A model-based approach for recipe design and scale

Transcript

5th International Conference on Lyophilization and Freeze Drying March 29 – 30, 2012, Bologna
A model‐based approach for recipe design and scale‐up of freeze‐drying processes
Davide Fissore, PhD
LYO
Research Team
LAB
Department of Applied Science and Technology
Outline
•
•
•
•
•
•
Recipe development
Scale‐up: the problem & the approaches
Mathematical modeling
Determination of model parameters
Recipe scale‐up: the procedure
Case study
Do I really need to scale‐up a recipe?
Would it be possible to directly obtain the recipe suitable for the industrial scale apparatus?
How to introduce/evaluate robustness?
How many experimental tests are really needed for scale‐up?
Which PAT tools are available to make scale‐up fast and easy?
Why do not take full advantage of modeling? and how to do it?
Recipe development
• An extended experimental campaign is generally carried out at lab‐scale to identify the values of the heating shelf temperature (Tshelf) and of the drying chamber pressure (Pc) that allow obtaining a product with acceptable quality.
• It is generally recognized that this result is achieved if product temperature is maintained below a limit value during primary drying, i.e. when the ice is removed from the frozen product by sublimation.
Recipe development
• Automatic control can allow recipe development in one step.
Input variables
Tfluid & Pc
Control system
Process
Output variables
T & Lfrozen
Monitoring system
Recipe development
-25
-30
-35
-40
-2
C
8°
20
C
Chamber
pressure, Pa
0°
15
-3
10
C
2°
5
-3
-45
C
4°
-3
C
6°
-3
C
8°
-3
Maximum product temperature, °C
• A design space can be constructed with few experiments.
-20
25
-25
30 -30
-5
-10
-15
Shelf
temperature, °C
Scale‐up: the problem
• Generally, the same recipe obtained in the lab‐scale equipment cannot be used (without modifications) to freeze‐dry the product in a pilot‐scale or in an industrial‐scale freeze‐dryer.
• Generally, the same dynamics of product temperature and of ice sublimation (i.e. the same primary drying duration) are not obtained in two different freeze‐dryers with the same recipe. Scale‐up: the problem
• The reasons at the basis of this are numerous, e.g.:
–
–
–
–
Radiation effect Chamber pressure
Heating and cooling rates
…
• The scale‐up problem is well identified, but the solutions proposed in the literature are not always simple and effective.
The reasonable man adapts himself to the world; the
unreasonable one persists in trying to adapt the
world to himself. Therefore, all progress depends on
the unreasonable man.
George Bernard Shaw, 1856-1950
Combining experiments and modelling
• A successful scale‐up of a recipe requires a thorough understanding of the relationship between the critical quality attributes and the manufacturing process. • Such a result can be achieved using: – a mathematical model of the process, to simulate product evolution for a selected recipe, – few experiments to determine model parameters and to characterize the different freeze‐dryers. If you can’t measure it,
you can’t improve it.
Lord Kelvin,1868
• A suitable model has to be selected.
The best material model of a cat is another, or preferably the same, cat (Wiener & Rosenblueth)
• The level of detail must be chosen according to the final use.
A theory has only the alternative of being right or wrong. A model has a third possibility: it may be right, but irrelevant (Egan)
• Parameters uncertainty and model complexity vs.
accuracy of the calculations.
1D Model
Pw,c
sublimation flux, Jw
dried layer
moving interface
Pw,i
frozen layer
TB
Tfluid
heat flux, Jq
1
Jw 
Pw ,i  Pw ,c 

Rp
heating shelf
Jq  K v  Tfluid  TB 
Overall heat transfer coefficient Kv
• Gravimetric test K v 
-2
40.00
45.00
50.00
Kv  A 
B  Pc
1  C  Pc
40
-2
K v, Wm K
-1
35.00
Av   Tfluid  TB dt
50
20.00
30.00
t
0
-1
Kv,W m K
25.00
m  H s
30
20
10
0
xa
xis
xis
a
y
• Kv is an effective coefficient that takes into account all the heat transfer mechanisms to the product.
Overall heat transfer coefficient Kv
• The Pressure Rise Tests (with MTM or DPE algorithm) can be used to get the value of Kv.
• The value of the sublimation flux (i.e. m/t) can be obtained using the Tunable Diode Laser Absorption Spectroscopy (TDLAS) in case the velocity profile in the duct is known (also in this case the temperature at the bottom of the vial has to be measured).
• In both cases the batch is assumed to be homogeneous and an average value is obtained.
Mass transfer resistance Rp
• Pressure Rise Test (+ MTM, DPE)
• Measurement of the sublimation flux (LyoBalance) and of product temperature
Rp 
p w , i  pw , c
Jw
o
___
DPE
Lyobalance
• Coupling a wireless miniaturized thermocouple and a soft‐sensor, a “smart vial” has been realized by POLITO. • It can be used:
– to measure the temperature of the product in vials in different positions over the shelf
– to estimate the residual amount of ice
– to evaluate Kv and Rp easily in different freeze‐dryers (including industrial‐scale freeze‐dryers)
See Poster by
Serena BOSCA and Coworkers
• It is:
–
–
–
–
compatible with automatic loading and unloading
usable for equipment qualification
suitable for process monitoring
suitable for advanced automatic control See Poster by
Serena BOSCA and Coworkers
Freeze‐dryers characterization (For homogeneous batch)
• Test in equipment "1" to determine the mean value of the heat transfer coefficient Kv for the vials of the batch.
• In case the gravimetric test is used to get Kv, at least other two tests, at different pressures, are needed in order to determine the pressure dependence of Kv.
• In case the PRT or TDLAS are used to get Kv, it is possible to get al the information in just one test.
Per aspera sic itur ad astra
(Seneca)
Freeze‐dryers characterization (For non-homogeneous batch)
4. One test in equipment "2" to determine the mean value of the heat transfer coefficient Kv.
Product characterization
5. One test to determine of the curve Rp vs. Ldried in equipment "1" (and, possibly, in equipment "2"). Recipe scale‐up
(Seneca)
TB  T fluid
T fluid
New recipe
1  1 L frozen



