Noninvasive Monitoring of a Freeze-Drying Process for tert-Butanol

Apr 27, 2016 - Freeze-drying from mixtures of water and organic solvents has been demonstrated to be beneficial to both product quality and process du...
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Noninvasive Monitoring of a Freeze-Drying Process for tert-Butanol/ Water Cosolvent-Based Formulations Roberto Pisano,* Davide Fissore, and Antonello A. Barresi Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Piedmont, Italy ABSTRACT: Freeze-drying from mixtures of water and organic solvents has been demonstrated to be beneficial to both product quality and process duration. The aim of this study was to develop a new model-based technology (referred to as valveless monitoring system) that makes it possible to monitor noninvasively the sublimation step in the case of lyophilization from both aqueous solutions and organic/ water cosolvent systems. This technology can directly measure the rate of sublimation and infer key quality variables, which cannot be measured online, from process variables (i.e., pressure inside the drying chamber and condenser) that are commonly measured during a freeze-drying cycle. These estimations are useful not only to monitor the process but also to design the cycle. In fact, the proposed monitoring system can also estimate either the heat transfer coefficient or the mass transfer resistance through two separate experiments. This study also shows how these two parameters (coupled with a mathematical model of the process) can be used to identify the values of the process conditions that allow maintenance of key quality variables within specified limits. Examples of application of this system to a tert-butanol/ water cosolvent-based formulation are presented and discussed to demonstrate the effectiveness of the proposed approach.

1. INTRODUCTION Today, various pharmaceutical products on the market are manufactured by freeze-drying from organic/water cosolvent systems.1 There are many reasons at the basis of this success. For example, the use of organic solvents can enhance chemical stability of lyophilized samples, beside increasing the rate of sublimation and thus decreasing the drying time. There are also various examples where the use of organic solvents is necessary to facilitate the wetting of hydrophobic ingredients.2 However, the use of these solvents causes several issues that have to be properly addressed by lyophilization professionals, e.g., it may require very low residual solvent content in the final product, special manufacturing facilities, and special care during solvent manipulation because of its flammability.1 Much research in recent years has focused on freeze-drying from organic/water cosolvent systems or from strictly organic solvents.1,3 In particular, the use of tert-butyl alcohol (TBA), both pure TBA or TBA/water mixtures, was found to be beneficial to product quality and process duration.2,4−14 Kasraian and DeLuca10 showed that the drying rate of sucroseand lactose-based formulations is highly increased if part of water is replaced by TBA. They observed that larger crystals of solvent are formed during freezing; after sublimation, these crystals produce larger pores in the dried cake, which then offer lower resistance to vapor flow and make the primary drying time shorter. At the same time, the use of TBA may be expected to lower the specific surface area and the secondary drying rate, increasing the secondary drying time. A compromise is thus necessary to achieve the effective freezedrying. Besides, the higher vapor pressure of the water/TBA system increases the driving force for mass transfer with respect to the pure aqueous system.6 Kasraian and DeLuca9 also observed that the above phenomena are influenced by the © XXXX American Chemical Society

composition of the water−TBA mixture, and the best results appear to be obtained using the eutectic composition, i.e., 20% TBA−80% water, because a uniform structure of TBA−ice crystals is obtained after freezing. This composition is used for various commercial drugs such as amoxicillin sodium,15 Aprostatil (CAVERJECT Sterile Powder),16 and Imexon.17 Beside safety issues, before moving from a pure aqueous system to a water/TBA system, it is necessary to check if the presence of TBA has negative effects on the collapse temperature of the formulation (when processing amorphous products) because product temperature has to remain below this value throughout the drying process to avoid dried cake collapse. In some cases, the addition of TBA was shown to have no effects on the collapse temperature, as for sucrose,10 whereas in other cases, the limit temperature was slightly decreased with respect to that of the pure water system, as for sulfobutylether-7-β-cyclodextrin.18 When developing a freeze-drying cycle, it is essential to choose those process conditions that on the one hand deliver the desired performance for the product and on the other hand improve the energy efficiency of the process. The experimental approach so far used for the development of a freeze-drying cycle in the case of organic/water cosolvent systems was far from optimal. Furthermore, there remains a need for an efficient method that can be used to monitor the key quality parameters of the product during the drying process. As concerns product quality, the appearance of the lyophilized plug is an important attribute to be considered Received: November 13, 2015 Revised: April 13, 2016 Accepted: April 27, 2016

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DOI: 10.1021/acs.iecr.5b04299 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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variables, e.g., the temperature of the product at the interface of sublimation and close to the bottom of the vial, the resistances to mass transfer, and the state of progress of the sublimation process. Furthermore, VMS, if coupled with thermocouple readings, can also be used to estimate the heat transfer coefficient for a specific container at a given pressure value. Although the use of organic/cosolvent systems allows a reduction in primary drying duration, a further improvement in energy savings can be achieved by process optimization similar to what has been already done for aqueous solutions.28 To this purpose, it is critical to select process conditions that can maintain the temperature of the product at its maximum allowed value beyond which product damage occurs. This study shows how VMS outcomes can be used to calculate the design space32−37 and achieve this objective; the design space is defined as the multidimensional combination of process parameters (and input variables) that have been demonstrated to provide assurance of quality. For a freeze-drying process, the design space is thus constituted by the values of temperature of the heat transfer fluid and of pressure in the drying chamber that produce a product with the desired characteristics at the end of the process. Experimental investigation, using a trial and error approach, can be used to find the design space, but mathematical modeling could be much more efficient, requiring only few tests to get the values of model parameters. The feasibility of this approach to a water/TBA formulation was shown by Bogdani et al.38

