Reactive Transport Modeling with Physics-Informed Machine Learning for Critical Minerals Applications

TL;DR

A physics-informed neural network framework for reactive transport modeling for simulating fast bimolecular reactions in porous media is presented for simulating fast bimolecular reactions in porous media.

Abstract

This study presents a physics-informed neural network (PINN) framework for reactive transport modeling for simulating fast bimolecular reactions in porous media. Accurate characterization of chemical interactions and product formation in surface and subsurface environments is essential for advancing critical mineral extraction and related geoscience applications.

Figures (16)

• Figure 1: Figure (A) shows the velocity field, with arrows indicating variations in direction and magnitude typical of an in situ leaching scenario. Flow through heterogeneous media creates channeling and recirculation zones that strongly affect reagent transport and mixing. (B) depicts the plume of product C (e.g., a metal–ligand complex) formed by a fast bimolecular reaction between reactants A (e.g., acid donor) and B (e.g., complexing agent). Concentrations are predicted using physics-informed neural networks (PINNs). The plume starts at the left boundary, where reactants enter, and sharpens moving right. Capturing these mixing-limited fronts is key to optimizing reagent injection, maximizing critical mineral extraction/recovery, and minimizing reagent use and by-products.
• Figure 1: Subsurface mass and reactive-transport for critical minerals and materials: The figure illustrates a range of scenarios involving fluid (gas and liquid) flow and transport within the Earth's subsurface---one of the largest porous media for fluid flow. The figure showcases various subsurface processes, including groundwater movement, renewable energy systems such as geothermal energy, geologic carbon storage, and reactive transport. The mineral phases can be clays, carbonates, Fe/Mn oxides, phosphates, and silicates. For instance within the critical mineral context cantrell1987rare, this may include $\text{Clay--Na} + \text{Li}^+ \rightarrow \text{Clay--Li} + \text{Na}^+$ or $\text{REE}^{3+} + \text{CO}_3^{2-} \rightarrow \text{REECO}_3^{+}$ within a much bigger multi-step reaction settings. This reaction focuses on a bimolecular complexation step in which a rare earth element (REE) forms a 1:1 carbonate complex in aqueous solution, commonly observed in alkaline or carbonate-rich environments.
• Figure 2: Modeling evolution: The figure illustrates the progression of modeling approaches over time. It begins with basic assumptions and advances to curve fitting. With the deeper understanding of physics and mechanics, simulation and computational mechanics emerged. Eventually, with the advent of advanced programming languages, data-driven and physics-informed machine learning has experienced significant growth.
• Figure 3: PINNs framework: The figure depicts the PINNs framework, which consists of a neural network (NN) structure and a physics-informed component. The input variables are processed through the NN to generate output variables. These outputs are evaluated against the governing equations of the system, including the PDE and boundary conditions. Residual losses are computed, and the weighted sum of these losses determines the total loss. If the total loss reaches its optimal minimum, the training concludes. Otherwise, the hyperparameters are updated based on the specified learning rate, and training continues until the maximum number of epochs is reached.
• Figure 4: Problem setup: The figure depicts the setup of the reaction subproblem within a square domain (or reaction tank) of dimensions $L_x$ and $L_y$, and the boundary $\partial\Omega$. The left boundary is prescribed with the concentration of chemical A in the upper half and chemical B in the lower half, as illustrated, while the remaining boundaries are subjected to zero flux $v_i ^\mathrm{p}(\mathbf{x})$. $f_i(\mathbf{x})$ is the volumetric source. The subscript $i$ denotes different chemical species considered in this study: A, B, and C.