메뉴 건너뛰기




Volumn 49, Issue 8, 2010, Pages 3862-3872

Fast high-resolution method for solving multidimensional population balances in crystallization

Author keywords

[No Author keywords available]

Indexed keywords

BATCH CRYSTALLIZATION PROCESS; CO-ORDINATE TRANSFORM; CO-ORDINATE TRANSFORMATION; CRYSTALLIZATION PROCESS; FUNCTIONAL FORMS; HIGH RESOLUTION; HIGH-RESOLUTION METHODS; MULTIDIMENSIONAL POPULATION BALANCE; NUMERICAL SOLUTION; POPULATION BALANCE EQUATION; SIZE DEPENDENCY; SOLUTION TIME; STABILITY REQUIREMENTS; TIME STEP;

EID: 79953321113     PISSN: 08885885     EISSN: 15205045     Source Type: Journal    
DOI: 10.1021/ie9016946     Document Type: Article
Times cited : (27)

References (33)
  • 1
    • 0004294969 scopus 로고    scopus 로고
    • 4th ed.; Butterworth- Heinemann: Oxford, U.K.
    • Mullin, J. W. Crystallization, 4th ed.; Butterworth-Heinemann: Oxford, U.K., 2001.
    • (2001) Crystallization
    • Mullin, J.W.1
  • 2
    • 52049114893 scopus 로고    scopus 로고
    • Modelling and control of combined cooling and antisolvent crystallization processes
    • Nagy, Z. K.; Fujiwara, M.; Braatz, R. D. Modelling and control of combined cooling and antisolvent crystallization processes. J. Process Control 2008, 18, 856-864.
    • (2008) J. Process Control , vol.18 , pp. 856-864
    • Nagy, Z.K.1    Fujiwara, M.2    Braatz, R.D.3
  • 3
    • 36849062583 scopus 로고    scopus 로고
    • Real-time optimal control of an anti-solvent isothermal semi-batch crystallization process
    • DOI 10.1016/j.ces.2007.09.049, PII S0009250907007683
    • Sheikhzadeh, M.; Trifkovic, M.; Rohani, S. Real-time optimal control of an anti-solvent isothermal semi-batch crystallization process. Chem. Eng. Sci. 2008, 63, 829-839. (Pubitemid 350235410)
    • (2008) Chemical Engineering Science , vol.63 , Issue.3 , pp. 829-839
    • Sheikhzadeh, M.1    Trifkovic, M.2    Rohani, S.3
  • 4
    • 0037438469 scopus 로고    scopus 로고
    • Dynamic optimization of batch processes: II. Role of measurements in handling uncertainty
    • Srinivasan, B.; Bonvin, D.; Visser, E.; Palanki, S. Dynamic optimization of batch processes: II. Role of measurements in handling uncertainty. Comput. Chem. Eng. 2003, 27, 21-44.
    • (2003) Comput. Chem. Eng. , vol.27 , pp. 21-44
    • Srinivasan, B.1    Bonvin, D.2    Visser, E.3    Palanki, S.4
  • 5
    • 68549085139 scopus 로고    scopus 로고
    • Model based robust control approach for batch crystallization product design
    • Nagy, Z. K. Model based robust control approach for batch crystallization product design. Comput. Chem. Eng. 2009, 33, 1685-1691.
    • (2009) Comput. Chem. Eng. , vol.33 , pp. 1685-1691
    • Nagy, Z.K.1
  • 6
    • 68949160852 scopus 로고    scopus 로고
    • A control oriented study on the numerical solution of the population balance equation for crystallization processes
    • Mesbah, A.; Kramer, H. J. M.; Huesman, A. E. M.; Van den Hof, P. M. J. A control oriented study on the numerical solution of the population balance equation for crystallization processes. Chem. Eng. Sci. 2009, 64, 4262-4211.
    • (2009) Chem. Eng. Sci. , vol.64 , pp. 4262-14211
    • Mesbah, A.1    Kramer, H.J.M.2    Huesman, A.E.M.3    Van Den Hof, P.M.J.4
  • 9
    • 50549203562 scopus 로고
    • Some problems in particle technology: A statistical mechanical formulation
    • Hulburt, H. M.; Katz, S. Some problems in particle technology: A statistical mechanical formulation. Chem. Eng. Sci. 1964, 19, 555-574.
    • (1964) Chem. Eng. Sci. , vol.19 , pp. 555-574
