Journal of Industrial and Engineering Chemistry, Vol.20, No.6, 3919-3946, November, 2014
CFD simulation of fluidized bed reactors for polyolefin production - A review
E-mail:
This literature survey focuses on the application of computational fluid dynamics (CFD) in various
aspects of the fluidized bed reactor. Although fluidized bed reactors are used in various industrial
applications, this first-of-its-kind review highlights the use of CFD on polyolefin production. It is shown that CFD has been utilized for the following mechanisms of polymerization: governing of bubble formation, electrostatic charge effect, gas.solid flow behavior, particle distribution, solid-gas circulation pattern, bed expansion consequence, mixing and segregation, agglomeration and shear forces. Heat and mass transfer in the reactor modeling using CFD principles has also been taken under consideration. A number of softwares are available to interpret the data of the CFD simulation but only few softwares possess the analytical capability to interpret the complex flowbehavior of fluidization. In this review, the popular softwares with their framework and application have been discussed. The advantages and feasibility of applying CFD to olefin polymerization in fluidized beds were deliberated and the prospect of future CFD applications was also discussed.
- Puettmann A, Hartge EU, Werther J, Chem. Eng. Process., 60, 86 (2012)
- Yang WC, Handbook of Fluidization and Fluid-Particle Systems, Marcel Dekker, Inc., New York (2003)
- Geldart D, Abdullah EC, Verlinden A, Powder Technol., 190(1-2), 70 (2009)
- Yang GQ, Du B, Fan LS, Chem. Eng. Sci., 62(1-2), 2 (2007)
- Bi HT, Ellis N, Abba IA, Grace JR, Chem. Eng. Sci., 55(21), 4789 (2000)
- Kashani AF, Abedini H, Kalaee MR, Chemical Product and Process Modeling, 6, 1934 (2011)
- Rokkam RG, Fox RO, Muhle ME, Powder Technol., 203(2), 109 (2010)
- Xie TY, Mcauley KB, Hsu JC, Bacon DW, Ind. Eng. Chem. Res., 33(3), 449 (1994)
- Choi KY, Ray WH, Chemical Engineering Science, 43, 2587 (1988)
- Kunii OLD, Fluidization Engineering, 2nd ed., Butterworth-Heinemann, Boston (1991)
- Geldart D, Gas Fluidization Technology, Wiley & Sons, Chichester (1986)
- Kiashemshaki A, Mostoufi N, Sotudeh-Gharebagh R, Chem. Eng. Sci., 61(12), 3997 (2006)
- Shamiri A, Hussain MA, Mjalli FS, Mostoufi N, Chem. Eng. J., 161(1-2), 240 (2010)
- Ibrehem AS, Hussain MA, Ghasem NM, Chem. Eng. J., 149(1-3), 353 (2009)
- Shamiri A, Hussain MA, Mjalli FS, Mostoufi N, Shafeeyan MS, Chem. Eng. Sci., 66(6), 1189 (2011)
- Davidson JFH, Harrison D, Fluidized Particles, Cambridge University Press (1963)
- Chatzidoukas C, Perkins JD, Pistikopoulos EN, Kiparissides C, Chem. Eng. Sci., 58(16), 3643 (2003)
- Zavala VM, Flores-Tlacuahuac A, Vivaldo-Lima E, Chem. Eng. Sci., 60(11), 3061 (2005)
- Hatzantonis H, Yiannoulakis H, Yiagopoulos A, Kiparissides C, Chem. Eng. Sci., 55(16), 3237 (2000)
- Xu X, Wu Y, Qiu Y, Dong C, Wu Gy, Wang H, European Polymer Journal, 42, 2791 (2006)
- Xuejing Zheng MSP, Weickert G, Loos J, European Polymer Journal, 68, 680 (2006)
- Luo ZH, Su PL, You XZ, Shi DP, Wu JC, Chem. Eng. J., 146(3), 466 (2009)
- Gobin AN, Simonin H, Llinas O, Reiling J, Selo VJ, Numerical Simulation of a Gas-Phase Polymerisation Reactor, Vienna, OIA (2012)
- Hulme I, Clavelle E, van der Lee L, Kantzas A, Ind. Eng. Chem. Res., 44(12), 4254 (2005)
- Anderson TB, Jackson R, Industrial and Engineering Chemistry Fundamentals, 6, 527 (1967)
- Elsdon R, Mitchell FRG, Journal of Physics D: Applied Physics, 9, 1445 (1976)
- Yiannoulakis H, Yiagopoulos A, Kiparissides C, Chem. Eng. Sci., 56(3), 917 (2001)
- Wang W, Lu BN, Zhang N, Shi ZS, Li JH, Int. J. Multiph. Flow, 36(2), 109 (2010)
- Hosseini SH, Shojaee S, Ahmadi G, Zivdar M, J. Ind. Eng. Chem., 18(4), 1465 (2012)
- Paul EL, Atiemo-Obeng VA, Kresta SM, Handbook of industrial mixing, John Wiley, New York (2004)
- Patel H, Ein-Mozaffari F, Dhib R, Comput. Chem. Eng., 34(4), 421 (2010)
- Reh L, Chem. Eng. Sci., 54(22), 5359 (1999)
- Gidaspow D, Multiphase Flow and Fluidization, Academic Press, San Diego, 1994p. 35.
