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Optimization of the Freeze-Drying Cycle: A New

Model for Pressure Rise AnalysisP. Chouvenc

ab, S. Vessot

a, J. Andrieu

a& P. Vacus

b

aLaboratoire dAutomatique et de Gnie des ProcdsLAGEP-UMR Q 5007 , CNRS U

Lyon1-CPE , Villeurbanne, Cedex, FrancebAventis Pasteur , Campus Mrieux , Marcy LEtoile, France

Published online: 06 Feb 2007.

To cite this article:P. Chouvenc , S. Vessot , J. Andrieu & P. Vacus (2004) Optimization of the Freeze-Drying C ycle:A New Model for Pressure Rise Analysis, Drying Technology: An International Journal, 22:7, 1577-1601, DOI: 10.1081/DRT-200025605

To link to this article: http://dx.doi.org/10.1081/DRT-200025605

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DRYING TECHNOLOGY

Vol. 22, No. 7, pp. 15771601, 2004

Optimization of the Freeze-Drying Cycle:

A New Model for Pressure Rise Analysis

P. Chouvenc,1,2 S. Vessot,1 J. Andrieu,1,* and P. Vacus2

1Laboratoire dAutomatique et de Ge nie des

Proce de sLAGEP-UMR Q 5007, CNRS UCB Lyon1-CPE,

Villeurbanne, Cedex, France2Aventis Pasteur, Campus Me rieux, Marcy LEtoile, France

ABSTRACT

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

*Correspondence: J. Andrieu, Laboratoire dAutomatique et de Ge nie des

Proce de sLAGEP-UMR Q 5007, CNRS UCB Lyon1-CPE, Bat. 308G, 43 Bd

du 11 Novembre 1918, 69622 Villeurbanne, Cedex, France; E-mail: andrieu@

lagep.cpe.fr.

1577

DOI: 10.1081/DRT-200025605 0737-3937 (Print); 1532-2300 (Online)

Copyright&2004 by Marcel Dekker, Inc. www.dekker.com

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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 experi-

mental 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 maxi-

mum difference of no more than 2C. The dried layer mass transferresistance 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 Wm2 K1 in accordance

with the published data for this type of vials and these experimental

freeze-drying conditions.

Key Words: Freeze-dryer control; PRA model; MTM model;

Pharmaceuticals freeze-drying; Ice sublimation temperature.

INTRODUCTION

During freeze-drying processes for pharmaceuticals, the precise

determination of the mean product temperature is the key-parameter

for the optimization of the process and its control. Then, it is important

to have a precise and significant estimation of this parameter in order to

maintain the product temperature as high as possible during the sublima-

tion period without going beyond the collapse temperature.[13] Insertion

of thermocouples or Pt100 sensors in a few vials is a widely used method

to measure this mean product temperature. Nevertheless, it is well known

that this sensor introduction modifies appreciably the elementary

phenomena of nucleation and of ice crystals growth,[2] by lowering the

degree of supercooling that leads to an increase of the average ice crystal

size in the frozen matrix. As a consequence, the mass transfer resistanceto water vapor flux through the dried layer in monitored vials is

considerably reduced and their drying kinetics are quite different from

the whole batch. Moreover, these monitored vials, for technical reasons,

are, most of the time, placed close to the loading door and, thereby,

1578 Chouvenc et al.

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submitted to wall effects. So, all these mechanisms tend to make the

monitored vials dry faster, preventing them from being representative of

the entire batch. Besides, this method required a manual process that may

compromise the product sterility when manufacturing pharmaceutical

products.

This is why the Pressure Rise Analysis method (PRA method),

derived from the MTM method originally proposed by Milton et al.[1]

and modified recently by Obert,[3] appears to be a very promising

method. Liapis et al.[4] have also published a similar method for deter-

mining mean product temperatures and temperature profiles in the frozen

layer. Indeed, it is a rapid, simple to implement, noninvasive, and

averaging temperature measurement method that requires a freeze-dryer

equipped with an external condenser and a very fast closing separatingvalve with closing times lower than 1 s. Process parameters such as the

temperature at the ice sublimation interface, Ti, the resistance to mass

transfer of the dried layer, Rp, and the overall heat transfer coefficient,

Kv, could be identified by fitting the experimental pressure rise data

obtained after the closing of the separating valvewith a transient

pressure response model.

Finally, this method has been proposed as a more precise predictive

way for determining the end of primary drying. One of the objectives of

this study was to point out the critical temperature increase of the

product during the PRA measurement at the end of primary drying

period and suggest an alternative way to determine the switch over from

primary drying to secondary drying period.

MATERIALS AND METHODS

Materials

Mannitol (reagent grade) was used as received from Sigma Aldrich

(Saint Louis, MO). Unstoppered 7 mL glass tubing vialshaving a

total mass of 8 gmanufactured by VerreTubex (France) were used for

this study.

