Conference Agenda

Reducing our carbon emissions to or below zero must be our main objective to mitigate the impact of climate change and retain a liveable environment for the coming generations. Carbon capture and utilization or storage is a promising approach to achieve this goal [1]. Amine-based solvents are already used in industrial settings owing to their high capacity to absorb carbon dioxide (CO₂) from flue gases, combined with a relatively easy regeneration to release and store the captured CO₂. However, the regeneration of the CO₂-loaded solvent is highly energy intensive, leading to around 30% of a power plant’s energy being lost. Thus, there is a high demand for new amine(s) or amine blends that can lower process costs and energy requirements.

To explore the vast chemical and process design space of possible solvents and operating conditions, we previously developed an integrated algorithm to optimize solvent structures and process conditions [2]. However, the non-linear relationships between structure, properties, and process limit the level of detail that could be considered in the process models. In this work, we use machine learning surrogates to improve the process model while maintaining tractability.

To preserve the structure-property relationship and enable the optimization of the solvent structure, we replaced the flash calculations in both columns with a low-dimensional ANN. Starting with a well-known system (monoethanolamine, MEA), we achieve up to a 50% speed-up in the optimization process while converging to equivalent process conditions. We explore the robustness of the surrogate-based model to the choice of starting point, a common challenge when considering process optimisation.

Ultimately, this approach will serve as a starting point in the integrated molecular and process design to achieve a fast and robust convergence while preserving the ranking of optimal solvent candidates.

References

[1] M. Bui, C. S. Adjiman, A. Bardow, E. J. Anthony, A. Boston, S. Brown, P. S. Fennell, S. Fuss, A. Galindo, L. A. Hackett, J. P. Hallett, H. J. Herzog, G. Jackson, J. Kemper, S. Krevor, G. C. Maitland, M. Matuszewski, I. S. Metcalfe, C. Petit, G. Puxty, J. Reimer, D. M. Reiner, E. S. Rubin, S. A. Scott, N. Shah, B. Smit, J. P. M. Trusler, P. Webley, J. Wilcox, N. Mac Dowell, Carbon capture and storage (CCS): the way forward, Energy Environ. Sci., 11, 5 (2018)

[2] L. Lee, A. Galindo, G. Jackson, C. S. Adjiman, Enabling the direct solution of challenging computer-aided molecular and process design problems: Chemical absorption of carbon dioxide, Comput. Chem. Eng., 174 (2023)

The computer-aided mixture/blend design (CAM^bD) framework has been widely applied for solvent mixture design problems over the past decades. To obtain the optimal solvent mixture for a specified process, a mixed-integer nonlinear programming (MINLP) model is usually developed by incorporating various constraints, such as property prediction model, phase equilibrium equations, a phase stability check, and design constraints on process conditions and property values. Group-contribution methods, e.g. UNIFAC, SAFT-g Mie, are often used in the model building, but embedding such thermodynamic model equations can significantly increase the computational cost required to solve these problems to global optimality. In particular, including a phase stability check constraint normally involves embedding an optimisation problem, such as the plane distance criterion, thus leading to a bilevel optimisation formulation. This can be approximated with a local stability check based on the derivatives of the chemical potential, at the cost of adding further to the nonconvexity. To develop more tractable problem formulations, a classifier-based surrogate of the tangent plane distance criterion was proposed in our previous work. The approach has yielded an accurate and computationally manageable approximation. The method is applicable to a specific thermodynamic model (UNIFAC in our work) with a predefined solvent mixture set. However, it remains to be expanded to other models and mixtures.

The potential of machine learning for predicting thermodynamic properties has been widely investigated in recent years. Even though high accuracy has been achieved with machine learning models, they can be difficult to use in CAM^bD as the feasibility of the generated molecules is not guaranteed. To address this, the concept of group-contribution machine learning (GC-ML) models was proposed by adopting the functional groups of GC methods as the input features. This approach combines the benefits of reliable predictions from machine learning and of generation of feasible molecules from the group-contribution representation, and it could in principle be applied in design. In this work, we build on the GC-ML concept to develop a surrogate model for phase stability whose inputs consist of the groups present in the mixture and its composition and temperature. This leads to a more general approach in terms of the source for datasets (thermodynamic model or experimental data) and in terms of the solvents that can be modelled. The performance of such a model is evaluated in terms of accuracy and prediction statistics, using the UNIFAC groups to represent the mixture. The surrogate model is then embedded into an optimisation problem which maximises the solubility of an active pharmaceutical ingredient (API), with the UNIFAC model to predict the solubility. Molecular connectivity and feasibility constraints are also included to ensure that physically feasible molecules are generated while satisfying the overall constraints. The computational expense to solve this surrogate-based model is also found to be competitive with other approaches to solving solvent design problems.

