parametric and cfd modeling of lyophilization process & plant · parametric and cfd modeling of...

1ISL-FD – Bologna, 2012 M. Galan

Parametric and CFD Modeling of Lyophilization

Process & Plant

ISL-FD 5th International Conference,Bologna, March 2012


EQUIPMENT AND PROCESS MODELLING

• The engineers that built this bridge did not use trial and error.

• The models told them how to do it right the first time.

• The Treasury (taxpayers) cannot accept “too expensive” bridges.

• Politicians cannot accept collapses.


Scope

• Lyo Process Constraints

• Parametric Models

• Understanding Our Lyo with CFD• Chamber and Shelves• Chamber-to-Condenser Duct• Ice Condenser

• Results & Conclusions


Validation• In 1987, the US Food and Drug Administration

issued its Guideline on General Principles of Process Validation, which defined Validation as:

“…establishing documented evidence which provides ahigh degree of assurance that a specific process willconsistently produce a product meeting its pre-determined specifications and quality attributes…”

• Over time, there has been a tendency for validation activities to become centered on documentation rather than on ensuring quality.


LyophilizationLimited understanding…

• We often read statements, such as…

• It is not infrequent that process development is ‘terminated’ with the recipe, and further work to define the production cycle is done empirically by the production team.

“In the lyophilization process, there are twoindependent variables, shelf temperature and chamberpressure, and once they are fixed, the dependentvariable, product temperature, becomes also fixed…”


• Usually we specify the recipe (shelf temperatures and chamber pressures vs. time) but…

• This doesn’t guarantee repeatable conditions for freezing

• This doesn’t guarantee that the sublimation parameters are repeatable

• Most importantly, this doesn’t guarantee scale-up and/or ‘smooth’ process transfer to another piece of equipment…

LyophilizationProcess Transfer Parameters…

Temperature & pressure vs. time are intensive magnitudes (independent of the system size), so, scaling a process without further investigation can

lead to unexpected results


• Insertion of a thin thermocouple in a few vials is a widely used method to measure the product (?) temperature during the process.

Disadvantages:• Intrusive for the product• Influence ice nucleation and

sublimation• Problems concerning the sterility of

the product• Difficult when using isolation

technology and impractical with automatic loading/unloading

• Using a thermocouple we can only measure the temperature at one point.

AND SUBLIMATION FLOW?

Classical Monitoring


Absolute Accuracy of Various Temperature Sensors in Degrees C

Temperature B type E type J type K type N type R type S type T type PRTD

-200 - - - 3.0 3.0 - - 3.0 0.55-100 - - - 2.5 2.5 - - 1.5 0.35 0 - 1.7 1.5 1.5 1.5 1.0 1.0 0.5 0.15 200 - 1.7 1.5 1.5 1.5 1.0 1.0 0.8 0.55 400 - 2.0 1.6 1.6 1.6 1.0 1.0 - 0.95 600 1.5 3.0 2.4 2.4 2.4 1.0 1.0 - 1.35 800 2.0 4.0 - 3.2 3.2 1.0 1.0 - 4.301000 2.5 - - 4.0 4.0 1.0 1.0 - - 1200 3.0 - - 9.0 9.0 1.3 1.3 - - 1400 3.5 - - - - 1.9 1.9 - - 1600 4.0 - - - - 2.5 2.5 - -

‘DPE’ (Dynamic Parameters Estimator) can be used to determine temperature when Automatic Loading Systems are employed



Primary Drying• Discrete temperature probes don’t measure ‘real’

temperature: sublimation front moves during primary drying.• The most critical parameter is ice temperature at sublimation

front (Tice). Collapse and/or melting, and sublimation speed depend directly on Tice.

Frozen product

Dry product

Temperature ºC

-25-24

-15Heated shelf at -10ºC

Heated shelf at -10ºC

-20

-10

-25-24

Frozeninterfacemoving

downwards

-20

-15

-10


Primary DryingHeat & Mass Transfer

FROZEN PRODUCT

Heating(cond+conv+rad)

Cooling(sublimation)

InterfaceProduct

TemperatureHeat Transfer Resistance

Dry Phase Vapor Flow Resistance

Lyophilizer Vapor Transport Resistance


Primary DryingHeat & Mass Transfer

ch i

chP

iP Cooling

(sublimation)

Shelf to vial

Glass

Frozen Product

Dry Phase

Stopper

Lyo

Heating(cond+conv+rad)

InterfaceProduct

Temperature

y y g

Glass vial

-25-24

-15

-20

-10

-25-24

-20

-15

-10

Frozeninterfacemoving

downwards

Hea

t Tra

nsfe

rS

ublim

atio

n Fl

ow

RESISTANCE

Frozen product

Dry product

Temperature ºC

P < P


Scope






Parametric Models• Estimate Interface Temperature (and Sublimation Rate)

– Introduce a perturbation (usually closing and opening the Chamber/Condenser isolation valve)

–Solve the equations of state–Extract process data

• Most recent techniques provide good accuracy throughout the entire primary drying process and on into secondary drying

But be aware…• They provide average values throughout the chamber

and provide no information on variability introduced by the geometrical configuration of the Lyophilizer.


