Freeze-Drying of Pharmaceutical Proteins in Vials: Modeling of Freezing and Sublimation Steps

The commercial finite element code FEMLAB was used to perform two-dimensional axisymmetric simulations of the temperature profiles and the moving front velocities of standard BSA (bovine serum albumin)-based formulations used to stabilize pharmaceutical proteins during the freeze-drying process. The simulations were validated with both experimental and numerical approaches.

In an initial step, the heat transfer phenomena taking place during the cooling of liquid solutions was studied in commercial size glass vials without freezing or sublimation.

Then, this model was extended and validated for the freezing process of aqueous BSA-based solutions encountered in the industrial freeze-drying processes with the same vials in order to confirm the identified values of the different thermal conductances between the product and the shelf and between the product and the surroundings.

Finally, the conductances between the product and the shelf and between the vial and the surroundings thus determined were used in a dynamic sublimation model with two zones and a moving sublimation front similar to the ones previously proposed in the literature.

The simulations showed a satisfactory agreement between experimental and simulated data.

The results of this study demonstrated that the freeze-drying process of pharmaceutical proteins in glass vials for standard industrial operating conditions was mainly controlled by the heat transfer from the shelf and the surroundings to the product sublimation front.     

Freeze-Drying of Pharmaceutical Proteins in Vials: Modeling of Freezing and Sublimation Steps

The commercial finite element code FEMLAB was used to perform two-dimensional axisymmetric simulations of the temperature profiles and the moving front velocities of standard BSA (bovine serum albumin)-based formulations used to stabilize pharmaceutical proteins during the freeze-drying process. The simulations were validated with both experimental and numerical approaches.

In an initial step, the heat transfer phenomena taking place during the cooling of liquid solutions was studied in commercial size glass vials without freezing or sublimation.

Then, this model was extended and validated for the freezing process of aqueous BSA-based solutions encountered in the industrial freeze-drying processes with the same vials in order to confirm the identified values of the different thermal conductances between the product and the shelf and between the product and the surroundings.

Finally, the conductances between the product and the shelf and between the vial and the surroundings thus determined were used in a dynamic sublimation model with two zones and a moving sublimation front similar to the ones previously proposed in the literature.

The simulations showed a satisfactory agreement between experimental and simulated data.

The results of this study demonstrated that the freeze-drying process of pharmaceutical proteins in glass vials for standard industrial operating conditions was mainly controlled by the heat transfer from the shelf and the surroundings to the product sublimation front.     

Experimental Study and Modeling of Freeze-Drying in Syringe Configuration. Part I: Freezing Step

This article concerns the experimental study and the modeling of the freezing step during freeze-drying of a model lyoprotectant formulation in syringe configuration. First, ice crystal morphology observations were carried out in a cold chamber equipped with stereomicroscopy to determine the ice crystal size distribution. We observed that the ice crystal morphology was homogeneous as a function of the radial position and that, contrary to our previous observations in glass vial configuration, no significant ice morphology differences existed between the bottom and the top of syringes. Thus, it seems that the gas cooling by free convection at the walls of the syringe during the freezing step led to higher homogeneity in the ice crystal morphology. These data allowed calculation of the mean ice crystal diameter (which was supposed to represent the mean porous diameter) and then the permeability of the freeze-dried cake. Moreover, a two-dimensional axisymmetric (2D) mathematical model in cylindrical geometry of the freezing step for aqueous sucrose solution was elaborated. It has been proved that this model was able to simulate quite precisely the whole temperature profiles during the freezing step, except the exothermic peak of nucleation. In the last part of this work on syringe geometry, the impact of annealing treatments on the freeze-dried matrix morphology was investigated. Some heterogeneity of sublimation rates was observed, with significant variation of residual humidity. Additionally, the water vapor mass transfer resistance values decreased if a convenient annealing treatment (shelf temperature at ?10°C) was applied.     