- Shi DP, Luo ZH, Guo AY, Ind. Eng. Chem. Res., 49(9), 4070 (2010)
- Ryu JB, Jung CY, Yi SC, J. Ind. Eng. Chem., 19(4), 1092 (2013)
- Elsdon R, Mitchell RG, Journal of Physics D: Applied Physics, 9, 1445 (1976)
- Zhao H, Castle GSP, Inculet II, Bailey AG, IEEE, 2, 835 (2000)
- Mountain JR, Mazumder MK, Sims RA, Wankum DL, Chasser T, Pettit Jr. PH, IEEE, 37, 778 (2001)
- Ahuja GN, Patwardhan AW, Chem. Eng. J., 143(1-3), 147 (2008)
- Wang TF, Wang JF, Jin Y, AIChE J., 52(1), 125 (2006)
- Roy S, Dhotre MT, Joshi JB, Chem. Eng. Res. Des., 84(A8), 677 (2006)
- Vejahati F, Mahinpey N, Ellis N, Nikoo MB, Can. J. Chem. Eng., 87(1), 19 (2009)
- Syamlal M, O’Brien TJ, Computer Simulation of Bubbles in a Fluidized Bed 22 (1989)
- Wen CY, Yu YH, Mechanics of Fluidization, p. 100. (1966)
- Ding J, Gidaspow D, AIChE Journal, 36, 523 (1990)
- Yan WC, Chen GQ, Luo ZH, Ind. Eng. Chem. Res., 51(46), 15132 (2012)
- Wei LH, Yan WC, Luo ZH, Powder Technol., 214(1), 143 (2011)
- Jakobsen HA, Grevskott S, Svendsen HF, Industrial and Engineering Chemistry Research, 36, 4052 (1997)
- Krishna R, van Baten JM, Chem. Eng. J., 82(1-3), 247 (2001)
- Fan La, Zhu C, Principles of Gas.Solid Flows, Cambridge University Press, Cambridge, UK (1998)
- Ranade V, Computational Flow Modeling for Chemical Reactor Engineering, Academic Press, New York, (2001)
- Lu HL, Liu WT, Li F, Zhao GB, He YR, Int. J. Energy Res., 26(15), 1285 (2002)
- Darton RC, Lanauze RD, Davidson JF, Harrison D, Transactions of the Institutions of Chemical Engineers, 55, 274 (1977)
- Busciglio A, Vella G, Micale G, Rizzuti L, Chem. Eng. J., 148(1), 145 (2009)
- Vegendla SNP, Heynderickx GJ, Marin GB, Comput. Chem. Eng., 35(7), 1192 (2011)
- Zhuang YQ, Chen XM, Luo ZH, Xiao J, Comput. Chem. Eng., 60, 1 (2014)
- Sun JY, Wang JD, Yang YR, Chem. Eng. Sci., 71, 507 (2012)
- Bin Y, Zhang MC, Dou BL, Song YB, Wu J, Industrial and Engineering Chemistry Research, 42, 214 (2002)
- Vun S, Naser J, Witt PJ, Yang W, Chem. Eng. Sci., 65(22), 5808 (2010)
- Gamwo IK, Soong Y, Lyczkowski RW, Powder Technol., 103(2), 117 (1999)
- Witt PJ, Perry JH, Schwarz MP, Applied Mathematical Modelling, 22, 1071 (1998)
- Chen XZ, Shi DP, Gao X, Luo ZH, Powder Technol., 205(1-3), 276 (2011)
- Aldaco R, Garea A, Irabien A, Chem. Eng. J., 134(1-3), 66 (2007)
- Cabezas-Gomez L, Milioli FE, Powder Technol., 132(2-3), 216 (2003)
- Doroodchi E, Galvin KP, Fletcher DF, Powder Technol., 156(1), 1 (2005)
- Jenck JF, Guisnet M, Barrault J, Bouchoule C, Duprez D, Perot G, Maurel R, Montassier C(Eds.), Gas.Liquid.Solid Reactors for Hydrogenation in Fine Chemicals Synthesis, Elsevier, p. 1. (1991)
- Addagatla SK, Computational study of Gas-Solid flow in riser section of circulating fluidized beds, Texas A & M University, Kingville (2008)
- Li TW, Garg R, Galvin J, Pannala S, Powder Technol., 220, 138 (2012)
- Wang W, Li JH, Chem. Eng. Sci., 62(1-2), 208 (2007)
- Wang W, Lu B, Li JH, Chem. Eng. Sci., 62(3), 814 (2007)
- Wardag ANK, Larachi F, AIChE J., 58(7), 2045 (2012)
