Machine Learning Methods Based Prediction of Breakthrough Curves in Reactive Porous Media from Peclet and Damköhler Numbers

Mathematical models of reactive flows in porous media are fundamental to a wide range of industrial, environmental and biomedical applications. Reactions occur at the pore scale, where it is often not possible to measure them directly. It is therefore important to establish correlations between microscale process parameters and macroscale measurements. Breakthrough curves, which represent the concentration of species at the flow outlet as a function of time, are key to parameter identification and optimization. Despite advances in pore-scale simulation algorithms, 3D computations remain time-consuming, making it difficult to solve inverse and optimal control problems. Machine learning and tensor methods, including Gaussian processes, neural networks and cross approximation, have shown promise in predicting breakthrough curves for 1D and 3D cases. This paper explores the use of machine learning methods to create surrogate models for convection- and diffusion-dominated regimes of 3D pore-scale reactive flow in (Peclet, Damköhler) parameter space. We show that regime-specific surrogate models are advantageous and extend the experiments to piecewise constant inlet concentrations. Our computational experiments, inspired by catalytic filter applications, are carried out using 3D geometries generated by specialized software, and conclude with a discussion of the performance of each method in different flow regimes.