during cycle development. To produce products that meet aesthetic requirements, it is fundamental to control both the temperature of the product and the duration of the primary drying. At laboratory scale, these parameters are monitored through thermocouples. However, thermocouples cannot be used at production scale where solutions are sterile filtered and aseptically filled into vials.19 A variety of technologies has been developed for freeze-drying from aqueous solutions. Two of these technologies (pressure rise test20−25 and tunable diode laser absorption spectroscopy)26,27 have received much attention from the lyophilization community, but a variety of factors limits their application at manufacturing scale. For example, the pressure rise test requires that for a short time interval (usually 30 s) the valve between the drying chamber and condenser is closed. This approach requires a fast closing valve in the duct, and care must be taken when setting the temperature of the heat transfer fluid because the product temperature increases as pressure increases during the test. This means that the primary drying stage has to be carried out at a temperature lower than its optimal value because an additional safety margin has to be used, and this can significantly increase the drying time.28 The tunable diode laser absorption spectroscopy requires the measurement of water concentration and gas velocity within the duct, and if the velocity profile within the duct is known, then it can estimate the sublimation flux. Furthermore, if product temperature is measured, then heat and mass transfer resistances can be estimated in-line. Unfortunately, the complex vapor dynamics within the duct, in particular in industrial-scale freeze-dryers, makes the estimation of product parameters less accurate,29 and the retrofit of existing freeze-dryers with the required hardware can be difficult (and expensive). Recently, a noninvasive method has been proposed by Pisano et al.30 to monitor in-line a freeze-drying cycle using the pressure decrease test. Similar to the pressure rise test, chamber pressure is modified for a short time, but in this case, chamber pressure decreases. This technique can effectively be used only if chamber pressure is regulated by nitrogen bleeding because it requires shut-off of the controlled leakage valve. The state of the product is retrieved looking for the best fit between calculated and measured values of chamber pressure, similar to the pressure rise test method. The advantage of pressure decrease test, with respect to the pressure rise test, is that no additional safety margin has to be used during cycle design because pressure deviations do not produce product overheating. All previously listed monitoring systems have been developed for the freeze-drying of aqueous solutions, although their application to freeze-drying from organic/water cosolvent systems has not been investigated yet and might require modifications that are not straightforward.31 This study aims to develop a fully noninvasive method for the monitoring of sublimation rate in the case of organic/water cosolvent systems. This method makes it possible to estimate the rate of sublimation without the need to insert a probe into the product (such as thermocouples), introduce a disturbance in the process (such as the pressure rise test or the pressure decrease test), or use expensive hardware. This method is referred to as valveless monitoring system (VMS) and is based on the measurement of the pressure difference between the drying chamber and condenser.31 This information is then combined with a mathematical model of the process in order to measure the rate of sublimation and estimate other key

2. MATERIALS AND METHODS 2.1. VMS Algorithm. VMS combines information coming from the real process with mathematical modeling in order to estimate the values of those variables that cannot be measured directly. In particular, VMS estimates the rate of sublimation from the pressure difference between the upstream side (Pc) and the downstream side (Pcond) of the freeze-dryer duct connecting the drying chamber and the condenser. The mathematical model used is derived from the mechanical energy balance, where the pressure difference is a function of the flow rate. In fact, because during primary drying the gas phase is mainly constituted by solvent vapor and composition gradients are very small,39 true diffusion can be considered of minor importance with respect to the bulk flow mechanism.40,41 In the case of viscous flow, the mechanical energy balance gives Js =

A sK sΔPP s ̅ Pc

(1)

where As is the cross-sectional area of the pipe connecting drying and condenser chambers, Js is the total mass flow rate of gas evacuated from the drying chamber, ΔPs is the pressure drop along the duct, and P̅ is the average pressure between the entrance and the exit of the duct. The conductance Ks is

Ks =

πDs4 ρgas 128Leq μgas

(2)

where Ds is the diameter of the pipe and Leq is an equivalent length that accounts for pressure loss due to the straight pipe, valves, fittings, bends in the pipe, and entrance/exit effects. The equivalent length varies with the type of equipment and can be determined by regression of experimental values for Jsμgas/ρgas B

DOI: 10.1021/acs.iecr.5b04299 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research versus ΔPsP̅/Pc. This task requires carrying out various experiments at different values of Pc and Tfluid, thus obtaining different values of Js, and then plotting Jsμgas/ρgas versus ΔPsP̅/ Pc; μgas and ρgas can be calculated from the measurement of pressure and temperature of the gas and from its composition. It is true that the measurement of gas composition is not always feasible; however, if pure solvents or solvent mixtures having eutectic composition are used, then we can hypothesize that the gas accumulated within the drying chamber has the same composition of the sublimating solvent. In the case of solvent mixtures having a composition different from the eutectic one, the composition of the gas within the drying chamber has to be measured or estimated. Furthermore, the following has to be remarked: (i) The calibration run can be carried out without using any drug but just the solvent because the duct conductance is independent of product characteristics. For the same reason, the result is not dependent on the characteristics of the container; this means that the calibration test can be carried out even once, and the result can be used when processing different products in different containers. (ii) The position of the sensors used to measure the pressure drop along the duct can strongly affect the estimation of the duct conductance. However, because the position of the sensors is not modified between the calibration test and the manufacturing runs, the result obtained after calibration can safely be used. Obviously, the duct conductance is equipment-specific; calibration is thus required for each type of unit. If pressure is very low, then the mean free path of molecules becomes comparable to the diameter of the duct, and the flow is governed by both molecular phenomena and by viscosity.42,43 In this case, eq 1 becomes

