Conference Agenda

Nucleophilic aromatic substitutions (SNAr) are crucial in medicinal and agrochemistry, especially for modifying pyridines, pyrimidines, and related heterocycles [1]. Identifying reliable, broadly applicable, and high-yielding methods for generating SNAr products remains a significant challenge, particularly at a process scale, due to high reagent costs, the need for elevated temperatures and extended reaction times, poor functional group tolerance, and strict water exclusion requirements [2]. In addressing these challenges, kinetic models play a vital role in providing a deep understanding of reaction mechanisms, which can facilitate the scale-up, optimisation and control of SNAr reactions [3].

Identifying a reliable kinetic model requires confirming the correct model structure before parameter estimation and validation. Conventional model-building approaches require the definition of pre-determined candidate model structures [4]. However, the reaction mechanism of SNAr—whether concerted or two-step—cannot be precisely confirmed, as it depends on the substrate, nucleophile, leaving group, and reaction conditions. This uncertainty makes it difficult to establish the exact mathematical form of the kinetic model [1].

We employ a DoE-SINDy [5] to address these challenges, allowing for generative modelling without a complete theoretical understanding. The benchmark case study involved the nucleophilic aromatic substitution (SNAr) of 2,4-difluoronitrobenzene with morpholine in ethanol (EtOH), producing a mixture of the desired ortho-substituted product, along with para-substituted and bis-adduct side products, formed through parallel and consecutive steps. In-silico measurements were generated using a ground-truth kinetic model, validated by Agunloye et al. [6], to investigate the performance of DoE-SINDy under various measurements conditions, including different noise levels and sampling intervals. Results show that the ‘true’ kinetic model for the SNAr reaction was successfully identified in a limited number of runs, and the DoE-SINDy framework allowed to quantify the effect of DoE factors, such as inlet concentrations, residence time and experimental budget on the performance of DoE-SINDy in model identification.

References

[1] Rohrbach, S., Smith, A. J., Pang, J. H., Poole, D. L., Tuttle, T., Chiba, S., & Murphy, J. A. (2019). Concerted Nucleophilic Aromatic Substitution Reactions. Angewandte Chemie International Edition, 58(46), 16368–16388.

[2] See, Y. Y., Morales-Colón, M. T., Bland, D. C., & Sanford, M. S. (2020). Development of SNAr Nucleophilic Fluorination: A Fruitful Academia-Industry Collaboration. Accounts of Chemical Research, 53(10), 2372–2383.

[3] Hone, C. A., Boyd, A., O’Kearney-Mcmullan, A., Bourne, R. A., & Muller, F. L. (2019). Definitive screening designs for multistep kinetic models in flow. Reaction Chemistry & Engineering, 4(9), 1565–1570.

[4] Asprey, S. P., & Macchietto, S. (2000). Statistical tools for optimal dynamic model building. Computers & Chemical Engineering, 24(2–7), 1261–1267.

[5] Lyu, W., & Galvanin, F. (2024). DoE-integrated Sparse Identification of Nonlinear Dynamics for Automated Model Generation and Parameter Estimation in Kinetic Studies. Computer Aided Chemical Engineering, 53, 169–174.

[6] Agunloye, E., Petsagkourakis, P., Yusuf, M., Labes, R., Chamberlain, T., Muller, F. L., Bourne, R. A., & Galvanin, F. (2024). Automated kinetic model identification via cloud services using model-based design of experiments. Reaction Chemistry & Engineering, 9(7), 1859–1876.