Equipment and Methods

The freeze-dryer used was a model SMH45 manufactured by

Usifroid (France). The freeze-drying chamber contained three shelves

providing a total shelf area of 0.45m2. The total pressure was

Freeze-Drying Cycle: A New Model for Pressure Rise Analysis 1579

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measured using a capacitance manometer MKS Baratron 622 (MKS

Instruments) having a typical time response as low as 4 ms. The water

vapor pressure measurements were realized by using a humidity

sensor PANAMETRICS M2LR (Chicago), the principle of which was

based on capacitance determination and providing data converted in

dew point temperature values in a range lying from 110C to 20C,

with a precision of 1C. Calibration curves for all the sensors were

supplied by the manufacturers. The temperature at the bottom of the

product inside 6 vials and the gas temperature inside the sublimation

chamber were monitored with K type thermocouples. A pneumatic

butterfly valve, with a closing time approximately equal to 0.5 s, was

mounted in the cylindrical duct connecting the freeze-drying chamberand the condenser chamber. During the PRA runs, the dynamic pressure

rise was monitored with a data acquisition systemmultimeter 2700

from Keithley (Keithley Instruments)allowing a sampling period as

low as 10ms.

A 5% mannitol w/w solution was prepared with distilled water. The

whole batch for standard freeze-drying runs contained 324 vials, each

containing 2 mL of solution corresponding to an initial product thickness L0of 1 cm. As recommended in the literature, the ratio chamber volume/ice

sublimating front area was equal to 1.28 m. After freezing the product down

to45C with a cooling rate of 1C/min, the product was freeze-dried at a

shelf temperature of 0C and with a total pressure equalto 38 Pa. Condenser

temperature was kept constant during all experiments at around60C.

The mean experimental product temperature was calculated byaveraging the temperature of five monitored vials. The temperature of

the vial located close to the Altuglass door of the freeze-dryer was

discarded from the calculation, because it was always 25C higher than

the mean product temperature due to door radiation effects. The chamber

leak rate was determined with an empty chamber by measuring the

pressure increase 2 h after closing the butterfly separating valve and a

mean leak rate equal to 0.13 Pa s1 was obtained.

MODELING OF PRESSURE RISE KINETICS

Literature Review

The first modeling of the pressure rise dynamics after rapidly closing

the separating valve was the MTM method proposed by Milton et al.,[1]


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expressed by the following equation state:

Pt PiTi PiTi Pc: exp N:A:R:Tv

MH2O:V:Rp: t

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflffl{TERM1

P iTi:Hs:MH2O

R:T2i:T

2 1

8

2: exp

kappa:2

L2 : t

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflffl{TERM2

PiTi:Hs:MH2O

R:T2

i

:1

Cp:L:c

:KvTshelf Tbottom : t

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl fflfflfflfflffl{TERM3 Fleak : tzfflfflffl}|fflfflffl{

TERM4

1

In a semi-empirical approach, this model assumes that four physical

phenomena influence independently the pressure rise inside the chamber.

The total pressure increase was assumed to result from four elementary

contributions: term 1, the ice sublimation at constant sublimation front

temperature,Ti; term 2, the equilibration of the thermal gradient in the

frozen layer; term 3, an increase in the ice temperature of the frozen

matrix due to the continuous heating during the measurement time

interval; term 4, the leak rate of the freeze-dryer directed from the

external atmosphere to the chamber inner. This model allowed these

authors to identify Ti and Rp values from experimental pressure rise

kinetics data obtained with mannitol, lactose, and potassium chloride

solutions; however, Milton et al.[1] observed that the values identified forthe overall heat transfer coefficient, Kv, were twice or three times higher

than the ones obtained by a direct measurement method and, thereby,

could not be identified from their model.

More recently, Obert[3] proposed a modification of the previous MTM

model by taking into account two other elementary physical phenomena:

. The desorption of the bound water in the dried layer during

primary drying which contributes to the increase of the total

pressure. It was expressed by the following simplified relationship:

dP=dt Ddes 2

where Ddes represents the desorption kinetics constant (Pa s1).

. The thermal inertia of the glass wall of the vial which was

introduced in the accumulation term on the heat balance of the

vial (term 3 of Eq. (1)).


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The overall heat transfer coefficient, Kv, was calculated from the

sublimation kinetics data by adopting the heat and mass transfer steady

state hypothesis:

Kv Pi Pc:Hs

Rp:Tshelf Tbottom 3

where Pi0 represents the water vapor partial pressure of water at the

interface before the valve closing. The term corresponding to the thermal

equilibration of the frozen layer after closing the valve was dropped

because it does not correspond to physical reality. So, the complete model

was expressed by the following equation (Eq. (4)):

Pt PiTi PiTi Pc: exp N:A:R:Tv

MH2O:V:Rp: t

PiTi:HS:MH2O

R:T2i:

PiTi Pc:HS

Cp:L:C mvial:Cpvial=A : Rp: t

Fleak: tDdes: t 4

The aim of our study was to set up a more advanced model taking

into account the increase in water vapor pressure at the sublimation

interface, notedPi, due to the overall product temperature increase as well

as the heat transfer coefficient variations during the dynamic pressure rise.