Js = A sK sΔPs

chemical component; thus, the rate of removal of each compound is proportional to its initial content in the solution.9 It follows that the method can be used as described only if the water/TBA system has eutectic composition; although this can seem a strong limitation, as discussed in the Introduction, most of the drugs currently processed using water/TBA solutions are initially dissolved in an eutectic solution of the two solvents. In any case, if the solvent mixture does not behave as a pure chemical component, then a corrective factor (that is productspecific) can be introduced so as to account for the different rates of sublimation of the various components. This corrective factor can easily be determined if the composition of the gas inside the drying chamber is measured. The time integration of Jsolv gives the amount of solvent that has been sublimated; thus, it allows the calculation of the residual solvent content into the dried product. During primary drying, this parameter is usually expressed in terms of ratio between the thickness of the frozen layer (Lf) and the initial thickness of the frozen product (Lt): Av Lf 1⎛ = ⎜⎜Lf(−1) − Lt Lt ⎝ (1 − ε/100)ρf

Ds3 6Ls

Tb = Tfluid −

(4)

where Ls is the geometrical length of the duct. Once Js is calculated by eqs 1 and 2 in the case of viscous flow or by eqs 3 and 4 in the case of Knudsen and transient regime, the rate of sublimation (Jsolv) can be calculated as follows 2

Jsolv ΔHsK v

(7)

where Kv is the heat transfer coefficient for the container-shelf system. Equation 7 is obtained from the energy balance of the frozen product, where steady-state conditions have been assumed, i.e., all the heat transferred to the product is used for solvent sublimation; this assumption is commonly accepted by freeze-drying practitioners because of the slow dynamics of the process. Equation 7 can still be used to roughly estimate the product temperature of mixtures of solvents having a composition different from the eutectic one, provided that a corrective factor is introduced to account for the effective enthalpy of sublimation of the mixture of solvents. This corrective factor can be determined from the composition of the gas into the drying chamber. During a lyophilization cycle, the temperature of the fluid is continuously monitored through Pt100 sensors, whereas the heat transfer coefficient, which is container-specific, cannot be calculated directly. Therefore, this last parameter has to be determined before the cycle is carried out. This parameter can be estimated, e.g., by eq 7, where the temperature of the product is measured through thermocouples and Jsolv is measured by eq 1. A further parameter of interest is the resistance to mass transfer (Rp), which correlates the rate of sublimation with the driving force for the mass transfer

2πRTgas

Jsolv = Js − Jleak − JN

(6)

where is the VMS estimation of frozen layer thickness at the previous sampling time. The rate of sublimation depends on the heat transferred to the product and thus on the temperature difference between the heat transfer fluid (Tfluid) and the product (Tb). As a consequence, the temperature of the product being dried can in principle be estimated from the vapor flow rate. The lumped model for heat and mass transfer previously described in Fissore et al.36 can be used for this purpose:

(3)

Mgas

⎞ Jsolv dt ⎟⎟ ⎠ i−1 ti

L(−1) f

It has to be remarked that in eq 3 the molecular flow and the viscous flow are not explicitly expressed because respectively they depend on the total pressure and on the partial pressure of the solvent. Nevertheless, this simplified approach was found to be adequate for the calculation of the solvent flux when pressure is very low. The conductance, Ks, can be calculated using the following equation: Ks =

∫t

(5)

where Jleak is the leakage rate of the equipment and JN2 is the flow rate of nitrogen bled into the drying chamber to adjust its pressure. The measurement has to be carried out under steadystate conditions, i.e., when the pressure in the chamber has reached its set-point value and remains at that value. The total flow rate of solvent, Jsolv, results from the contribution of all the components of the solvent mixture, i.e., water and other organic solvents. If the mixture of water and other organic solvents has eutectic composition, e.g., water and tert-buthyl alcohol form two eutectic mixtures at 20 and 90% (w/w) of TBA, then the solvent mixture behaves as a pure

Rp = C

(Pi − Psolv) Jsolv

(8) DOI: 10.1021/acs.iecr.5b04299 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research where Pi is the equilibrium pressure of the mixture of solvents at the interface of sublimation and is a function of the product temperature.12,44 Ideal behavior of the solid−vapor system is assumed, i.e., the vapor pressure of the mixture is given by the sum of the vapor pressure of each component, each of them multiplied by the respective molar fraction. Furthermore, as we are considering mixtures at eutectic composition, the mole fraction of each component in the mixture is constant with time. This hypothesis has been confirmed in the Results section of this paper. Furthermore, we assumed that all the gas inside the chamber is made of solvent, i.e., the inert air fraction is negligible; thus, Psolv is equal to Pc. The resistance to mass transfer is product-specific and for a given product is not constant during a cycle because this resistance increases with the thickness of the porous dried layer, and this dependence might be nonlinear because of within-vial product heterogeneity. Generally, the following equation is used to express this dependence:

