Modelling and Analysis
As a new graduate, you have recently started your first employment with the industrial giant, Mitsubishi Chemical. Mitsubishi is committed to sustainability through their KEITEKI principles, and have a far-reaching vision is to produce platform chemicals from renewable feedstocks. As such, Mitsubishi has sourced a renewable supply of isobutyraldehyde from the emerging sustainable aviation fuel industry, where the isobutyraldehyde is produced via the gasification of biomass. This renewable supply of isobutyraldehyde needs to be oxidised to isobutyric acid using a novel isothermal enzyme reactor pioneered by Mitsubishi.
Figure 1 - Isothermal enzyme reactor for the sustainable production of isobutyric acid from renewable isobutyraldehyde.
The slurry reactor is aerated with air to ensure the availability of excess O2 (A) (Figure 1), uniformly suspending a whole-cell solid catalyst within the variable reactor volume. The whole-cell catalyst contains an engineered P450 enzyme with a high kinetic rate for oxidising isobutyraldehyde to isobutyric acid at ambient operating temperature.
Reaction 1 represents the enzyme-catalysed oxidation of isobutyraldehyde (B) to isobutyric acid (P), simplified to equation 2 for ease of notation.
At this early stage of sustainable process development, the Department has minimal insight into the model structure of the kinetic rate equation. Table 1 details the representative process parameters the Department have used in their scale-down experiments in their laboratory.
Table 1 - Process parameters for the isothermal enzyme reactor (Figure 1).
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Description
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Value
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Engineering Unit
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Concentrated isobutyraldehyde feed (Cb1)
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24.9
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[mol·dm-3]
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Dilute isobutyraldehyde feed (Cb2)
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0.1
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[mol·dm-3]
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Further facilitating the scale-down experiments in the lab, the Department has normalised the feeds to the enzyme reactor’s cross-sectional area. The constant manipulated variables and the initial condition are detailed in Table 2.
Table 2 - Initial condition for laboratory experiments and constant manipulated variable flow rates.
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Initial condition
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Unit
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Value
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State variables
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h
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[dm]
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40
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CB
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[mol·dm3]
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0.1
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Manipulated variables
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w1
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[dm·min-1]
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1
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w2
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[dm·min-1]
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1
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An experienced engineer scientist in your team has derived the below ordinary differential equations to model the enzyme reactor (Figure 1), where equation 3 is the liquid volume balance and equation 4 is the species balance for isobutyraldehyde. She has kindly provided a template Simulink model (EnzymeReactor_Assignment3.slx) as a starting point for your model parameter estimation.
Given the model structure for the reaction rate (equation 4), rb, is unknown at this early stage of process development, the Department harvested experimental time series data using the process conditions outlined in Table 2. This time series represents 54 samples taken over 100 [min] from the enzyme reactor for gas chromatography (GC) analyses of isobutyraldehyde concentration, Cb. The GC analyses and their 95% confidence limits are contained in the file ‘Slurry Enzyme Reactor Experimental Results.xlsx’ . Unfortunately, the isobutyric acid concentration, Cp, could not be measured given the lab’s HPLC instrument is not operational. However, the experienced engineering scientist knows from previous experimental work that rb is only a function of Cp and Cb. Therefore, she’s asked you to derive the ODE for Cp using the stoichiometry of the reaction.
The experienced engineering scientist has tasked you to devise a neural network surrogate model for the reaction kinetics associated with the P450 enzyme catalyst. In the absence of fundamental first principles insight into the reaction mechanism, rb in equation 4 needs to be estimated using a feedforward radial basis function neural network. Avoiding overfitting, she’s advised you to minimise the number of hidden neurons to less than four. The experienced engineering scientist believes that the Cb time series contains sufficient state variable information for extracting a black box kinetic reaction rate term for equation 4. She’d like to use the resulting dynamic equations for future optimisation of the process towards maximising the techno-economics. You agree with her, and you’re confident that the integration of ODEs with artificial intelligence will make the most of the available experimental data.
Deliverables
Submit a single report as your individual assessment of a radial basis function neural network as a model structure for the kinetic rate equation for the slurry enzyme reactor. Underpinning your conclusion, submit:
1. A technical report of no more than 750 words, addressing the mark scheme requirements.
2. All Matlab Simulink files supporting your report and recommendations.
INDIVIDUAL ASSESSMENT MARK SHEET
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Assignment 3 mark scheme
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Simulink modelling
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Systematic use of subsystems for modelling, compartmentalising the model to make the structure accessible to other engineers at Mitsubishi.
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3.0
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Correct modelling for the ODE for isobutyric acid and the feedforward radial basis function neural network architecture as surrogate model for the reaction kinetics.
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18.0
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Consideration for a suitable numerical integration algorithm.
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3.0
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Neural network surrogate model architecture
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Demonstrated sound engineering science judgement for the selection of inputs to the neural network surrogate model.
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8.0
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Presented an evidenced rational for the number of radial basis function hidden neurons.
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12.0
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Neural network model parameter estimation
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Effective normalisation of the inputs variables to the neural network.
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5.0
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Conducive initialisation of the weights ofthe neural network.
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5.0
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Selected neural network model parameters suited to exploring the solution space during optimisation.
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5.0
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Appreciably minimised the sum square error (SSE) between the model and experimental data using an optimisation algorithm.
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5.0
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Model parameter estimation outcome
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Model parameter optimisation led to a representative neural network surrogate model.
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8.0
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Assessed the statistical significance of the model digitisation, given confidence limits of the experimental results.
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5.0
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Evaluated the robustness of interpolation and extrapolation with respect to alternate w1 and w2.
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8.0
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Technical Writing
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Discussion on selected neural network architecture.
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5.0
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Discussion on optimisation of neural network model parameters, reflecting on how representative and robust the surrogate model is.
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5.0
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Technical report structure aligned with formal scientific report format.
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5.0
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