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 hybrid-modeling approach to monoclonal antibody (mAb) production processes design using automated bioreactor equipment. Experimental data covering a reasonable yet broad range of cultivation conditions was collected by the equipment. Using the data, a model applicable to a wide range of cultivation conditions was developed. In the modeling, a data-driven model was applied to describe complicated/unknown phenomena that could not be captured by previously proposed mechanistic models. In the hybrid model, while maintaining the mass balance of the mechanistic model, coefficients of the equations were estimated with random forest regression. Overall, the model could describe the dynamic concentration profiles of product mAb and quality-relevant impurities depending on the media/glucose feeding conditions. The model was then applied to determine an optimal condition that maximized product mAb concentration and satisfied the impurity constraints. The work can further supp... [more]

Extended Dynamic Mode Decomposition (EDMD) and its variant, the pqEDMD, which uses a p-q-quasi norm reduction of polynomial basis functions, are attractive tools to derive linear operators approximating the dynamic behavior of nonlinear systems. This study highlights how this methodology can be applied to data-driven modeling and control of bioprocesses by discussing the selection of several ingredients of the method, such as the polynomial basis, order, data sampling, and preparation for training and testing, and ultimately, the exploitation of the model in linear model predictive control.

Global biomanufacturing is projected to expand rapidly in the coming decade due to advancements in DNA sequencing and manipulation. However, the complexity of cellular behaviour introduces difficulty in modelling and optimizing biomanufacturing processes. Phenomenological models that represent the physics of the system in empirical equations suffer from poor robustness, while their machine learning (ML) counterparts suffer from poor extrapolative capability. On the other hand, hybrid models allow us to leverage both physical constraints and the flexibility of ML. This work describes a new approach for hybrid modeling that integrates the time-variant parameter estimation and ML model training into a singular step. We implement this approach on a proposed scheme for the cell-mediated conversion of a lignin derivative into a bioplastic precursor and show that our integrated hybrid model outperforms the traditional two-step hybrid, phenomenological, and ML model counterparts. Lastly, we de... [more]

Hybrid modelling utilizes advantageous aspects of both mechanistic (white box) and data-driven (black box) modelling. Combining the physical interpretability of kinetic modelling with the power of a data-driven Artificial Neural Network (ANN) yields a hybrid (grey box) model with superior accuracy when compared to a traditional mechanistic model, while requiring less data than a purely data-driven model. This study demonstrates the construction a hybrid model with transfer learning for the predictive modelling and optimization of a high-cell-density microalgal fermentation process for lutein production. Dynamic optimization was conducted to identify a feeding strategy that maximized final lutein production. The results were then experimentally validated. Overall, this work presents a novel digital twin application that can be easily adapted to general bioprocesses for model predictive control and process optimization.

Process control can be one of the most exciting and engaging chemical engineering undergraduate courses! This paper describes our experience transforming Chemical Process Control into Data Analytics, Optimization, and Control at the University of Notre Dame (second semester required course in the junior year). Our modern course is built around six hands-on experiments in which students practice data-centric modeling and analysis using the Arduino-based Temperature Control Lab (TCLab) hardware. We argue that state-space dynamic modeling and optimization are more critical for educating modern chemical engineers than topics such as frequency domain analysis and controller synthesis emphasized in many classical undergraduate control courses. All the course material is available online at https://ndcbe.github.io/controls.

The increasing complexity of industrial biotechnology demands advanced modeling techniques capable of capturing the intricate dynamics of bioreactors. Traditional regression-based and empirical methods often fall short when confronted with the highly nonlinear behavior and limited experimental data characteristic of bioprocesses. Addressing these challenges requires a more intelligent approach—one that leverages domain knowledge to model complex bioprocess dynamics effectively, even with sparse data, while maintaining interpretability and robustness. In this study, we introduce a process-informed, data-driven methodology for modeling the dynamics of industrial bioreactors, leveraging the capabilities of the rising field of Scientific Machine Learning (SciML). Our approach leverages Physics-Informed Neural Networks (PINNs) to seamlessly integrate domain knowledge encoded in physical laws with sparse experimental data and deep learning techniques, enabling precise simulation and modeling... [more]