- Wardag ANK, Larachi F, Chem. Eng. J., 179, 349 (2012)
- Chalermsinsuwan B, Chanchuey T, Buakhao W, Gidaspow D, Piumsomboon P, Chem. Eng. J., 189, 314 (2012)
- Hernandez-Jimenez F, Gomez-Garcia A, Santana D, Acosta-Iborra A, Chem. Eng. J., 215, 479 (2013)
- Alobaid F, Strohle J, Epple B, Adv. Powder Technol., 24(1), 403 (2013)
- Alobaid F, Epple B, Particuology, 11, 514 (2013)
- Jalalinejad F, Bi XTT, Grace JR, Int. J. Multiph. Flow, 44, 15 (2012)
- Zhong HB, Gao JS, Xu CM, Lan XY, Powder Technol., 230, 232 (2012)
- Chang J, Wang G, Gao JS, Zhang K, Chen HG, Yang YP, Powder Technol., 217, 50 (2012)
- Hamidipour M, Chen JW, Larachi F, Chem. Eng. Sci., 78, 167 (2012)
- Herzog N, Schreiber M, Egbers C, Krautz HJ, Comput. Chem. Eng., 39, 41 (2012)
- Khongprom P, Aimdilokwong A, Limtrakul S, Vatanatham T, Ramachandran PA, Chem. Eng. Sci., 73, 8 (2012)
- Yusuf R, Halvorsen B, Melaaen MC, Can. J. Chem. Eng., 90(3), 544 (2012)
- Cloete S, Johansen ST, Amini S, Powder Technology, 215, 15 (2012)
- Asegehegn TW, Schreiber M, Krautz HJ, Powder Technol., 219, 9 (2012)
- Yan WC, Li J, Luo ZH, Powder Technol., 231, 77 (2012)
- Wang S, Hao ZH, Lu HL, Yang YC, Xu PF, Liu GD, Int. J. Multiph. Flow, 39, 159 (2012)
- Guo Y, Wu CY, Thornton C, AIChE Journal, 89, 1075 (2012)
- Feng YQ, Swenser-Smith T, Witt PJ, Doblin C, Lim S, Schwarz MP, Powder Technol., 219, 78 (2012)
- Acosta-Iborra A, Sobrino C, Hernandez-Jimenez F, de Vega M, Chem. Eng. Sci., 66(15), 3499 (2011)
- Peng B, Zhu J, Zhang C, Industrial and Engineering Chemistry Research, 51, 2152 (2011)
- Chalermsinsuwan B, Gidaspow D, Piumsomboon P, Chem. Eng. J., 171(1), 301 (2011)
- Esmaili E, Mahinpey N, Advances in Engineering Software, 42, 375 (2011)
- Bhuiya MMK, Chowdhury MSU, Islam M, Ahamed JU, Khan MJH, Sarker MRI, Saha M, International Communications in Heat and Mass Transfer, 39, 1505 (2012)
- Bhuiya MMK, Chowdhury MSU, Ahamed JU, Khan MJH, Sarkar MAR, Kalam MA, Masjuki HH, Shahabuddin M, International Communications in Heat and Mass Transfer, 39, 818 (2012)
- User Guide FLUENT 14.5.7, Fluent Inc. (2013)
- Caspar JV, Meyer TJ, Journal of Physical Chemistry, 87, 952 (1983)
- Stewart PH, Larson CW, Golden DM, Combustion and Flame, 75, 25 (1989)
- Magnussen BF, Hjertager BH, Olsen JG, Bhaduri D, On Mathematical Models of Turbulent Combustion with Special Emphasis on Soot Formation and Combustion, The Combustion Institute, USA (1976)
- Zacca JJ, Debling JA, Ray WH, Chem. Eng. Sci., 51(21), 4859 (1996)
- Li NN, Fane AG, Ho WSW, Matsuura T, Advanced Membrane Technology and Application, John Wiley & Sons Inc., New York, USA (2008)
- Incropera FP, DeWitt DP, Bergman TL, Lavine AS, Fundamentals of Heat and Mass Transfer, 6th ed., John Wiley & Sons Inc., New York (2007)
- Bird R, Transport Phenomena, 2nd ed., John Wiley & Sons, Inc., Lightfoot, New York (2002)
- McAuley KB, MacGregor JF, Hamielec AE, AIChE Journal, 36, 837 (1990)
- McAuley KB, Talbot JP, Harris TJ, Chem. Eng. Sci., 49(13), 2035 (1994)
