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.     

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).     

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

Dynamic and spatially multi-dimensional mathematical models of the primary and secondary drying stages of the freeze-drying of pharmaceutical crystalline and amorphous solutes in vials, are constructed and presented in this work. The models account for the removal of free and bound water and could also provide the geometric shape of the moving interface and its position. It is proved that the temperature of the moving interface can not be constant if the flux of heat flow to the sides of the vial is not zero. It is also proved that the slope of the free surface (moving interface) at the edge of the vial is always curved downward.

The numerical solution of the nonlinear partial differential equations of the models would allow model simulations that could indicate design conditions, operating conditions, and control strategies that could provide high drying rates and could lead to a series of novel experiments in freeze-drying.     

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).     

Experimental and Modeling Study During Freeze Drying of Aqueous tert-Butanol–Based Formulations in Vials

In this study, using COMSOL Multiphysics software, we set up a two-dimensional model for the sublimation step a frozen aqueous organic cosolvent tert-butyl alcohol (TBA) formulation without a dissolved active principal ingredient contained in 4-mL glass vials. This model, based on the hypothesis of a sublimation process mainly governed by the conductive heat transfer between the shelf and the sublimation front, allowed precise prediction of the sublimation kinetics and the sublimation front movement for different operating conditions. Next, this modeling was validated by many experimental runs under operating conditions corresponding to very low total gas pressures (5 to 50 Pa) and low shelf temperatures (0 to ?20°C) generally encountered during industrial freeze drying of thermosensible pharmaceuticals (vaccines, diagnostic proteins, serums, etc.).     

A Binary Gas Transport Model Improves the Prediction of Mass Transfer in Freeze Drying

Monitoring partial vapor pressure in the freeze-drying chamber is a cheap, global, and non-intrusive way to assess the end of the primary drying stage. Most existing dynamic freeze-drying models which predict this partial pressure describe mass transfer between the product and the condenser via a mass transfer resistance or a mass transfer coefficient. Experimental evidence suggests that such models can be significantly in error for some values of the sublimation flux, leading to physically inconsistent predictions and possibly incorrect assessment of primary drying termination, with potential risk of product damage if moving to secondary drying and increasing shelf temperature while some ice is still present. Assuming a binary gas transport model for vapor and inert gas leads to improved and consistent predictions and explains the apparent variation of the mass transfer resistance with total pressure, shelf temperature, and product sublimation area.     

MASS TRANSFER THROUGH PERMEABLE WALLS: A NEW INTEGRAL EQUATION APPROACH FOR CYLINDRICAL TUBES WITH LAMINAR FLOW

Mass transfer through cylindrical semipermeable walls is analyzed. The solution is obtained in terms of integral equations. Despite the existence of a non-homogeneous boundary condition on the semipermeable wall, the solution thus obtained is particularly advantageous since the associated eigenvalue problem is independent of the Sherwood number. This parameter takes into account the main conductances at the tube wall.

The approach is applied to the case of mass transfer from the interior of a capillary tube with semipermeable walls to an external fluid. The flow in the tube is laminar, and the external flow is assumed turbulent.

The mathematical methodology employed provides a framework to develop numerical schemes of fast and sure convergence.     

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.     

A MONTE-CARLO APPROACH TO THE INTERPRETATION OF BUBBLE PROBE SIGNALS IN FREELY BUBBLING FLUID BEDS†

The interpretation of the signals generated by a double probe may be done by the three characteristic times method:

t₁ the time duration of the pulses;

t₂ the time shift between the signals of the two probes;

t₃ the time interval between two pulses on one channel.

Each of these times is largely dispersed and the corresponding histograms may be constructed.

The present work is a trial to go over from the time histograms to physical properties of the bubbles combining a Monte-Carlo simulation and a flexible simplex optimisation procedure.

As a result, the percentage of oblique bubbles cutting just one level, the bubble size distribution, the average velocity-size relation, and the individual dispersion around it may be defined.

The procedure is finally applied to experimental results obtained with a light probe in a fluid bed of glass beads.     