Accurate mechanistic models provide valuable physical insight and are crucial for efficient process scale-up and optimisation, but their identification requires lengthy experimental data collection, model construction, validation and discrimination. Traditional black-box machine learning transfer methods leverage prior knowledge but lack interpretability and physical insights. To address this, we propose a novel approach using artificial neural network feature attribution to automatically locate corrections and symbolic regression to make structural modifications to an inaccurate or low-fidelity mechanistic model. In a comprehensive in-silico case study, the framework adapted a kinetic model from one biochemical system to a different but related one, enhancing predictive accuracy. Integrated within an iterative model-based design of experiments routine, it minimised the number of new experiments required. The study also discusses the impact of the inductive bias trade-off and alternati... [more]

The optimization of the power conversion system, responsible for thermal-to-electrical energy conversion, for a pulsed fusion power plant is presented. A spherical tokamak is modelled as three heat sources, all pulsed, with different stream temperatures and available amounts of heat. A thermal energy storage system is considered in the design to compensate for the lack of thermal power during a dwell. Thermal storage enables continued power generation during a dwell and can avoid thermal transients in sensitive components like turbomachines. Multiple lower grade heat sources are integrated into the process through parallel preheating trains. The evaluation of a dynamic model of the power conversion system is used to define an objective function with multiple criteria. A bi-objective optimization problem is defined to investigate the trade-off between the size of the thermal energy storage system and the variability in turbine power output during a dwell. The set of non-dominated design... [more]

Solar Thermal Power Plants (STPPs) use solar energy for large-scale electricity production but face significant operational challenges. These include variations in solar radiation, cloud cover, electricity demand fluctuations, and the need for frequent shutdowns if energy storage is inadequate. Deciding an optimal STPP operating conditions is challenging due to these factors. While revenue maximization has been used as an objective in existing literature, current models are often static and fail to capture the dynamic nature of STPPs. In contrast, this work proposes a dynamic model-based revenue optimization approach that accounts for plant dynamics and operational constraints, such as solar radiation variability and changing electricity demand. The objective function is designed to maximize revenue while considering power generation and fluctuating electricity prices. A simulation model of 1 MWe hybrid solar thermal power plant in Gurgaon, India, featuring two solar fields—Parabolic T... [more]

The transition to a circular economy (CE) requires agents in circular supply chain (SC) networks to take a variety of different initiatives, many of which are dynamic in nature. We use a system dynamics (SD)-based approach to develop a generic framework for dynamic modeling of CE networks and propose a prototypical circular SC network by combining dynamic models for five actors: a manufacturer, consumer, material recovery facility (MRF), recycling facility, and the Earth. We apply this framework to the supply chain for Polyethylene Terephthalate (PET) plastic packaging by considering different scenarios over a 65-year time horizon in the US. We include both "slow-down-the-loop" initiatives (i.e., those that extend product use time through demand reduction or reuse) and "close-the-loop" initiatives (i.e., those that reintroduce product to the supply chain through recycling) by the consumer, as well as sorting and recycling capacity expansion. We find that, given the current recycling in... [more]

Demographic shifts and increased automation in chemical plants are reducing the experience and skill levels of plant operators. Therefore, BASF has implemented Operator Training Simulators (OTS) to allow operators to practice and improve their skills in this safe and controlled environment. The OTS consists of a dynamic model of the process, a control system and safety logics. This paper describes the learnings from using OTS at BASF, where they are used to train operators in process understanding, optimization, procedural training, and disturbance handling. Benefits include reduced training costs, minimized risks and improved efficiency. Also organizational guidelines are provided to ensure that the mentioned benefits are realized in industrial practice. Additionally, high-accuracy OTS models support HAZOP, debottlenecking, and optimization studies.