R p = R p,0 +

ALd 1 + BLd

detector (LaserGas II SP Monitor, Neo Monitors, Lørenskog, Norway). The maximum allowable product temperature was determined by differential scanning calorimetry (DSC, type Q200, TA Instruments, New Castle, DE, USA); the samples were initially frozen at −60 °C, and then heated up to room temperature in inert atmosphere at 10 °C min−1. 2.3. Case Study. All runs were carried out using a sucrosebased formulation. The solid content was 5% (w/w), whereas the solvent is a mixture of water and TBA at the eutectic composition, i.e., 20% of TBA. All reagents were purchased from Sigma-Aldrich and used as received. Solutions were filtered through 0.2 μm PES membrane and filled in tubing vials (ISO 80426 6R, Vidrio Soplado Manuel Perez, Rubi,̀ Spain). The filling volume was 3 mL; thus, the initial thickness of the frozen product was 10.5 mm. Vials were loaded directly on the heating shelves and were partially stoppered with igloo stopper (West Pharmaceutical Services, Horsens, Denmark). During freezing, the temperature of the heat transfer fluid was lowered to −50 °C. Then, an annealing process (at Tfluid = −7 °C for 1 h) was introduced to eliminate product stresses and potential metastable forms of TBA.9 However, it must be pointed out that the presence of metastable forms does not affect the performances of the VMS method. After that, the temperature of the heat transfer fluid was decreased to −50 °C and held for 2 h. Primary drying was carried out at Tfluid = 0 °C and Pc = 10 Pa, whereas secondary drying was carried out at Tfluid = +20 °C and Pc = 5 Pa. In all the tests carried out in this study, the Knudsen diffusion within the duct was negligible because the Knudsen number, given by the ratio between the gas mean free path and the duct diameter, was significantly lower than 1. 2.4. Protocol of Validation. The ability of VMS to monitor the process was tested upon three parameters: rate of sublimation, drying time, and temperature of the product. As concerns the first parameter, the VMS estimations of the rate of sublimation has been compared with experimental data obtained by the gravimetric procedure. Furthermore, VMS estimates the completion of solvent sublimation as the time at which the thickness of the frozen product is zero. This estimation was compared with the evolution of (i) the concentration of water inside the drying chamber as measured by a laser detector and (ii) the difference in pressure between the upstream side and downstream side of the duct. Both the concentration of water and the pressure drop dramatically decrease as primary drying nears completion. In contrast, the VMS estimation of the product temperature was compared with the value measured through thermocouples, at least until their measurement is reliable. In this study we did not compare the estimations obtained with the VMS with those obtained using the pressure rise test or the pressure decrease test. This choice is motivated by the fact that all these methods have been validated against direct measurements of the variables of interest; thus, the differences between the estimated variables are expected to be very small and of the same order of magnitude of the uncertainty of a direct experimental measure. Nevertheless, these methods are not equivalent, and the VMS has some specific advantages with respect to other monitoring techniques: (i) The calibration is very simple, and the in-line application does not involve complex calculations (i.e., nonlinear optimizations). (ii) No expensive hardware is required. (iii) Product dynamics are not affected by the measurement.

(9)

Furthermore, this parameter depends on process conditions. Fissore and Pisano45 showed that beside freezing the drying conditions can also modify the relationship between Rp and the thickness of the dried product Ld. For example, the use of aggressive heating conditions can promote microcollapse phenomena and thus can dramatically reduce the values of Rp. Because VMS can estimate both the rate of sublimation and the product temperature (given the value of Kv), the calculation of Rp by eq 8 is straightforward, whereas Rp,0, A, and B in eq 9 are obtained by regression of experimental values for Rp versus Ld. In this framework, it has to be highlighted that the parameters A and B do not depend on chamber pressure: In fact, the sublimation flux in the dried product is mainly due to Knudsen diffusion,46 and as it has been recently shown by Fissore and Pisano,45 it is possible to calculate A and B as follows A=

RTi0.5 a ,B= 1 a0Msolv K (1 − ε) a0

(10)

where Ti is product temperature at the sublimation interface, a0 and a1 are structural parameters used to describe pore size distribution along the dried layer, K is a constant whose value is 22.9 m/s K0.5, and (1 − ε) is the dried cake void fraction (ε being the solid content). The key thermodynamic properties of the water/TBA system required to solve model equations (sublimation enthalpy and vapor pressure) are given in Bogdani et al.12 2.2. Equipment and Instrumentation. All the lyophilization cycles were carried out in a laboratory freeze-dryer (LyoBeta 25, Telstar Technologies, Terrassa, Spain). The apparatus was equipped with miniature thermocouples (T type, Tersid, Milan, Italy), Pt100 sensors, and two capacitance manometers (Baratron 626A, MKS Instruments, Andover, MA, USA). The leak rate of the equipment is 1.1 × 10−3 mbar L s−1, the diameter of the duct (that contains a butterfly valve) is 0.1 m, and its geometrical length is 0.3 m. Pressure inside the drying chamber is controlled by bleeding of nitrogen, and its flow rate is monitored through a mass flow meter (MB100 type, MKS Instruments, Andover, MA, USA). The concentration of water inside the drying chamber was monitored by a laser D

