In this paper, the problem of magnetic nanoparticles injection into a water–oil two–phase flow under an external permanent magnetic field is investigated. The mathematical model of the problem under consideration has been developed. We treat the water-nanoparticles suspension as a miscible mixture while it is immiscible with the oil phase. The magnetized phase pressure includes an additional pressure term with the conventional thermodynamic pressure. The countercurrent imbibition flow problem is taken as an example. Physical variables including water–nanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat deposited nanoparticles are investigated under the influence of the magnetic field.
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