Desalination by natural freezing

This paper presents a technique for desalination by natural freezing that can be used in relatively warm climates with ambient temperatures above freezing. The reasons for the freezing of water are discussed and theoretical calculations are given to predict the time required to reach the freezing temperature. Experimental results are given which show that the technique works. The melted ice water from a single freezing without a wash step has three to six times less salt than the feed. Possible suitable locations, a preliminary economic analysis, and methods of increasing the product purity by washing the ice are discussed.     

Influence of Freezing Temperature on Product Parameters of Solid Dosage Forms Prepared via the Freeze‐Casting Technique

The freeze‐casting technique was used to formulate porous solid bodies containing theophylline as an active pharmaceutical ingredient, potato starch as a filler and citric acid or saccharose as binding agents. Aqueous suspensions of the ingredients were frozen at three different temperatures. The aim of this work was to investigate the influence of the freezing temperature on the ice crystal growth rate of the suspensions and the resulting porosity of the freeze‐casted samples. The impact of the freezing temperature on the solidification of the suspensions was analyzed via contact angle measurements. The rate of ice crystal growth was expressed as an overall linear growth rate. The porosity of the freeze‐casted bodies was determined by high‐pressure mercury porosimetry. A close correlation was found between the freezing temperature and the investigated product parameters. Lower cooling temperatures resulted in higher final porosities. The lowest temperature, at which final product properties could be regulated by varying the cooling regimes, was –30 °C. The influence of the freezing temperature and the impact of the additives were not remarkable at a freezing temperature lower than –30 °C. Therefore, it can be concluded that the optimum freezing temperature of the suspensions investigated in this study is in the temperature range between –20 °C and –30 °C.     

Determination of the solubility of a monomer in water by multiple headspace extraction gas chromatography

In water‐based polymerization (suspension, microsuspension, emulsion, miniemulsion, and microemulsion polymerization), the solubility of the monomer in the aqueous phase can have profound effects on the final polymer product. This article demonstrates a novel method for the determination of monomer solubility in water with headspace gas chromatography (GC). In this method, an excess amount of an organic solute of interest was added into a closed headspace vial containing a given volume of water. The organic solute and water in the vial was well mixed by strong hand shaking; then, the equilibrated vapor solute in the vial at a desired temperature was measured by headspace GC with a multiple headspace extraction mode. In each headspace extraction, a part of the vapor phase in the vial was vented for GC analysis and replaced with an inert gas. The excess amount of solute in aqueous solution was eventually removed from the vial after multiple headspace extractions, and the solute concentration in water reached its saturation point. After that point, the concentration of the solute in the vapor dramatically decreased in each subsequent headspace extraction. By plotting vapor concentration versus headspace extraction number, we determined the transition point. The vapor concentration at this point corresponded to the solute solubility, which was calculated through a calibration. This method was very simple and automated; it could easily be used for organic solute solubility measurement at an elevated temperature. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 1296–1301, 2006     

Ice Sublimation in Vial Lyophilization

Ice sublimation in vial lyophilization was studied experimentally and theoretically. A theoretical dynamic and two-dimensional axisymmetric model that comprised both the vial and its content was developed. The model included the curvature of the bottom of the vial, the temperature of the ice surface as a function of the chamber pressure, and physical models for the heat of sublimation, thermal conductivity of gases at low pressure, thermal conduction, and thermal radiation. The coefficients in the model were based on physical constants, except for vials on the periphery of the shelf, where an overall heat transfer coefficient derived from experimental data was used to model the transport of heat from the walls of the freeze dryer. The study demonstrated that the sublimation was, apart from the shelf temperature and the chamber pressure, also influenced by the curvature of the bottom of the vial, the position on the shelf, and the atmosphere in the freeze dryer.     

