Conference Agenda

Due to increasing demand for biosurfactants, which are more environmentally friendly than surfactants derived from non-renewable raw materials, there is a growing need for studies proposing new processes for their production or aiming at the optimization of existing ones. In this context, the mathematical modeling of enzymatic reactors for the esterification of fatty acids with sugars in the production of biosurfactants has been a useful tool for studying and optimizing the process. In particular, artificial neural networks and fuzzy systems emerge as promising methods for developing models for those processes [1]. Thus, this work aimed at the development of hybrid-neural models and a fuzzy model for enzymatic esterification reactors associated with biosurfactant production. For the development of artificial neural networks, experimental data provided by Lima et al. [2] were employed, pertaining to the kinetics of xylose ester synthesis obtained through the esterification of oleic or lauric acid in tert-butyl alcohol medium. In the case of artificial neural networks application, the coupling of networks to reactor mass balances was considered in hybrid models to infer reactant concentrations over time. To achieve this, the Runge-Kutta method was employed for the integration of the material balance differential equations. Computationally, an algorithm was constructed incorporating material balances, neural reaction rates and numerical integration. In the case of applying fuzzy logic for modeling and optimizing the conversion of fatty acid esterification with sugars as a function of operational process parameters (time, temperature, molar ratio of substrates and enzyme loading), a study was conducted based on the available set of experimental data [2]. All computational development was carried out using Matlab. In the application of hybrid-neural models, neural networks were able to predict the kinetic behavior of the xylose esterification process in biosurfactant synthesis by applying them to reactor mass balances, obtaining R^2 values above 0.94, indicating a good predictive capacity. The trained fuzzy models were able to simulate the relationships between input variables and the output variable, enabling the construction of various response surface combinations and estimating the optimal operational condition at 60 h of reaction, 55°C, molar ratio of substrates of 5:1 and enzyme loading of 37.5 U/g. The same condition was obtained when applying the particle swarm optimization algorithm. Thus, this study demonstrated the capability of computational intelligence in modeling, simulation and optimization of biosurfactant synthesis.

References

[1] Alice de C.L. Torres, Rafael A. Akisue, Lionete N. de Lima, Paulo W. Tardioli, Ruy de Sousa Júnior, Computational intelligence applied to the mathematical modeling of enzymatic syntheses of biosurfactants, Editor(s): Ludovic Montastruc, Stephane Negny, Computer Aided Chemical Engineering, Elsevier, Volume 51, 2022, Pages 139-144, https://doi.org/10.1016/B978-0-323-95879-0.50024-2.

[2] Lima LN, Vieira GNA, Kopp W, Tardioli PW, Giordano RLC. Mono- and heterofunctionalized silica magnetic microparticles (SMMPs) as new carriers for immobilization of lipases. Journal of molecular catalysis B, Enzymatic. 2016 Nov;133:S491–499.