冷冻干燥过程强化中冷冻阶段优化的研究进展

冷冻干燥产品质量高,但时间长、能耗高。本文综述了冷冻干燥过程强化中冷冻阶段的优化方法,控制冷冻速率、调节冰晶成核和退火处理可以获得大而均匀的冰晶从而提高升华干燥阶段速率,但物料内部比表面积的减小会降低解吸干燥阶段速率,这类常规的冷冻阶段优化方法对弱吸湿性的物料有一定的强化效果。有机溶剂具有较高的蒸气压,作为共溶剂时可以增加传质推动力,但较低的有机溶剂残留量要求阻碍了其进一步应用。“初始非饱和多孔介质冷冻干燥”的技术思想是将液体物料首先制备成具有一定初始孔隙的冷冻物料,然后再进行冷冻干燥。物料具有的初始孔隙为水蒸气的迁移提供了便捷的通道,而且纤薄的固体基质也有利于结合水的解吸,可以同时强化升华干燥阶段和解吸干燥阶段。该技术思想是过程低消耗和产品高质量的完美结合,为解决冷冻干燥过程速率低的问题提供了新的方案。     

APPLICATION OF UF TECHNOLOGY TO LARGE-SCALE SYNTHESIS OF GT 267-004, A SEQUESTRANT FOR C. DIFFICILE TOXIN

GT 267-004 is a nonabsorbed, nonantibiotic, high molecular weight anionic polymer that is undergoing clinical evaluation as a Clostridium difficile toxin sequestrant. The API is a mixed salt form that consists of approximately 30 to 50% potassium and 70 to 50% sodium as the counterions on the polymer.

The initial polymerization process results in an aqueous polymer solution with the polymer in the 100% sodium form. It also contains some oligomeric impurities. UF technology was applied in a novel way to convert the single-salt polymer to the mixed salt form and to simultaneously remove the oligomers below the required specification limits in a single-unit operation.

Experiments with a UF lab unit validated the concept of simultaneously performing ion exchange and purification. An appropriate amount of potassium chloride was added to the polymer solution to carry out the ion exchange considering the selectivity of the polymer for the potassium ion over the sodium ion. The resulting mixed salts in solution were removed using ultrafiltration membranes. The process produced the API in excellent purity.

The lab data were used to scale up the process to produce several hundred kg of the API. The engineering analysis of the large-scale UF operation was carried out to run the UF process in the cyclic mode and in the diafiltration mode. The UF operation was optimized with respect to time, water usage, operability, and the concentration of product solution required for the subsequent processing.

The optimized UF process was found to be a very cost-effective and time-efficient route to produce the new API.     

药品真空冷冻干燥过程监控技术研究进展

对药品冻干过程进行优化的关键是在保证药品质量不受损害的情况下尽量缩短干燥时间。因此,对冻干过程进行准确的监控是十分重要的,既要保证药品的温度保持在合理的范围内,对干燥结束时间进行准确地判断,同时又要对冻干过程压力和温度进行良好的控制以达到冻干过程的最优化。本文对近年来药品真空冷冻干燥过程监控技术的研究进展进行了综述,主要有基于动态参数估计法(DPE)的监控系统、基于卡尔曼滤波法的监测系统、露点法判断一次干燥结束点、模型预测控制法(MPC)。提出药品真空冷冻干燥监控技术的研究应着重于以下几点:考虑辐射、对流和导热3种传热方式在冻干传热过程中所占的比重,建立二维、三维冻干模型以更加精确地监测药品冻干过程的参数,在此基础上研究对加热隔板温度和冻干室压力的实时最优控制策略,以对药品冻干过程进行及时、有效地控制。     

SIMULATION AND DESIGN 0f HEATING PROFILSS IN HEAT CONTROLLED FREEZE-DRYING OF PHARMACKUTICALS IN VIALS BY THE APPLICATION OF A SUBLIMATION SEMISPHERICAL MODEL.