- Trambouze P, in: Pilavachi PA (Ed.), Computational Fluid Dynamics Applied to Chemical Reaction Engineering, Springer, Netherlands, p. 1122. (1993)
- Kolaczkowski ST, Chao R, Awdry S, Smith A, Chem. Eng. Res. Des., 85(A11), 1539 (2007)
- Frassoldati A, Frigerio S, Colombo E, Inzoli F, Faravelli T, Chem. Eng. Sci., 60(11), 2851 (2005)
- Goh YR, Zakaria R, Yang YB, Nasserzadeh V, Swithenbank J, J. Inst. Energy, 76(508), 72 (2003)
- Rudniak L, Machniewski PM, Milewska A, Molga E, Chem. Eng. Sci., 59(22-23), 5233 (2004)
- Warnecke HJ, Schafer M, Pruss J, Weidenbach M, Chem. Eng. Sci., 54(13-14), 2513 (1999)
- Jiang Y, Khadilkar MR, Al-Dahhan MH, Dudukovic AP, AIChE J., 48(4), 701 (2002)
- Eriksson EJG, McKenna TF, Ind. Eng. Chem. Res., 43(23), 7251 (2004)
- Gerogiorgis DI, Ydstie BE, Chem. Eng. Res. Des., 83(A6), 603 (2005)
- Canu P, Vecchi S, AIChE J., 48(12), 2921 (2002)
- Hayes RE, Kolaczkowski ST, Introduction to Catalytic Combustion, Gordon and Breach Science Publishers, USA (1997)
- Lettieri P, Cammarate L, Micale GDM, Yates J, International Journal of Chemical Reactor Engineering, 1, 1542 (2003)
- Sahu JN, Rama Krishna Chava VS, Hussain S, Patwardhan AV, Meikap BC, J. Ind. Eng. Chem., 16(4), 577 (2010)
- Taghipour F, Ellis N, Wong C, Chem. Eng. Sci., 60(24), 6857 (2005)
- Londono A, Londono C, Molina A, Chejne F, Simulation of Gas-Solid Fluidized Bed Hydrodynamics using OpenFOAM, Beaumont House, UK (2007)
- Passalacqua A, Fox RO, Powder Technol., 213(1-3), 174 (2011)
- Syamlal M, O’Brien TJ, Benyahia S, Gel A, Pannala S, Modelling and Simulation in Engineering (2008)
- Syamlal M, Rogers W, O’Brien TJ, MFIX Documentation Theory Guide, p. Medium: ED; Size: 49 p. (1993)
- Syamlal M, MFIX Documentation, User’s Manual, National Technical Information Service, Springfield, VA (1994)
- Syamlal SVM, Cho SM, in: Ciang SH (Ed.), Modeling of Coal Conversion in a Carbonizer, University of Pittsburgh, Pittsburgh, PA, p. 1309. (1996)
- Guenther MSC, Syamlal M, Longanbach J, Cicero D, Smith P, in: Proceedings of the 19th Annual Pittsburgh Coal Conference, Pittsburgh, PA (2002)
- Gidaspow D, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions, Academic Press, New York, NY (1994)
- Fan LSZ, Principles of Gas-Solid Flows, Cambridge University Press, New York (2005)
- Bi HTT, Chem. Eng. Sci., 62(13), 3473 (2007)
- Darelius A, Rasmuson A, van Wachem B, Bjorn IN, Folestad S, Chem. Eng. Sci., 63(8), 2188 (2008)
- Zhang K, Brandani S, Bi J, Progress in Natural Science, 15, 42 (2005)
- Zhang K, Brandani S, Bi J, Jiang J, Progress in Natural Science, 18, 729 (2008)
- Gera D, Gautam M, Powder Technol., 84(3), 283 (1995)
- Kuipers JAM, van Duin KJ, van Beckum FPH, van Swaaij WPM, Computers and Chemical Engineering, 17, 839 (1993)
- Pain CC, Mansoorzadeh S, de Oliveira CRE, Int. J. Multiph. Flow, 27(3), 527 (2001)
- Peirano E, Delloume V, Leckner B, Chem. Eng. Sci., 56(16), 4787 (2001)
- Shen LH, Johnsson F, Leckner B, Chem. Eng. Sci., 59(13), 2607 (2004)
- Li Y, Zhang JP, Fan LS, Chem. Eng. Sci., 54(21), 5101 (1999)