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mass before loading into the freeze-drying chamber and after 6 h of sublimation. The mass variation observed gives a direct estimation of the average rate of sublimation and hence of Js. Figure 1 shows an example of results for the equipment used in this study. The flow rate of gas evacuated from the drying

VMS can also estimate the resistance to either heat transfer or mass transfer. As concerns the heat transfer coefficient, the VMS estimations were compared with those obtained by the gravimetric procedure. However, the VMS estimations of Rp (as a function of the thickness of the dried layer) were compared with those obtained via pressure rise test for aqueous solutions. This comparison has not been done for the TBA−water system because the use of the pressure rise test technique in the presence of mixtures of water and organic solvents requires a high-freqency acquisition system to track the evolution of the organic solvent concentration during the pressure rise test, and this system was not available for the eperimental apparatus used in this study. However, an example of VMS estimations of Rp versus Ld was given for a placebo formulation made of sucrose 5% (processed from a mixture of water and TBA at eutectic composition). 2.5. Cycle Design. As described in the Introduction, VMS can be used to monitor the product state during the process or to estimate the resistance to heat (Kv, that is container-specific) and mass transfer (Rp, that is product-specific). These last two parameters can then be used by a mathematical model of the process to develop the cycle, e.g., using the design space method. As previously described in Fissore et al.,36 the design space was calculated from the energy balance at the sublimation interface (assuming steady-state conditions, i.e., no energy accumulation in the frozen product): K v(Tfluid − Tb) = ΔHs

Pi − Psolv Rp

Figure 1. Comparison between model predictions (solid line) and experimental data (■) for gas flow rate vs pressure drop along the duct when the flow is viscous. The equivalent length (Leq) is 2.15 m.

chamber (normalized accounting for its viscosity and mass density, Jsμgas/ρgas) varied linearly with the pressure drop along the duct (ΔPsP̅/Pc). This result confirms that the conductance of the duct is independent of process conditions as shown in eq 1 but only depends on the equipment used via Leq. This last parameter can be obtained by regression of experimental values of Jsμgas/ρgas versus ΔPsP̅/Pc. For the apparatus used in this study, Leq is 2.15 m. Figure 1 also confirms that eqs 1 and 2 can effectively describe the fluid dynamics in the duct when the flow is viscous and a mixture of water and TBA is used. Model predictions (obtained by eqs 1 and 2 and using the optimal value of Leq above determined) agreed with experimental data. A similar result was previously obtained for the freeze-drying from pure water.30 Even if this task has been done for the pressure decrease test, the results obtained are still valid for the VMS because they refer to those relationships that describe the fluid dynamics through the duct and that are common for both methods. 3.2. Thermal Characterization of the Container. To monitor the product state, the value of the heat transfer coefficient is necessary. There are various methods for the estimation of Kv; the most common method is the gravimetric procedure, which is very accurate but also time- and workdemanding. VMS can also be used to this purpose, provided that the temperature of product is measured, as demonstrated in the following. A first cycle was carried out where VMS was used to measure Js, and Pt100 sensors and thermocouples (directly inserted into the product being dried, close to the vial bottom) were used to monitor the evolution of the temperature of the heat transfer fluid and of the product, respectively. This information was then used to estimate the value of the heat transfer coefficient at a given pressure. An example of results is shown in Figure 2 where it can be observed that although the VMS estimations were somewhat affected by noise in the data the average value

(11)

If the heat flux to the product is written as a function of Tb, then eq 11 becomes −1 ⎛ 1 L⎞ 1 + f ⎟ (Tfluid − Ti ) = ΔHs (Pi − Psolv) ⎜ kf ⎠ Rp ⎝ Kv

(12)

Pi is a function of Ti, Rp is a function of Ld, and Lf = Lt − Ld. It follows that the temperature of the product at the moving interface can be calculated if the values of Tfluid, Psolv, and Ld are known. For a given value of Psolv and thus of Kv, the limit value Tfluid * is the one that brings the product temperature to the limit value (Tmax): ⎛ P(T ) − Psolv L⎞ * = Tmax + ⎜ 1 + f ⎟ΔHs i max Tfluid K k Rp ⎝ v f⎠

(13)

For a given value of pressure, it is possible to calculate T*fluid as a function of Rp and thus of Ld. It follows that we can calculate the evolution of the design space curve as the drying goes ahead minimizing the computational effort. Of course the determination of the design space curve requires that this calculation is repeated varying the value of chamber pressure.

3. RESULTS 3.1. Characterization of the Equipment. Various runs were carried out in order to investigate the relationship between Js and ΔPs in the case of freeze-drying from the TBA/ water cosolvent system at eutectic composition, i.e., 20% of TBA. For each run, the mass flow rate Js was measured by gravimetric procedure, whereas ΔPs was measured by two independent capacitance manometers that were connected to the drying chamber and condenser chamber, respectively. The gravimetric procedure implies the measurement of the product E

