Conference Agenda

A Digital Twin (DT) is a digital representation of a physical entity that employs data, algorithms, and software to enhance operations, forecast failures, and evaluate new designs through the simulation of real-world scenarios (Attaran et al., 2023). DTs have the potential for real-time monitoring, simulation, and optimization. However, traditional DTs often rely on mechanistic models (Bárkányi et al., 2021). These mechanistic models are complex because of their non-linearity, imposing time and budget constraints (Beisheim et al., 2019). This results in challenges of high computational demands, complex model structures, and slow response time, making the DTs, both complex and resource-intensive. Surrogate models, on the other hand, are the simplified approximations of more complex, higher-order models. These approximations are typically constructed using data-driven approaches, such as Random Forest Regression (Garg et al., 2023), facilitating faster simulations and simpler deployment.

This study aims to analyze the complexity of mechanistic and surrogate modeling approaches in the context of DTs to aid in model selection. A model with reduced complexity is capable of improving computational efficiency, simplifying implementation and maintenance, and enabling ease in real-time monitoring and predictive maintenance. To improve the performance of DTs by selecting a less complex model, a complexity analysis is necessary. This involves evaluating complexity metrics including analytical, structural, space, behavioral, training, and prediction complexity. By assigning complexity scores to models, an overall complexity score can be determined, helping to identify the most suitable model. Using a centrifugal pump as a use case, the mechanistic model is compared to a surrogate model to quantify complexity scores and select a less complex model for DT development.

Future work will focus on accuracy analysis and data augmentation to enhance the framework with additional model selection metrics. The developed complexity evaluation framework can be applied to complex DTs of entire process plants, enabling the identification of components that can be effectively modeled using surrogate models for enhanced efficiency, as well as those that require detailed mechanistic models for greater accuracy and precision.

References

Attaran, M., Attaran, S., Celik, B.G., 2023. The impact of digital twins on the evolution of intelligent manufacturing and Industry 4.0. Advances in Computational Intelligence 3, 11. https://doi.org/10.1007/s43674-023-00058-y

Bárkányi, Á., Chován, T., Németh, S., Abonyi, J., 2021. Modelling for Digital Twins—Potential Role of Surrogate Models. Processes 9. https://doi.org/10.3390/pr9030476

Beisheim, B., Rahimi-Adli, K., Krämer, S., Engell, S., 2019. Energy performance analysis of continuous processes using surrogate models. Energy 183, 776–787. https://doi.org/10.1016/j.energy.2019.05.176

Garg, A., Mukhopadhyay, T., Belarbi, M.O., Li, L., 2023. Random forest-based surrogates for transforming the behavioral predictions of laminated composite plates and shells from FSDT to Elasticity solutions. Composite Structures 309, 116756. https://doi.org/10.1016/j.compstruct.2023.116756

In chemical production processes, some crucial variables are often difficult to measure in real time through instrumentation, necessitating soft sensing techniques. Data-driven models, such as neural networks, have been widely applied in soft sensing scenarios due to their strong fitting capabilities. However, these models often suffer from limitations such as poor interpretability and limited extrapolation capability, primarily due to their lack of process-specific domain knowledge. This study addresses these challenges by proposing a hybrid modeling approach that integrates mechanistic models into neural network frameworks, with the distillation unit serving as a case study. First, an equilibrium stage model was selected as the mechanistic model, incorporating Murphree efficiency to correct model deviations. Next, parameter estimation of Murphree efficiency was performed using the training dataset, targeting the soft-sensing objective within the equilibrium stage model. Based on the relationship between Murphree efficiency and the column hydraulics, a first-tier network model was developed to predict Murphree efficiency. Subsequently, the estimated Murphree efficiency was used in the equilibrium stage model to produce low-precision soft-sensing results, which were then fed as inputs to a second-tier network model that provided the final soft-sensing predictions. This methodology was applied to an actual distillation system for phenylenediamine, yielding favorable results that demonstrated the applicability of the proposed hybrid model. The integration of mechanistic knowledge within the neural network not only improved predictive accuracy but also enhanced the model's interpretability and robustness in a complex production environment.

Ammonia nitrogen from domestic and industrial wastewater can lead to eutrophication, water pollution, and oxygen depletion in aquatic systems when released into the environment without any post-treatment. The removal of ammonia nitrogen from wastewater is particularly challenging and energy-intensive since it requires specialized treatment processes such as biological approaches. These technologies are known to face challenges due to the high sensitivity of microorganisms to environmental changes as well as the need for large areas and significant infrastructure [1]. Recently, alkaline electrolyzers for removing ammonia from aqueous solutions have been investigated. Electrolyzers are compact systems that enhance space efficiency and reduce the use of chemicals, leading to cost savings and a decreased environmental impact. However, due to their direct reliance on electricity, electrolyzers still have high energy consumption and incur substantial electricity costs.