- Panneerselvam R, Savithri S, Surender GD, Chem. Eng. J., 132(1-3), 159 (2007)
- Jiradilok V, Gidaspow D, Breault RW, Chem. Eng. Sci., 62(13), 3397 (2007)
- Cheung SCP, Yeoh GH, Tu JY, Chem. Eng. Sci., 62(17), 4659 (2007)
- Laborde-Boutet C, Larachi F, Dromard N, Delsart O, Schweich D, Chem. Eng. Sci., 64(21), 4399 (2009)
- Sun JY, Zhou YF, Ren CJ, Wang JD, Yang YR, Chem. Eng. Sci., 66(21), 4972 (2011)
- Hosseini SH, Zhong W, Esfahany MN, Pourjafar L, Azizi S, Journal of Fluids Engineering 132 041301 (2010)
- Li P, Lan X, Xu C, Wang G, Lu C, Gao J, Particuology, 7, 269 (2009)
- Hamzehei M, Rahimzadeh T, Ind. Eng. Chem. Res., 48(6), 3177 (2009)
- Gidaspow D, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions, Academic Press, New York (1994)
- Syamlal M, O’Brien T, Computer Simulation of Bubbles in a Fluidized Bed, p. 22. (1989)
- Hosseini MZSH, Rahimi R, Samimi A, Chemical Product and Process Modeling, 4, 1934 (2009)
- Miroliaei AR, Shahraki F, Atashi H, Karimzadeh R, J. Ind. Eng. Chem., 18(6), 1912 (2012)
- Jung JW, Gidaspow D, Gamwo IK, Chem. Eng. Commun., 193(8), 946 (2006)
- Jiradilok V, Gidaspow D, Breault RW, Shadle LJ, Guenther C, Shi SP, Chem. Eng. Sci., 63(8), 2135 (2008)
- Jiradilok V, Gidaspow D, Damronglerd S, Koves WJ, Mostofi R, Chem. Eng. Sci., 61(17), 5544 (2006)
- Jung J, Gidaspow D, Gamwo IK, Ind. Eng. Chem. Res., 44(5), 1329 (2005)
- Tagliaferri LMC, Lettieri P, Marzocchella A, Olivieri G, Salatino P, Chemical Engineering Science, http://dx.doi.org/10.1016/j.ces.2013.1008.1015. (2013)
- Rao DA, Sivashanmugam P, J. Ind. Eng. Chem., 16(1), 157 (2010)
- Kashyap M, Gidaspow D, Koves WJ, Chem. Eng. Sci., 66(2), 183 (2011)
- Wadnerkar D, Utikar RP, Tade MO, Pareek VK, Adv. Powder Technol., 23(4), 445 (2012)
- Onishi R, Takahashi K, Vassilicos JC, Journal of Computational Physics, 242, 809 (2013)
- Rathore SK, Das MK, Int. J. Heat Mass Transf., 61, 365 (2013)
- Wang LM, Zhang B, Wang XW, Ge W, Li JH, Chem. Eng. Sci., 101, 228 (2013)
- Xiong QG, Li B, Zhou GF, Fang XJ, Xu J, Wang JW, He XF, Wang XW, Wang LM, Ge W, Li JH, Chem. Eng. Sci., 71, 422 (2012)
- Mudde RF, Groen JS, Vandenakker HE, Chem. Eng. Sci., 52(21-22), 4217 (1997)
- Cui Z, Fan LS, Chem. Eng. Sci., 59(8-9), 1755 (2004)
- Cui Z, Fan LS, Industrial and Engineering Chemistry Research, 44, 1150 (2004)
- Liu DY, Bu CS, Chen XP, Comput. Chem. Eng., 58, 260 (2013)
- Xie J, Zhong WQ, Jin BS, Shao YJ, Huang YJ, Adv. Powder Technol., 24(1), 382 (2013)
- Boemer A, Qi H, Renz U, Int. J. Multiph. Flow, 23(5), 927 (1997)
- Lun CKK, Savage SB, Jeffrey DJ, Chepurniy N, Journal of Fluid Mechanics, 140, 223 (1984)
- Cooper S, Coronella CJ, Powder Technol., 151(1-3), 27 (2005)
- Jang HT, Park TS, Cha WS, J. Ind. Eng. Chem., 16(3), 390 (2010)
- Mostafazadeh M, Rahimzadeh H, Hamzei M, Powder Technol., 239, 422 (2013)
- Basesme EA, Levy EK, Powder Technology, 72, 45 (1992)
- Fernandes FAN, Lona LMF, J. Appl. Polym. Sci., 81(2), 321 (2001)
- Tsuchiya K, Song GH, Fan LS, Chemical Engineering Science, 45, 1429 (1990)
- Gibilaro LG, Rowe PN, Chemical Engineering Science, 29, 1403 (1974)