Lithium-metal batteries (LMBs) are a promising alternative to lithium-ion batteries (LIBs) for energy storage applications due to their high theoretical capacity (3,860 mAh g⁻¹ for lithium metal vs. 372 mAh g⁻¹ for graphite) and low electrochemical potential (-3.404 V vs. SHE) [1, 2]. However, their practical use is limited by poor cycle stability and safety concerns, such as short circuits or explosions during prolonged use. A significant challenge is the instability of the solid electrolyte interphase (SEI) layer, which cracks during repeated lithium deposition and stripping. These cracks enable dendrite growth, leading to further SEI formation and depletion of active lithium [3]. Additionally, as dendrites are stripped during discharge, some become electrochemically inactive, forming "dead lithium." This dead lithium reduces the effective diffusion coefficient, hindering lithium-ion movement and degrading the overall performance of LMBs [4]. Nevertheless, very few studies have addressed these issues in a mathematical modeling context in contrast to LIBs. To bridge this gap, we develop an LMB model based on the Doyle-Fuller-Newman (DFN) model [5] on COMSOL Multiphysics. The key difference from the conventional DFN model is that we model the lithium-metal electrode by considering only the electrode surface. We also express the effective diffusion coefficient as a function of the amount of dead lithium, which captures the tortuous pathways of lithium ions in the electrolyte. We simulate the dynamic behavior of LMBs and interpret the capacity loss over repeated cycles. We validate the model by comparing predicted voltage-capacity curves and cycle retention results with our experimental data from a Li/NMC-811 coin cell, demonstrating its ability to simulate degradation phenomena accurately.

1. Hao, F., A. Verma, and P.P. Mukherjee, Mechanistic insight into dendrite-SEI interactions for lithium metal electrodes. Journal of Materials Chemistry A, 2018. 6(40): p. 19664-19671.

2. Liu, G.Y. and W. Lu, A Model of Concurrent Lithium Dendrite Growth, SEI Growth, SEI Penetration and Regrowth. Journal of the Electrochemical Society, 2017. 164(9): p. A1826-A1833.

3. Mao, M.L., et al., Anion-enrichment interface enables high-voltage anode-free lithium metal batteries. Nature Communications, 2023. 14(1).

4. Chen, K.H., et al., Dead lithium: mass transport effects on voltage, capacity, and failure of lithium metal anodes. Journal of Materials Chemistry A, 2017. 5(23): p. 11671-11681.

5. Doyle, M., T.F. Fuller, and J. Newman, Modeling of Galvanostatic Charge and Discharge of the Lithium Polymer Insertion Cell. Journal of the Electrochemical Society, 1993. 140(6): p. 1526-1533.

An essential problem in precision agriculture is to accurately model and predict root-zone (top 1 m of soil) soil moisture profile given soil properties and precipitation and evapotranspiration information. This is typically achieved by solving agro-hydrological models. Nowadays, most of these models are based on the standard Richards equation (RE) [1], a highly nonlinear, degenerate elliptic-parabolic partial differential equation that describes irrigation, precipitation, evapotranspiration, runoff, and drainage through soils. Recently, the standard RE has been generalized to time-fractional RE by replacing the first-order time derivatives with any fractional order between 0 and 2 [2]. Such generalization allows the characterization of anomalous soil exhibiting non-Boltzmann behavior due to the presence of preferential flow.

This work addresses the pressing issue of inverse modeling of time-fractional RE; that is, how to accurately estimate the fractional order and soil property parameters of the fractional RE given soil moisture content measurements. Inverse problems are generally ill-posed due to insufficient and/or inaccurate measurements, thereby posing significant computational challenges. In this work, we propose a novel Bayesian variational autoencoder (BVAE) framework that synergistically integrates our in-house developed physics-based, data-driven global random walk (DRW) fractional RE solver [4] and adaptive Fourier decomposition (AFD) [6] to accurately estimate the parameters of time-fractional RE. Our proposed BVAE framework consists of a probabilistic encoder, latent-to-kernel neural networks and convolutional neural networks. The probabilistic encoder projects the input data (i.e., soil moisture measurements) to a latent space. To preserve useful mathematical properties and physical insights, we further restrict the latent space to its reproducing kernel Hilbert space (RKHS) via the use of latent-to-kernel neural networks. The AFD-based convolutional neural networks are applied to the resulting RKHS as decoder for parameter estimation. These neural networks are trained end-to-end, in which the training data are soil moisture profiles produced by our DRW fractional RE solver. The entire BVAE framework is theoretically justified and explainable using the AFD theory, a novel signal processing technique that achieves superior computationally efficiency. Through illustrative examples, we demonstrate the efficiency and reliability of our BVAE framework.

