# An improved mathematical model for hypothetical oil reservoir for optimum oil recovery using magnetic nanomaterials

## TL;DR

This paper presents a new mathematical model to improve oil recovery in complex reservoirs using magnetic nanoparticles and 3D geometries.

## Contribution

The study introduces an enhanced magnetohydrodynamic model with magnetic field-induced pressure and 3D hexagonal prism geometry for unconventional reservoirs.

## Key findings

- A 29.08% increase in oil recovery was observed using nanoflooding compared to water flooding.
- Porosity and flow rate significantly influence recovery performance in the model.
- Magnetic field proximity to cavity structures enhances oil recovery rates.

## Abstract

In the oil and gas industry, enhanced oil recovery (EOR) strategies for unconventional reservoirs, characterized by complex geometries, differ significantly from those used in conventional reservoirs. This research focuses on the impact of 3D hexagonal prism geometries on EOR in hypothetical oil reservoirs using silicon dioxide (SiO₂) magnetic nanoparticles under liquid-phase flow conditions, a topic not extensively explored in existing literature. We developed an improved magnetohydrodynamic (MHD) mathematical models to simulate oil recovery processes in these geometries, using ANSYS Fluent for finite volume analysis. We developed an improved magnetohydrodynamic (MHD) model by incorporating magnetic field-induced pressure terms, nanoparticle transport losses, and a 3D hexagonal prism geometry that reflects complex reservoir behavior. These enhancements extend beyond traditional Darcy-based models by integrating magnetic permeability, viscosity alteration, and magnetic field-pore interactions. The model evaluates the impact of key reservoir parameters including porosity (ϕ = 0.1–0.4), injection flow rate (0.01–0.05 mL/min), and nanoparticle concentration (Ψ = 0.01–0.04), under different magnetic field configurations. Porosity and flow rate were also found to significantly influence recovery performance, highlighting the practical adaptability of the model for diverse reservoir conditions. Findings indicate that proximity of a magnetic field to cavity structures enhances oil recovery rates, with a significant 29.08% increase in recovery from nanoflooding compared to water flooding.Future research will extend this framework to study green, eco-friendly nanoparticles under elevated temperature and pressure, aiming to improve thermal stability, reduce environmental risks, and enhance recovery efficiency in more extreme reservoir conditions.