This supplementary material contains tables and figures with the data necessary to replicate the results described in the manuscript.

The source code contains a run_experiments.sh script, which can be used to replicate the results described in the manuscript.

This is the MATLAB source code for the SATvac (Stochastic Agent-based T-cell Vaccination) model, a stochastic agent-based framework for simulating CD8+ T cell dynamics following vaccination. This model captures main immune response phases including activation, expansion, and contraction. It also tracks T cell differentiation into effector and memory cell types and explains the variability observed in immune responses by modeling stochasticity at the single cell level.

Maintenance is critical for industrial plants to ensure operational reliability and worker safety. In process industries, fouling, the accumulation of solid residues in equipment, poses a significant challenge, causing inefficiencies and productivity losses. Effective modeling of fouling evolution over time is essential for maintenance planning to prevent equipment from operating under suboptimal conditions. Traditional approaches to fouling prediction include equation-based models, which offer high precision but may struggle with continuously changing process bound-aries, and machine learning techniques, which are more adaptable but less effective at capturing rapidly evolving trends driven by complex underlying physics. This study introduces an innova-tive hybrid machine learning approach for predictive maintenance, combining the strengths of both methods. Pressure differential is modeled using an equation-based approach that links pressure data with fouling thickness, while the foul... [more]

Mathematical modeling is essential for the effective control of many chemical engineering processes, including crystallization. However, most existing crystallization models used in industry and academia assume ideal mixing. As a result, the unclear effects of imperfect mixing on crystallization, reported in experimental studies, remain largely unexplained. In this work we aim to address this gap in understanding by examining antisolvent crystallization processes on a general theoretical level, using a novel dimensionless model. To address the impact of mixing on crystallization, we employ the Engulfment model coupled with a population balance, and we nondimensionalize the model equations. Using this model, we explore the dependence of the mean particle size on the homogenization rate, represented by the Damköhler number for crystallization. Moreover, we study the impact of mixing at various values of the model's kinetic parameters to simulate difference in properties of individual pro... [more]

Tableting is a dry granulation process for compacting powder blends into tablets. In this process, a blend of active pharmaceutical ingredients (APIs) and excipients are fed into the hopper of a rotary tablet press via feeders. Inside the tablet press, rotating feed frame paddle wheels fill powder into dies, with tablet mass adjusted by the lower punch position during the die filling process. Pre-compression rolls press air out of the die, while main compression rolls apply the force necessary for compacting the powder into tablets. In this paper, process variables such as feeder screw speeds, feed frame impeller speed, lower punch position during die filling, and punch distance during main compression have been systematically varied. Corresponding responses, including pre-compression force, ejection force, and tablet porosity have been evaluated to optimize the tableting process. After implementing an open platform communications unified architecture (OPC UA) interface, process variab... [more]

Understanding the complex dynamics of continuous processes in pharmaceutical manufacturing is essential to ensure product quality across the production line. This paper presents a data-driven modeling approach using Sparse Identification of Nonlinear Dynamics with Control (SINDYc) to capture the dynamics of a continuous direct compression (CDC) tableting line. By incorporating delayed control inputs into the candidate function library, the model effectively captures deviations from steady state in response to dynamic changes. The proposed model was developed by finding a balance between accuracy and sparsity, with focus on the ability to generalize to a wide range of operating conditions.

This work presents a kinetic model of drug substance synthesis considering slug flow characteristics in Stevens oxidation. The developed model is also applied to determine the feasible range of the process parameters. Flow experiments were conducted to obtain kinetic data, varying the inner diameter, temperature, and residence time. A kinetic model was developed for the change in concentrations of the starting material, products, and catalysis. In the kinetic model, slug flow was considered by including a volumetric mass transfer coefficient during this flow. In the initial experiments, early-stage kinetic data were insufficient, conducting additional experiments at shorter residence times. Furthermore, the initial model could not reproduce the residual of the starting material, introducing the oxidant consumption that inhibits the starting material consumption and improving the initial model. The improved model could reproduce experimental results and demonstrated that, as the inner d... [more]