用升华与蒸发联合法干燥食品的物理性质

Drying is an important unit operation in processing of biological resources. The drying process may influence the product properties and quality, which may shrink, break or undergo rheological, physical and biochemical changes. The important parameters responsible for such changes are drying conditions, type of drying technology and residence drying time. Thermal conductivity, thermal-mass diffusivity, enthalpy, porosity and density are the main material property and heat-mass transfer parameters, which are essential for understanding the changes in product quality and for designing and dimensioning the drying processes. In this paper physical properties of food products undergoing a combined sublimation and evaporation were studied. Pieces of vegetables and potatoes were dried in a heat pump fluidized bed dryer at combined modes with temperatures below the freezing point in the beginning and a final drying step at temperatures above the freezing point. Samples of products were tested at different moisture contents with respect to physical properties. Physical properties of leek and potato samples were measured and mass diffusivities were determined from drying kinetic data. Based on bulk density and rehydration measurements it was clearly observed that drying temperature and modes influenced the final product physical properties. The potato cuberun dried with initial atmospheric freeze-drying step had rehydration ability 430% above a run dried only above the freezing point. The average effective mass diffusivity for 5 mm slabs of leek was 0.5×10^-11m^2·s^-1 for the sublimation stage and 2.2×10^-11m^2·s^-1 for the evaooration stage.     

THE DYNAMIC BEHAVIOR OF A FIXED-BED STEAM-OXYGEN COAL GASIFIER DISTURBED BY WATER INFLUX II. MODEL DEVELOPMENT AND VERIFICATION

A one-dimensional transient model has been developed to simulate the unsteady-state behavior of a fixed-bed coal gasifier disturbed by water injection. The resulting set of differential equations was solved numerically using a finite difference method. The validity of the model was first tested against the steady-state experimental data on the product gas composition and the gas production rate for different feed conditions, and the model has been further extended to include transient operation of the gasifier. The dynamic analysis includes the quantitative validation of the system response to changes in the feed condition—either a step change or a rectangular-pulse type change. The simulation results show that the dynamic behavior has a quite different trend in the product gas composition than equilibrium models predict. Such a discrepancy occurs because dynamic behavior is controlled by the changes in the gasification reaction rate rather than a shift in equilibrium The controlling mechanism can be elucidated in terms of the relative contribution by each gasification reaction.     

微孔发泡塑料挤出成型中聚合物—气体均相体系形成研究

微孔发泡塑料是一种内部含有很多小泡孔的新型材料，具有很多优异性能。在微孔塑料挤出成型加工过程中，聚合物－气体均相体系能否形成是保证产品质量的关键因素之一。对其进行分析和计算，推导出挤出过程中聚合物－气体均相体系形成所需时间计算公式。结果表明，通过增加挤出压力，从而获得泡孔细密的泡沫塑料。     

Synthesis and characterization of (S)-3-benzoylthio-2-methylpropionic acid

以硫代乙酸、甲基丙烯酸为原料,经过缩合、水解-酯化得到3-苯甲酰巯基-2-甲基丙酸的消旋体,经化学拆分得到(S)-3-苯甲酰巯基-2-甲基丙酸。综合考察了缩合、水解-酯化、拆分过程中影响反应的因素,结果表明：硫代乙酸与甲基丙烯酸摩尔比为1.4︰1,反应时间为2 h、反应温度为93 ℃条件下,可以得到收率为95.6%的3-乙酰巯基-2-甲基丙酸（缩合物A）;控制釜温不超过20 ℃,将缩合物A加入11.8%的氢氧化钠水溶液中进行水解,水解完成后将下层钠盐投回釜内,然后在低温下滴加苯甲酰氯,反应进行2 h后将釜液调至酸性,产品逐渐析出,计算得水解-酯化总收率为96.7%;利用拆分剂D-(+)-N-苄基-α-苯乙胺对产品拆分,拆分收率为36.0%,综合以上三步总收率可达33.3%。其结构经核磁、质谱、红外分析确认且由X射线衍射分析结晶度非常高。     

Sublimation Kinetics during Freeze-Drying of Pharmaceutical Protein Formulation

The influence of total gas pressure and shelf temperature on sublimation kinetics of BSA-based formulation in glass vial as geometrical configuration was determined with a pilot freeze-dryer in standard operating freeze-drying conditions.