Parametric Transient Modelfor Drying in Vials

( )H t

0

L

z

bottomq

driedlayer I

frozenlayer II

sideq

topq

Both transient heat and mass transfer equations defined for the two layers of product:

For the dried layer I:

For the frozen layer II:

2I,gl gl I,gl gl,I,

I I,gl2 2 2gl ,gl gl ,gl gl, gl,

gl, 4 4I,gl2 2

gl ,gl gl, gl,

2

21

ii

P P e i

eW

P e i

T T RhT T

t c cz R R

RF T T

c R R

ñ ñ

ñ

2II,gl gl II,gl gl,II,

II II,gl2 2 2gl ,gl gl ,gl gl, gl,

gl, 4 4II,gl2 2

gl ,gl gl, gl,

2

21

ii

P P e i

eW

P e i

T T RhT T

t c cz R R

RF T T

c R R

ñ ñ

ñ


Analysis of Perturbation


Validation of Results

• Comparison between experimental and estimated temperatures at the vial bottom.

• Pirani-to-Baratron pressure ratio is shown.


Advantages & LimitationsAdvantages:• Consistent results up to the end of Primary Drying• Applicable to both R&D and Production• Robust monitoring tool able to help in assessing production

process variations• Can be used when placing probes is not practical

Limitations:• Indirect (?) measuring method• Inaccuracy slightly increases at the end of primary drying (if

there are large heterogeneities between vials)• Model (as it is) only valid for vials and bulk, but not applicable

for lyophilization of granules• Provide only average values (not ‘spread’ or ‘tolerances’)


Scope






Shelf Interdistance

• Case study: Pilot freeze dryer–Shelves: 4+1: 450 x 450 mm (17.7” x 17.7”)

• Bulk drying in trays

• Pressure: 10 Pa (0.1 mbar/75 mtorr)

• Free flow interdistance:–Case 1: 57 mm (2.24”)–Case 2: 17 mm (0.67”)–Case 3: 7 mm (0.28”)


Pilot Lyophilizer Mesh


Pressure Contours on ShelvesCase 1 57 mm (2.24”)

0.2

Pa


Velocity Profile (vectors)

• Batch homogeneous

• Vapor flows throughout the shelf to the bottom of the chamber

• Duct influences more than free distance

Case 1


Pressure Contours on Shelves

• Maximum pressure in the middle of the shelf

Case 2 17 mm (0.67”)0.

7 P

a


Velocity profile (vectors)

• Batch less homogeneous

• Vapor flows throughout the shelf to the back and to the front of the chamber

• Both duct and free distance have influence

Front Rear

Case 2



• Maximum pressure in the middle of the shelf

Case 3 7 mm (0.28”)4.

7 P

a


Shelf Interdistance• Case study: Industrial freeze dryer

–Shelves: 1,500 x 1,800 mm (59.1” x 70.9”)

• Drying in Vials

• Pressure: 10 Pa (0.1 mbar/75 mtorr)

Case Shelves Free Flow Interdistancemm (in)

L1 14 + 1 67.0 (2.64)L2 15 + 1 57.0 (2.24)L3 16 + 1 50.5 (1.99)L4 17 + 1 42.0 (1.65)



• Operating pressure 10Pa• Mass flux 1 kg/h·m2


Contour plot of Absolute Pressure

L1

L4

Shelf 1 11 14

Shelf 1 13 17


Pressure Profiles across Shelves

Pressure profiles over some shelves of an industrial lyophilizer along the depth of the shelf along the centerline(the numbers identify the shelf, starting from the bottom)


Questioning an Observation…

“The vials closer to the duct dry slower due to cold temperature radiation received from the ice condenser...”

In the examples shown, even in the best case scenario (L1, 67mm of free space) the actual pressure over these vials can be 2Pa lower.

Depending on the pressure regime in which the process is performed, this can equate to a difference of 2ºC (colder)

In the worst case scenario (L4, 42mm of free space) the temperature difference could approach 4ºC


Scope






Butterfly Valvewith Simple Geometry

A simple disc was first used to define the mesh for the CFD calculations.


CFD Simulations

Velocity Mach Number


CFD with a ‘Real’ Valve

Velocity Mach number


Mass Flux for a Certain Duct Geometry

Complex geometry reduces the flow by 4-5%; maximum flow strongly depends on inlet pressure.


