In this paper, the problem of magnetic nanoparticle injection into a water-oil two-phase flow under an external permanent magnetic field is investigated numerically. The mathematical model of the problem under consideration has been developed. We treat the water- nanoparticle suspension as a miscible mixture while it is immiscible with the oil phase. The magnetization, density, and viscosity of ferrofluids are obtained using immiscible mixture relations. On the other hand, the magnetized phase pressure will have additional pressure terms relative to the conventional thermodynamic pressure, namely, the ferrofluid phase dynamic pressure, the fluid magnetic pressure, and the magneto-strictive pressure, while, the magnetic normal pressure is neglected in this study. Physical variables including water-nanoparticle suspension saturation, nanoparticle concentration, and pore wall/throat deposited nanoparticle, are investigated under the influence of the magnetic field. From our results, we found that magnetic field has a significant effect on the physical quantities of the model. Therefore, a magnet can be implemented for enhanced oil recovery.

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