The sublimation rate curves showed three different periods with a plateau corresponding to a stationary regime. These kinetics data were mainly dependent on the shelf temperature and slightly influenced by the total gas pressure. Thus, the sublimation process in our conditions was mainly governed by overall heat transfer rate from the plate and from the surroundings to the sublimation front.

Moreover, it proved that the water vapor mass transfer mechanism through the dried layer occurs by molecular diffusion in Knudsen regime.

Finally, these experimental sublimation kinetics data were found in a quite fair agreement with the set up results. They confirm the validation of previous modeling of mean product temperature profiles during the freeze-drying by using the finite element code FEMLAB in real vial geometry (2-D).     

(S)-3-苯甲酰巯基-2-甲基丙酸的合成及表征

以硫代乙酸、甲基丙烯酸为原料,经过缩合、水解-酯化得到3-苯甲酰巯基-2-甲基丙酸的消旋体,经化学拆分得到(S)-3-苯甲酰巯基-2-甲基丙酸。综合考察了缩合、水解-酯化、拆分过程中影响反应的因素,结果表明:硫代乙酸与甲基丙烯酸摩尔比为1.4︰1,反应时间为2 h、反应温度为93℃条件下,可以得到收率为95.6%的3-乙酰巯基-2-甲基丙酸(缩合物A);控制釜温不超过20℃,将缩合物A加入11.8%的氢氧化钠水溶液中进行水解,水解完成后将下层钠盐投回釜内,然后在低温下滴加苯甲酰氯,反应进行2 h后将釜液调至酸性,产品逐渐析出,计算得水解-酯化总收率为96.7%;利用拆分剂D-(+)-N-苄基-α-苯乙胺对产品拆分,拆分收率为36.0%,综合以上三步总收率可达33.3%。其结构经核磁、质谱、红外分析确认且由X射线衍射分析结晶度非常高。     

Optimal cure steps for product quality in a tire curing process

Numerical algorithms and computer programs have been developed to determine optimal cure steps in a tire curing process. A dynamic constrained optimization problem was formulated with the following ingredients: (1) an objective function that measures product quality in terms of final state of cure and temperature history at selected points in a tire; (2) constraints that consist of a process model and temperature limits imposed on cure media; (3) B‐splines representation of a time‐varying profile of cure media temperature. The optimization problem was solved using the complex algorithm along with a finite element model solver. Numerical simulations were carried out to demonstrate the procedure of determining optimal cure steps for a truck/bus radial tire. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 2063–2071, 1999     

Sublimation Kinetics during Freeze-Drying of Pharmaceutical Protein Formulation

The influence of total gas pressure and shelf temperature on sublimation kinetics of BSA-based formulation in glass vial as geometrical configuration was determined with a pilot freeze-dryer in standard operating freeze-drying conditions.

The sublimation rate curves showed three different periods with a plateau corresponding to a stationary regime. These kinetics data were mainly dependent on the shelf temperature and slightly influenced by the total gas pressure. Thus, the sublimation process in our conditions was mainly governed by overall heat transfer rate from the plate and from the surroundings to the sublimation front.

Moreover, it proved that the water vapor mass transfer mechanism through the dried layer occurs by molecular diffusion in Knudsen regime.

Finally, these experimental sublimation kinetics data were found in a quite fair agreement with the set up results. They confirm the validation of previous modeling of mean product temperature profiles during the freeze-drying by using the finite element code FEMLAB in real vial geometry (2-D).     