K v  K v k frozen



1
T
fluid
 Ti 
 1 L frozen 
Kv 

TB  Ti

K

k
v
frozen



 1 L frozen 
Kv 

1

K

k
v
frozen


Kv is used to characterize freeze‐dryer "2"
Lfrozen, Ti and TB in freeze‐dryer "1" have to be known
Experiments
1. Gravimetric test in equipment "1" to determine the heat transfer coefficient Kv in each vial of the batch.
2. Identification of the groups of vials in equipment "1".
3. At least other two gravimetric tests in equipment "1" at different pressures in order to determine the pressure dependence of Kv (i.e. the parameters A, B and C)
(Seneca)
4. One gravimetric test in equipment "2" to determine the heat transfer coefficient Kv as a function of the vial position over the shelf.
5. Identification of the groups of vials in equipment "2".
6. Determination of the parameter A for the various groups of vials in equipment "2".
(Seneca)
Product characterization
7. One test to determine of the curve Rp vs. Ldried in equipment "1" (and, possibly, in equipment "2"). Recipe scale‐up
8. Identification of the target dynamics.
(Seneca)
Temperature, K
-25
vial b
vial c
vial d
vial e
-30
-35
-40
Tb by DPE+
-45
e
e
e
d
d
e
d
b
0
d
b
c
b
4
6
8
10
time, h
c
d
b
2
(Seneca)
a
Case study: the freeze‐dryers
A. A laboratory scale freeze‐dryer: vacuum‐tight chamber volume = 0.2 m3, 4 shelves (area of a heating shelf = 0.16 m2)
B. A pilot‐scale freeze‐dryer: vacuum‐tight chamber volume = 1.15 m3, 17 shelves (area of a heating shelf = 0.7 m2)
C. An industrial scale freeze‐dryer: 15 shelves (area of a heating shelf = 2.7 m2).
Case study: the product
• Freeze‐drying of a pharmaceutical product containing an antiviral drug (with a solid content of 11% w/w). • A fixed volume (i.e. 1.5 mL) of such a solution was filled in glass tubing vials that are directly loaded on the heating shelves and arranged in clusters of hexagonal arrays.
Case study: loading
Case study: Kv
D
E
B
C
Filled symbols refer to
the values measured
in freeze-dryer A,
while empty symbols
to those observed in
the freeze-dryer B.
Case study: recipe design
Ldried/L = 1%
Ldried/L = 12%
Ldried/L = 99%
Case study: recipe design
0
-5
-10
-15
-20
-25
-30
-35
-40
scale-up
Lfrozen, mm
Tfluid, °C
Uniform batch (or only core vials considered)
Ti, °C
Case study: recipe scale‐up
-32
-34
-36
-38
-40
-42
10
No scale‐up
8
6
4
2
0
0
2
4
6
8 10 12 14 16
time, h
0
2
4
6
8 10 12 14 16
time, h
• In this case Kv was higher in the large‐scale freeze‐
dryer and, thus, Tfluid had to be lowered to avoid product overheating.
• Often Kv is lower in large‐scale freeze‐dryer: recipe transfer is safe in this case (lower product temperature) but not efficient as drying time is longer
(the recipe can be optimised increasing the shelf temperature).
Freeze-dryer A
Freeze-dryer B
Conclusions
Do I really need to scale‐up a recipe?
Would it be possible to directly obtain the recipe suitable for the industrial scale apparatus?
How to introduce/evaluate robustness?
How many experimental tests are really needed for scale‐up?
Which PAT tools are available to make scale‐up fast and easy?
Why do not take full advantage of modeling? and how to do it?
Conclusions
Process
understanding
Mathematical
modelling
Experiments
Process
Analytical
Technology
Research Team
Torino
LAB
LYO
Department of Applied
Science and Technology
Antonello Barresi
Serena Bosca
Davide Fissore
Daniele Marchisio
Miriam Petitti
Roberto Pisano
Tereza Zelenkova
Departiment of Electronics
Simone Corbellini
Marco Parvis
Alberto Vallan

A model-based approach for recipe design and scale

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