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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