Performing experiments to improve the model not the process
The guiding principle of model-targeted experimentation (also known as model-centric experimentation) is that experimentation used to improve the accuracy of the model rather than to improve the process itself. The model is then used to optimize the process design or operation.
If the empirical parameters – for example, reaction kinetic parameters, heat transfer coefficients – of a model are made as accurate and scale-invariant as possible, the model can be used to examine a wide design space much more rapidly and effectively than via experimentation alone.
Model-targeted experimentation is also a key component of model-based innovation (MBI), a similar procedure applied at R&D level typically for early-stage process or product development.
What does model-targeted experimentation involve?
In a nutshell, model-targeted experimentation starts with a high-fidelity predictive model of the experimentation process and the key phenomena being studied.
Experimental data is fitted to these models to calculate parameter values. Related model-based data analysis facilities also provide parameter confidence information, showing how accurately the proposed model represents what is observed.
If there is significant uncertainty in the parameters:
- the model may not accurately reflect what is happening in real life. For example, a proposed reaction set may be missing one or two key reactions.
- the experimental data may not contain sufficient or sufficiently-accurate data to calculate accurate and independent parameter values. In this case, the confidence information can be used as a guide in the design of subsequent experiments targeted at maximizing parameter accuracy.
Model-targeted experimentation – step-by-step
The key steps in model-targeted experimentation are:
Step 1. Construct first-principles models of the experiment
This involves building a first principles model of the experimental setup used for gathering data, including representation of the key fundamental phenomena being studied (e.g. a detailed reaction set model).
For example, the model of a simple bench-scale stirred reactor experiment may involve:
- a model of the stirred tank, complete with heat and material balances
- a model of the cooling/heating jacket, with appropriate heat transfer equations
- the reaction rate equations and species balance for the reactions occurring in the vessel.
The experiment model is constructed in a modular form allowing the components to be easily be implemented within the full equipment model in Step 3.
Initial reaction kinetic parameter values, if not readily available, are typically found by literature search. The initial values are progressively refined in the steps below.
Models may be written from scratch – for example, using equations found in research literature – but are typically taken from libraries such as the PSE Advanced Model Library for Fixed-Bed Catalytic Reactors (AML:FBCR).
An important note: when conducting model-targeted experiments, it is essential to use small-scale experimental apparatus where the phenomena being studied can be isolated as far as possible.
For example, experiments aimed at determining reaction kinetic parameter value should be as close to isothermal as possible to minimise temperature effects.
Likewise, equipment should be small-scale to minimise the impact of mixing effects on results.
Step 2(a). Estimate the model parameters from data and analyse uncertainty
The model constructed in Step 1 is used to estimate model parameters – typically kinetic constants or heat transfer coefficients – from initial experimental data using gPROMS’ parameter estimation techniques.
In addition to parameter values, model-based data analysis techniques built into the parameter estimation facility also yield estimates of the accuracy of these values in the form of confidence intervals, as well as estimates of the error behaviour of the measurement instruments.
This information is used to determine whether the parameters are sufficiently accurate for subsequent design and operational purposes. It is in fact possible to relate key performance indicators (KPIs) for the process back to uncertainty in parameter values, providing an indication of where further experimentation should be concentrated in order to minimise subsequent design risk.
Step 2(b). Design additional experiments, if necessary
If the data analysis in Step 2 identifies areas of data uncertainty that are not within acceptable risk limits, additional experiments may need to be carried out.
These experiments can now be designed specifically to maximize information in the areas of interest, either informally or by using the model-based experiment design (MBED) techniques provided as a gPROMS option.
MBED takes advantage of the significant amount of information that is already available in the form of the mathematical model to design the optimal next experiment that yields the maximum amount of parameter information (i.e. to minimise the uncertainty in the estimated parameters).
MBED helps to achieve the required parameter accuracy with the minimum number – and hence time and cost – of experiments.
Model-targeted experimentation may require a shift in thinking. Rather than aiming experiments at, for example, maximizing the yield of main product, more useful model information may be obtained by maximizing the yield of an impurity. The latter provides richer information for the model in characterising side reactions, which will be important in subsequent optimization calculations.
Step 2(c). Execute experiments and iterate if necessary
Now carry out the experiment designed in Step 2(b). Repeat Steps 2(a)-2(b)-2(c)-2(a) until parameter values are within acceptable accuracy.
Repeating the cycle at different scales
Steps 1 and 2 may be repeated to develop sub-models at different scales, covering different phenomena. Typically this proceeds in sequential fashion, keeping the parameters previously estimated constant at each subsequent stage.
For example, in a catalytic bed reactor, initial experiments may focus on small samples of catalyst in isolated conditions. The kinetic parameters estimated from these experiments are then fixed in subsequent experiments – for example to determine bed heat transfer characteristics.
Moving on to Step 3
If experiments have been conducted under suitable conditions (e.g. small-scale, isothermal experiments for determining kinetic parameters), at the end of Step 2 you will have:
- high-fidelity models of all key phenomena that closely represent the experimental data
- scale-invariant parameters, meaning that the model can predict phenomena accurately over a range of scales and conditions
- a good understanding of where the design risk lies and where further experimentation – if any – is required.
The model has effectively been validated against experimental data. Now, and only now, are you ready to build the full equipment model and proceed with design or operational analysis.