New Pressure Rise Dynamics Modeling: PRA Model

In a more rigorous approach, we propose to delete the arbitrary

hypothesis of additivity of the four mechanisms contributing to the total

pressure increase and to set up a new modeling based on elementary

heat and mass transfer balances coupled with the constitutive equations

expressing the heat and mass fluxes during the desiccation process.

Two gas species contribute independently to the pressure rise dynamics

during PRA runs: the water vapor and the inert gas.

The water vapor accumulated in the product chamber was generated

by the sublimation of ice crystals and, to a lower extent, by the desorption

of the bound water from the dried layer. Assuming a rapid valve closing

and that the gas phase obeyed the ideal gas law, the rate of total pressureincrease was described by the relationship:

dPwatert

dt

NARTv

MH2OVRpPiTi Pwt Ddes 5


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whereNrepresents the number of vials,A the sublimation interface area

for one vial, R the universal gas constant, Pi and Pw, respectively the

water vapor pressure in equilibrium with the interface temperatureTiand

in the sublimation chamber. The rate of desorption of the bound water

from the dried layer, notedDdes(Pa s1), was assumed to remain constant

during the PRA run and Antoines law was used to express Pi as a

function ofTi:

lnPi A1

TiB1 6

where A1 and B1 are constants respectively equal to 6320.1517 and

29.5578 in S.I. units.[5] Assuming that there was only water vapor in the

chamber before closing the butterfly valve, the inert gas partial pressure

increase was only due to the leak of the freeze dryer chamber:

dPinertt

dt Fleak 7

where Fleak represents the constant chamber leak rate.

Finally, the total gas pressure was obtained by adding the partial

pressures of both species:

Pt Pwatert Pinertt 8

Heat Balance for One Vial

During a PRA experiment, the total heat flux dQ/dt transferred

from the shelves to the product contributed mainly to the ice sublimation

and, to a least extent, to the product and the glass vial temperature

increase and to the desorption of the bounded water. Assuming that

the temperature increase at the interface dTi/dt was the same as the

mean product temperature rise, the heat balance for a whole vial was

expressed by:

dQ

dt AKvTshelf Tbottom cCpLAmvial:Cpvial

dTit

dt

A:Hs

Rp PiTi Pwt

VMH2OHdes

NRTv Ddes 9

The total mass of one vial was 8 g but due to the poor thermal

conductivity of glass, it was assumed that the mass contributing to the

overall temperature increase was only the mass of the glass wall in


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contact with the frozen matrix. Globally, this mass was estimated to 2 g.[6]

Combining Eqs. (6) and (9), we finally obtained:

dTit

dt

1

cCpL mvial Cpvial

A

KvP:Tshelf Tbottom Hs

Rpexp

A1

Tit B1

Pwt

VMH2OHdes

NARTvDdes

10

dPwatert

dt

NARTv

MH2 O VRpexp

A1

Tit

B1 Pwt Ddes 11Heat Flux Expression

The literature data about heat transfer modeling during freeze-drying

expressed the total heat transferred from the surroundings and the shelf

to the vial as the result of three basic mechanisms: conductive heat

transfer by contact between the vial and the shelf, radiative flux from the

surroundings to the vial and the gas-conduction heat transfer at low

pressure through the gas layer between the bottom of the vial and the

shelf. Consequently, the overall heat transfer coefficient, noted Kv, was

expressed, in a first approach, by the following relationship under the

hypothesis of additivity of these mechanisms[7]:

Kv Kcont Krad Kgas-cond 12

where the heat transfer coefficients Kcont and Krad were constant for a

given type of vial and a given geometrical pattern of the vials on the

shelves.[7]

However, the gas-conduction heat transfer coefficient was dependent

on the gas nature and on the total pressure inside the freeze-drying

chamber and described by the following equation[7]:

Kgas-cond 0P

1 0lsepP=gas0

13

where is an adimensional coefficient characterizing the heat transfer

efficiency,lsepis the equivalent mean distance between the shelf and thebottom of the vial, 0 is the molecular thermal conductivity of the gas

and 0,gasis the gas thermal conductivity at atmospheric pressure, these

two last parameters being intrinsic values characteristic of the gas nature.

It is worth noting that the vial heat transfer coefficient, Kv, could be


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also calculated from the mass transfer resistance value, Rp, and from the

total water vapor partial pressure driving force by the following equation:

Kv0 1

Tshelf Tbottom

Pi0 Pc:Hs

Rp

VMH2OHdes

NARTvDdes

14

The temperature at the bottom of the vial, noted Tbottom, was

assumed to be constant during the PRA run and calculated from the

steady state heat transfer hypothesis through the frozen layer by the

following relationship:

Tbottom evial

vial

L

c :Pi0 Pc:Hs

RpTi0 15

The variation ofKv as a function of the total pressure was obtained

by differentiating Eq. (13), namely:

dKvP

dP

0

1 0lsep=gaz0 P

2 16The final equation set, Eqs. (6)(8), (11), and (14)(16), subject to the

following initial conditions:

Tijt0 Ti0;Pijt0 Pi0;Pjt0 Pc;Kvjt0 Kv0;

Pwaterjt0 Pc;Pinertjt0 0

was integrated using Matlab software. A nonlinear regression analysis

based on Marquardt-Levenberg algorithm was used to minimize the

objective function Fsdefined as the sum of the error function. This error

function was expressed as the difference between the experimental total

pressure values and the corresponding calculated ones.