    • Hulburt, H.M.1    Katz, S.2
  • 10
    • 0031214085 scopus 로고    scopus 로고
    • Description of aerosol dynamics by the quadrature method of moments
    • PII S0278682697000330
    • McGraw, R. Description of Aerosol Dynamics by the Quadrature Method of Moments. Aerosol Sci. Technol. 1997, 27, 255-265. (Pubitemid 27327931)
    • (1997) Aerosol Science and Technology , vol.27 , Issue.2 , pp. 255-265
    • McGraw, R.1
  • 11
    • 0038625401 scopus 로고    scopus 로고
    • Quadrature method of moments for population-balance equations
    • DOI 10.1002/aic.690490517
    • Marchisio, D. L.; Pikturna, J. T.; Fox, R. O.; Vigil, R. D.; Barresi, A. A. Quadrature method of moments for population-balance equations. AIChE J. 2003, 49, 1266-1276. (Pubitemid 36583119)
    • (2003) AIChE Journal , vol.49 , Issue.5 , pp. 1266-1276
    • Marchisio, D.L.1    Pikturna, J.T.2    Fox, R.O.3    Vigil, R.D.4    Barresi, A.A.5
  • 12
    • 70349339181 scopus 로고    scopus 로고
    • Combined quadrature method of moments and method of characteristics approach for efficient solution of population balance models for dynamic modeling and crystal size distribution control of crystallization processes
    • Aamir, E.; Nagy, Z. K.; Rielly, C. D.; Kleinert, T.; Judat, B. Combined Quadrature Method of Moments and Method of Characteristics Approach for Efficient Solution of Population Balance Models for Dynamic Modeling and Crystal Size Distribution Control of Crystallization Processes. Ind. Eng. Chem. Res. 2009, 48, 8575-8584.
    • (2009) Ind. Eng. Chem. Res. , vol.48 , pp. 8575-8584
    • Aamir, E.1    Nagy, Z.K.2    Rielly, C.D.3    Kleinert, T.4    Judat, B.5
  • 13
    • 10044271895 scopus 로고    scopus 로고
    • Solution of population balance equations using the direct quadrature method of moments
    • DOI 10.1016/j.jaerosci.2004.07.009, PII S0021850204003052
    • Marchisio, D. L.; Fox, R. O. Solution of population balance equations using the direct quadrature method of moments. J. Aerosol Sci. 2005, 36, 43-73. (Pubitemid 39601424)
    • (2005) Journal of Aerosol Science , vol.36 , Issue.1 , pp. 43-73
    • Marchisio, D.L.1    Fox, R.O.2
  • 14
    • 58949095935 scopus 로고    scopus 로고
    • Solution of the population balance equation using the sectional quadrature method of moments (SQMOM)
    • Attarakih, M. M.; Drumm, C.; Bart, H. Solution of the population balance equation using the sectional quadrature method of moments (SQMOM). Chem. Eng. Sci. 2009, 64, 742-752.
    • (2009) Chem. Eng. Sci. , vol.64 , pp. 742-752
    • Attarakih, M.M.1    Drumm, C.2    Bart, H.3
  • 15
    • 0031553395 scopus 로고    scopus 로고
    • On the solution of population balance equations by discretization - III. Nucleation, growth and aggregation of particles
    • PII S0009250997003072
    • Kumar, S.; Ramkrishna, D. On the solution of population balance equations by discretization-III. Nucleation, growth and aggregation of particles. Chem. Eng. Sci. 1997, 52, 4659-4679. (Pubitemid 28056225)
    • (1997) Chemical Engineering Science , vol.52 , Issue.24 , pp. 4659-4679
    • Kumar, S.1    Ramkrishna, D.2
  • 16
    • 63449114224 scopus 로고    scopus 로고
    • On the solution of population balances for nucleation, growth, aggregation and breakage processes
    • Qamar, S.; Warnecke, G.; Eisner, M. P. On the solution of population balances for nucleation, growth, aggregation and breakage processes. Chem. Eng. Sci. 2009, 64, 2088-2095.
    • (2009) Chem. Eng. Sci. , vol.64 , pp. 2088-2095
    • Qamar, S.1    Warnecke, G.2    Eisner, M.P.3