- Norouzi HR, Mostoufi N, Mansourpour Z, Sotudeh-Gharebagh R, Chaouki J, Chem. Eng. Res. Des., 89(6A), 817 (2011)
- Norouzi HR, Mostoufi N, Sotoudeh-Gharebagh R, Journal of Chemical and Petroleum Engineering, 46, 111 (2012)
- Norouzi HR, Mostoufi N, Sotudeh-Gharebagh R, Powder Technol., 225, 7 (2012)
- Zhang SX, Ray WH, AIChE J., 43(5), 1265 (1997)
- Javad H, Nayef MG, Wan MAWD, Ind. Eng. Chem. Res., 43(19), 6048 (2004)
- Kemmere MF, Meuldijk J, Drinkenburg AAH, German AL, J. Appl. Polym. Sci., 79(5), 944 (2001)
- Azadi M, J. Ind. Eng. Chem., 17(2), 229 (2011)
- Wells GJ, Ray WH, AIChE J., 51(12), 3205 (2005)
- Kolhapure NH, Fox RO, Chem. Eng. Sci., 54(15-16), 3233 (1999)
- Rhodes MJ, Wang XS, Nguyen M, Stewart P, Liffman K, Chem. Eng. Sci., 56(8), 2859 (2001)
- Zhang Y, Jin BS, Zhong WQ, Ren B, Xiao R, Chem. Eng. Res. Des., 88(5-6A), 757 (2010)
- Zhang Y, Jin BS, Zhong WQ, Chem. Eng. Process., 48(3), 745 (2009)
- Wu CL, Zhan JM, Journal of Hydrodynamics: Series B, 19, 335 (2007)
- Mazzei L, Marchisio DL, Lettieri P, AIChE J., 58(10), 3054 (2012)
- Ahmadzadeh A, Arastoopour H, Teymour F, Strumendo M, Chem. Eng. Res. Des., 86(4A), 329 (2008)
- Kotoulas C, Kiparissides C, Chem. Eng. Sci., 61(2), 332 (2006)
- Mazzei L, Casillo A, Lettieri P, Salatino P, Chem. Eng. J., 156(2), 432 (2010)
- Wang S, Liu GD, Lu HL, Sun LY, Xu PF, Chem. Eng. Sci., 71, 185 (2012)
- Zhong Y, Wang Z, Guo Z, Tang Q, Powder Technology (2013)
- Moritz HU, Chemical Engineering and Technology, 12, 71 (1989)
- Wang S, Hao ZH, Lu HL, Liu GD, Wang JX, Xu PF, AIChE J., 58(2), 440 (2012)
- Soliman MA, Aljarboa T, Alahmad M, Polymer Engineering and Science, 19, 1454 (1994)
- Hulme I, Kantzas A, Powder Technol., 147(1-3), 20 (2004)
- Dong L, Zhao Y, Luo Z, Duan C, Wang Y, Yang X, Zhang B, International Journal of Mining Science and Technology, 23, 227 (2013)
- Almendros-Ibanez JA, Pallares D, Johnsson F, Santana D, Powder Technol., 197(1-2), 73 (2010)
- Hull AS, Chen ZM, Fritz JW, Agarwal PK, Powder Technol., 103(3), 230 (1999)
- Busciglio A, Vella G, Micale G, Rizzuti L, Chem. Eng. Sci., 65(16), 4782 (2010)
- Fung AS, Hamdullahpur F, Powder Technology, 74, 121 (1993)
- Mitra-Majumdar D, Farouk B, Shah YT, Chem. Eng. Sci., 52(24), 4485 (1997)
- Geldart D, Kelsey JR, Powder Technology, 6, 45 (1972)
- Syamlal M, O'Brien TJ, AIChE J., 49(11), 2793 (2003)
- Laux HJ, Johansen ST, Computer Simulation of Bubble Formation in a Gas-Solid Fluidized Bed, The Minerals, Metals & Materials Society, Durango, CO, p. 517. (1998)
- Reuge N, Cadoret L, Coufort-Saudejaud C, Pannala S, Syamlal M, Caussat B, Chem. Eng. Sci., 63(22), 5540 (2008)
- Hassani MA, Zarghami R, Norouzi HR, Mostoufi N, Powder Technol., 246, 16 (2013)
- Bokkers GA, Annaland MVS, Kuipers JAM, Powder Technol., 140(3), 176 (2004)
- Gobin AN, Simonin H, Llinas O, Reiling J, Selo VJ, Numerical Simulation of a Gas-Phase Polymerisation Reactor; European Congress on Computational Methods, Wales (2001)