新型矿井冻结施工温度监测方法的研究

对新型矿井冻结施工过程中温度监测方法进行研究,分析了影响温度变化的因素,阐述了ANASY在冻结施工中的应用与采用的网格划分模式,将得出的影响温度变化的因素以中排、外1排之间的范围为例进行详细的求解,得出影响温度变化的主要因素,为今后这方面的研究提供借鉴。     

水热耦合对冻土区埋地管道土壤温度场的影响

冻土区埋地热油管道最常见的安全问题是冻害破坏。当环境温度降至冰点以下,土壤中水分的冻结将伴随着水分向冻结前锋迁移,产生不均匀冻胀,加之周期性不可逆的冻融循环,极易造成管道失稳甚至破裂。研究管道冻害成因,应先预测埋地管道周围土壤冻融过程中温度场的变化,以及温度场与水分场的变化关系。采用有限体积法,建立土壤多孔介质水热耦合相变模型,利用SIMPLER算法进行数值求解,为了研究水分对土壤温度场的影响,这里对无水土壤和饱和含水土壤两种极限情况进行对比分析,结果表明：在输油管道运行初期,两种情况土壤温度场接近,随着运行时间的延长,饱和含水土壤温度场偏高,水分迁移和冰水相变对土壤温度场具有一定影响。     

Optimization of the Freeze-Drying Cycle: A New Model for Pressure Rise Analysis

The principal aim of this study was to evaluate the Pressure Rise Analysis (PRA) method as a nonintrusive method for monitoring the product temperature during primary drying of the freeze-drying process of model pharmaceutical formulations. The principle of this method, based on the MTM method initially published by Milton et al.1 consisted in interrupting rapidly the water vapor flow from the sublimation chamber to the condenser chamber and by analyzing the resulting dynamics of the chamber total pressure increase. A new physical model, named PRA model, based on elementary heat and mass balance equations and on constitutive equations expressing the elementary fluxes, was proposed and validated in this study for interpreting the experimental pressure rise data. It was possible to identify very precisely the values of some key parameters of the freeze-drying process such as the ice sublimation interface temperature, the mass transfer resistance of the dried layer and the overall heat transfer coefficient of the vial. The identified ice front temperatures were compared with experimental data obtained from vial bottom temperatures measured by thin thermocouples during freeze-drying runs of 5% w/v mannitol solutions. These two sets of data were found consistent with a maximum difference of no more than 2°C. The dried layer mass transfer resistance increased linearly as a function of its thickness, and the values were coherent with the few literature data published for this system. The method also led to reliable values of the vial overall heat transfer coefficient of approximately 20 Wm^-2 K^-1 in accordance with the published data for this type of vials and these experimental freeze-drying conditions.     

DYNAMIC OPTIMAL CONTROL OF BATCH RICE DRYING PROCESS

The drying of paddy rice may result in quality degradation, expressed as a head kernel yield, leading to significant commercial depreciation of the product. A mathematical model of the drying and of the quality degradation process was combined with a dynamic optimization algorithm to determine the drying conditions (air temperature and relative humidity as functions of time) that ensured the highest possible final product quality for a specified drying time and a specified final moisture content. The robustness of the optimal drying strategy with respect to the initial state of the product, to the model parameters and to the initialization of the optimization algorithm was verified. The compromise between the highest achievable final quality and the allowed total drying time was studied. The combination of simulation and optimization yielded a new insight in the rice drying process and in the quality preservation strategies.     

一种活性染发剂的制备与应用

以酸性黄73、环氧氯丙烷、硫氢化钠为原料,采用两步法合成活性染料,考察了反应时间、反应温度、原料摩尔比对第1步反应产物收率的影响,得到的较佳反应条件为:n(环氧氯丙烷)∶n(酸性黄73)=20∶1,80℃下反应4 h,在此条件下第1步反应产物的收率为65%。再用硫氢化钠对第1步反应产物进行改性,得到巯基改性的酸性黄73。用红外光谱和液质联用对2步反应产物进行结构表征,并将巯基改性的酸性黄73用于染发剂中考察其染发效果。结果表明,目标产物可以与头发结合,且水洗牢度良好。