  • 17
    • 0037872052 scopus 로고    scopus 로고
    • Multivariate population balances via moment and Monte Carlo simulation methods: An important sol reaction engineering bivariate example and "mixed" moments for the estimation of deposition, scavenging, and optical properties for populations of nonspherical suspended particles
    • Rosner, D. E.; McGraw, R.; Tandon, P. Multivariate Population Balances via Moment and Monte Carlo Simulation Methods: An Important Sol Reaction Engineering Bivariate Example and Mixed Moments for the Estimation of Deposition, Scavenging, and Optical Properties for Populations of Nonspherical Suspended Particles. Ind. Eng. Chem. Res. 2003, 42, 2699-2711. (Pubitemid 36667383)
    • (2003) Industrial and Engineering Chemistry Research , vol.42 , Issue.12 , pp. 2699-2711
    • Rosner, D.E.1    McGraw, R.2    Tandon, P.3
  • 18
    • 0030128282 scopus 로고    scopus 로고
    • On the solution of population balance equations by discretization - I. A fixed pivot technique
    • Kumar, S.; Ramkrishna, D. On the solution of population balance equations by discretization-I. A fixed pivot technique. Chem. Eng. Sci. 1996, 51, 1311-1332. (Pubitemid 126660704)
    • (1996) Chemical Engineering Science , vol.51 , Issue.8 , pp. 1311-1332
    • Kumar, S.1    Ramkrishna, D.2
  • 19
    • 0030127313 scopus 로고    scopus 로고
    • On the solution of population balance equations by discretization - II. A moving pivot technique
    • Kumar, S.; Ramkrishna, D. On the solution of population balance equations by discretization-II. A moving pivot technique. Chem. Eng. Sci. 1996, 51, 1333-1342. (Pubitemid 126660705)
    • (1996) Chemical Engineering Science , vol.51 , Issue.8 , pp. 1333-1342
    • Kumar, S.1    Ramkrishna, D.2
  • 20
    • 44349124408 scopus 로고    scopus 로고
    • The cell average technique for solving multi-dimensional aggregation population balance equations
    • DOI 10.1016/j.compchemeng.2007.10.001, PII S009813540700244X
    • Kumar, J.; Peglow, M.; Wamecke, G.; Heinrich, S. The cell average technique for solving multidimensional aggregation population balance equations. Comput. Chem. Eng. 2008, 32, 1810-1830. (Pubitemid 351749667)
    • (2008) Computers and Chemical Engineering , vol.32 , Issue.8 , pp. 1810-1830
    • Kumar, J.1    Peglow, M.2    Warnecke, G.3    Heinrich, S.4
  • 21
    • 38149073208 scopus 로고    scopus 로고
    • A two-level discretisation algorithm for the efficient solution of higher-dimensional population balance models
    • Pinto, M. A.; Immanuel, C. D.; Doyle, F. J., III. A two-level discretisation algorithm for the efficient solution of higher-dimensional population balance models. Chem. Eng. Sci. 2008, 63, 1304-1314.
    • (2008) Chem. Eng. Sci. , vol.63 , pp. 1304-1314
    • Pinto, M.A.1    Immanuel, C.D.2    Doyle III, F.J.3
  • 22
    • 0032193202 scopus 로고    scopus 로고
    • Finite-element methods for steady-state population balance equations
    • Nicmanis, M.; Hounslow, M. J. Finite-element methods for steadystate population balance equations. AIChE J. 1998, 44, 2258-2272. (Pubitemid 29047589)
    • (1998) AIChE Journal , vol.44 , Issue.10 , pp. 2258-2272
    • Nicmanis, M.1    Hounslow, M.J.2
  • 23
    • 8544278921 scopus 로고    scopus 로고
    • High resolution algorithms for multidimensional population balance equations
    • DOI 10.1002/aic.10228
    • Gunawan, R.; Fusman, I.; Braatz, R. D. High resolution algorithms for multidimensional population balance equations. AIChE J. 2004, 50, 2738-2749. (Pubitemid 39490549)
