1 Handling Uncertainty in the Development and Design of Chemical Processes David Bogle, David Johnson and Sujan Balendra Centre for Process Systems Engineering Dept of Chemical Engineering University College London Collaborating Company : Pharmacia

2 Summary Objectives Process Development Methodology A Multiphase reactor Complete Manufacturing Processes Conclusions

3 Objectives Process development Integrated model-based approach Impact of uncertainty Management of uncertainty

4 Chemical and clinical trials Simultaneous scale-up and production Resources and Divisions Difficulty in implementing changes Process development issues

5 Sequence of batch operations Complex fundamental mechanisms Multiphase

6 Generic model-based approach 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)?

7 Uncertainty Incomplete process knowledge  lack of suitable data  not having rigorous models Impact Management

8 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

9 Methodology

10 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

11 Optimisation approach Optimisation objectives : key UA criteria Off-line decisions : scenario independent control variables s.t. deterministic constraints stochastic (binary) constraints

12 Methodology

13 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%)

14 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

15 Optimal reduction in uncertainty  decision variables – fractions of original values of parameters which characterise spread of uncertainties Max   st +   dt Subject to deterministic model uncertainty space characterisation stochastic inequality constraint FW(F) < a FW (F)’ (width between 5% and 95% fractiles)

16 Case study : Bromopropyl amination (Sano et al. 1999) Semi-batch reactor with constant addition First order parallel-series reaction First order dissolution kinetics Isothermal A + B C main A + C Dsub

17 Uncertainty analysis : nominal optimisation Uncertainty : kinetic parameters10 % dissolution parameters 10 % feed purity1.5 % temperature control1 %

18 CF plot : Yield C - nominal solution

19 CF plot : Final time - nominal solution

20 Optimal isothermal conditions CriteriaNominal optimal operation Uncertain optimal operation Scenarios Mean-variance {Y C } [E{Y C } (%), Var{Y C }][94.35, 50.4][94.30, 26.9] E{Y D } (%) E{t f } (hr) FW{Y C } (%) FW{Y D } (%) FW{t f } (hr) [Pr pass {Y D  2.0}, Pr pass {t f  8.0}] [0.59, 0.59][0.53, 0.98] [E viol {Y D  2.0}, E viol {t f  8.0}] [1.39, 4.49][1.25, 0.05] Decisions t add (hr) T iso (K)

21 Robust optimisation Key uncertainties main and sub-reaction kinetic parameters : Ea main, Ea sub Objective function :

22 CF plot : Yield C - robust solution

23 CF plot : Final time - nominal solution

24 CF plot : Final time - robust solution

25 CF plot : Yield D - robust solution Yield D - not improved with robust optimisation  insensitive to available controls

26 Critical uncertainty reduction on Yield D criteria

27 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

28 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

29 Process development methodology

30 Typical Pharmaceutical Plant Reaction 1 stage Dilution | Quench | Phase separation Solvent exchange 7 stages 3 stages 4 stages Purification | Isolation API Crystals PP Data

31 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?

32 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

33 Acknowledgements EPSRC, Pharmacia, Aspentech