Errort Pexperimentalt Pt 17

FSX

jErrortj 18

This new advanced model, set up from constitutive and balance

equations of the whole system, allowed the identification of the parameters

values which characterized the desiccation kinetics: the sublimation fronttemperature,Ti, the resistance to mass transfer of the dried layer,Rp, all

along the freeze-drying cycles by implementing different PRA runs. The

overall heat transfer coefficientKvcan also be calculated from the steady

state equations as previously suggested by Obert.[3]


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RESULTS AND DISCUSSION

Total Pressure Rise Dynamics

Figures 1A and B depict a comparison of the different model

predictions for a typical set of experimental data obtained after 5 H of

primary drying (Fig. 1A) and after 11 H (Fig. 1B). Estimated thicknesses

of the dried layer were respectively 3 and 9 mm. Experimental pressure

rise curves showed two distinct parts as shown on this same figure. The

first part was observed for times smaller than 8 s, during which the total

pressure increased rapidly and resulted mainly from ice sublimation at

the interface. Then, a second part was observed when the total pressure

rose more slowly, mainly resulting from the product temperature increasedue to continuous vial heating as the total chamber pressure approached

the water vapor pressure in equilibrium with ice at the sublimation

interface.

At the beginning of primary drying, all the three previously described

models, with identified parameter values gathered on Table 1, fitted

very well to the experimental data points so that no noticeable dif-

ference between them can be observed on Fig. 1A. A poorer fit for

higher temperature values was observed for Miltons model as shown

on Fig. 1B. However, these results supported the apparent validity of these

mathematical models.

The three models led to similar values ofTi, significantly higher than

the mean experimental product temperatures by 1 to 2C. Besides,

identifiedRpvalues were comparable with a maximum variation of 20%

from one to another. Kv values, calculated from the identified Tiand Rpvalues instead of identifying it from experimental data, were in the same

order of magnitude but Miltons model seemed to slightly overestimate

this parameter in comparison with the other two models. Finally, the

desorption rate values identified from the two models that take this

phenomena into account in their mathematical expression, differed from a

large factor of 400. Indeed, the PRA model identified Ddesvalues leading

to a negligible pressure rise as compared to all the other sources. Whereas

Oberts model could be contested as it did not take this parameter

into account in the heat balance, the PRA model provided values in

agreement with previous studies which reported that the amount of

bound water during primary drying was negligible with respect to theamount of water removed by sublimation[4,8]. Therefore, the PRA model

was rewritten waving the desorption term from Eqs. (5), (9)(11), and

(14) and compared to the original one. A comparison of the two analyses

is presented on Table 2.


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Figure 1. (A) Experimental data () fit by the PRA model (solid line), Oberts

model (dash line), and Miltons model (dot dash black). Tshelf 0C, P 38Pa.

Data fit for a mean experimental product temperature equal to 249.5K after

280 min, (B) Experimental data () fit by the PRA model (solid line), Oberts

model (dash line), and Miltons model (dot dash black, pointed by an arrow).

Tshelf 0C, P 38 Pa. Data fit for a mean experimental product temperature

equal to 256K after 680 min.(View image in color online.)


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It proved that no significant differences could be observed for the

identified parameter values, that the calculation times decreased and that

the numerical stability of the model increased (data not shown).

Consequently, the PRA model which did not take into account the

desorption phenomena, was chosen for the final study as it offered the

advantage to identify only two parameters Tiand Rp, instead of three for

all the other models.

Temperature Measurements

The main advantage of this rapid transient method was the

estimation of the mean temperature of the sublimation interface, Ti,

without any intrusive sensor. From this estimation, it seems possible to

adjust the operating parameters (shelf heating rate) in order to maintain

the mean product temperature, estimated by the ice front temperature, as

high as possible and below the collapse temperature all along the primaryand the secondary drying periods. Experimental Tivalues were calculated

from the mean values given by thermocouple probes, assuming that

Tthermocouple Tbottom i.e., that the probe was in close contact with the

vial bottom and that the thermocouple introduction all along the central

Table 1. Comparison between the identified parameters values from the

three models for a 5% w/v mannitol solution after 280 min of primary drying.

Freeze-drying conditions: Tshelf 0C, P 38Pa.

Model Ti(K)

Rp(kPam2 s kg1)

Kv(W m2 K1)

Ddes(Pas1)

PRA 251.9 312 22.8 6.26 104

Milton et al.[1] 250.6 256 28.7 N.A.

Obert[2] 251.3 276 22.7 0.260

Table 2. Comparison between PRA models with and without desorption term.