    • (2004) AIChE Journal , vol.50 , Issue.11 , pp. 2738-2749
    • Gunawan, R.1    Fusman, I.2    Braatz, R.D.3
  • 24
    • 33646174027 scopus 로고    scopus 로고
    • A comparative study of high resolution schemes for solving population balances in crystallization
    • Qamar, S.; Eisner, M. P.; Angelov, I. A.; Warnecke, G.; SeidelMorgenstern, A. A comparative study of high resolution schemes for solving population balances in crystallization. Comput. Chem. Eng. 2006, 30, 1119-1131.
    • (2006) Comput. Chem. Eng. , vol.30 , pp. 1119-1131
    • Qamar, S.1    Eisner, M.P.2    Angelov, I.A.3    Warnecke, G.4    SeidelMorgenstern, A.5
  • 25
    • 34447542581 scopus 로고    scopus 로고
    • Adaptive high-resolution schemes for multidimensional population balances in crystallization processes
    • DOI 10.1016/j.compchemeng.2006.10.014, PII S0098135406002882
    • Qamar, S.; Ashfaq, A.; Warnecke, G.; Angelov, I.; Eisner, M. P.; Seidel-Morgenstern, A. Adaptive high-resolution schemes for multidimensional population balances in crystallization processes. Comput. Chem. Eng. 2007, 57, 1296-1311. (Pubitemid 47077485)
    • (2007) Computers and Chemical Engineering , vol.31 , Issue.10 , pp. 1296-1311
    • Qamar, S.1    Ashfaq, A.2    Warnecke, G.3    Angelov, I.4    Elsner, M.P.5    Seidel-Morgenstern, A.6
  • 26
    • 44649170892 scopus 로고    scopus 로고
    • Parallel high-resolution finite volume simulation of particulate processes
    • DOI 10.1002/aic.11484
    • Gunawan, R.; Fusman, I.; Braatz, R. D. Parallel high-resolution finite volume simulation of particulate processes. AIChE J. 2008, 54, 1449-1458. (Pubitemid 351774791)
    • (2008) AIChE Journal , vol.54 , Issue.6 , pp. 1449-1458
    • Gunawan, R.1    Fusman, I.2    Braatz, R.D.3
  • 29
    • 84984082305 scopus 로고
    • Crystal size distributions in continuous crystallizers when growth rate is size dependent
    • Abegg, C. F.; Stevens, J. D.; Larson, M. A. Crystal size distributions in continuous crystallizers when growth rate is size dependent. AIChE J. 1968, 14, 118-122.
    • (1968) AIChE J. , vol.14 , pp. 118-122
    • Abegg, C.F.1    Stevens, J.D.2    Larson, M.A.3
  • 30
    • 0037073056 scopus 로고    scopus 로고
    • On the solution of population balance equations (PBE) with accurate front tracking methods in practical crystallization processes
    • DOI 10.1016/S0009-2509(02)00236-1, PII S0009250902002361
    • Lim, Y.; Le Lann, J.; Meyer, X.; Joulia, X.; Lee, G.; Yoon, E. On the solution of population balance equations (PBE) with accurate front tracking methods in practical crystallization processes. Chem. Eng. Sci. 2002, 57, 3715-3732. (Pubitemid 35212399)
    • (2002) Chemical Engineering Science , vol.57 , Issue.17 , pp. 3715-3732
    • Lim, Y.I.1    Le Lann, J.2    Meyer, X.M.3    Joulia, X.4    Lee, G.5    Yoon, E.S.6
  • 31
    • 33749335929 scopus 로고    scopus 로고
    • Fokker-Planck equation for particle growth by monomer attachment
    • Matsoukas, T.; Lin, Y. Fokker-Planck equation for particle growth by monomer attachment. Phys. Rev. E 2006, 74, 031122.
    • (2006) Phys. Rev. E , vol.74 , pp. 031122
    • Matsoukas, T.1    Lin, Y.2
  • 33
    • 0015967197 scopus 로고
    • Programmed cooling crystallization of potassium sulphate solutions
    • Jones, A. G.; Mullin, J. W. Programmed cooling crystallization of potassium sulphate solutions. Chem. Eng. Sci. 1974, 29, 105-118.
    • (1974) Chem. Eng. Sci. , vol.29 , pp. 105-118
    • Jones, A.G.1    Mullin, J.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.