Dynamic or Programmable Catalysis is an innovative strategy to improve heterogeneous catalysis processes by modulating the binding energies (BE) of adsorbates on a catalytic surface. The technique enables the periodic favoring of different reaction steps, overcoming limitations imposed by the Sabatier Principle and allowing for higher overall reaction rates, otherwise unattainable. Previously, we implemented a simultaneous simulation approach using the algebraic modeling language Pyomo and the solver IPOPT to obtain cyclic steady state results for a unimolecular reactive system with up to four-order of magnitude increases in computational performance compared to the previously reported sequential approach. The flexibility of the method allowed for the investigation of the influence of forcing signal parameters on system behavior and provided a framework for waveform design. In this study, we use a hybrid framework that combines the sequential and the simultaneous simulation approaches... [more]

This study presents an economic analysis of a blue H2-N2 production system, using a novel intensified reformer system with a hydrogen production efficiency of 80%. The system’s ability to produce both high-purity H2 and N2 creates opportunities for small-scale blue H2 and distributed ammonia production. The system consists of three identical, optimized fixed-bed reforming reactors, a heat recovery system, and shift reactors. A dynamic model was developed to simulate three small-scale H2 production systems: 2.8 tpd, 7.1 tpd, and 17.1 tpd, enabling an evaluation of their economic viability. The results indicate that the cost of H2 production ranges from 2.7 to 3.1 USD/kgH2. Sensitivity analysis reveals that natural gas and CO2 transportation costs have a significant impact on the variability of H2 price. This research provides valuable insights into the economic feasibility of small-scale blue hydrogen production, offering a pathway to support the broader adoption of hydrogen technologie... [more]

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. This study presents a comprehensive dynamic thermodynamic model that is capable of simulating the tank system across all operating conditions and, therefore, enables thermodynamic analysis of drive cycles. The core of the model is a differential-algebraic equation system that describes the thermodynamic state of the hydrogen in the tank. Additionally, surrogate models based on artificial neural networks are applied to efficiently describe quasi-steady-state heat exchangers integrated into the tank system. Several use... [more]

Power-to-Ammonia technology offers sustainable pathways for energy storage and chemical production, with fixed-bed reactors being critical components for efficient synthesis. Understanding reactor dynamics under varying conditions is essential for optimizing these systems, particularly when integrated with intermittent renewable energy sources. This study aims to develop and validate a 2D axisymmetric CFD model for analysing the dynamic response of a ruthenium-catalysed ammonia synthesis reactor to thermal perturbations. The model incorporates detailed reaction kinetics, multicomponent mass transport, and heat transfer mechanisms to predict system behaviour under transient conditions. Results reveal that a step increase in wall temperature from 400°C to 430°C enhances NH3 concentration by 136% (from 2.2 to 5.1 vol.%), with rapid system stabilization achieved within 0.5 seconds. The thermals response maintains consistent heat transfer patterns, exhibiting ~400K differentials between inl... [more]

This study proposes a model-based approach utilizing a hybrid population balance model (PBM) to optimize temperature profiles for minimizing agglomeration and enhancing crystal growth. The PBM incorporates key mechanisms—nucleation, growth, dissolution, agglomeration, and deagglomeration—and is ap-plied to the crystallization of an industrial active pharmaceutical ingredient (API), Compound K. Parameters were estimated through prior design of experiments (DoE) and refined via additional thermocycle experiments. In-silico DoE simulations demonstrate that the hybrid PBM outperforms traditional methods in assessing process performance under agglomeration-prone conditions. Results confirm that thermocycles effectively reduce agglomeration and promote bulk crystal formation, though their efficiency plateaus be-yond a certain cycle number. This model-based approach provides a more robust strategy for agglomeration control compared to conventional methods, offering valuable insights for indus... [more]

This model uses the CHEMCAD unit operation Batch Column together with tools for data reconciliation and optimization. Some experimental data is included.
It is used as a template in the course Green Processes at Berlin University of Applied Science (BHT), where students use it to regress measured data from lab experiments and to design an optimal process.

This model uses standard CHEMCAD unit operations and thermodynamic models to simulate the separation of ethanol and water from a fermenter broth.
It is used as a template in the course Green Processes at Berlin University of Applied Science (BHT), where students use it to regress measured data from lab experiments and to design an optimal process.

