Numerical Solution and Stability Analysis of the Modified Linear Adsorption Model for Nanoparticles Transport in Porous Media Using the Crank-Nicolson Method

The transport and retention of nanoparticles in porous media are essential processes that impact the outcomes of Enhanced Oil Recovery (EOR). A Modified Linear (ML) adsorption model was formulated to examine nanoparticle transport using a simplified linear association between adsorbed and aqueous concentrations, resulting in a modified advection-dispersion equation that includes an effective retention term. This study reformulates and resolves the modified linear model applying the Crank-Nicolson finite difference method. All physical and numerical parameters are derived directly from literature related to four fundamental flood research studies employing coated silica and iron oxide nanoparticles in Boise sand packs. The research confirms that the Modified Linear Model, discretised by Crank-Nicolson, accurately represents the delayed breakthrough, plateau behaviour, and post-flush decrease observed in experiments, showing consistent numerical performance.