Simulations at Constant Inlet Pressure


Mass Flow as a function of the Condenser Pressure

• Straight duct, DN700. The transition to sonic flow condition, with constant mass flow are indicated by the dashed line.


Scope






Modeling Approach

• Even for a preliminary investigation of the general hydrodynamics, it was determined that was not possible to neglect the ‘disappearance’ of the water vapor due to ice condensation, because it was not possible to establish an alternative reasonable outlet condition that gave simulations with reasonable pressure values.

• The approach used models water deposition as a finite rate wall surface reaction, in which the limiting step of the overall process is considered the mass transfer of water molecules to the condenser walls. The resistance has been modeled by adopting the simplified approach of the film theory and by assuming a linear concentration profile in the film.


Geometry and Mesh of Pilot Unit


Temperature and Water Fraction

Contours of static temperature (K)sublimation rate: 0.4 kg m-2 h-1.

Contours of water mass fraction (dimensionless)sublimation rate: 0.4 kg m-2 h-1.


Ice Deposition Rate

Contours of surface deposition rate of ice (kg/ m2 s)sublimation rate: 0.4 kg m-2 h-1.


Industrial Condenser

The two chemical species (water vapor and nitrogen) enter the condenser from its inlet, the inert gas representing the 5% of the overall mass flow.


ResultsContours of water mass fraction (dimensionless)

plane y=0 plane z=0.3 m

plane x=0


ResultsContours of surface deposition rate of ice (kg/ m2 s).


Contours of the Velocity Vectors


Scope






Results• By means of CFD it is possible to calculate the local

pressure over the various shelves in the drying chamber, given the operating conditions (water flow rate fromthe vials, temperature, pressure) and the geometry of the equipment.

• The use of CFD requires time, and the availability of a suitable software to perform the calculations.

• Is it possible to ‘generalize’ the results obtained by means of CFD, i.e. to identify correlations that can provide a quick evaluation of the effect of the design parameters and of the operating conditions on the pressure distribution in the chamber?


Results

• Given the CFD results (i.e. the pressure values over the shelves) of one specific piece of equipment (i.e. a ‘fingerprint’ of the equipment), we would like to determine how local pressure is affected by:

• Distance between the shelves• Size of the shelf• Sublimation flow rate• Chamber pressure

…without doing more CFD calculations!


Results• For example, if our interest is focused on:

–The maximum local pressure in the chamber (usually on the shelf located furthest from the vapor duct);

–The ‘distribution’ of the pressure over the shelf.

• A formula can be derived with the form:

P = f (Pchambersublimation flowsize of the shelfdistance between the shelves)


Equipment Design Approach• Selection of the nominal chamber pressure for maximum

expected sublimation flow rate


Equipment Design Approach• Operating chamber pressure and sublimation flow rate are

generally given as process specifications. At high sublimation rates ‘choked’ flow conditions can occur.

• A preliminary check can easily be done using simplified jet-flow calculations to correlate maximum mass flow density (mass flow rate in the duct divided by the duct cross section) with the chamber pressure. From the mass flow density, the required nominal diameter of duct and valve can be calculated.

Jet flow approximation: Calculation of critical mass flow density for water vapor at different inlet velocities for a given inlet static temperature

0

10

20

30

40

50

60

0 10 20 30 40

mass flow density, g/h cm2

cham

ber P

ress

ure,

Pa

Jet Oetjen

air 239 K

air 273 K

air 293 K

water 239 K

water 273 K

water 293 K



expected sublimation flow rate• Evaluation of pressure conditions over shelves


Equipment Design Approach• If the pressure profile is not disturbed by the duct location, it is

symmetric; then the maximum overpressure over the shelf and the maximum pressure difference along the shelf coincide, and can be calculated

Pressure profiles over the bottom shelf (left) and the duct shelf (right) for the L3 configuration (16+1 shelves; 50.5mm/1.99” free flow interdistance). The profiles along three parallel axes (x3 is the median) and through the whole chamber are shown; the shelf zone is between the vertical dotted lines.


Equipment Design Approach• Case 1: The bottom shelf is close to the ideal situation; the

maximum overpressure (increase with respect to the reference pressure at the point of maximum pressure over the shelf; relevant for evaluating the maximum product temperature in a vial) and the maximum pressure variation over the shelf (the difference between the minimum and maximum pressure, affecting the variance between vials) are very similar.

Maximum overpressure (filled symbols) and maximum pressure difference (open symbols) over the bottom shelf of the lyo, for different shelf configurations.


Equipment Design Approach• Case 2: ‘Duct’ shelf is very different; in this case the maximum

overpressure (increase with respect to the reference pressure at the point of maximum pressure over the shelf; relevant for evaluating the maximum product temperature in a vial) is limited and the maximum pressure variation over the shelf (the difference between the minimum and maximum pressure, affecting the variance between vials) is much larger.