Improving existing tools for process simulation and optimization is a critical task to enable the restructuring of the chemical industry toward sustainability. Recently, there has been an ascending trend toward coupling machine-learning models (i.e., surrogate models) and well-established mathematical programming techniques to optimize process simulations [1]. Such approaches can overcome known issues of simulation-optimization approaches, such as lack of analytical formulations, potentially noisy calculation, unconverged simulation, and high computation expenses.

Traditionally, process simulation surrogates can be generated at three levels of abstraction: system, unit, and property [2]. With the decreasing reference system complexity (from system- to property-wide), the mapping between input and output variables is expected to become simpler at the cost of potentially propagating surrogate modeling errors. Overall, optimizing the surrogate models is often easier than the original process simulation, yet selecting the appropriate surrogacy level and building accurate surrogates might become challenging.

Here, we propose an alternative method for building surrogates. In essence, we introduce the concept of open-loop plant surrogate building, i.e., replacing the whole system with all iterative calculations (e.g., recycles) turned off and converging the simulation using the surrogates. This alleviates the computationally intensive and failure-prone simulation problems listed above. Similar ideas have been considered in derivative-based optimization, where iterative calculations are added as constraints in the optimization problem [3]. Additionally, we propose using model-based adaptive sampling to enhance the performance of the open-loop surrogates to approximate closed-loop simulations by enforcing sampling near convergence. We use this quasi-closed-loop data to more accurately fit the objective functions and constraints from the process design problem with ReLU (rectified linear unit) neural networks. These are formulated as mixed-integer linear programming (MILP) problems through the OMLT Python package [4] and solved to global optimality.

The proposed open-loop surrogate modeling and optimization approach is applied to mathematical benchmark and sustainable chemical process design problems and compared with system-level and open-loop surrogates without active learning enhancement. We found that the larger datasets generated from the computationally cheaper (orders of magnitude) open-loop simulations lead to more accurate neural network surrogates. Adaptive sampling allowed tailoring data generation and modeling performance in regions closer to the converged simulation and consistently improved the optimization results across all case studies. Moreover, the values for the closed recycle given some simulation degrees of freedom can be accurately estimated using the surrogates. We conclude that avoiding the simulation iterative calculations in an open-loop surrogacy level jointly with adaptive sampling can improve surrogate modeling and be a promising alternative for automated chemical process design.

References

[1] A. Bhosekar and M. Ierapetritou, “Advances in surrogate based modeling, feasibility analysis, and optimization: A review,” Computers & Chemical Engineering, 108, 250–267, 2018.

[2] R. Misener and L. Biegler, “Formulating data-driven surrogate models for process optimization,” Computers & Chemical Engineering, 179, 108411, 2023.

[3] L.T. Biegler, I.E. Grossmann, and A.W. Westerberg, Systematic Methods of Chemical Process Design. Prentice Hall PTR, 1997.

[4] F. Ceccon et al., “OMLT: Optimization & Machine Learning Toolkit,” Journal of Machine Learning Research, 23, 349, 1–8, 2022.

Liquid-liquid extraction (LLX) is a crucial technique for the separation of mixtures that are susceptible to high temperatures, highly diluted, or exhibit azeotropic behavior (Sattler, 2012). Despite its widespread industrial application, the design and optimization of liquid-liquid extraction (LLX) processes remain challenging, especially due to kinetic phenomena, e.g. fluid dynamics and mass transfer limitations (Kampwerth et al., 2020). In contrast to distillation, where equilibrium-based (EQ-based) models with constant values for the height-equivalent to a theoretical stage (HETS) are well established and yield accurate results, the beforementioned phenomena in LLX systems can lead to a reduction in model accuracy. Non-equilibrium (NEQ) models, which provide a more detailed description of mass transport and fluid dynamics, offer a superior representation but are associated with a substantial increase in complexity. This results in the generation of highly nonlinear and non-convex optimization problems. Additionally, the necessary consideration of solvent recovery in a closed-loop process further increases the challenges for an optimization-based design. This complexity represents a significant obstacle to the frequent use of NEQ models in process optimization, particularly in the context of large-scale industrial applications.