Model Ti(K)

Rp(kPam2 s kg1)

Kv(W m2 K1)

Ddes(Pas1)

PRA 251.9 312 22.8 6.26 104

PRA (without desorption) 251.7 319 18.4 N.A.


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axis of the vial had no significant effect on the recorded experimental

temperature:

TiThermocouple TThermocouple Kv:LTshelf TThermocouple

c19

whereL represents the thickness of the frozen layer and, c, its apparent

thermal conductivity.

Figure 2 shows an example of the data collected during the primary

drying of a 5% w/v mannitol solution.

Unlike the results reported by Milton et al. [1] for a 5% mannitol

solution, the interface temperatures identified by the three models were

systematically 1 to 3C higher than experimental ones during the primary

drying. Such differences were greater than the numerical model

uncertainties and the experimental errors. Several hypotheses could

explain this discrepancy. Vials used for this study were smaller than the

ones used for previously reported MTM studies so that the introduction

of a thermocouple became a more important relative perturbation thanin the case of larger vials, which could considerably modify the freeze-

drying behavior of monitored vials. Indeed, the tip of the thermocouple

in contact with the bottom of the vial acted as a heterogeneous nucleation

site and decreased the degree of supercooling during the freezing stage.

242

244

246

248

250

252

254

256

258

0 100 200 300 400 500 600 700

Time (min)

Ti(K)

Figure 2. Ice sublimation front temperature. Comparison between PRA

model (diamonds), Miltons model (triangles), Oberts model (circle), and mean

product temperatures (squares) measured by thermocouples. (View image in

color online.)


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The mean ice crystal size of such vials had the tendency to increase,

lowering the mass transfer resistance of the dried layer.[2] Moreover, the

body of the probe itself created a preferential pathway for the water

vapor flux from the ice front to the top of the dried layer, which also

decreased the mass transfer resistance. These artefacts on the dried layer

structure for monitored vials led to faster sublimation kinetics and to a

lower product temperature at steady state. Therefore, considering these

possible artifacts and the great sensitivity of the PRA model to parameter

Ti value, the corresponding identified values were expected to be more

representative of the overall behavior of the whole batch in such

experimental conditions.

The difference between experimental and identifiedTivalues from all

models was almost constant for L 0.2 cm. However, when reaching theend of primary drying, experimental values became even higher than

the identified ones as shown on Fig. 2. This behavior could be partly

explained by the fact that the thermocouples were not exactly in contact

with the vial bottom so that they lost contact at some point with the

remaining frozen layer. In addition, side vials on the tray completed their

sublimation significantly earlier. In order to compensate for the reduction

of the effective sublimation area, which was assumed to be constant,

all models tended to underestimate parameter Ti. Furthermore, this

imprecise evaluation of Ti appeared to be correlated to a poor fit of

experimental data by these models as shown Fig. 1B. Therefore, the PRA

model allowed a more appropriate determination ofTivalues on a larger

product temperature range, while identifying only two parameters instead

of three needed for Miltons and Oberts models.

Overall Heat Transfer Coefficient

The heat flux transferred from the chamber walls and from the

shelves to the vials during the PRA measurement period provided the

sublimation latent heat and was also responsible of the frozen layer

temperature increase. This temperature increase, which contributed to

maintain a water vapor driving force for the sublimation, and the leak

rate toward the chamber, mainly determined the total pressure rise during

the second half period of the PRA experiment. Nevertheless, Milton et al.reported Kv values from regression analysis 23 times higher than the

values calculated by direct measurements.[9] This tendency has also been

observed in this study by identifying their model to our experimental data

as shown Fig. 3.


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It may be observed that the identifiedKvvalues from Miltons model

are very scattered and varied from the lower bound imposed, namely

Kv 0, up to Kv 40 W/m2/K, which is twice the value obtained by the

two other models. Moreover, when product temperature got over 20C,

Miltons model could not properly fit experimental data as shown by

Fig. 1B and the identified Kv values were not reliable. This scattering

reflected the lack of precision of their model, due to terms 2 and 3 of

Eq. (1), which determined the product temperature increase as a func-

tion of time and mainly influenced the second part of the total pressure

dynamics curves. On the other hand, PRA model and Oberts model

calculated the initial overall heat transfer coefficient values, noted Kv0,

assuming steady state transfer mechanisms between two runs.[3] Both

models led to stable values between 18 and 22 W/m2/K, independently of

the initial product temperature. These results were in agreement with

the experimental Kv values obtained by gravimetric method, namely

Kv 20W/m2/K, in the exact same experimental conditions.[6] Pikal

et al.[9] reported Kv values equal to 27 W/m2/K for tubing vials and

18 W/m2

/K for moulded vials. Furthermore, in order to develop a morerealistic and precise heat transfer model, the PRA model described

the evolution of the Kv values during the PRA runs by using Eqs. (14)

and (16). Variations ofKv values as a function of time after closing the

separating valve are presented on Fig. 4.

0

5

10

15

20

25

30

35

40

45

0 100 200 300 400 500 600 700 800

Time (min)

Kv(W/m/K)

Figure 3. Overall heat transfer coefficient values identified by PRA model

(diamonds) by Miltons model (triangles) and by Oberts model (circles). (View

image in color online.)


