Two-phase concentric annular tube flow is investigated. We study the case when one of the phases is Newtonian, e.g. oil, and the other non-Newtonian fluid, e.g. solution of an EOR polymer. The kinetic theory-based FENE-P dumbbell model is used to describe the polymer rheology. Both possibilities are considered: when the phase in the core is non-Newtonian and when it is Newtonian.

The system of differential equations governing the dynamics of the phases is solved analytically, and the fractional flows of the phases are determined. Further, the concept of relative permeability is generalized. It is demonstrated how Darcy’s law can be extended to take non-Newtonian effects into account. It is illustrated that the relative permeabilities of the phases depend not only of their saturation, but also on the pressure gradient in the flow direction, due to the polymeric phase rheology.

Finally, the role of the normal stresses in the non-Newtonian phase is discussed. We show that in a cylindrical tube the normal forces do not contribute to the pressure drop in the flow direction and, therefore, do not affect the dynamics of the phases; but, in slightly more complicated geometries the impact of normal stresses on the fluid dynamics can be essential.


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