Polyhydroxyalkanoates (PHAs) are microbial bioplastics that are fully biodegradable, biocompatible and can be produced by renewable feedstocks through fermentation. These are all desirable attributes for the replacement of current fossil-based plastics. Strong mathematical models describing bioprocesses are invaluable tools that can be used for enhancing bioprocess understanding as well as optimization. In this study, polyhydroxybutyrate (PHB), by Cupriavidus necator DSM 545 was produced using glycerol and ammonium sulphate (AS) as the sole carbon and nitrogen sources, respectively. In addition, a kinetic bioprocess model was developed. The kinetic parameters of the model were calibrated with five fermentation experiments with different initial conditions (e.g. variable glycerol and AS concentrations) in order to properly establish the inhibition regions and provide a generalized model as much as possible. The model was successfully validated by three independent experiments, two with... [more]

A one-dimensional homogeneous reactor model for a cocurrent flow nonadiabatic catalytic membrane reactor operating water gas shift reaction (WGSR) is developed. The model is used to predict the performance of the reactor and estimate the optimal hydrogen flux profiles required to maximize the CO conversion, and control the temperature rise due to the exothermicity. Under the optimized condition, the secured optimal hydrogen flux is found to be a bang-bang type suggesting constructing reactors of different hydrogen permeabilities. To control the reactor temperature, the activity of the reaction side is diluted by distributing axially certain fractions of inert solid, i.e. 0.35, 0.45 and 0.50. The total volume fraction of the inert solid required to maintain the temperature at 320oC (593.15 K) is 0.50 and the profile is obtained to be a singular-arc type with an observed maximum activity at the reactor inlet.

The use of waste heat from electrolysis can significantly increase process efficiency. Alkaline and PEM electrolyzers, the most mature technologies, produce low-temperature waste heat. Most studies focus on using this waste heat for low-temperature applications like district heating. Alternatively, this waste heat can be upgraded to a temperature that can be usable in the chemical industry, e.g., for steam generation. The combination of an alkaline electrolyzer with a heat pump has been recently investigated to supply both hydrogen and medium-temperature heat. Optimizing electrolyzers for both hydrogen and heat production (combined design) has been shown to have advantages over optimizing for hydrogen only and upgrading the waste heat a posteriori (separate design). However, the effects of electrolyzer pressure and hydrogen compression were not considered, and it remains unclear if similar benefits apply to PEM electrolyzers. This work further analyzes the combined system (i.e., electr... [more]

Climate change, driven by increasing CO2 emissions, necessitates innovative mitigation strategies, particularly for hard-to-abate industries. Carbon Capture and Utilization technologies offer promising solutions by capturing CO2 from industrial flue gases and converting it into value-added products. Among capture methods, membrane separation stands out for its compact design, energy efficiency, and scalability. Following capture, CO2 can be converted into chemicals like formic acid using electrocatalytic processes, enabling energy storage from renewable sources. This study proposes the design of an industrial demonstrator for a CO2 recycling plant targeting hard-to-abate sectors such as textile and cement industries. The system integrates polymeric membranes for CO2 capture and a 100 cm² electrochemical reactor for CO2 electroreduction into formic acid. Experimental data from both stages are used to develop predictive models based on artificial neural networks (ANN), optimizing system... [more]

Sustainable development goals have spurred advancements in bioprocess design, driven by improved process monitoring, data storage, and computational power. High-fidelity models are essential for advanced process system engineering, yet accurate parametric models for bioprocessing remain challenging due to overparameterization, often resulting in poor predictive accuracy. Hybrid modeling, combining parametric and non-parametric methods, offers a promising solution by enhancing accuracy while maintaining interpretability. This study explores hybrid models for succinic acid fermentation by Escherichia coli, a critical process for sustainable bio-based chemical production. The research presents a structured exploration of hybrid model architectures and their robustness under varying conditions. Experimental data were preprocessed to remove noise and outliers, and hybrid model structures were developed with differing levels of hybridization (from one to all reaction rates). Kinetic paramete... [more]

Catalysis design and reaction condition optimization are considered the heart of many chemical and petrochemical processes and industries; however, there are still significant challenges in these fields. Advances in machine learning (ML) have provided researchers with new tools to address some of these obstacles, offering the ability to predict catalyst behaviour, optimal reaction conditions, and product distributions without the need for extensive laboratory experimentation. In this contribution, the potential applications of ML in heterogeneous catalysis and photocatalysis are explored by analysing datasets from different reactions, including Fischer-Tropsch synthesis and photocatalytic pollutant degradation. First, datasets were collected from literature. After cleaning and preparing the datasets, they were employed to train and test several models. The best model for each dataset was selected and applied for optimization.

