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Handling Uncertainty in the Development and Design of Chemical Processes
David Bogle,David Johnson and
Sujan Balendra
Centre for Process Systems EngineeringDept of Chemical Engineering
University College London
Collaborating Company : Pharmacia
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Summary
• Objectives
• Process Development
• Methodology
• A Multiphase reactor
• Complete Manufacturing Processes
• Conclusions
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Objectives
• Process development
• Integrated model-based approach
• Impact of uncertainty
• Management of uncertainty
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• Chemical and clinical trials
• Simultaneous scale-up and production
• Resources and Divisions
• Difficulty in implementing changes
Process development issues
Process deve lopment
Sca le up Sca le upSca le up
Make chemical product
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Process development issues
Reaction
Isolations
Fina l purifica tionSubs tra te
Large uncertainty Non-reproducible Inadequate data for
proces s deve lopment
• Sequence of batch operations
• Complex fundamental mechanisms
• Multiphase
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Generic model-based approach
Develop models Identify da ta Improve mode ls
Process deve lopment
Sca le up Sca le upSca le up
Why? • Efficient process development
• Structure/document process knowledge
• Improve understanding and process potential
• Identify important areas where knowledge is lacking
• Future application to validation (FDA)?
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Uncertainty
• Incomplete process knowledge
lack of suitable data
not having rigorous models
Phys ical propertiesTrans fer
ThermodynamicsKine tic s
Impact Management
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Dealing with Uncertainty in Process Development
• Utilise the available information
• What can be done?
manipulate available decisions
improve the model - reduce uncertainty
alternative process/route
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Methodology
Systematic model development
Improve model
Get data
Process models Uncertainty
characterisation Feedback
Stochastic system
Risk Analysis: Uncertainty Analysis quantify uncertainty
Sensitivity Analysis identify contributors
Optimal input uncertainty reductions identify reduction to meet
desired output performance uncertainty limits
Implement Get new data
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Input effect Uncertainty characterisation : normal, uniform
Define uncertainty space :
Correlation structures :
Sampling : Hammersley
Output effect Uncertainty analysis :
constraint violation
Sensitivity indicators : linear, non-linear
Risk analysis approach
V
, ,2
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Optimisation approach
max , , , , , , max , , , , , ,, , , ,u t
s mu t
s m ms s
E Q x x y u J Q x x y u d
Not based on extreme scenarios
Dynamic and non-linear behaviour
Computa tiona l is sues
• Optimisation objectives : key UA criteria
• Off-line decisions : scenario independent control variables
s.t. deterministic constraints stochastic (binary) constraints
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Methodology
(5) Initial conditions Operating policy
(8) Validation of the stochastic system and the
relevant deterministic process model(s)
(regarding Steps 1 to 6)
(1b) Assume parameter uncertainties
Perturbation Analysis
(1a) Estimate characteristics of model parameter uncertainties
(3) Sampling procedure
(4) Solve stochastic model (6) Solve deterministic model of complete process
(2) Define the stochastic system with significant uncertain inputs
(7) Convergence test
Uncertainty Analysis over complete
process sequence
Data
collection
Performance criteria distribution parameters
(9) Sensitivity Analysis
(10) Optimal reduction in key parameter uncertainties for
desired output uncertainty limits
Key contributors to predicted output uncertainties
Compare distributions to independent data
Data drivers
Required source reductions to meet target levels
Development of individual process models
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Uncertainty Analysis
• Estimate characteristics based on local
linearisation and approx. confidence region
• Hammersley sampling procedure
• Solve stochastic model to give expected
values of statistics for output variables
• Continue sampling until mean and variance
are unchanging (<1%)
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Validation and Sensitivity Analysis
• Estimate ranking priority of inputs contributing
to uncertainty
• Use
• Correlation coefficients – linear measures of input
contribution
• Standardised regression coefficient – fraction of
output variability explained by input variability not
due to any of the other inputs
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Optimal reduction in uncertainty