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placebo solution containing 5% (w/w) of sucrose. The solvent is a mixture of water and TBA at the eutectic composition (20% of TBA). As a first attempt, VMS has been tested upon its capability to monitor the rate of sublimation. To this purpose, a group of three vials were regularly extracted by a “sample thief”, and the mass of solvent removed was determined by back weighing. As can be seen in Figure 3, VMS estimations of vapor flow rate agreed with those obtained by gravimetric procedure. All the extracted samples have been analyzed utilizing DSC. The DSC profile showed that the addition of TBA to the sucrose solution did not change the critical temperature of the formulation, i.e., the glass transition temperature of sucrose at −33 °C. In addition, all the profiles showed an endothermic peak at about −6 °C, corresponding to the melting point of the TBA−water eutectic at 20% w/w. For example, Figure 4 shows Figure 2. Comparison between the value of heat transfer coefficient for the vial used in this study as estimated by VMS and thermocouples (●) and that measured by gravimetric procedure (solid line). The comparison was carried out at Pc = 10 Pa and Tfluid = 0 °C using vials ISO 80426 6R.

of Kv fairly agreed with the value of heat transfer coefficient measured by the gravimetric procedure (solid line). As concerns the last part of the drying, we can observe that the decrease in Kv was more marked after 10 h. This trend could be related to the strong reduction in the vapor flow rate (Figure 3); it follows that after 10 h the uncertainty in the measurement

Figure 4. DSC thermogram of sucrose 5% (w/w) in 20% TBA−80% water system after 4 h of drying.

the DSC thermogram of the sample after 4 h of drying. This result confirmed that both TBA and water molecules sublimed at the same rate; thus, the TBA−water mixture (at the eutectic composition) behaves as a single chemical component. If water molecules sublimed faster than TBA molecules or vice versa, then a second peak would appear in the DSC profiles, but that is not the case. In the first part of the drying, the flow rate of solvent released by sublimation steeply increased as the temperature of the product increased from the low temperature of freezing to a new steady-state value. Then, the rate of sublimation remained almost constant. Actually, the rate of sublimation slightly decreased because of the increase in the resistance to mass transfer, which in turn is the consequence of an increase in the thickness of the dried product. Finally, Jsolv dramatically decreased as the primary drying neared completion, i.e., after 10 h of drying. The rate of sublimation is close to 0 after 14.5 h, which corresponds to the completion of ice sublimation for the entire batch of vials. VMS can also estimate the residual content of solvent by the time integration of the sublimation rate. That information is complementary to the rate of sublimation and useful to determine the time at which the primary drying nears completion; thus, the temperature of the heat transfer fluid can be raised to promote solvent desorption, i.e., the secondary drying stage. Figure 5 shows a good agreement between the

Figure 3. Evolution of the rate of sublimation as estimated by VMS (solid line) and as measured by the gravimetric procedure (○). Error bars represent standard deviation. Data refer to the freeze-drying of a 5% (w/w) sucrose solution (in 20% TBA−80% water system) processed at Pc = 10 Pa and Tfluid = 0 °C in vials ISO 80426 6R.

of the pressure drop was more marked. Thus, the uncertainty on the VMS estimation of Kv was much higher, approximately 10%. Apart from the first 10 min of drying, this agreement is quite good for the entire duration of the cycle, making this method more reliable than other technologies proposed in literature. For example, the pressure rise test technique gives good estimations of Kv only in the central part of the cycle, whereas it underestimates or overestimates the value of Kv at the beginning and at the end of the cycle, respectively. 3.3. Experimental Validation of VMS. In this section, VMS has been used to monitor the primary drying stage of a F

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refers to average properties of the batch, whereas the thermocouples refer to individual vials. Therefore, the VMS estimations average the temperature of vials that have already finished drying with that of vials that are still sublimating, and the contribution of this last group becomes smaller and smaller as the drying proceeds toward its completion. The uncertainty in the VMS estimation of the product temperature is determined by that of the pressure sensor; the accuracy of the pressure sensor used in this study was 0.01 Pa, which corresponds to ±0.5 °C uncertainty in Tb. Finally, VMS can estimate the resistance of dried product to vapor flow. Knowledge of this parameter is essential to understand better the drying behavior of the product investigated. As can be seen in Figure 7A, the VMS estimations

Figure 5. Evolution of (a) concentration of water inside the drying chamber as measured by the laser detector, (b) pressure drop along the duct, and (c) thickness of the frozen layer as estimated by VMS. The vertical line represents the drying time, i.e., 14.5 h.

drying time as estimated by VMS (as the time at which the thickness of the frozen layer is zero) and that determined by monitoring the composition of the gas inside the drying chamber or that deducted by the analysis of evolution of the pressure drop. Figure 6 compares the temperature of the product (close to the vial bottom) as measured through thermocouples in three

Figure 7. Impact of Ld on Rp for lyophilized sucrose from (A) water and (B) a mixture of water and TBA (20% w/w). In graph A, VMS (circles) and pressure rise test (line and triangles) estimations are compared.

of Rp versus Ld are in fairly good agreement with those obtained through the pressure rise test technique, showing that VMS can effectively estimate such a parameter. This comparison was given only for those samples containing water as solvent; however, in theory a similar comparison might be done also for water−TBA mixtures, provided that the freeze-dryer is equipped with a high-frequency system for the acquisition of both the total pressure within the drying chamber and the partial pressure of either water or the cosolvent (TBA). Because this system was not available for the freeze-dryer used in this study, a direct comparison between VMS and pressure rise test could not be shown for water−TBA mixtures. However, an example of VMS estimations of Rp versus Ld for a sucrose solution, containing 80% water and 20% TBA as solvent, was shown in Figure 7B. It can be observed that the value of Rp sharply increased (within the first 2 mm) with the thickness of the dried product. Furthermore, the values of Rp versus Ld in the case of freeze-drying from a mixture of water and TBA were much lower than those previously observed in graph A. Therefore, the addition of TBA to the sucrose solution allows a more rapid rate of sublimation and thus a shorter lyophilization cycle. This may be because the addition of TBA to the sucrose solution changed the crystal habit of ice. As can be observed in Figure 8, the internal structure of lyophilized sucrose is more open when 20% (w/w) TBA was added, giving a lower resistance of the dried cake. In particular, the addition of TBA