This study introduces a data-driven modelling approach using Multi-Task Gaussian Process (MTGP) models to predict biogas production and other key performance indicators in a continuous anaerobic digester fed with hydrothermal carbonization (HTC) products. The feedstock consists of hydrochar and HTC liquor derived from sewage sludge and agro-industrial waste, which exhibit significant variability in composition and degradation profiles, complicating predictive modelling. A Gaussian Process (GP) based approach is utilised because of its capacity to manage intricate and uncertain systems. While GPs have been applied in various fields, their use in predicting biogas production from HTC products has not yet been tested. This problem is critical given the need for reliable models to optimise biogas production from highly variable waste materials. Inputs include operational parameters like dilution rate, soluble chemical oxygen demand (SCOD) at the inlet, and organic loading rate. The GP model predicts biogas production, SCOD in the output, and volatile fatty acid (VFA) concentration. Using an MTGP framework, the model jointly predicts these outputs by leveraging correlations between them, enhancing prediction accuracy. The probabilistic nature of the GP framework allows for the prediction of mean output values along with uncertainties, captured through confidence intervals. This is particularly valuable in dynamic systems like AD, where uncertainties arise from variations in feedstock and microbial activity. The MTGP model extends standard GP regression to handle multiple outputs through the Linear Model of Coregionalization (LMC), which shares a latent structure among tasks via a common kernel, while allowing for task-specific variations. By jointly modelling multiple outputs, the MTGP benefits from shared information across tasks, leading to improved predictions, especially when one output, such as VFA, is difficult to predict independently. The GP model was trained using 164 days of experimental data from a lab-scale anaerobic digester. Results were compared with a previously developed mechanistic model. While the mechanistic model, which incorporates biological kinetics, effectively captures broad trends in biogas production and reactor performance, it is parameter-dependent and assumes specific system dynamics. It struggles with uncertainties in input conditions and process variability. In contrast, the GP model provides a non-parametric, flexible alternative, capable of adapting to complex, nonlinear relationships without prior knowledge of system dynamics. The performance of the GP model was evaluated based on Mean Absolute Error (MAE) and R2 values and compared to the mechanistic model. The GP model yielded: SCOD (MAE = 0.108, R2 = 0.984), VFA (MAE = 0.311, R2 = 0.988), and Biogas (MAE =0.131, R2 = 0.935), indicating a strong fit. In contrast, produced less accurate results, including SCOD (MAE = 0.307, R2 = 0.5), VFA (MAE = 0.2.311, R2 = 0.455), and Biogas (MAE =0.359, R2 = 0.538. The GP model was able to accurately capture the biogas production trend while providing predictive intervals that encapsulate the observed fluctuations in SCOD and VFA concentrations. In conclusion, this study highlights the potential complementarity between data-driven models like MTGPs and mechanistic models. Combining the flexibility of GPs with mechanistic insights could lead to hybrid models that enhance predictive accuracy and robustness in AD systems.

Abstract

Fluid Catalytic Cracking (FCC) is a crucial process in the refining industry, capable of converting lower-quality feedstocks such as Vacuum Gas Oil (VGO) into higher-value products like gasoline and diesel. Due to the changes in feedstock properties and market prices of products, there is a need to adjust and optimize the FCC unit in a timely manner. Accurate modelling of the FCC unit facilitates this optimization, potentially leading to significant economic benefits. However, the complexity of the feedstock and the reactions during the cracking process introduce considerable nonlinearity to the FCC unit (Khaldi et al., 2023). Data-driven modelling approaches are increasingly preferred for their effectiveness in modelling these nonlinear systems. Compared to mechanism models, deep learning models such as Multiple Layer Perceptron (MLP) and Recurrent Neural Network (RNN) generally offer higher accuracy and prediction speed (Yang et al., 2023). However, due to the limited range of actual plant operations and the black-box nature of data-driven models, relying solely on these models for optimization may lead to contradictory decisions.

To address these challenges, we propose incorporating the gradient information of product yields into the training process of data-driven models. Specifically, during the model training process, we not only predict the yields but also calculate the gradients of yields with respect to key variables using the forward difference method. The deviation between the predicted and actual gradients is then integrated into the loss function. We utilize the gradients from the mechanism model Petro-SIM as the ground truth. Given the impracticality of using Petro-SIM to calculate gradients for all points in the training set due to high computational costs, we develop a surrogate model for Petro-SIM to enhance computational speed. Additionally, we employ Bayesian optimization to sample the key variables over a broader range when building the surrogate model, thereby reducing the number of sampling instances needed. The results demonstrate that the surrogate model for Petro-SIM achieves high prediction accuracy, with a mean absolute percentage error (MAPE) of just 0.003, ensuring reliable gradient calculations. More importantly, compared to a purely data-driven model, our hybrid model accurately predicts the gradients of yields with respect to key variables, facilitating the optimization of operating conditions.