To tackle this problem, we suggest a novel electrolyzer-pressure retarded membrane distillation (E-PRMD) process. The PRMD process is designed to simultaneously produce water and electricity, while the electrolyzer removes ammonia nitrogen and produces hydrogen [2]. The electrical energy produced by the PRMD can power the alkaline electrolysis, resulting in a more economically efficient integrated process. A mathematical model was developed for the E-PRMD process, incorporating reaction kinetics, mass and energy balances. Each unit model was validated using experimental results to ensure accurate model predictions. The developed model for the ammonia electrolyzer was used to predict the amounts of N₂ and H₂ gas generation rate at each cathode and anode side, which were then used to assess the ammonia removal rates and impurities. The percentage of impurities in the produced hydrogen by the E-PRMD ranges from 0.1% to 3%, depending on the operating current density of 0 to 5 kA/m². Furthermore, simulation results show that an optimal flow rate exists in terms of maximum net energy density, while the average water flux increases as the feed flow rate in the PRMD system increases.

Therefore, the E-PRMD system, which combines the two systems, not only removes ammonia nitrogen from wastewater but also enhances energy efficiency through the additional electrical energy generated. The additional production of hydrogen and high-quality freshwater further underscores the multi-functionality of the E-PRMD system. Using the developed model for the integrated system, further variations in the process configurations will be explored to investigate the interactions between the PRMD and electrolyzer systems under a wide range of operating conditions. This will allow us to identify the key variables in maximizing ammonia removal, hydrogen production, and energy production through the integrated E-PRMD process.

References

1. Y. Dong, H. Yuan, R. Zhang, N. Zhu, Removal of ammonia nitrogen from wastewater: A review, Trans ASABE 62 (2019).

2. K. Park, D.Y. Kim, D.R. Yang, Theoretical Analysis of Pressure Retarded Membrane Distillation (PRMD) Process for Simultaneous Production of Water and Electricity, Ind Eng Chem Res 56 (2017).

Increasing global demand for bio-based products requires development of efficient bioprocesses that achieve techno-economic feasibility at scale. To achieve this, biopharmaceutical industries have been using model-based methods to understand and control the process. Depending on the available amount of prior process knowledge and the quantum of data, a spectrum of process modelling techniques ranging from purely statistical to purely mechanistic can be used. Purely mechanistic models suffer from the curse of dimensionality, as the amount of data required to fit the model increases exponentially with an increase in parameters to describe the biological phenomena. On the other hand, purely data-driven techniques demonstrate poor performance at low data availability and often fail to provide understanding of the process. Hybrid modelling strategies that combine mechanistic models with data-driven approaches to reap the benefits of both paradigms are receiving much attention¹. In this study, we explore a new hybrid modelling framework that combines metabolic networks with latent variable models to provide understanding about the metabolic state of the cells and demonstrate the ability of the framework to predict the time evolution of microalgal growth dynamics in photoautotrophic regime.

Latent variable models are a class of data driven models that assume a latent structure in the provided data to model the posterior distribution of the observed data. In this study, we use multi-dimensional microalgal growth data to model the distribution of the latent space that is mechanistically mapped to the metabolic state. One key advantage of latent variable models is the ability to generate data (x) from the latent space (z) by modelling the conditional likelihood p(x | z). This methodology has been applied on other scientific fields for anomaly detection and understanding underlying behavior.

The latent variable is connected to the mechanistic model through a reduced metabolic network. DRUM (dynamic reduction of unbalanced metabolism) is a metabolic modelling framework that can address intracellular metabolite accumulation by dividing the complete metabolic network into subnetworks within which the quasi-steady state assumption is valid. This allows us to construct a structured mechanistic model of microalgal growth in the form of ODEs which operate with relatively limited number of variables².

In this study, we combine a structured model describing microalgal growth in a photobioreactor with various kinds of latent variable models to construct hybrid models that can accurately predict the growth profile of various state variables. We also explore the potential of these models in describing complex metabolic effects observed in photoautotrophic regime, eg. night biomass loss and the diurnal cycle. Future work will explore the usability of these models in process optimization and scale up.

References:

1. Solle D, Hitzmann B, Herwig C, et al. Between the Poles of Data-Driven and Mechanistic Modeling for Process Operation. Chem Ing Tech. 2017;89(5):542-561. doi:10.1002/cite.201600175

2. Baroukh C, Muñoz-Tamayo R, Steyer JP, Bernard O. DRUM: A New Framework for Metabolic Modeling under Non-Balanced Growth. Application to the Carbon Metabolism of Unicellular Microalgae. PLOS ONE. 2014;9(8):e104499. doi:10.1371/journal.pone.0104499

The call to reduce industrial CO₂ emissions has driven the development of advanced CO₂ capture and utilisation technologies, with electrochemical CO₂ reduction (eCO₂R) standing out for its ability to convert CO₂ into various fuels and chemicals. A promising solution for industrial decarbonisation is the synthesis of green methanol (MeOH) from CO₂ and renewable energy. However, the development of eCO₂R technology for green methanol production is only at the laboratory stage, making it difficult to cope with large-scale industrial production situations, especially in the development of CO₂ electrolysers, process design, system optimsation, economic analysis and environmental assessment Therefore, it is important to compare different green MeOH production routes based on different system configurations to explore their performance, economic feasibility and environmental sustainability.

