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Mechanistic Modeling

the ultimate QbD tool for process understanding

Marcus Degerman, Lars Sejergaard, Ernst Broberg Hansen, Ann-Merete Ludvig, Else Bang Riis, Janus Krarup, Arne Staby WCBP 2011

Modeling in Process I ndustry

Products

• Ethylene
• Propylene
• Every 4 hours the process is

re-optimized.

• Training room

Cracker plant in Stenungsund Feedstock

• Naphtha
• Ethane
• Propane
• Butane

Definition of Quality by Design

“A systematic approach to development that begins with predefined objectives and emphasizes product and process understanding and process control, based on sound science and quality risk management.”

• Q8, Pharmaceutical Development, ICH

W hat is a m odel?

• one who is employed to display clothes or other merchandise
• a description or analogy used to help visualize something

that cannot be directly observed

• a system of postulates, data, and inferences presented as a

mathematical description of an entity or state of affairs; also: a computer simulation based on such a system

from http: / / www.merriam-webster.com/ Basic principles & theories Assum ptions Data

”I've always seen modeling as a stepping stone.”

• Tyra Banks

Basic QbD elem ents

Models DoE One-parameter evaluation CQAs CPPs PAT etc… Release testing

Process understanding Risk assessm ent Control space Design space

Parameter ranges

Case study - Size Exclusion Chrom atography

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 1.2 1.4

Volume (CV) UV absorption

• HMW P
• dim er
• m onom er
• total UV
• Pooling

Risk Assessm ent

• CQAs
• Potency
• Pool concentration
• Impurities
• Dimers
• HMWP
• CPPs
• Flow rate
• Column length
• Feed volume
• Feed concentration*
• Peak collection

* CQA for previous step

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 1.2 1.4

Volume (CV) UV absorption

Chrom atography m odel

1. Basic principles/ theories

• Convection and dispersion in the

packed column

• Mass transfer into the particles
• Diffusion within the pores
• (Adsorption/ desorption kinetics)
• (Steric Mass Action)

2. Assumptions

• Homogeneous column
• Lumped mass transfer kinetics
• Aggregates
• dimer
• ctamer
• No aggregate formation during

processing

3. Data

• Varying flow rate
• Varying column length
• Varying load volume
• Hypothesis
• Function
• Interaction effects
• Test of hypothesis
• Calibration

Mechanistic m odel

( )

p p

c c st t c

1 1 1 1

− = ∂ ∂

( )

1 1

1 2 2 1 1 1 1

= ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ ⋅ − ∂ ∂ + ∂ ∂ ⋅ ⋅ − ⋅ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ ⋅ c x Pe x c t c k c t

p P d

ε ε ε

Packed Colum n: Pore diffusion:

Calibration experim ents

• Experim ent
• Sim ulation

0.5 1 1 2 3 CV OD

Experiment 1

0.5 1 0.5 1 1.5 2

CV OD

Experiment 2

0.5 1 0.5 1 1.5 2 2.5

CV OD

Experiment 3

0.5 1 1 2 3

CV OD

Experiment 4

Design of Sim ulations

• Column length: 2 levels
• Flow rate: 2 levels
• Pooling front: 3 levels
• Pooling trailing edge: 3 levels
• Feed concentration: 6 levels
• Level of dimers and aggregates set at highest level in

feed.

216 ”experiments”

Sensitivity analysis

0.2 0.4 0.2 0.4 2 4 20 30 40 1 2 0.5 1 0.02 0.04 0.02 0.04 0.6 0.8 1

Yield Aggregates Dim er Pool conc. Flow rate Length Feed conc. Pool front Pool T.E.

Pool concentration

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 2 3 4 5 Fe e d conce ntr a tion ( g/ L) Pool concentration ( g/ L)

Yield

50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100% 1 2 3 4 5 Fe e d conce ntr a tion ( g/ L) Yield

Aggregates

0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 1 2 3 4 5

Fe e d conce ntr a tion ( g/ L) HMWP ( total)

Feed concentration Pooling front

Lab verification experim ents

High load High concentration Set point High aggregate level Low pool concentration Low yield

Effect

~3 ~3 1.5 0.75 0.5

Feed concentration

3% 5 2% 4 5% 3,6,7 9% 2 5% 1

Feed volume #

• “W orst case” conditions
• All experim ents at low colum n length and high flow rate

Pool concentration ( g/ L)

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0.00 0.20 0.40 0.60 0.80 1.00 Sim ulation Experim ental

Process is robust w ith regard to concentration

Feed concentration 0.5g/ L gives a worst case pool concentration of 0.35g/ L.

dim er + HMW P

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 0.0 % 0.5 % 1.0 % 1.5 % 2.0 % 2.5 % 3.0 % 3.5 % 4.0 % Sim ulation Experim ental

Process is robust w ith regard to HMW P

• Process is robust
• Feed concentration of

0.75 g/ L confirmed as worst case regarding HMWP.

• Error at low HMWP due to
• analysis error
• dimer, octamer

Docum entation

Risk assessm ent

• CPPs

Model report

• Theory
• Assumptions
• Data (Calibration)

Process verification study protocol

• Full factorial study by simulation
• Model reduced experimental design

Process verification report

• Verification of process
• Verification of model
• Parameter ranges
• CPP/ KP/ non-CPP

W hat do w e m odel?

• Chromatography
• Ion exchange
• Size exclusion
• Hydrophobic interaction
• Reversed-phase
• Reactions
• Acylation
• PEGylation
• Activation
• We just started with
• Freeze-drying
• Freezing-thawing

Mechanistic m odels are versatile tools

• Knowledge space
• Model space
• Design space
• Control space

1 . Process understanding 2 . Model-based developm ent 3 . Process control 4 . Process support / Trouble shooting

Mechanistic m odeling is sound science

• Process understanding anchored in theories/ first

principles

• supported by the scientific community
• Interaction effects built into the models

Mechanistic Modeling

the ultimate QbD tool for process understanding

Marcus Degerman, Lars Sejergaard, Ernst Broberg Hansen, Ann-Merete Ludvig, Else Bang Riis, Janus Krarup, Arne Staby WCBP 2011