The freeze-drying of a certain pharmaceutical contained in vials in industrial like conditions has been described by a sublimation model under analogous semispherical configuration. Several operating strategies were proved on the basis of considering three different stages during freeze-drying in relation with the modification of heating and product temperacure evolutions. The model offers interesting perspectives to obtain orientative simulated results in heating strategies analysis in order to reduce drying time.     

RECIRCULATING REACTOR FOR THE STUDY OF MULTIPHASE KINETICS

A new laboratory reactor was set up to measure kinetic coefficients in a solid (catalyst)-liquid-gas reacting system.

The reactor consists of two parts: an absorber, where the liquid is partially saturated by the gas reactant and a reacting zone, where the liquid alone, containing the dissolved gas, flows through a fixed bed of catalyst.

The ricircle of the liquid in the absorber maintains a high concentration of the gas reactant in the liquid also in the zone of reaction, allowing the use of a high mass of catalyst (significative from a statistical point of view) and the achievement of sufficiently high conversion.

The tested reaction is the catalysed hydrogenation of ∝-metylstyrene: in order to consider a drastic situation and to verify the results with the literature data, the experimental conditions examined corresponded to very high chemical reaction rate (instantaneous reaction) at the surface of the pellets.

The tests were carried out with the reactor working both in batchwise and in continuous operative mode (steady state); the results show the reliability of the new reactor above all when the steady state operation is considered. For the use of the reactor in batchwise condition, the accumulation of the product inside the catalyst particles must be considered for an accurate measurement of the kinetic parameters,     

EVALUATION OF CONDUCTIVE HEAT TRANSFER MECHANISMS BETWEEN AN IMMERSED SURFACE AND THE ADJACENT LAYER OF PARTICLES IN BUBBLING FLUIDIZED BEDS

The evaluation of the heat transfer coefficient h_wp between a heat exchanging surface immersed in a gas fluidized bed and the adjacent layer of dense phase particles is analyzed in this contribution. Gas convective and radiant effects are not included in the present analysis.

The inclusion of h_wp, or an equivalent formation, in mechanistic models describing heat transfer has been necessary because the sudden voidage variation close to the immersed wall restrains significantly the heat transfer rate. However, there is not at present a widely accepted expression to evaluate h_wp.

A precise formulation for h_wp accounting for transient conduction inside spherical particles, the Smoluchowski effect, the concentration of particles in the adjacent layer (N_p) and an effective separation gap (l₀) is developed here.

Although N_p can be estimated, in principle, from experimental evidence in packed beds, and it is reasonably expected that l₀ = 0, the analysis of experimental heat transfer rates in moving beds, packed beds, and bubbling fluidized beds indicate that values of h_wp are, in general, smaller than expected from these assumptions. Appropriate values of l₀ and N_p are then stimated by fitting the experimental data.

The probable effect of surface asperities is also discussed by analyzing a simplified geometrical model. It is concluded that the parameter l₀ can be also effective to account for particle roughness, independently of thermal properties.     

A Review on Freeze Drying of Drugs with tert-Butanol (TBA) + Water Systems: Characteristics,Advantages, Drawbacks

Organic cosolvent systems have been evaluated for their potential and increasing use for freeze drying of solutions to produce stabilized powders of marketed pharmaceutical products. The formulations most often investigated include tert-butanol (TBA) + water mixtures. These organic cosolvent systems present many interesting advantages: high freezing temperatures, very short sublimation time, low sublimation enthalpies, high equilibrium vapor/solid pressure values, and low toxicity.

Thus, some main characteristics of water + TBA systems have been reviewed, especially regarding its interesting thermodynamic properties (sublimation enthalpy, equilibrium vapor pressure), impact of freezing conditions on morphological properties of frozen formulations (nucleation, crystal size and shape), influence of operating parameters (total pressure, temperature) on sublimation times, and organic cosolvent and water residual contents.

The crystal morphology of frozen formulations prepared with TBA revealed unexpected results compared with the results reported in the literature for water-based formulations in terms of the complex relationships between freezing rates, supercooling, nucleation temperatures, and solvent crystal morphology (size and shape).