To match the growing demand for biomethane production, anaerobic digestors need an optimal and time-varying adaptation of the input diet. Dynamic co-digestion constitutes a hard challenge for the limited instrumentation and control equipment typically installed aboard full-scale plants. The development of prediction models is foreseen to support process (optimal) design and control. In this work, a rigorous framework is applied to take full-scale applicability into account while dealing with the design and training of both high-fidelity and control-oriented first-principle/grey-box models, intended to be exploited for real-time optimization and actual process control respectively.

Designing a digital twin will be crucial in developing automation-based future manufacturing systems. The design of digital twins involves data-driven modelling of individual manufacturing units and interactions between the various entities. The goals of future manufacturing units such as zero waste at the plant scale can be formulated as a model-based optimal control problem by identifying the necessary state, control inputs, and manipulated variables. The fundamental assumption of any model-based control scheme is the availability of a “reasonable model”, and hence, assessing the goodness of the model in terms of stability and sensitivity around the optimal parameter value becomes imperative. This work analyses the data-driven model of an acetaminophen production plant obtained from SINDy, a nonlinear system identification algorithm using sparse identification techniques. Initially, we linearize the system around optimal parameter values and use local stability analysis to assess the... [more]

Antibody therapies are important in treating life-threatening ailments such as cancer and autoimmune diseases. Purity of the antibody is essential for successful applications and Protein A selective resin extraction is the standard step for antibody recovery. Unfortunately, such resins can cost up to 30% of the total cost of antibody production. Hence, the optimal design of this purification step becomes a critical factor in downstream processing to minimize the size of the column needed. An accurate predictive model, as a digital twin representing the purification process, is necessary where changes in the flow rates and the inlet concentrations are modeled via the Method of Moments. The system uncertainties are captured by including the stochastic Ito process model of Brownian motion with drift. Pontryagin’s Maximum Principle under uncertainty is then applied to predict the flowrate control strategy for optimized resin use, column design, and efficient capturing of the antibodies. In... [more]

Machine learning presents opportunities to improve the scale-specific accuracy of mechanistic models in a data-driven manner. Here we demonstrate the use of a machine learning technique called Sparse Identification of Nonlinear Dynamics (SINDy) to improve a simple mechanistic model of algal growth. Time-series measurements of the microalga Chlorella Vulgaris were generated under controlled photobioreactor conditions at the University of Technology Sydney. A simple mechanistic growth model based on intensity of light and temperature was integrated over time and compared to the time-series data. While the mechanistic model broadly captured the overall growth trend, discrepancies remained between the model and data due to the model's simplicity and non-ideal behavior of real-world measurement. SINDy was applied to model the residual error by identifying an error derivative correction term. Addition of this SINDy-informed error dynamics term shows improvement to model accuracy while maint... [more]

Within an Industry 4.0 framework, a variety of new considerations are of increasing importance, such as securing processes against cyberattacks on the control systems or utilizing advances in image processing for image-based control. These new technologies impact relationships between process design and control. In this work, we discuss some of these potential relationships, beginning with a discussion of side channel attacks and what they suggest about ways of evaluating plant design and instrumentation selection, along with controller and security schemes, particularly as more data is collected and there is a move toward an industrial Internet of Things. Next, we highlight how the 3D computer graphics software tool set Blender can be utilized to analyze a variety of considerations related to ensuring safety of plant operation and facilitating the design of assemblies with image-based sensing.

The (bio-)pharmaceutical industry is facing crossroads in an effort to ramp up its global capacity, while working to meet net-zero targets and to ensure continuous drug supply. Beyond geopolitical challenges faced worldwide, (bio-)pharmaceutical processes have been historically very complex to design, optimise and integrate in a global distribution network that is resilient and adaptable to changes. In this paper we offer a perspective of how Process Systems Engineering (PSE) tools can support and advance (bio-)pharma practices with an outlook towards 3-fold sustainability. The latter is considering three main pillars, namely social (drug supply), economical and environmental sustainability. We discuss PSE contributions that have revolutionised process design in this space, as well as the optimisation of distributions networks in pharmaceuticals. We do this by means of example cases: one on model-based unit operation design and a second one on sustainable supply chain networks in the... [more]