References

Khaldi, M.K., Al-Dhaifallah, M., Taha, O., 2023. Artificial intelligence perspectives: A systematic literature review on modeling, control, and optimization of fluid catalytic cracking. Alexandria Engineering Journal 80, 294–314. https://doi.org/10.1016/j.aej.2023.08.066

Yang, F., Xu, M., Lei, W., Lv, J., 2023. Artificial Intelligence Methods Applied to Catalytic Cracking Processes. Big Data Mining and Analytics 6, 361–380. https://doi.org/10.26599/BDMA.2023.9020002

Sustainability is a thriving global topic of concern and following the advancement of technological progress and increased standards of living, the demands for energy, fuels, chemicals and other requirements have increased significantly. Methanol is one such chemical which has seen increases in demand due to its importance as a precursor in the development of other widely used chemicals such as formaldehyde as well its use in the solvent industry. As a result of this, ample research has been conducted in order to develop new production pathways and to further improve the efficiency of previous production routes. CO and CO₂ hydrogenation has shown promise as a potential sustainable method for producing CH₃OH due to its potential for achieving high selectivity and to mitigate environmental issues (recycling of CO₂ to generate green fuels and reduce greenhouse emissions).

In order to gain insight into the reaction mechanisms driving the process, it is beneficial to develop kinetic models that accurately describe the system for several reasons: (i) to develop understanding of variable relationships; (ii) to facilitate control and optimisation; (iii) to conduct model-based design of experiments (MBDoE) and reduce experimental burdens; and (iv) to expedite scale up and scale down of processes. Two commonly used reaction rate models are the power law and Langmuir-Hinshelwood expressions. The former being popular within industrial contexts due to its simplicity to implement and integrate further effects such as mass transfer and heat transfer, however, retains the disadvantage of reduced generalisability as the reaction orders may change significantly under different operating conditions. The latter is commonly used within the field of heterogeneous catalysis as they describe the adsorption of reactants on an ideal catalyst surface. The strong assumptions imposed when developing such kinetic models may limit their predictive performance through the introduction of inductive bias (i.e. model structural uncertainty).

A solution to counter these drawbacks is the inauguration of a data-driven component within the kinetic modelling framework such that any complex, less understood kinetics can be instead learnt from historical data by a machine learning model. This framework is referred to as hybrid modelling and has shown success within the literature in the fields of bioprocessing and biotechnology, requiring lower quantities of data and increased interpretability than traditional black box models. It also removes the necessity for complex, less understood kinetics to be approximated via strong assumptions. However, much less effort has been made to investigate the advantages of hybrid modelling in chemical reaction engineering applications. Therefore, in order to identify the pros and cons associated with each kinetic and hybrid modelling strategies for chemical reaction network modelling, a thorough comparison was made in this work using syngas methanol production as a case study. By constructing different kinetic models and hybrid models, it was observed that hybrid models offer clear advantages over kinetic models for prediction and uncertainty estimation and show greater capability to generalise to unseen conditions when trained with limited data, thus indicating their potential for use in the field of chemical reaction kinetics.

In real-world applications, many optimisation problems are inherently difficult to find feasible solutions due to the lack of exact information, the presence of noisy data distributions, and parameter uncertainties. As a result, data-driven optimisation approaches are increasingly adopted to efficiently explore solution spaces and identify improved outcomes. Chance constraint programming (CCP) is an optimisation approach that ensures stochastic constraints are met with a predetermined probability of satisfaction amongst all possible scenarios (Li et al. 2008; Calfa et al. 2015). Numerous studies have successfully integrated specifically with various optimisation problems (Bianco et al. 2019). Copulas are data-driven coupling functions that capture the dependence structure between multiple univariate marginal distributions under certain correlations. Incorporating copula formulations into CCP makes it possible to better model dependencies between variables under different scenarios when underlying data exhibits complex distributions or non-trivial dependencies, such as correlated risks or non-linear relationships, thereby improving the accuracy of decision-making in optimisation problems with the presence of uncertain parameters. In recent years, the integration of copula and CCP has shown significant promise (Hosseini et al., 2020; Khezri and Khodayifar, 2023).

In this work, we present a copula-based chance-constrained optimisation framework designed to achieve good efficiency and accuracy in estimating demand levels for integrated planning and scheduling problems. Our approach ensures feasible decision-making within a defined risk threshold. We validated this framework within the context of data-driven optimisation, leveraging the DOMINO framework (Beykal et al., 2020), which is a data-driven grey-box algorithm for addressing generic constrained bilevel optimisation problems. Our experiments demonstrate that the proposed approach is capable of identifying robust solutions that result in higher joint satisfaction rates for products and near-optimal performance, all while significantly reducing computational time compared to exact methods and other simulation-based software. The efficiency and effectiveness of our approach are further validated through a number of case studies across a range of optimisation problems.

