An asymptotic model for the primary drying stage of vial lyophilization

详细信息    查看全文

• 作者：M. Vynnycky
• 关键词：Asymptotics ; Freeze ; drying ; Vial ; Pharmaceuticals
• 刊名：Journal of Engineering Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：96
• 期：1
• 页码：175-200
• 全文大小：1,002 KB
• 参考文献：1.Muzzio CR, Dini NG (2011) Simulation of freezing step in vial lyophilization using finite element method. Comput Chem Eng 35:2274–2283CrossRef
  2.Sheehan P, Liapis AI (1998) Modelling of the primary and secondary drying stages of the freeze-drying of pharmaceutical product in vials: numerical results obtained from the solution of a dynamic and spatially multidimensional lyophilisation model for different operational policies. Biotechnol Bioeng 60:712–728CrossRef
  3.Pikal MJ, Cardon S, Bhugra C, Jameel F, Rambhatla S, Mascarenhas WJ, Akay HU (2005) The nonsteady state modeling of freeze drying: in-process product temperature and moisture content mapping and pharmaceutical product quality applications. Pharm Dev Tech 1:17–32CrossRef
  4.Pikal MJ (1985) Use of laboratory data in freeze-drying process design: heat and mass transfer coefficients and the computer simulation of freeze-drying. J Parenter Sci Tech 39:115–139
  5.Millman MJ, Liapis AI, Marchello JM (1985) An analysis of the lyophilisation process using a sorption sublimation model and various operational policies. AIChE J 31:1594–1604CrossRef
  6.Mascarenhas WJ, Akay HU, Pikal MJ (1997) A computational model for finite element analysis of the freeze-drying process. Comput Meth Appl Mech Eng 148:105–124CrossRef MATH
  7.Song CS, Nam JH, Kim CJ, Ro ST (2002) A finite volume analysis of vacuum freeze drying processes of skim milk solution in trays and vials. Dry Tech 20:283–305CrossRef
  8.Song CS, Nam JH, Kim CJ, Ro ST (2005) Temperature distribution in a vial during freeze-drying of skim milk. J Food Eng 67:467–475CrossRef
  9.Brülls M, Rasmuson A (2009) Ice sublimation in vial lyophilization. Dry Tech 27:695–706CrossRef
  10.Zhai S, Su H, Taylor R, Slater KH (2005) Pure ice sublimation within vials in a laboratory lyophiliser; comparison of theory with experiments. Chem Eng Sci 60:1167–1176CrossRef
  11.Hottot A, Peczalski R, Vessot S, Andrieu J (2006) Freeze-drying of pharmaceutical proteins in vials: modeling of freezing and sublimation steps. Dry Tech 24(5):561–570CrossRef
  12.Velardi SA, Barresi AA (2008) Development of simplified models for the freeze-drying process and investigation of the optimal operating conditions. Chem Eng Res Design 86:9–22CrossRef
  13.Lopez-Quiroga E, Antelo LT, Alonso AA (2012) Time-scale modeling and optimal control of freeze-drying. J Food Eng 111(4):655–666CrossRef
  14.Jackson R (1977) Transport in porous catalysts. Elsevier, Amsterdam
  15.Mason EA, Malinauskas AP (1983) Gas transport in porous media: the dusty-gas model. Elsevier, New York
  16.Gloor PJ, Crosser OK, Liapis AI (1987) Dusty-gas parameters of activated carbon adsorbent particles. Chem Eng Commun 59:95–105CrossRef
  17.Kast W, Hohenthanner CR (2000) Mass transfer within the gas-phase of porous media. Int J Heat Mass Transfer 43:807–823CrossRef MATH
  18.Liapis AI, Bruttini R (1995) Freeze-drying of pharmaceutical crystalline and amorphous solutes in vials: dynamic multi-dimensional models of the primary and secondary drying stages and qualitative features of the moving interface. Dry Tech 13:43–72CrossRef
  19.Sheehan P (1998) Internal report No. 10. Tech. Rep., Department of Chemical Engineering, University of Missouri-Rolla, Rolla, MO
  20.Mitchell SL, Vynnycky M (2009) Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems. Appl Math Comput 215:1609–1621MathSciNet MATH
  21.Mitchell SL, Vynnycky M (2012) An accurate finite-difference method for ablation-type Stefan problems. J Comput Appl Math 236:4181–4192MathSciNet CrossRef MATH
  22.Mitchell SL, Vynnycky M, Gusev IG, Sazhin SS (2011) An accurate numerical solution for the transient heating of an evaporating droplet. Appl Math Comput 217:9219–9233MathSciNet MATH
  23.Vynnycky M (2009) An asymptotic model for the formation and evolution of air gaps in vertical continuous casting. Proc R Soc A 465:1617–1644ADS MathSciNet CrossRef MATH
  24.Wagner W, Saul A, Pruss A (1994) International equations for the pressure along the melting and along the sublimation curve of ordinary water substance. J Phys Chem Ref Data 23:515–527ADS CrossRef
  25.Boss EA, Filho RM, de Toledo ECV (2004) Freeze drying process: real time model and optimization. Chem Eng Process 43:1475–1485CrossRef
  26.Sadikoglu H, Liapis AI (1997) Mathematical modelling of the primary and secondary drying stages of bulk solution freeze-drying in trays: parameter estimation and model discrimination by comparison of theoretical results with experimental data. Dry Tech 15:791–810CrossRef
  27.Bruttini R, Rovero G, Baldi G (1991) Experimentation and modelling of pharmaceutical lyophilization using a pilot plant. Chem Eng J 45:B67–B77CrossRef
  28.Nail SL (1980) The effect of pressure on heat transfer in the freeze-drying of parenteral solutions. J Parenter Drug Assoc 34:358–368
  29.Demirel Y, Saxena SC (1996) Heat transfer through a low-pressure gas enclosure as a thermal insulator: design considerations. Int J Energy Res 20:327–338CrossRef
  30.Gan KH, Bruttini R, Crosser OK, Liapis AI (2004) Heating policies during the primary and secondary drying stages of the lyophilization process in vials: effects of the arrangements of vials in clusters of square and hexagonal arrays on trays. Dry Tech 22:1539–1575CrossRef
  
• 作者单位：M. Vynnycky (1) (2)
  
  1. Mathematics Applications Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, Limerick, Republic of Ireland
  2. Division of Casting of Metals, Department of Materials Science Engineering, Royal Institute of Technology, Brinellvägen 23, 100 44, Stockholm, Sweden
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Applications of Mathematics
  Analysis
  Mathematical Modeling and IndustrialMathematics
  Numeric Computing
  
• 出版者：Springer Netherlands
• ISSN：1573-2703

文摘

Asymptotic methods are employed to analyse a commonly used one-dimensional transient model for coupled heat and mass transfer in the primary drying stage of freeze-drying (lyophilization) in a vial. Mathematically, the problem constitutes a two-phase moving boundary problem, in which one of the phases is a frozen porous matrix that undergoes sublimation, and the other is a low-pressure binary gaseous mixture. Nondimensionalization yields a model with 19 dimensionless parameters, but a systematic separation of timescales leads to a reduced model consisting of just a second-order differential equation with two initial conditions for the location of a sublimation front; the temperature and gas partial pressures can be found a posteriori. The results of this asymptotic model are compared with those of earlier experimental and theoretical work. Most significantly, the current model would be a computationally efficient tool for predicting the onset of secondary drying.