References

[1] L.A. Richards, Capillary conduction of liquids through porous mediums, Physics, 1931, 1(5): 318-333.

[2] Ł. Płociniczak, Analytical studies of a time-fractional porous medium equation: Derivation, approximation, and applications, Communications in Nonlinear Science and Numerical Simulation, 2015, 24(1-3): 169-183.

[3] M.T. Van Genuchten, A closed‐form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Science Society of America Journal, 1980, 44(5): 892-898.

[4] Z. Song, Z. Jiang, A Novel Data-driven Numerical Method for Hydrological Modeling of Water Infiltration in Porous Media, arXiv preprint arXiv:2310.02806, 2023.

[5] D.P. Kingma, M. Welling, Auto-encoding variational bayes, arXiv preprint arXiv:1312.6114, 2013.

[6] W. Qian, W. Sprößig, J. Wang, Adaptive Fourier decomposition of functions in quaternionic Hardy spaces, Mathematical Methods in the Applied Sciences, 2012, 35(1): 43-64.

The electrification of chemical processes is known to have great potential to reduce global carbon dioxide emissions. Conventional combustion units, which emit large amounts of carbon dioxide in the process of reaching chemical equilibrium, can particularly benefit from electrification. Additionally, the utilisation of CO₂ emitted in the industrial and energy sectors can be used for the sustainable production of carbon-based chemicals. This can be achieved by various catalytic reactions, one of which is the reverse water-gas shift (RWGS) reaction, where CO₂ reacts with hydrogen to be converted into synthesis gas ^[1].

In this study, we develop a computationally efficient simulation approach for an electrified reverse water gas shift reactor and compare it with experimental results for model validation. The washcoat catalyst allows us to attain relatively uniform temperature across the catalyst which reduce the possibility of coke formation. However, its suboptimal mass transfer efficiency requires system optimisation. Many studies on electrified reactors use computational fluid dynamics (CFD), which requires large computational resources and calculation time. This makes CFD modelling methods inappropriate for optimisation that requires iterative calculations. Hence,we build a computationally efficient simulation workflow by combining two-dimensional (2D) mass and energy balances and a one-dimensional (1D) kinetic model. Reactions are applied as a source term in the mass balance model to the reactor walls, where the catalyst is assumed to be located. This is done by assuming a zero washcoat thickness (ZWT) model for rapid computation with reasonable accuracy. Most of the studies consider the physical thickness of the catalyst, which produces precise results but requires three computational domain (gas, catalyst and reactor wall) while ZWT model requires two (gas and reactor wall) ^[2].

The model was validated through two experiments. The first involved a dry run of the joule heating furnace and the second was a packed bed reaction. Experimental data were employed to fit the boundary heat flux in the energy balance model, as well as the pre-exponential factor and activation energy of the reaction kinetics. As a results, axial temperature profile appears as a parabolic form in the dry run simulation. After applying reactions, a distorted temperature profile appear due to the heat of the reaction and the diffusion of product from the washcoat to gas phase can be obseved. Furthermore, we reduce the calculation time from 20 minutes to 3 minutes compared to the CFD simulation due to the absence of catalyst domain calculation. These results demonstrate that our simulation methodology provides fast and accurate outcome, indicating its potential to be used as a platform for optimisation or control simulations. In future study, this model will be used to propose operating condition and reactor design to maximise the syngas production and minimise energy consumption.

Reference

[1] Thor Wismann, Larsen KE, Mølgaard Mortensen. Electrical Reverse Shift: Sustainable CO₂ Valorisation for Industrial Scale. Angew Chem Int Ed. 2022

[2] Michael J. Stutz, Dimos Poulikakos Optimum washcoat thickness of a monolith reactor for syngas production by partial oxidation of methane. Chem Eng Sci. 2008