Reference:

Beykal, B., Avraamidou, S., Pistikopoulos, I. P., Onel, M., & Pistikopoulos, E. N. (2020). Domino: Data-driven optimization of bi-level mixed-integer nonlinear problems. J. Glob. Optim., 78, 1-36.

Bianco, L., Caramia, M., & Giordani, S. (2019). A chance constrained optimization approach for resource unconstrained project scheduling with uncertainty in activity execution intensity. Comput. Ind. Eng., 128, 831-836.

Calfa, B. A., Grossmann, I. E., Agarwal, A., Bury, S. J., & Wassick, J. M. (2015). Data-driven individual and joint chance-constrained optimization via kernel smoothing. Comput. Chem. Eng., 78, 51-69.

Hosseini Nodeh, Z., Babapour Azar, A., Khanjani Shiraz, R., Khodayifar, S., & Pardalos, P. M. (2020). Joint chance constrained shortest path problem with Copula theory. J. Comb. Optim., 40, 110-140.

Khezri, S., & Khodayifar, S. (2023). Joint chance-constrained multi-objective multi-commodity minimum cost network flow problem with copula theory. Comput. Oper. Res., 156, 106260.

Li, P., Arellano-Garcia, H., & Wozny, G. (2008). Chance constrained programming approach to process optimization under uncertainty. Comput. Chem. Eng., 32(1-2), 25-45.

Hydrogen-powered heavy-duty trucks have a high potential to significantly reduce CO₂ emissions in the transportation sector. Therefore, efficient hydrogen storage onboard vehicles is a key enabler for sustainable transportation as achieving high storage densities and extended driving ranges is essential for the competitiveness of hydrogen-powered trucks. Cryo-compressed hydrogen (CcH2), stored at cryogenic temperatures and high pressures, emerges as a promising solution. To fully exploit this technology, understanding the thermodynamic behavior of CcH2 storage systems is critical for optimizing operational strategies. This study presents a comprehensive thermodynamic model implemented in MATLAB, which is capable of simulating the tank system across all operating conditions and, therefore, enables thermodynamic analysis and optimization of drive cycles.

The considered CcH2 tanks consist of an aluminum liner wrapped in carbon fiber and insulation material. Further, these tanks are equipped with two heat exchangers. The first heat exchanger heats up the hydrogen that is discharged from the tank to power the truck in a fuel cell. The second heat exchanger is used for pressure control by providing heat to the hydrogen stored within the tank, which is essential for maintaining the hydrogen at the required minimum pressure level.

With the applied MATLAB model, the thermodynamic state of the hydrogen in the onboard tank system can be simulated in all typical operating scenarios (discharge, refueling, dormancy) and real-life drive cycles consisting of these base operations. The core of the model is a differential-algebraic equation system that describes the thermodynamic state of hydrogen in the tank. Additionally, surrogate models based on artificial neural networks are applied to efficiently describe the heat exchangers integrated into the tank system. These surrogate models accurately replicate the performance of larger individual component models, allowing for fast and flexible simulation. Their integration into the overall tank system enables advanced process analysis and optimization.

Several use cases are explored to demonstrate the model's ability to simulate the thermodynamic behavior during real-live drive cycles and to find optimal operating strategies. As such, an optimal stop density is determined, when to stop driving and refuel the tank to maximize overall driving ranges. Real-live drive cycles are considered, taking into account the limited availability of refueling stations in early market applications as well as longer periods of dormancy. By analyzing the simulation results, preliminary conclusions regarding optimal operation depending on the desired requirements, like driving range and loss-free holding time, are drawn. For instance, refueling right before a dormancy period will reduce the loss-free holding time of the cryogenic tank, but will also extend the driving range of the subsequent discharge period.

These results provide valuable insights into how operational strategies can be tailored to maximize driving range, minimize hydrogen losses, and improve overall system efficiency, ultimately supporting the adoption of hydrogen in long-haul transportation.