Adaptive Time-Stepping and Machine Learning Approach for Pore-Scale Reactive Transport Simulations

Pore-scale reactive transport simulations are typically computationally very expensive, which limits their application to complex heterogeneous systems. To solve the computational bottleneck, an adaptive time-stepping algorithm is developed and combined with machine learning-derived surrogate models for geochemical calculations. The time-step is adapted by monitoring the evolution of the diffusion field and the precipitation reactions and by exploiting intermediate stationary states of the system. The algorithm is benchmarked on a system relevant to cement-claystone interaction with the geochemical reaction being the precipitation of Calcium-Silicate-Hydrates (C-S-H) in the pore space of a claystone. The precipitation of C-S-H is modeled as a solid solution, and it is possible to calculate and trace the local Ca/Si ratio of C-S-H, as well as the local amount of gel porosity. In the reactive transport simulations presented here, the geochemical surrogate models alone lead to acceleration factors of up to two orders of magnitude. The adaptive time-stepping algorithm leads to an additional acceleration of three to five orders of magnitude maintaining the relative deviation below 2%. The overall combined acceleration is demonstrated to be six to seven orders of magnitude having a profound impact and opening new computational avenues. Supplementary Information: The online version contains supplementary material available at https://doi.org/10.1007/s11242-026-02287-4.