decision variables – fractions of original values of parameters which characterise spread of uncertainties
Max st + dt
Subject todeterministic modeluncertainty space characterisation
stochastic inequality constraintFW(F) < a FW (F)’
(width between 5% and 95% fractiles)
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Case study : Bromopropyl amination(Sano et al. 1999)
• Semi-batch reactor with constant addition
• First order parallel-series reaction
• First order dissolution kinetics
• Isothermal
aqueous Bsolid A
methanol solvent
A + B C main
A + C D sub
B
A
addition T
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Uncertainty analysis : nominal optimisation
• Uncertainty : kinetic parameters 10 %
dissolution parameters 10 %
feed purity 1.5 %
temperature control 1 %
Nomina l Mean Fractile diffe rence Exp. Viola tion
97.1 Yie ld C (%) 94.3 81 - 99 -
6.8 Fina l time (h) 9.4 2 - 27 3.5 (8h)
1.4 Yie ld D (%) 2.8 0.3 - 9.1 1.4 (2%)
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CF plot : Yield C - nominal solution
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CF plot : Final time - nominal solution
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Optimal isothermal conditions
Criteria Nominal optimal operation
Uncertain optimal operation
Scenarios 456 418
Mean-variance {YC} 0 0.234
[E{YC} (%), Var{YC}] [94.35, 50.4] [94.30, 26.9]
E{YD} (%) 2.75 2.77
E{tf} (hr) 9.34 2.35
FW{YC} (%) 18.73 15.92
FW{YD} (%) 8.83 7.55
FW{tf} (hr) 24.97 5.17
[Prpass{YD 2.0}, Prpass{tf 8.0}] [0.59, 0.59] [0.53, 0.98]
[Eviol{YD 2.0}, Eviol{tf 8.0}] [1.39, 4.49] [1.25, 0.05]
Decisions
tadd (hr) 1.79 1.12
Tiso (K) 296.8 312.4
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Robust optimisation
Key uncertainties
main and sub-reaction kinetic parameters : Eamain, Easub
Objective function : max,
min minT
robust
no al
robust
no aladdition
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2
Nominal Robus t
Tiso (K) 297 312
addition (h) 1.8 1.1
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CF plot : Yield C - robust solution
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CF plot : Final time - nominal solution
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CF plot : Final time - robust solution
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CF plot : Yield D - robust solution
Yield D - not improved with robust optimisation
insensitive to available controls
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Critical uncertainty reduction on Yield D criteria
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Recap
• What information has been obtained?
quantified effect of model uncertainty and system variability
a priori robust control solution
whether further model development may be useful and where
sensitivity of key risk criteria- range of sources- potential reduction in the critical source
• Information may be available before pilot plant run
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Why is this information useful?
• Formal recognition of the problem of uncertainty
• Opportunity to improve the potential of the process
• Aims to reduce the pilot plant laboratory iteration
• Purpose of modelling, and the limitations
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Process development methodology
Systematic model development
Improve modelGet dataProcess models
Uncertaintycharacterisation
Feedback
Optimal input uncertainty reductions identify key reduction requirements to meet desired output performance uncertainty limits
Risk Analysis:Uncertainty Analysis quantify uncertainty
Sensitivity Analysis identify contributors
Stochastic system
Flowsheet optimisation
Process modelsImportant uncertainty
space
Optimisation under uncertainty
Stochastic optimisation problems:
Optimal output performance prediction identify operating policy
Optimal control error tolerance identify maximum control uncertainty within performance constraints
Importance of potential knowledge estimate Value of Perfect
Information
Comparison betweenflowsheet alternatives
ImplementGet new data
Optimise process
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Typical Pharmaceutical Plant
Reaction
1 stage
Dilution | Quench | Phase separation
Solvent exchange
7 stages
3 stages4 stages
Purification | Isolation
API
Crystals
PP Data
PP Data
PP Data PP Data
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Process design systems are typically modular and data comes as error bounds around a data
point – use interval methods
Input
N stream
Cost
P -Input Parameters
r-Residuals
MODULE
Output
M stream
Real values
Gradient values
Interval Bounds
Real values
Gradient values
Interval Bounds
But how conservative?
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Conclusions
• Process development
• Methodology for quantifying and minimising uncertainty
• Uncertainty analysis and identification of potential
uncertainty reduction
• Case study of semi batch reactor
• Contrast of stochastic and interval approaches
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Acknowledgements
EPSRC, Pharmacia, Aspentech