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We observed that, during the 20 s time interval of a standard PRA

experimental run, Kv values increased from 23 to 29 W/m2/K due to the

gas thermal conductivity increase. In order to verify the relevance of

introducing a variable Kv parameter in the model, the identification was

also carried out with the PRA model considering that Kv remained

constant and equal to the initial overall heat transfer coefficient, Kv0.

Results are presented on Table 3. Identified Rp values varied of about10% and a 0.2C difference was observed on Ti0values. These variations

were not significant considering experimental errors so that, practically,

the PRA model could be more simplified by assuming constant Kvvalues

all along the PRA run.

Figure 4. Evolution of the vial overall heat transfer coefficient during a PRA

measurement.Tshelf 0C, P 38Pa,Texp 249.5K, t 280min.(View image in

color online.)

Table 3. Comparison between identified parameters by the new MTM model

for different configuration of Kv Tshelf 0C, P 38Pa, Texp 249.5K,

t 280min.

Ti0 (K) Rp (KPamskg1)

VariableKv 251.9 312

ConstantKv 252.1 337


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Mass Transfer Resistance Measurements

Several techniques to estimate the mass transfer resistance values,Rp,

were reported in the literature.[9] They were all based on gravimetric

method and used either a single or a limited number of vials. Estimation

of Rp from the PRA model allowed the determination of the mean

product mass transfer resistance for the whole vial batch, averaging the

heterogeneity of the cake structures generated by the random freezing

phenomena inside each vial. In order to calculate Rpas a function of the

dry layer thickness, the position of the sublimation interface and the

thickness of the dry layer were estimated as a function of time by using

the following relationship:

Lt cAL0

Pit=tacqi1 KvA:Tshelfi Tbottomi=Hs:tacq

cA

20

As shown on Fig. 5, a typical set ofRpvalues identified by the PRA

model was compared with the two previous MTM models predictions.

As previously observed in the case of a 5% w/v mannitol solution,[9]

the product resistance identified by the PRA model increased continuously

0

100000

200000

300000

400000

500000

600000

700000

800000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

ex10(m)

Rp(Pa.m

.s/Kg)

Figure 5. Product resistance as a function of the thickness of the dry layer

identified by PRA model (diamonds), Miltons model (triangles), Oberts model

(circle), and calculated from published data[9] (solid line). (View image in color

online.)


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and linearly as a function of the dry layer thickness. Mass transfer

resistance of the dried layer was empirically correlated to our data as

follows (S.I. units):

Rp 5:528107e4:8104 21

Experimental data correlation lines are passing close to the axis

origin, so that we did not consider any significant crust effect with this

system and with these freezing and freeze-drying conditions. Besides, Rpvalues derived from the three models were similar for e< 0.8 cm and

slightly lower than values found in the literature. However, Rp values

from Oberts model were underestimated for e> 0.8 cm and were 50%

lower than literature values while PRA and Milton models continued

providing consistent values. Therefore, the PRA model provided moreconsistent Rp values on a wider product temperature range than other

literature models.

Mean Product Temperature Increase During PRA Runs

The temperature of the sublimation interface was calculated at each

time increment from the identified parameters values as shown on Fig. 6.

It was observed that during the first 3 s of the PRA run duration

time, the product temperature increase was low because most of the

heat supplied to the vial was used for the sublimation of ice. Then, the

estimated product temperature increased linearly as a function of time.

Therefore, it was possible to compare calculated and experimental mean

product temperature increase during a 20 s measurement time interval,

as shown on Fig. 7.

Experimental data were obtained by averaging the temperature

increases given by thermocouples in 2 monitored vials located at the tray

centre. We observed that experimental and calculated values were in very

good agreement during the first 9 h of the primary drying. Temperature

increase was quite constant all along this period, ranging from 0.4 to

0.8C. However, when reaching the end of primary drying, the product

temperature increase reached a value of 1.6C whereas the PRA model

predicted a temperature increase of only 0.8C. As the model under-

estimated the product temperature increase when very little ice remained,

this last observation could confirm the hypothesis that only the glass wallof the vial in contact with the frozen product has to be taken into account

in the vial heat balance

Furthermore, according to Milton et al., product temperature increase

during the 20 s time interval of a MTM experiment was less than 1C.


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Figure 6. Modeling of the evolution of the ice sublimation interface temperature

during PRA measurement. Tshelf 0C, P 38Pa, Texp 249.5K, t 280 min.

(View image in color online.)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 200 400 600 800

Time (min)

Temperatureincrease

(K)

Figure 7. Overall product temperature increase during a standard PRA

experiment. Observed experimentally (squares) and simulated by PRA model(diamonds).(View image in color online.)


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We observed that this happened to be true only during the early stage

whereas this value was 23 times higher at the end of the primary drying.

