Recent advances on the numerical modeling and simulation of nanoparticle-assisted CO₂ enhanced oil recovery

Nanoparticle-assisted CO₂ flooding is a promising enhanced oil recovery (EOR) technique that also sequesters carbon, but its complex multiscale physics and chemistry pose challenges for modeling. This paper reviews and analyzes numerical simulation methods and theoretical modeling approaches used to study nanoparticle-assisted CO₂ enhanced oil recovery (NPs-CO₂-EOR). It presents flow regimes including laminar flow, Darcy's law, multiphase flow and foundational models for nanoparticle transport in porous media, explores chemical and physical interactions at multiple scales, and outlines the mechanisms by which nanofluids enhance oil recovery. The study discusses both macroscopic and microscopic simulation techniques including Darcy-based transport equations, chemical reaction equilibrium modeling, computational fluid dynamics (CFD), and molecular dynamics simulations. Numerical results and case studies are highlighted to demonstrate model effectiveness in predicting oil recovery and reservoir behavior. Special attention is given to recent advances in machine learning (ML) and hybrid physics-ML modeling, which have been employed to accelerate reservoir simulation, predict nanoparticle retention, and forecast oil recovery performance in NPs-CO₂-EOR. Finally, key challenges and potential directions for future research are also discussed.