- van Wachem BGM, Schouten JC, Krishna R, van den Bleek CM, Computers and Chemical Engineering 22 (Suppl. 1) S299. (1988)
- Di Renzo A, Cello F, Di Maio FP, Chem. Eng. Sci., 66(13), 2945 (2011)
- Lyczkowski RW, Bouillard JX, Gamwo IK, Torpey MR, Montrone ED, Industrial and Engineering Chemistry Research, 49, 5166 (2009)
- Sitnai O, Chemical Engineering Science, 37, 1059 (1982)
- Zhou YF, Ren CJ, Wang JD, Yang YR, Dong KZ, Powder Technol., 235, 9 (2013)
- Li J, Kuipers JAM, Powder Technol., 127(2), 173 (2002)
- Godlieb W, Deen NG, Kuipers JAM, Powder Technol., 182(2), 250 (2008)
- Zhang JP, Li Y, Fan LS, Powder Technol., 112(1-2), 46 (2000)
- Mansourpour Z, Karimi S, Zarghami R, Mostoufi N, Sotudeh-Gharebagh R, Particuology, 8, 407 (2010)
- Floyd S, Choi KY, Taylor TW, Ray WH, Journal of Applied Polymer Science, 32, 2935 (1986)
- Computers and Chemical Engineering, McKenna TF, Cokljat D, Wild P, Computers and Chemical Engineering 22 (Suppl. 1) S285., 22 (1998)
- McKenna TF, Soares JBP, Chem. Eng. Sci., 56(13), 3931 (2001)
- Tioni E, Broyer JP, Spitz R, Monteil V, McKenna TFL, Macromolecular Symposia, 285, 58 (2009)
- Eriksson EJG, McKenna TFL, Macromolecular Symposia, 285, 28 (2009)
- Kaneko Y, Shiojima T, Horio M, Chem. Eng. Sci., 54(24), 5809 (1999)
- Karimi S, Mansourpour Z, Mostoufi N, Sotudeh-Gharebagh R, Part. Sci. Technol., 29(2), 163 (2011)
- Ibrehem AS, Chemical Product and Process Modeling, 4, 1934 (2009)
- Behjat Y, Shahhosseini S, Hashemabadi SH, International Communications in Heat and Mass Transfer, 35, 357 (2008)
- Hutchinson RA, Ray WH, Journal of Applied Polymer Science, 34, 657 (1987)
- Wang Y, Yuan F, Journal of Industrial and Engineering Chemistry, http://dx.doi.org/10.1016/j.jiec.2013.06.037. (2013)
- Huilin L, Gidaspow D, Bouillard J, Wentie L, Chem. Eng. J., 95(1-3), 1 (2003)
- Mickley HS, Fairbanks DF, AIChE Journal, 1, 374 (1955)
- Di Natale F, Lancia A, Nigro R, Powder Technol., 195(2), 135 (2009)
- Liu MX, Zhang YM, Bi HT, Grace JR, Zhu YD, Chem. Eng. Sci., 65(11), 3485 (2010)
- Gunn DJ, International Journal of Heat and Mass Transfer, 21, 467 (1978)
- Patil DJ, Smit J, Annaland MV, Kuipers JAM, AIChE J., 52(1), 58 (2006)
- Syamlal M, Gidaspow D, AIChE Journal, 31, 127 (1985)
- Brown SL, Lattimer BY, Experimental Thermal and Fluid Science, 44, 883 (2013)
- Dehnavi MA, Shahhosseini S, Hashemabadi SH, Ghafelebashi SM, International Communications in Heat and Mass Transfer, 35, 1375 (2008)
- Dehnavi MA, Shahhosseini S, Hashemabadi SH, Ghafelebashi SM, International Communications in Heat and Mass Transfer, 37, 437 (2010)
- Chiesa M, Mathiesen V, Melheim JA, Halvorsen B, Comput. Chem. Eng., 29(2), 291 (2005)
- Patankar SV, Numerical Heat Transfer and Fluid Flow, 1st ed., Hemisphere Publishing, Washington, DC (1980)
- Hou QF, Zhou ZY, Yu AB, Ind. Eng. Chem. Res., 51(35), 11572 (2012)
- Zhou ZY, Yu AB, Zulli P, AIChE J., 55(4), 868 (2009)
- Hendrickson G, Chem. Eng. Sci., 61(4), 1041 (2006)
- Yao L, Bi HT, Park AH, Journal of Electrostatics, 56, 183 (2002)
- Salama F, Sowinski A, Atieh K, Mehrani P, Journal of Electrostatics, 71, 21 (2013)