Consequently, it seemed that using this method to determine the end point

of the primary drying[3] or to optimize the shelf temperature during the

process by monitoring with the material collapse temperature was very

efficient when freeze-drying robust products. Nevertheless, it could be

quite hazardous when freeze-drying very sensitive pharmaceutical

products such as vaccines, which cannot generally suffer temperature

increase as high as 2C, even for a short time period.

Complementary Method for Determining the

End of Primary Drying

The previous critical analysis of the transient methods (PRA or

MTM) for the control of freeze-drying processes of sensitive pharmaceu-

ticals, in spite of their numerous advantages, has shown some limitations

due to the product temperature increase during the duration of the

pressure rise test, mainly at the end of the primary drying. Therefore, in

the perspective of a complete process control, it seemed necessary to set

up a complementary method to the PRA method in order to determine

precisely andnoninvasively the end of primary drying. A control procedure

was tried by recording continuously the water vapor pressure in the

sublimation chamber by using a capacitance sensor (PANAMETRICS)

and by assessing the end of the sublimation period for the batch as a whole

to a sharp drop of the water vapor partial pressure in the chamber. The use

of this kind of sensor for such an application was first reported by Roy and

Pikal[10] who were able to detect the presence of a very small amount of ice,

down to 0.3% of vials in a batch having residual ice. More recent studies

reported by Bardat et al.[11] showed that this type of sensor had also a

greater sensitivity than other known methods such as Pirani gauge

determinations[12] and product temperature monitoring by thermo-

couples. Therefore, this technique was used during a cycle in order to

check its applicability to our pilot and for the investigated product. Figure

8 shows the graph obtained for the freeze-drying cycle of a 5% w/v

mannitol solution during which the product temperature and the water

vapor partial pressure were monitored.

PRA runs appeared as spikes in the total pressure and in the waterpartial pressure curves but they did not introduce any significant

perturbation in the control of the process itself. Indeed, the time response

of used sensors was fast enough to follow the dynamics of such runs and

to get back to the nominal values before activating the alarms of the


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process. The end of sublimation in monitored vials by thermocouple

corresponded to a sharp temperature increase (1) and occurred about 5 H

before observing a noticeable change in the water vapor partial pressure

given by the moisture sensors (2). The end point of the sublimation

corresponded to the time when the partial pressure of water stabilized to

its lower value (3). The PRA method and the moisture sensor did not

interfere one with the other and could effectively be coupled in order to

get an optimal process control system, able to monitor in real time critical

drying parameters and to determine the end point of sublimation.

CONCLUSIONS

In this study, PRA method was evaluated as a method for

monitoring the freeze-drying cycles of vaccines in small vials. The mainadvantages of this technique rely on its rapidity and on its noninvasive

principle. A new physical model for analyzing the dynamics of the

sublimation chamber total pressure increase was presented and validated.

This model allowed the identification of the main key-parameters of

-40

-30

-20

-10

0

10

20

30

40

13 15 16 18 20 21 22 24 25 26 29 31 33 34

Time (Hours)

Temperature(C)

0

100

200

300

400

500

600

700

800

Pressure(bar)

12

3

Figure 8. Freeze-drying cycle of a 5% mannitol during a standard PRA

experiment.Tshelf 0C,P 38 Pa,Texp 249.5K,t 280 min. Shelf temperature

(diamonds), product temperatures of two vials (solid lines), total chamber

pressure (X), and water partial pressure () are represented. (View image in color

online.)


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the freeze-drying process, namely the sublimation front interface

temperature, the mass transfer resistance of the dried layer and the

overall vial heat transfer coefficient on a wider product temperature range

than previous MTM models. Identified ice front temperature values were

close to the experimental data within a range of about 28C, while mass

transfer resistances and overall heat transfer coefficients were consistent

with values from the literature. Furthermore, we showed that the

desorption phenomena during primary drying was not significant enough

to be taken in account by the pressure rise analysis method and that it

could be practically neglected for the PRA modeling.

Besides, we showed experimentally and theoretically that the product

temperature increase during the time period of the PRA test was not

negligible at the end of the primary drying (up to 2C). This is why theindustrial implementating of this PRA method could be hazardous

for very sensitive products like vaccines, etc. So, in these cases we

recommend the monitoring of industrial freeze-drying cycles by measur-

ing and following on-line the water vapor partial pressure in the

sublimation chamber with a capacitance type sensor.

NOMENCLATURE

A Ice sublimation front area of one vial (m2)

A1 Constant of Antoines law (Dimensionless)

B1 Constant of Antoines law (Dimensionless)Cp Frozen layer specific heat (J/kg/K)

Cpvial Vial glass specific heat (J/kg/K)

Ddes Desorption constant during primary drying (Pa/s)

e Thickness of the dried layer (m)

Error(t) Cf. Eq. (17) (Pa)

Fleak Freeze dryer leak rate (Pa/s)

lsep Mean separation distance between the vial and the

shelf (m)L Thickness of the remaining frozen layer (m)

L0 Initial thickness of the frozen layer (m)

kappa Miltons model constant (J/s/m2/K)

Kcont

Contact heat transfer coefficient for one vial (W/m2/K)