Physics-Informed Symbolic Regression (PISR) offers a pathway to discover human-interpretable solutions to partial differential equations (PDEs). This work investigates three fitness metrics within a PISR framework: PDE fitness, Bayesian Information Criterion (BIC), and a fitness metric proportional to the probability of a model given the data. Through experiments with Laplace’s equation, Burgers’ equation, and a nonlinear wave equation, we demonstrate that incorporating information theoretic criteria like BIC can yield higher fidelity models while maintaining interpretability. Our results show that BIC-based PISR achieved the best performance, identifying an exact solution to Laplace’s equation and finding solutions with R2-values of 0.998 for Burgers’ equation and 0.957 for the nonlinear wave equation. The inclusion of the Bayes D-optimality criterion in estimating model probability strongly constrained solution complexity, limiting models to 3-4 parameters and reducing accuracy. Thes... [more]

Random signals are crucial in chemical and process engineering, where industrial plants generate big data that can be used for process understanding and decision-making. This makes it necessary to unveil the underlying probability histograms from these signals with a finite number of bins. However, the search for the optimal number of bins is still based on empirical optimisation and general rules of thumb. In this work, we introduce an alternative and general method to unveil probability histograms. Our method employs a novel variable-order QMOM, which adapts automatically based on the relevance of the information contained in the random data. The number of bins used to recover the underlying histogram is found to be proportional to the information entropy, where a search algorithm is developed that generates bins and assigns probabilities to them. The algorithm terminates when no more significant information is available for assignment to the newly created nodes, up to a user-defined... [more]

The performance of chemical plants is inevitably related to knowledge about the current state of the system. However, both process and equipment drifts may distort state information. Deviations of process values caused by equipment malfunction may be misinterpreted as process drifts and vice versa. Determining the cause of the drift is further complicated by the fact that equipment drifts typically occur in combination with process drifts. This paper presents a method that uses available additional equipment data to reliably detect and decouple combined equipment and process drifts in chemical plants by combining statistical methods with model-based approaches. The utility of additional equipment information is assessed based on its effect on the decoupling of process and equipment drifts. First results demonstrate the feasibility of the approach in a real plant.

Industrial process monitoring can benefit from utilizing historical data, providing insights for decision-making and operational efficiency. This study develops a soft-sensor-based approach leveraging multi-fidelity modeling to correct discrepancies between online sensors and laboratory analyses. A Gaussian process-based strategy is used to predict deviations between high-frequency low-fidelity sensor data and less frequent high-fidelity laboratory measurements. By exploring static and dynamic modeling frameworks, we assess their suitability for capturing process dynamics and addressing time-dependent variability. The multi-fidelity soft sensor noticeably improves predictive accuracy, outperforming high-fidelity and low-fidelity methods. This approach demonstrates applicability across various industrial settings where integrating diverse data sources enhances real-time process control and monitoring, reducing reliance on costly laboratory sampling.

Uncertainty plays a crucial role in strategic supply chain design. In this study, we explore robust approaches to model uncertainty when the non-deterministic parameters are placed in the independent term, on the right-hand side (RHS) of the constraints. We consider the "disjunctive adjustable column-wise robust optimization" (DACWRO), a disjunctive formulation introduced previously in our group, and compare it with the adjustable column-wise robust optimization (ACWRO) formulation, a specific technique for solving robust optimization problems when the original robust optimization approach may assume too-conservative results. Given that the proposed method is based on the generalized disjunctive programming (GDP) technique, it is a higher lever modelling approach that represents the discrete nature of the decision process. In addition, it provides alternative MILP representations that can be further tested and compared. The analysis assesses the computational performance and reformulat... [more]