- Boland D, Geldart D, Powder Technology, 5, 289 (1972)
- Giffin A, Mehrani P, Journal of Electrostatics, 68, 492 (2010)
- Sowinski A, Miller L, Mehrani P, Chem. Eng. Sci., 65(9), 2771 (2010)
- Tiyapiboonchaiya P, Gidaspow D, Damronglerd S, Ind. Eng. Chem. Res., 51(25), 8661 (2012)
- Wang F, Wang JD, Yang YR, Ind. Eng. Chem. Res., 47(23), 9517 (2008)
- Briens CL, Bergougnou MA, Inculet II, Baron T, Hazlett JD, Powder Technology, 70, 57 (1992)
- Ali FS, Ali MA, Ali RA, Inculet II, Journal of Electrostatics, 45, 139 (1998)
- Moughrabiah WO, Grace JR, Bi XT, Industrial and Engineering Chemistry Research, 48, 320 (2008)
- Al-Adel MF, Saville DA, Sundaresan S, Ind. Eng. Chem. Res., 41(25), 6224 (2002)
- Shih YT, Gidaspow D, Wasan D, AIChE Journal, 33, 1322 (1987)
- Lim EWC, Zhang Y, Wang CH, Chem. Eng. Sci., 61(24), 7889 (2006)
- Fan R, Fox RO, Muhle ME, Role of Intrinsic Kinetics and Catalyst Particle Size Distribution in CFD Simulations of Polymerization Reactors, ECI, Vancouver, Canada, p. 993. (2007)
- Sowinski A, Mayne A, Mehrani P, Chem. Eng. Sci., 71, 552 (2012)
- Yu X, Li W, Xu Y, Wang J, Yang Y, Xu N, Wang H, Industrial and Engineering Chemistry Research, 49, 132 (2009)
- Sowinski A, Salama F, Mehrani P, Journal of Electrostatics, 67, 568 (2009)
- Liao CC, Hsiau SS, Huang TY, Powder Technol., 208(1), 1 (2011)
- Alobaid F, Apple B, Particuology, 11, 514 (2013)
- Rabinovich E, Kalman H, Powder Technol., 207(1-3), 119 (2011)
- Ashrafi O, Mostoufi N, Sotudeh-Gharebagh R, Chem. Eng. Sci., 73, 1 (2012)
- Ashrafi O, Nazari-Pouya H, Mostoufi N, Sotudeh-Gharebagh R, Adv. Powder Technol., 19(4), 321 (2008)
- Arastoopour H, Huang CS, Weil SA, Chemical Engineering Science, 43, 3063 (1988)
- Hatzantonis H, Goulas A, Kiparissides C, Chem. Eng. Sci., 53(18), 3251 (1998)
- Yan WC, Luo ZH, Lu YH, Chen XD, AIChE J., 58(6), 1717 (2012)
- Chen XZ, Luo ZH, Yan WC, Lu YH, Ng IS, AIChE J., 57(12), 3351 (2011)
- Mikami T, Kamiya H, Horio M, Chem. Eng. Sci., 53(10), 1927 (1998)
- Kuwagi K, Horio M, Chem. Eng. Sci., 57(22-23), 4737 (2002)
- Mishra BK, Thornton C, Bhimji D, Minerals Engineering, 15, 27 (2002)
- Groger T, Tuzun U, Heyes DM, Powder Technol., 133(1-3), 203 (2003)
- Wang XS, Rhodes MJ, Chem. Eng. Sci., 59(1), 215 (2004)
- Limtrakul S, Rotjanavijit W, Vatanatham T, Chem. Eng. Sci., 62(1-2), 232 (2007)
- Yang RY, Yu AB, Choi SK, Coates MS, Chan HK, Powder Technol., 184(1), 122 (2008)
- Li S, Marshall JS, Liu G, Yao Q, Progress in Energy and Combustion Science, 37, 633 (2011)
- Mansourpour Z, Mostoufi N, Sotudeh-Gharebagh R, Can. J. Chem. Eng., 91(3), 560 (2013)
- Mansourpour Z, Mostoufi N, Sotudeh-Gharebagh R, Chemical Engineering Research and Design, 92, 102 (2013)
- Dahl SR, Hrenya CM, Chem. Eng. Sci., 60(23), 6658 (2005)
- Annaland MV, Bokkers GA, Goldschmidt MJV, Olaofe OO, van der Hoef MA, Kuipers JAM, Chem. Eng. Sci., 64(20), 4237 (2009)
- Fan R, Fox RO, Chem. Eng. Sci., 63(1), 272 (2008)
- Tagami N, Mujumdar A, Horio M, Particuology, 7, 9 (2009)