Kgas-cond Gas conduction heat transfer coefficient for one vial

(W/m2/K)Krad Radiative heat transfer coefficient for one vial (W/m

2/K)

Kv Overall heat transfer coefficient for one vial (W/m2/K)


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Kv0 Overall heat transfer coefficient before closing the

separation valve (W/m2/K)MH2O Molecular weight of water (kg/kmol)

mvial Mass of one vial (kg)

N Number of vials for a whole batch

P Total pressure in the lyophilization chamber (Pa)

Pc Initial total pressure in the lyophilization chamber (Pa)

Pi Water vapor partial pressure at the interface (Pa)

Pi0 Water vapor partial pressure at the interface before

closing of the separation valve (Pa)Pinert Inert gas partial pressure in the lyophilization chamber

(Pa)

Pw Water vapor partial pressure in the lyophilizationchamber (Pa)

Q Thermal energy (J)

R Universal gas constant (J/kmol/K)

Rp Resistance to mass transfer of the dried layer

(Pam2 s kg1)t Time (s)

Tbottom Temperature of the frozen layer at the bottom of the

vial (K)Texp Mean experimental product temperature (K)

Ti(t) Temperature at the sublimation front (K)

Ti0 Initial temperature of the sublimation front before

closing the separation valve (K)Tv Temperature of gas in the lyophilization chamber (K)

Tshelf Shelf temperature (K)

V Volume of the lyophilization chamber (m3)

Greek Letters

Efficiency coefficient for heat transfer (Dimensionless)

Hs Enthalpy of ice sublimation (J/kg)

t PRA measurements interval (s)

T Temperature gradient between the bottom of the frozen

product and the sublimation front (K)c

Thermal conductivity of the frozen layer (W/m/K)gas

0 Thermal conductivity of water vapor at atmospheric

pressure (W/m/K)c Ice density (kg/m

3)

0 Water vapor molecular thermal conductivity (W/m2/Pa/K)


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ACKNOWLEDGMENT

The authors wish to thank Aventis Pasteur and Re gion Rhone-Alpes for

their financial support and their interest in this work.

REFERENCES

1. Milton, N.; Pikal, M.J.; Roy, M.L.; Nail, S.L. Evaluation of

manometric temperature measurement as a method of monitoring

product temperature during lyophilization. PDA Journal of

Pharmaceutical Science and Technology 1997, 51 (1), 716.

2. Pikal, M.J. Freeze-drying of proteins, part I: process design.

Biopharm1990, 3, 1827.

3. Obert, J.P. Mode lisation, Optimisation et Suivi en Ligne du Proce de

de Lyophilisation. Application a` lAme lioration de la Productivite

et de la Qualite des Bacte ries Lactiques Lyophilise es. Ph.D. thesis,

INRA, Paris-Grignon, 2001; 186.

4. Liapis, A.I.; Sadikoglu, H. Dynamic pressure rise in the drying

chamber as a remote sensing method for monitoring the temperature

of the product during the primary drying stage of freeze-drying.

Drying Technology 1998, 16 (6), 11531171.

5. Perry, R.H.; Chilton, C.H. Chemical Engineers HandBook, 5th Ed.;

McGraw Hill, 1973.

6. Chouvenc, P. Optimisation du Proce de de Lyophilisation desLiposomes. Ph.D. thesis, Universite Claude Bernard Lyon 1,

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7. Pikal, M.J. Heat and mass transfer in low pressure gases: applications

to freeze-drying. In Transport Processes in Pharmaceutical Systems;

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2000; 611686.

8. Sheehan, P.; Liapis, A.I. Modeling of the primary and secondary

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vials: numerical results obtained from the solution of a dynamic

and spatially multi-dimensional lyophilization model for different

operational policies. Biotechnology and Bioengineering 1998, 60,

712728.9. Pikal, M.J. Use of laboratory data in freeze-drying process design:

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of freeze-drying. Journal of Parenteral Science and Technology.

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10. Roy, M.L.; Pikal, M.J. Process control in freeze-drying: determina-

tion of the end point of sublimation drying by an electronic moisture

sensor. Journal of Parenteral Science and Technology Mar.Apr.

1989, 43 (2), 6066.

11. Bardat, A.; Biguet, J.; Chatenet, E.; Courteille, F. Moisture

measurement: a new method for monitoring freeze-drying cycles.

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47 (6), 293299.

12. Nail, S.L. Methodology for in process determination of residual

water in freeze-drying products. International Symposium on

Biological Product Freeze-Drying and Formulation, Bethesda,

USA, 1990; Dev. Biol. Stand: Karger, Basel, 1991; 74, 137151.

13. Liapis, A.I.; Pikal, M.J.; Bruttini, R. Research and developmentneeds and opportunities in freeze drying. Drying Technology 1996,

14 (6), 12651300.

14. Sadikoglu, H.; Liapis, A.I. Mathematical modeling of primary and

secondary drying stages of bulk solution freeze-drying in trays:

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of theoretical results with experimental data. Drying Technology

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