Maximum overpressure (filled symbols) and maximum pressure difference (open symbols) over the duct shelf of the lyo, for different shelf configurations



expected sublimation flow rate• Evaluation of pressure conditions over shelves• Estimation of the chamber resistance and pressure drop

through the chamber


Equipment Design Approach• The pressure drop through the chamber is generally small, but

with two different contributions:– Variation from the ‘reference pressure’, (corresponding to the value

measured by a pressure gauge located remote from inert gas inlet or condenser duct) and the chamber exit.

– A much more significant pressure drop in the first zone of the duct (strong velocity variations and development of a new velocity profile)

Lyo chamber pressure drop correlations

Pressure variation on the middle plane of the chamber for the industrial scale apparatus. The operating pressure is 10 Pa and the mass flux is 1 kg m-2 h-1



expected sublimation flow rate• Evaluation of pressure conditions over shelves• Estimation of the chamber resistance and pressure drop

through the chamber• Calculation of actual flow, as a function of chamber

pressure (and condenser pressure)


Equipment Design Approach• Case of a straight duct (L/D dependent). Left graph plots the

mass flow density as a function of condenser pressure (each curve corresponds to a value of chamber pressure). The horizontal line corresponds to critical flow conditions (choked flow). The symbols corresponds to the subcritical region.

• Right graph plots the mass flow density as a function of chamber pressure (each curve corresponds to a value of condenser pressure). The limit curve with red symbols corresponds to critical flow conditions.


Scale-up• Development performed in a pilot plant

– Self size 350mm x 480mm (13.8” x 18.9”)– Free distance top of vial to shelf: 57mm (2.24”)– Pressure: 10 Pa (0.1 mbar, 75 mtorr)

• Production:– Shelf size 1,500mm x 1,800mm (5’ x 6’)– Free distance top of vial to shelf: 51mm (2.01”)– Pressure: 10 Pa (0.1 mbar, 75 mtorr)

• Vial in pilot unit: 14.9 Pa• Vial in production unit: 18 Pa• T ≈ 2ºC

18.0

17.2

16.4

15.6

14.8


Aggressive Cycle Development• Development performed in a pilot plant (using few vials)

– Sublimation flow: 0.8 kg/h·m2

– Developed at 10 Pa (0.1 mbar, 75 mtorr)

• Production:– Shelf size 1,500mm x 1,800mm (5’ x 6’)– Shelves (17 + 1): 45.9 m2 (494 sq.ft.)– Pressure: 10 Pa (0.1 mbar, 75 mtorr)– Duct: D: 700mm (27.6”)

• Pch > 13 Pa• Not able to follow recipe


Other ResultsSeveral simulations have been carried out introducing an inert gas (nitrogen)

– Typically inert gas is used to control the pressure in the drying chamber (measured by sensors placed in the chamber). Depending on the proportion ofgas, the distribution of the gas inthe chamber varies, but what it isimportant to say is that thechamber can not be considereda perfectly mixed system.

– The concentration is very highclose to the inert inlet and thereare zones, far from the inlet,where the inert concentrationis almost zero.


Conclusions

• CFD models of Lyophilizer vessels have been developed to investigate the effect of geometrical parameters on the vapor fluid dynamics. These models have given a better understanding of:

– The influence of shelf interdistance and dimensions;– The influence of the vapor duct, in terms of its position and dimensions;– The hydrodynamics and performance of the ice condenser;– The distribution of inert gas throughout the system.

• From the CFD model for a particular piece of equipment, simple formulae can be derived which enable the effect of a change to be assessed without running CFD.

• Effects have been identified from CFD simulations which have not hitherto been fully considered in process studies.

• Combination of Parametric and CFD approaches could lead to advanced control systems.



• The engineers that built this bridge did not use trial and error.


• The Treasury (taxpayers) cannot accept “too expensive” bridges.

• Politicians cannot accept collapses.



• The engineers that developed this process did not use trial and error.


• The Patients cannot accept “too expensive” medicines.

• Reg. Authorities cannot accept collapses.


Acknowledgements...

• Antonello Barresi• Serena Bosca• Davide Fisore• Daniele Marchisio• Miriam Petitti• Roberto Pisano• Valeria Rasetto

The Research Group of the LyoLab atPolitecnico di Torino

Department ofMaterial Sciences and Chemical Engineering


Thank you for your attention

Any questions?

“Before I came here, I was confused about this subject. After listening to your lecture I am still confused, but at a higher level.”

Enrico Fermi

Miquel [email protected]

parametric and cfd modeling of lyophilization process & plant · parametric and cfd modeling of...

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