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Better Management of Computer Experiments

using Design Expert

David Nicolaides

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5 Quick Company Overview

Computer Experiments

A Chemical Reaction and its Challenges

Simulation of the Reaction Kinetics

DOE and Analysis

Conclusions and Questions

Contents

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Our Company

a ScientificcompanyCombining Science, Technology and Art for a sustainable society

14,000passionate people• 108 nationalities• One global R&D / 43 labs • Game changing 3DEXPERIENCE

solutions

190,000enterprise customers• 12 industries in 140 countries• >10 million on premise users• >100 million online users

3,500partners• Research & Education • Software & Technology• Sales & Services

Long-termdriven• Majority shareholder control • Revenue: $ 2.8 Bn*• Operating margin: 31.5%*

* Non-IFRS

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Computer Experiments

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A Chemical Reaction The reaction at right has been studied

for a variety of different purposes (antitumoral drugs, indicators of enantiomeric excess, etc.) and for a variety of different ligands. Reference [1] was the first to explore the kinetics in a detailed fashion, including reporting values for the rate coefficients ki.

The complexity of the reaction means that there are many intermediates, which have to be dealt with in subsequent purification steps.

[1] “Solution behaviour, kinetics and mechanism of the acid-catalysed cyclopalladation of imines”, Montserrat Gómez, Jaume Granell and Manuel Martinez, J. Chem. Soc., Dalton Trans., 1998, Pages 37–43

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Purification Issues The issues can be clarified by considering the

kinetics of the reaction. At right we see results from [2] which used spectroscopic methods and kinetic theory to analyse this reaction, and note that if we were willing to wait for a very long time (reaction times are on the order of days) then we could simplify the purification problem.

As usual, it comes down to a trade-off between cost of reaction and cost of purification. We would like to find an “optimal” quench time, so that we get a reasonable amount of product which is still easy to purify.

[2] “Combining hard- and soft-modelling to solve kinetic problems”, Anna de Juan, Marcel Maeder, Manuel Martınez, Roma Tauler, Chemometrics and Intelligent Laboratory Systems 54 2000. 123–141

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Simulating Reactions in Modelica Modelica is an open-source,

object-oriented system for simulating dynamic (time-dependent, or “1D”) systems. As well as a robust differential equation solver it includes algebraic equation solving. The systems simulated can be quite complex (e.g. thousands of simultaneous coupled equations).

Solving the equations of kinetic theory is “a doddle”, with only a few lines of code needed.

“Tutorial on the fitting of kinetics models to multivariate spectroscopic measurements with non-linear least-squares regression”, Graeme Puxty, Marcel Maeder and Konrad Hungerbühler, Chemometricsand Intelligent Laboratory Systems 81 (2006) 149–164.

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DOE of Computer Experiments We can profitably use Design Expert to ensure that our

simulations give us the maximum information with the least effort.

In this case we know the key parameters, the kinetic coefficients. We also know how these parameters depend on those accessible to the chemist, mainly T (reaction temperature) and P (pressure) (we keep the solvent fixed for this study).

Accepted wisdom (e.g. [3]) is that for computer experiments there is no reason to expect a particular functional form for the model, therefore the DOE should be one of the “space-filling” type (Optimal, Distance-based in DX). However, we also chose a number of experiments sufficient to support a relatively complex (e.g. cubic) model form, if that was found to be significant.

[3] Design and Analysis of Experiments, Douglas C. Montgomery, 7th edition. Wiley. See, e.g. section 11.5

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Details about the Factors and Responses The working range of T and P was taken from the experimental work [1].

Note that these reactions are run at moderate T, but very high P (hundreds of atomospheres). The data on the kinetic coefficients k1, k2, and k3reported in [1] was fit to a simple Arrhenius form, allowing values to be determined for the ki at any design point.

We took as fixed a “quench time” of 12 hours (an overnight run). Given this quench time we can calculate the responses.

For the responses, three were considered: Conversion: the amount of the desired product. Selectivity: a ratio of the amount of desired product to the amounts of two of the

intermediates, regarded as the most problematic to purify. Cost: a simple “model” (or equation) incorporating the understanding that greater T

and P don’t come for free.

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The Experiments

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Analysis For Conversion (0 – 1, shown at right),

logit transform was used, and a cubic model was found to be significant.

For Selectivity Box-Cox analysis suggested a log transform, and again a cubic model was significant.

With these choices the residuals showed no dangerous trends, and leverages were all small.

More sophisticated statistical methods (e.g. “Gaussian Process Models”) thus don’t seem to be warranted.

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Optimization The simplest summary of the

analysis is the ‘Graphical Optimization’ chart, showing an obvious region for meeting the experimental goals of

Conversion > 0.95 Selectivity > 100 Cost < 150

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Conclusions We have found Design Expert to be a very useful tool in the design and analysis

of effective computer experiments (a.k.a. simulations). We found the distance-based optimal designs satisfactory in this case, though with

hindsight a more traditional design might also have worked. We found no need (yet) for more complex models (e.g. GPM).

The DOE, simulations and analysis performed here only took a small amount of time, but we expect that with the increasing use of simulation in industrial R&D, the time-savings offered by this approach will only increase.

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