB risers:Extension of EMMS drag model to binary gas-solid flow,Chem.Eng.Sci.122(2015)637-651.
[33]J.Wang,W.Ge,J.Li,Eulerian simulation of heterogeneous gas-solid flows in CFBrisers:EMMS-based sub-grid scale model with a revised cluster description,Chem.Eng.Sci.63(2008)1553-1571.
[34]Y.Zhao,H.Li,M.Ye,Z.Liu,3D numerical simulation of a large scale MTO fluidized bed reactor,Ind.Eng.Chem.Res.52(2013)11354-11364.
[35]K.Hong,S.Chen,W.Wang,J.Li,Fine-grid two-fluid modeling of fluidization of Geldart A particles,Powder Technol.296(2016)2-16.
[36]B.Lu,H.Luo,H.Li,W.Wang,M.Ye,Z.Liu,J.Li,Speeding up CFD simulation of fluidized bed reactor for MTO by coupling CRE model,Chem.Eng.Sci.143(2016)341-350.
[37]B.Lu,J.Zhang,H.Luo,W.Wang,H.Li,M.Ye,Z.Liu,J.Li,Numerical simulation of scale-up effects of methanol-to-olefins fluidized bed reactors,Chem.Eng.Sci.171(2017)244-255.
[38]H.Luo,B.Lu,J.Zhang,H.Wu,W.Wang,A grid-independent EMMS/bubbling drag model for bubbling and turbulent fluidization,Chem.Eng.J.326(2017)47-57.
[39]Y.Tian,J.Geng,W.Wang,Structure-dependent analysis of energy dissipation in gas-solid flows:Beyond nonequilibrium thermodynamics,Chem.Eng.Sci.171(2017)271-281.
[40]S.Mori,C.Y.Wen,Estimation of bubble diameter in gaseous fluidized beds,AICHE J.21(1975)109-115.
[41]S.Karimipour,T.Pugsley,A critical evaluation of literature correlations for predicting bubble size and velocity in gas-solid fluidized beds,Powder Technol.205(2011)1-14.
[42]J.B.Romero,L.N.Johanson,Factors affecting fluidized bed quality,Chem.Eng.Prog.Symp.Ser.58(1962)28-37.
[43]A.Whitehead,A.Young,Fluidization performance in large scale equipment,Proceedings of the International Symposium on Fluidization 1967,pp.284-293.
[44]D.Geldart,The effect of particle size and size distribution on the behaviour of gasfluidised beds,Powder Technol.6(1972)201-215.
[45]C.Fryer,O.E.Potter,Experimental investigation of models for fluidized bed catalytic reactors,AICHE J.22(1976)38-47.
[46]C.X.Yacono,An X-ray study of bubbbles in gas-fluidised beds of small particles,Ph.D.Dissertation,University of London,1975.
[47]J.Werther,Hydrodynamics and mass transfer between the bubble and emulsion phases in fluidized beds of sand and cracking catalyst,in:R.Toei(Ed.),Fluidization,New York Engineering Foundation,1983.
[48]P.Cai,M.Schiavetti,G.De Michele,G.C.Grazzini,M.Miccio,Quantitative estimation of bubble size in PFBC,Powder Technol.80(1994)99-109.
[49]M.Horio,A.Nonaka,A generalized bubble diameter correlation for gas-solid fluidized beds,AICHE J.33(1987)1865-1872.
[50]R.Krishna,J.M.van Baten,Using CFD for scaling up gas-solid bubbling fluidised bed reactors with Geldart A powders,Chem.Eng.J.82(2001)247-257.
[51]F.Johnsson,S.Andersson,B.Leckner,Expansion of a freely bubbling fluidized bed,Powder Technol.68(1991)117-123.
[52]D.Geldart,The size and frequency of bubbles in two-and three-dimensional gasfluidised beds,Powder Technol.4(1970)41-55.
[53]G.Yasui,L.N.Johanson,Characteristics of gas pockets in fluidised beds,AICHE J.4(1958)445-452.
[54]W.H.Park,W.K.Kang,C.E.Capes,G.L.Osberg,The properties of bubbles in fluidised beds of conducting particles as measured by an electroresistivity probe,Chem.Eng.Sci.24(1969)851-865.
[55]A.R.Abrahamsen,D.Geldart,Behaviour of gas-fluidized beds of fine powders part II.Voidage of the dense phase in bubbling beds,Powder Technol.26(1980)47-55.
[56]H.Cui,N.Mostoufi,J.Chaouki,Gas and solids between dynamic bubble and emulsion in gas-fluidized beds,Powder Technol.120(2001)12-20.
[57]K.Hilligardt,J.Werther,Influence of temperature and properties of solids on the size and growth of bubbles in gas fluidized beds,Chem.Eng.Technol.10(1987)272-280.
[58]S.Chiba,T.Chiba,A.W.Nienow,H.Kobayashi,The minimum fluidisation velocity,bed expansion and pressure-drop profile of binary particle mixtures,Powder Technol.22(1979)255-269.
[59]B.Formisani,G.D.Cristofaro,R.Girimonte,A fundamental approach to the phenomenology of fluidization of size segregating binary mixtures of solids,Chem.Eng.Sci.56(2001)109-119.