A comparative assessment is conducted on various green MeOH synthesis routes using direct air-captured (DAC) CO₂ and renewable energy sources, focusing on the technology readiness for near-future deployment. This work provides an overview of techno-economic analysis (TEA) and life-cycle analysis (LCA) over the fossil-fuel based conventional process. Four models were designed and analyzed, including (1) one-step electrochemical conversion of CO₂ into MeOH, (2) two-step MeOH synthesis from H₂O electrolysis to produce H₂ followed by CO₂ hydrogenation, and (3) three-step synthesis i.e., H₂O electrolysis to produce H₂, CO₂ electrolysis to produce CO, followed by hydrogenation of CO₂ and CO. In addition, a conventional methanol synthesis route using natural gas reforming is set as a benchmark. The surrogate models for H₂ and CO₂ electrolysers, developed in MATLAB, are integrated into the main processes modelled in Aspen Plus. We set the operating temperature and pressure of methanol reactor to 250 °C and 70 bar respectively. Response surface methodology (RSM) is employed to obtain the surrogate models that characterise the effects of operating temperature, cell voltage, and CO₂ residence time on current density, Faraday efficiency (FE), and single-pass conversion in H₂ and CO₂ electrolysers. Four key process metrics are selected to evaluate the economic feasibility of a green methanol synthesis technology versus a commercial baseline of natural gas to methanol, including levelised cost of methanol (LCOM), levelised amount of CO₂ consumed, energy efficiency, and technology readiness level (TRL). The levelised CO₂ consumed for conventional route is 1.63 kg CO₂ per kg MeOH produced,which ranges from 1.88 to 2.35 CO₂ per kg MeOH produced in the other three cases. Compared to the unit methanol production cost of $0.77 per kg MeOH produced from fossil fuel-based processes, the one-step methanol production method, with a cost of $0.69 per kg MeOH produced is more economically feasible despite its relatively low single-pass conversion and energy efficiency. The three-step green methanol synthesis (Case 3) demonstrates comparatively improved performance, with a levelised cost of methanol (LCOM) of $0.64 per kg MeOH produced, a levelised CO₂ consumption of 2.13 kg CO₂ per kg MeOH produced, and a levelised cost of renewable electricity (LCOE) of 6.78 kWh per kg MeOH produced.

Oscillatory baffled reactors (OBR) are attracting attention for their process intensification effects, such as high mixing performance at low flow rates and long residence time due to the vortices generated by the interaction between the oscillating flow and the baffles. The oscillatory Reynolds number (Reo) is dimensionless parameter for design of the OBR. On the other hand, when frequency and amplitude differ with the same Reo number, it has showed that the difference influence the flow pattern inside the reactor and behavior of the reaction process in our previous studies. Although it is well known that computational fluid dynamics simulations are effective in designing the internal structure of process equipment, there is a problem in that calculations for unsteady processes require a high computaional load.

Therefore, we came up with application of machine learning using data for flow visualization as a method for predicting unsteady flow patterns. In this study, we investigated methods for dynamic analysis of spatiotemporal data acquired by Particle Image Velocimetry (PIV) to determine inputs and outputs for neural network model. The proper orthogonal decomposition (POD) is a numerical method that enables a reduction in the complexity of computer intensive simulations such as computational fluid dynamics. In order to investigate applicability of POD to dynamic analysis of oscillatory flow patterns, we collected PIV measurement data under conditions of low Reo from 40 to 762. The amplitude of oscillation was varied in the range of 5 to 15 mm.

In the POD analysis of time-series data of velocity vectors in a flow field, the eigenvalues ​​of the covariance matrix calculated from the data matrix are sorted in descending order, and the eigenvector for each eigenvalue is called “Mode”. As a result of POD analysis of the above-mentioned collected data, the cumulative contribution rate of Modes 1 to 3, which have the largest contribution rate, was about 80%. When Reo was 762 and the amplitude was 5 mm, the periodic time-variation of the mode coefficients was seen for the three modes. It was found that the flow pattern for Mode 1 represents profile of vertical flow and the flow pattern for Mode 2 represents profile of generation of vortices in the upper and lower parts.

Next, we developed the multi-layered neural network model with three outputs of Mode 1 – 3 that were extracted above. In the modeling, Reo, amplitude, frequency, velocity ratio for oscillatory flow and local velocity vectors were set as inputs. When traing was implemented by changing the number of hidden layers from 1 to 10 and the number of hidden nodes from 3 to 96, results with high predictive performance were obtained for the generation, size, and movement of vortices. On the other hand, poor predictive performance was observed when Reo was lower. Hence, it was demonstrated that three sets of modes and mode coefficients extracted by the POD could be useful for dynamic analysis and prediction of time-variant flow pattarens in OBR that was operated under low Reo.