Catalytic processes are immensely important to the chemical industry, with more than 95% of products using a catalyst at some part of the manufacturing process. Maximizing of product yields (and/or quality) while minimizing of costs, particularly in terms of energy consumption is becoming increasingly important considering the current global economic context of rising energy cost and requirements of reducing CO2 emissions. That is why, new catalyst generation are developed periodically to improve activity or selectivity.

Predictive reactor models are required for process design optimization, which often implies some extent of extrapolation beyond the range of available experimental data. Models must therefore be not only precise, i.e. within the acceptable range for the calibration and validation datasets, but also robust, i.e. avoiding aberrant model predictions when extrapolating. This is particularly challenging when the number of experimental data points limited and/or characterization of the reaction network is difficult due to the complexity of the feedstocks. For example, this is the case for VGO hydrocracking which is a chemical process that breaks down heavy hydrocarbons into lighter, more valuable products, using feedstocks such as vacuum gas oil (VGO) or renewable sources like vegetable oil and animal fat. Although existing hydrocracking models, developed over years of research, can achieve high accuracy and robustness once calibrated and validated [1-3], significant challenges persist. These include the inherent complexity of the feedstocks (containing billions of molecules), high computational costs, and limitations in analytical techniques, particularly in differentiating between similar compounds like iso and normal alkanes. These challenges result in extensive experimentation, higher costs, and considerable discrepancies between physics-based model predictions and actual measurements.

The following equation shows the used kinetic model .

dy/dt=-k0exp(-Ea/RT)ppH2^myⁿf(Feed)g(OperatingCondition, Feed)

Where:

• y: concentration of a pseudo component (lump) (% m/m)
• t: contact time (h)
• T: temperature (K)
• ppH2 : Partial pressure of H2 (bar)
• k0: pre exponential factors
• Ea: Activation of Energy
• n: reaction order
• m: pression order
• f: A semi physical formula modelling the feed reactivity and the competition between all the pseudo components. It depends only on the feed composition.
• g: A semi physical formula modelling some operating conditions effects (ex : thermodynamic limitation).

The main problems regarding such models are:

1. This model is not accurate far from the calibration database because the structure of the f and g functions and their inputs are chosen by the process engineer by trial and error without a strong scientific justification. This choice is then not objective nor optimal.
2. The different sources of data do not span the wide range of feeds and possible operating conditions, nor is it feasible to conduct a structured experimental campaign to complete the data manifold (the number of feeds is limited). This results in a biased dataset.

To overcome these limitations, effective approximations are needed that integrate both empirical data and established process knowledge. A preliminary investigation into purely data-driven models revealed difficulties in capturing the fundamental behavior of the hydrocracking reaction, motivating the exploration of a hybrid modeling approach. Among various hybrid modeling frameworks [4], physics-informed neural network (PINN) was selected for in-depth examination, as it can leverage well-established first-order principles, represented by ordinary differential equations (ODEs), to guide data-driven models. This method can improve approximations of real-world reactions, even when the first-order principles do not perfectly match the underlying, complex processes [5].

This work introduces a novel hybrid modeling approach that employs physics-informed neural networks (PINNs) to address the challenges of hydrocracking reactor modeling. The performance is compared against a traditional kinetic model and a range of purely data-driven models, using data from 120 continuous pilot plant experiments as well as simulated scenarios based on the existing first-order behavior model developed at IFPEN [2].

Several criteria are used to compare and optimize the suggested methods:

1. Accuracy: the aim is to test the kinetic and the developed hybrid model on the test data base
2. Interpretability: Trend analysis are carried out. The aim is to show that known trend: pressure, temperature, flowrate, feed impacts are respected.
3. Extrapolation: the aim is to test the kinetic and the developed model on a test data base far from the training data base.
4. Model development time.

In all scenarios, the proposed approach outperformed the kinetic model and purely data-driven models. Furthermore, the hybrid models demonstrated that constraining data-driven models, such as neural networks (NNs), with known first-order principles can lead to more robust outcomes. This approach proposes a new methodology for modeling uncertain reactor processes by leveraging general a priori knowledge alongside data. The aim is not to replace the kinetic models but to show that the development time is much lower using hybrid model. This model can then be used quickly. It will then be replaced by a kinetic model when the pilot plant experiments will be available.

References

[1] Chinesta, F., & Cueto, E. (2022). Empowering engineering with data and AI: a brief review.

[2] Becker, P. J., & Celse, B. (2024). Combining industrial and pilot plant datasets via stepwise parameter fitting. Computer Aided Chemical Engineering, 53, 901-906.

[3] Becker, P. J., Serrand, N., Celse, B., Guillaume, D., & Dulot, H. (2017). Microkinetic model for hydrocracking of VGO. Computers & Chemical Engineering, 98, 70-79.

[4] Bradley, W., et al. (2022). Integrating first-principles and data-driven modeling. Computers & Chemical Engineering, 166, 107898.

[5] Tai, X. Y., Ocone, R., Christie, S. D., & Xuan, J. (2022). Hybrid ML optimization for catalytic processes. Energy and AI, 7, 100134.