Figure 6. Comparison between the product temperature as estimated by VMS (○) and that as measured through thermocouples (dashed line) inserted in three different vials.

different vials with that estimated by VMS. These results were obtained using the value of heat transfer coefficient previously determined. A fairly good agreement can be observed between thermocouple readings and VMS estimation, confirming that VMS can effectively monitor both the state of progress of the primary drying as well as the temperature of the product. However, it can be noted that the VMS estimations seemed to underestimate the product temperature after 9 h of drying, i.e., when some of the vials of the batch (those containing thermocouples) completed the sublimation of ice. This behavior is reasonable if we account for the fact that VMS G

DOI: 10.1021/acs.iecr.5b04299 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 9. (A) Values of T*fluid vs Ld/Lt (at Pc = 30 Pa) for sucrose freeze-drying from a mixture of water and TBA. The blue line refers to Tfluid = −20 °C, and the shaded area indicates the margin of safety for Tfluid. (B) Design space calculated for sucrose freeze-drying from a mixture of water and TBA.

maximum allowed value. If a simple approach is preferred, then the temperature of the fluid can be maintained constant throughout the primary drying stage and equal to the limit value when Ld/Lt= 1, i.e., −20 °C for the case here investigated. If at least three tests at three different values of chamber pressure are carried out using VMS to evaluate Kv, then it becomes possible to estimate the dependence of Kv on Pc that is generally expressed by means of the following equation: K v = C0 +

Figure 8. Magnification of the internal structure of lyophilized sucrose from (top picture) pure water and (bottom picture) a mixture of water and TBA (20% w/w).

C1Pc 1 + C2Pc

(14)

The three parameters C0, C1, and C2 are calculated looking for the best fit between calculated and measured values of Kv. Then, once the values of these parameters are known, the calculations of the design space can be repeated for different values of chamber pressure, thus obtaining the design space shown in Figure 9B. If the cycle is carried out at the limit of the design space, then small and unexpected variations in process conditions might bring the product above its maximum allowable temperature, promoting its collapse. It is therefore fundamental to select an appropriate combination of process conditions that is close to but not at the limit of the design space curve so as to minimize the risk of failure. The margin of safety, the distance between the value of Tfluid used to carry out the cycle and the limit value shown by the DS curve throughout the primary drying stage, can easily be determined using the same design space shown in Figure 9. This margin of safety is directly related to the robustness of the cycle because it gives an estimation of the maximum deviation on process conditions that can occur without compromising the quality of the product. As can be seen in Figure 9A (shaded area), if a static cycle is used for primary drying (i.e., the temperature of the heat transfer fluid is not modified during the sublimation step), then the margin of safety is very large at the beginning of the drying and tends to decrease as the drying goes ahead. To give an example, if Tfluid is −20 °C and Pc is 30 Pa, then the margin of safety for Tfluid is about 20 °C at the beginning and is lower than 5 °C after 20% of drying; therefore, the cycle is very robust only in the first part of the drying.

(at eutectic composition) did not promote the formation of pores larger than those obtained from aqueous solutions, but produced a spongelike structure that offered lower resistance to mass transfer. A similar result was also observed by Kasraian and DeLuca10 for a similar formulation. This fact makes organic/water cosolvent systems a good alternative to aqueous solutions; for example, we observed that the addition of a small amount of TBA to an aquesous solution of sucrose can dramatically reduce the duration of the primary drying and thus its energy cosumption. For example, we have carried out a cycle similar to that described above but using pure water as solvent, and we observed that the primary drying duration was 40% longer than that observed in the presence of TBA as cosolvent. However, we observed that the addition of TBA to the water solution made the lyophilized samples more brittle than those obtained from the aqueous solution; this result was also observed in the literature6,47 and was likely due to the more open porous structure promoted by TBA. 3.4. Cycle Design. Because VMS can provide values of model parameters Kv and Rp, then it could effectively be used to calculate the design space. Figure 9A shows an example of the results that can be obtained when the pressure inside the drying chamber is 30 Pa. It is possible to see that in order to minimize the drying time it is required to manipulate continuously the temperature of the heating fluid in such a way that product temperature remains always as close as possible to the H