To address these challenges, this work proposes an integrated approach that combines NEQ modeling with EQ-based superstructure optimization for a hybrid extraction-distillation process. The objective is to develop a more practical method for process optimization that captures the essential features of mass transfer and fluid dynamics in the LLX without the computational burden of full rate-based modeling throughout the entire design process. In the initial phase, an NEQ representation of an LLX column is employed to calculate HETS values specific to the selected solvent and contingent on the operational conditions, namely temperature and phase ratio (Kampwerth et al., 2022). Based on the generated data, HETS correlations are developed and incorporated into an EQ-based extraction-distillation superstructure model (Kruber et al., 2018), thereby enabling an accurate yet simplified representation of mass transport phenomena in combination with a rigorous closed-loop process optimization.

The efficacy of the proposed design approach is illustrated through its application to the separation of a diluted acetone-water mixture. The optimal process designs for a range of solvents are evaluated, with a particular focus on the specific HETS values. Furthermore, the method is benchmarked against a conventional superstructure optimization approach, which employs a constant HETS value across all solvents and operating conditions.

References

Kampwerth, J., Weber, B., Rußkamp, J., Kaminski, S., Jupke, A., 2020. Towards a holistic solvent screening: On the importance of fluid dynamics in a rate-based extraction model. Chem. Eng. Sci. 227, 115905.

Kampwerth, J., Roth, D., Polte, L., Jupke, A., 2022. Model-Based Simultaneous Solvent Screening and Column Design Based on a Holistic Consideration of Extraction and Solvent Recovery. Ind. Eng. Chem. Res. 61 (9), 3374–3382.

Kruber, K.F., Scheffczyk, J., Leonhard, K., Bardow, A., Skiborowski, M., 2018. A hierarchical approach for solvent selection based on successive model refinement. Comput. Aided Chem. Eng. 43, 325–330.

Sattler, K., 2012. Thermische Trennverfahren. John Wiley & Sons, Hoboken.

Global distribution of fusion power plants has the potential to provide a limitless supply of low-carbon energy and be revolutionary in tackling today’s climate crisis. Deuterium-Tritium (DT) fusion is currently the leading fusion reaction towards commercialisation of fusion power plants, being able to produce the highest energy output at the “lowest” temperature requirement [1]. In 2022, the National Ignition Facility in California achieved “net” energy production for the first time ever from their breakthrough DT fusion experiments [2]. Unfortunately, tritium - one of the two main feedstocks of this reaction - is a scarcely available, very expensive, and radioactive isotope of hydrogen, which introduces a series of additional feasibility and safety challenges into a commercial fusion power plant’s design.

The fusion fuel cycle is an essential component of a fusion power plant design. The fuel cycle is required to continuously recover unburnt tritium from a fusion reactor’s plasma exhaust gases, and safely recycle it back into the fusion reactor’s fuelling systems as a 50/50 molar mixture of deuterium and tritium with minimal impurities, including protium. Cryogenic distillation is a leading technology candidate for the separation and rebalancing of hydrogen isotope mixtures within the fuel cycle. Cryogenic distillation is advantageous for this application due to having a very high separation efficiency, being a well-established technology, and its design being easily scalable and adaptable for different fuel cycle requirements [3]. However, the main drawback of this technology is that the liquid hold-ups within the columns will contain very large inventories of tritium [4]. High tritium inventory within the fuel cycle is problematic for the feasibility and safety of fusion power plant operation. Therefore, accurate modelling of the fuel cycle, as well as quantification of the tritium inventory requirements, is an essential part of ensuring the feasibility of fusion power plant operation.

In this work, dynamic optimisation of the cryogenic distillation processes for hydrogen isotope separation was performed and an optimal control framework was proposed to minimise tritium inventory, without compromising on separation efficiency, under uncertainty. The effects of parameters such as the number of stages, side stream flow rates, condenser and boiler heat duties, feed location, etc were investigated. These optimization problems are complex and demand specialized optimization techniques. Mathematically, they are formulated as mixed-integer nonlinear programming (MINLP) problems and implemented using the General Algebraic Modelling System (GAMS). A key consideration in developing mathematical models for optimization-based design is the handling of uncertainty in the experimental data used for model development.

References:

1. ITER. WHAT IS ITER. ABOUT 2023; Available from: https://www.iter.org/proj/inafewlines.

2. The Indirect Drive, I.C.F.C., et al., Achievement of Target Gain Larger than Unity in an Inertial Fusion Experiment. Physical Review Letters, 2024. 132(6): p. 065102.

3. Day, C., et al., The pre-concept design of the DEMO tritium, matter injection and vacuum systems. Fusion Engineering and Design, 2022. 179: p. 113139.

4. Schwenzer, J., et al., Operational tritium inventories in the EU-DEMO fuel cycle. Fusion Science and Technology, 2022. 78(8): p. 664-675.