Due to the intermittent nature of most renewable energy sources, developing good and flexible control structures for green electrolysis systems is crucial for maintaining efficient and safe plant operation. This work uses the “top-down” section of Skogestad’s plantwide control procedure to propose a suitable control architecture for PEM electrolysis systems based on advanced regulatory control. Advanced regulatory control structures, such as active constraint control, may offer several advantages over MPC and AI-based control methods as they are computationally less expensive, less affected by model accuracy, easier to scale, and offer fast disturbance rejection. In our approach, we first mapped the constraint regions for the system. Then, we reduce the complexity by reformulating the optimization problem slightly, to remove some constraint regions to obtain a simpler solution structure that gives a negligible loss. Finally, we propose an active constraint control architecture using PI... [more]

Model-based control and optimisation strategies can play a key role in improving energy efficiency and reducing emissions into produced water re-injection facilities. However, building a model that adequately describes the plant is challenging and can also be used in online decision-making procedures. This work proposes a simple model based on a real water re-injection facility operating on the Norwegian continental shelf. The results demonstrate the model's flexibility, which could be fitted to different plant operating points while being fast to solve when embedded in optimisation problems. The developed model is expected to aid the implementation of strategies like self-optimising control and real-time optimisation on produced water re-injection facilities.

As demand for long and accurate molecular simulations increases so too does the computation demand. Beyond using new, enterprise scale processor developments - such as the ARM neoverse chips – or performing simulations leveraging Graphics Processing Unit compute, there exists a potentially faster and more power efficient option in the form of custom hardware. Using hardware description languages it is possible to transform existing algorithms into custom, high performance hardware layouts. This can lead to faster and more efficient simulations but compromises on the required development time and flexibility. In order to take the greatest advantage of the potential performance gains, the focus should be on transforming the most computationally expensive parts of the algorithms. When performing molecular dynamics simulations in a polar solvent like water, non-bonded electrostatic calculations dominate each simulation step, as the interactions between the solvent and the molecular structu... [more]

Process simulation is essential for optimizing chemical processes, offering a cost-effective alternative to the experimental approach. This study presents a co-current hollow fibre membrane model for CO2 separation, integrated into Aspen HYSYS® using the CAPE-OPEN standard. A one-dimensional boundary value problem (BVP) is solved through the shooting method, ensuring accuracy for complex gas separation processes. The unit is implemented in C++, facilitating interoperability, error handling, and optimization of key performance indicators like energy consumption and separation efficiency. Appropriate output variables are employed in the Aspen HYSYS® environment to enable direct sensitivity analysis and optimization within the process simulator. Results Sensitivity analysis results demonstrate that the co-current hollow fiber membrane unit improves methane recovery compared to a pressure swing water absorption (PSWA) column for biogas upgrading to biomethane. While membrane technology sho... [more]

The increasing global population has resulted in the scramble for more energy. Hydrogen offers a new revolution to energy systems worldwide. Considering its numerous uses, research interest has grown to seek sustainable production methods. However, hydrogen production must satisfy three factors, i.e., energy security, energy equity, and environmental sustainability, referred to as the energy trilemma. Therefore, this study seeks to investigate the sustainability of hydrogen production pathways through the use of a Multi-Criteria Decision- Making model. In particular, a modified Simultaneous Evaluation of Criteria and Alternatives (SECA) model was employed for the prioritization of 19 options for hydrogen production. This model simultaneously determines the overall performance scores of the 19 options and the objective weights for the energy trilemma in a South African context. The results obtained from this study showed that environmental sustainability has a higher objective weight v... [more]

Real-time carbon accounting is crucial for advancing policies that effectively meet sustainability objectives. This work introduces a carbon tracking tool specifically designed for the European electricity grid. The tool collects hourly data on electricity consumption and generation, cross-border power exchanges, and weather information to assess the real-time environmental effects of electricity use, employing locally-specific emission factors for the generation sources. It utilizes weather data from various stations across Europe to produce week-ahead forecasts of carbon intensity in the grid. Predictions are created using a random forest regressor, integrated within the optimal controller of an operational industrial batch process. This prediction-based optimizer seeks to reduce total emissions tied to the process schedule's electricity consumption by implementing a rolling horizon strategy. By leveraging enhanced energy flexibility, the controller provides significant opportunities... [more]