DOI: 10.1021/acs.iecr.5b04299 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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4. CONCLUSIONS This paper shows a new process analytical technology (valveless monitoring system) for the monitoring of the primary drying stage in the case of organic/water cosolvent systems at the eutectic composition. In principle, this technology can also be used to monitor the freeze-drying process from a strictly organic solvent system or from an aqueous solution. VMS was demonstrated to give quantitative accurate estimations of sublimation rate. We also showed that this information coupled with thermocouple readings can be used to estimate the heat transfer coefficient for a specific container and at a given pressure. Once the heat transfer coefficient of the container has been estimated, VMS can be used to estimate a number of parameters hardly measurable during a production cycle, e.g., the temperature of the product, the thickness of the frozen layer, and the heat/mass transfer coefficients. In this paper, we found that VMS can effectively estimate all these parameters. In this study, the pressure drop was determined from the pressure measured (using two separated sensors) at the upstream side and the downstream side of the duct. It follows that the accuracy of the VMS method is dictated by that of the two pressure sensors used. A regular calibration of the two sensors is therefore recommended in order to improve the reliability of the method. As an alternative, a differential capacitance manometer can be used, provided that it is compatible with sterilization treatment. Also, the minimum value of vapor flow rate that can be detected by VMS depends on the accuracy and resolution of the pressure sensor. For the case study here discussed, this minimum value is 3 × 10−4 kg h−1. During primary drying, the mass flux usually varies from 0.1 kg h−1 m−2 (precautionary cycle) to 1 kg h−1 m−2 (aggressive cycle). It follows that VMS can give accurate results if the sublimating area is greater than 3 × 10−4 m2 for aggressive cycles and 3 × 10−3 m2 for precautionary cycles, corresponding to a minimum load from 1 up to 9 vials. Finally, we showed how VMS outcomes can be used to calculate the design space of a specific product and thus properly define process conditions (temperature and pressure) that maintain the product temperature at its maximum allowable value. This approach makes it possible to carry out the freeze-drying cycle at its maximum rate of sublimation and thus optimize the energy consumption of the process.

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Ds = internal diameter of the duct, m ΔHs = enthalpy of sublimation, J kg−1 J = mass flow rate, kg s−1 K = parameter used in eq 10, m s−1 K−0.5 Ks = conductance of the duct, s m−1 Kv = heat transfer coefficient, W m−2 K−1 kf = thermal conductivity of the frozen product, W m−1 K−1 Ld = thickness of the dried product, m Leq = equivalent length, m Lf = thickness of the frozen product, m Ls = geometrical length of the duct, m Lt = total thickness of the product, m Mgas = molecular weight of the gas, kg kmol−1 Msolv = molecular weight of the solvent, kg kmol−1 P̅ = average pressure along the duct, Pa Pc = pressure inside the drying chamber, Pa Pcond = pressure inside the condenser chamber, Pa Pi = equilibrium pressure, Pa Psolv = partial pressure of the mixture of solvent inside the drying chamber, Pa ΔPs = pressure drop along the duct, Pa R = ideal gas constant, J kmol−1 K−1 Rp = resistance to mass transfer, m s−1 Rp,0 = parameter used to calculate Rp in eq 9, m s−1 Tb = temperature of the product close to the vial bottom, K T*fluid = maximum fluid temperature, K Tfluid = temperature of the heat transfer fluid, K Tgas = temperature of the gas, K Ti = product temperature at the sublimation interface, K Tmax = limit product temperature, K t = time, s Greek letters

ε = solid content, % μgas = viscosity of the gas, kg m−1s−1 ρf = mass density of frozen product, kg m−3 ρgas = mass density of the gas, kg m−3 Subscripts

leak = leakage of the equipment s = duct solv = mixture of water and TBA Abbreviations

AUTHOR INFORMATION

Corresponding Author

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*E-mail: [email protected]. Tel.: +39-011-0904679. Fax: +39-011-0904699. Notes

DSC = differential scanning calorimetry TBA = tert-buthyl alcohol VMS = valveless monitoring system

REFERENCES

(1) Teagarden, D. L.; Baker, D. S. Practical aspects of lyophilization using non-aqueous co-solvent systems. Eur. J. Pharm. Sci. 2002, 15, 115−133. (2) Nuijen, B.; Bouma, M.; Henrar, R. E. C.; Floriano, P.; Jimeno, J. M.; Talsma, H.; Kettenes-van den Bosch, J. J.; Heck, A. J. R.; Bult, A.; Beijnen, J. H. Pharmaceutical development of a parenteral lyophilized formulation of the novel antitumor agent aplidine. J. Pharm. Sci. Technol. 2000, 54, 193−208. (3) Teagarden, D. L.; Wang, W.; Baker, D. S. Practical aspects of freeze-drying of pharmaceutical and biological products using nonaqueous cosolvent systems. In Freeze-drying/Lyophilization of Pharmaceutical and Biological Products; Rey, L.; May, J. C., Eds.; Informa Healthcare: London, 2010. (4) Baldi, G.; Gasco, M. R.; Pattarino, F. Statistical procedures for optimizing the freeze-drying of a model drug in tert-butyl alcohol:water mixtures. Eur. J. Pharm. Biopharm. 1994, 40, 138−141.

The authors declare no competing financial interest.

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ABBREVIATIONS A = parameter used to calculate Rp in eq 9, s−1 As = cross-sectional area of the duct, m2 Av = cross-sectional area of the vial, m2 a0 = parameter used in eq 10, m a1 = parameter used in eq 10, m−1 B = parameter used to calculate Rp in eq 9, m−1 C0 = parameter used to calculate Kv in eq 14, W m−2K−1 C1 = parameter used to calculate Kv in eq 14, W m−2K−1 Pa−1 C2 = parameter used to calculate Kv in eq 14, Pa−1 Cw = water concentration in the gas inside the drying chamber, mg m3 I

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K

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