Rapid modelling of reactive transport in porous media using machine learning: limitations and solutions

TL;DR

This paper addresses the computational bottleneck in reactive transport simulations caused by per-grid-cell geochemical calculations. It evaluates a range of ML surrogates, finding that while one-shot predictions can be accurate, rollout stability requires physics-informed strategies; the authors demonstrate that simple, non-intrusive corrections—especially enforcing charge balance and selective re-running of the full geochemical solver—substantially improve rollout accuracy. The main contribution is a practical recipe: use an ML surrogate (XGBoost with a residual connection) together with physics-based constraints and careful dataset generation to achieve reliable, accelerated rollout simulations for a cation-exchange problem. The approach yields at least an order of magnitude speed-up and provides guidance for extending surrogate-based geochemical modules to more complex systems.

Abstract

Reactive transport in porous media plays a pivotal role in subsurface reservoir processes, influencing fluid properties and geochemical characteristics. However, coupling fluid flow and transport with geochemical reactions is computationally intensive, requiring geochemical calculations at each grid cell and each time step within a discretized simulation domain. Although recent advancements have integrated machine learning techniques as surrogates for geochemical simulations, ensuring computational efficiency and accuracy remains a challenge. This work investigates machine learning models as replacements for a geochemical module in a simulation of reactive transport in porous media. As a proof of concept, we test this approach on a well-documented cation exchange problem. While the surrogate models excel in isolated predictions, they fall short in rollout predictions over successive time steps. By introducing modifications, including physics-based constraints and tailored dataset generation strategies, we show that machine learning surrogates can achieve accurate rollout predictions. Our findings emphasize that even for a simple sorption equilibrium reaction (cation exchange problem), machine learning surrogates alone fail in predicting over successive time-steps. Incorporating simple physics-based modifications enables us to overcome this limitation. A detailed analysis of the limitations and potential mitigation strategies is presented in this work.

Figures (17)

• Figure 1: Coupling between the flow and transport simulator (IC-FERST) and the geochemical simulator (PHREEQC).
• Figure 2: Schematic of the cation exchange in a small portion of the porous space. The outflow from the schematic will be the inflow in the next portion of the domain in the next time step.
• Figure 3: Inputs and outputs of the geochemical reaction in the cation exchange problem. The reaction is performed for each grid cell at each time step.
• Figure 4: Two-dimensional domain and mesh used to represent the cation exchange problem (as in yekta:21reactive). We show a snapshot in time of the concentration of K+.
• Figure 5: Cation exchange results generated by the coupling between IC-FERST and PHREEQC.