It has been proved that optimum freeze-drying cycles are established by simultaneously taking into account the impact of formulation variables, especially the tert-butanol content, and classical freeze-drying variables during the freezing step (nucleation temperatures, freezing rates) and the sublimation step (shelf temperature, total pressure) to maximize the drying rates and to minimize the residual solvent levels while preserving the main quality attributes of the freeze-dried powder.     

HEAT AND MASS TRANSFER DURING SAPWOOD DRYING ABOVE THE FIBRE SATURATION POINT

Pine sapwood was dried in an air convection kiln at temperatures between 60-80 °C. Temperature and weight measurements were used to calculate the position of the evaporation front beneath the surface. It was assumed that the drying during a first regime is controlled by the heat transfer to the evaporation front until irreducible saturation occurs. Comparisons were made with CT-scanned density pictures of the dry shell formation during initial stages of drying of boards.

The results indicate a receding evaporation front behaviour for sapwood above approximately 40-50% MC when the moisture flux is heat transfer controlled. After that we finally reach a period where bound water diffusion is assumed to control the drying rate.

The heat transfer from the circulating air to the evaporation front controls the migration flux. In many industrial kilns the heating coils therefore have too small heat transfer rates for batches of thin boards and boards with high sapwood content.     

混合型烷醇酰胺组成对油/水动态界面张力的影响

为了探究混合型烷醇酰胺复杂组成对油/水界面张力的作用机制,采用GC-MS联用分析了混合型烷醇酰胺(GYD)的组成,并用自制的不同烷基链长醇酰胺(简记为C_nDEA,n=8,10,12,14,16)在大庆原油条件下研究了GYD组成对油/水界面张力的影响规律。结果表明,降低油/水界面张力能力强弱为C₁₄DEA> C₁₂DEA≈GYD> C₁₆DEA> C₁₀DEA> C₈DEA,C₁₄DEA、C₁₂DEA和GYD在一定浓度范围内能降低油/水界面张力至10^-3mN/m数量级;C_nDEA之间复配体系的界面活性取决于体系中各单分子结构烷醇酰胺相对含量,其中C₁₄DEA/C₁₂DEA相对含量是影响体系油/水界面活性的关键因素,当C₁₄DEA/C₁₂DEA复配比大于1时,体系达到超低界面张力浓度窗口更宽,界面动态特性更好;适量助剂(月桂酸和二乙醇胺)的加入对体系降低界面张力有一定的协同效应;GYD/C₁₄DEA复配体系随C₁₄DEA浓度增加,体系界面活性明显改善。     

MERCURY REMOVAL FROM OILS

Heavy condensate or oil can contain significant amounts of mercury which causes marketing, processing and environmental concerns.

We have developed an effective process to remove all kinds of mercury compounds in heavy condensate. At the conditions tested, the total mercury content in a condensate was reduced from 3,000 to lO ppb, representing 99.7% mercury removal.

In the process, the condensate is pumped upflow through a reactor filled with activated carbon and polysulfide solution at mild conditions. The effluent is a clear, low mercury product.

The theory and principles of the process are developed and verified with experiments. Process variables were also explored to define the preferred region of operation.     

An Interactive Tool for the Optimization of Freeze-Drying Cycles Based on Quality Criteria

Among existing dehydration methods, freeze-drying has unique benefits for the stabilization and preservation of biological activity of pharmaceutical products but remains an expensive and time-consuming process. A user-friendly software tool was developed, allowing for interactive selection of process operating condition profiles in order to maximize process productivity while insuring product quality preservation. The software is based on a dynamic, one-dimensional heat and mass transfer model, which can accurately represent both the primary and secondary drying stages and the gradual transition between them. The model was validated in a wide range of operating conditions: ? 25 to + 25°C shelf temperature and 10 to 34 Pa total pressure. By comparing a reference sucrose solution with a formulated pharmaceutical product containing polyvinylpyrrolidone (PVP), it is shown that controlling product properties such as glass transition temperature and sorption isotherm can reduce the minimum achievable cycle duration by 12 h (33%).