In the present paper, a mathematical model and numerical simulation to describe the nanoparticles-water suspension imbibes into a water-oil two-phase flow in a porous medium is introduced. We extend the model to include the negative capillary pressure and mixed relative permeabilities correlations to fit with the mixed-wet system. Also, buoyancy and capillary forces as well as Brownian diffusion are considered. Throughout this investigation, we monitor the changing of the fluids and solid properties due to addition of the nanoparticles and check for possible enhancement of the oil recovery process using numerical experiments.

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