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Abstract <p>This study presents a physics-informed neural networks (PINNs) 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. The proposed methodology sequentially addresses the flow and diffusion–reaction subproblems. The flow field is computed using a mixed formulation, while the diffusion–reaction system is modeled via two uncoupled tensorial diffusion equations reformulated in terms of chemical invariants. PINNs are employed to solve the governing equations, enabling data-efficient, mesh-free prediction of chemical concentration fields. The framework is validated through a series of benchmark problems involving flow in heterogeneous porous media. Initial verification is conducted using patch tests for the flow field, followed by validation of the transport problem with emphasis on preserving non-negativity of concentrations. The complete fast bimolecular reaction scenario is then solved, yielding spatial distributions of reactants and product species. Results demonstrate that the PINNs-based approach effectively captures sharp, mixing-limited reaction fronts and dispersive mixing behavior, offering reliable predictions of reactive plume evolution. These capabilities are crucial for evaluating long-term subsurface behavior in applications such as fluid storage, energy extraction, and efficient extraction of critical minerals.</p> Graphical Abstract <p>Figure (A) shows the velocity field, with arrows indicating variations in direction and magnitude typical of an <i>in situ</i> 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. </p>

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

  • 期刊论文

  • 发表日期：

    2026年3月13日

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  • Kripa Adhikari,
  • Md. Lal Mamud,
  • Maruti Kumar Mudunuru,
  • Kalyana B. Nakshatrala

摘要

Abstract

This study presents a physics-informed neural networks (PINNs) 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. The proposed methodology sequentially addresses the flow and diffusion–reaction subproblems. The flow field is computed using a mixed formulation, while the diffusion–reaction system is modeled via two uncoupled tensorial diffusion equations reformulated in terms of chemical invariants. PINNs are employed to solve the governing equations, enabling data-efficient, mesh-free prediction of chemical concentration fields. The framework is validated through a series of benchmark problems involving flow in heterogeneous porous media. Initial verification is conducted using patch tests for the flow field, followed by validation of the transport problem with emphasis on preserving non-negativity of concentrations. The complete fast bimolecular reaction scenario is then solved, yielding spatial distributions of reactants and product species. Results demonstrate that the PINNs-based approach effectively captures sharp, mixing-limited reaction fronts and dispersive mixing behavior, offering reliable predictions of reactive plume evolution. These capabilities are crucial for evaluating long-term subsurface behavior in applications such as fluid storage, energy extraction, and efficient extraction of critical minerals.

Graphical Abstract

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.