## Séminaire d'Alex Hansen (NTNU, Trondheim, Norvège)

**The co-moving velocity, a new concept in immiscible two-phase flow in porous media**

Alex Hansen

PoreLab, Department of Physics, NTNU, Trondheim, Norway

Since 1936, relative permeability theory has been the leading description of immiscible two-phase flow in porous media at scales much larger than the pore scale. Central to this theory are the two relative permeabilities, one for each fluid, which measures the reduction of mobility each fluid experiences due to the presence of the other fluid. The theory assumes the two relative permeabilities to be functions of the saturation (i.e., relative concentration) alone. When there are saturation gradients present, a third parameter comes into play, the capillary pressure. This is also assumed to depend on the saturation alone.

Such a theory is clearly quite limited in that it makes many strong assumptions. Yet, it is essentially the only one that is used for practical calculations. Can one do better ? That is, come up with a theory that is closer to the physics that is going on and at the same does not drown in complexity ? My answer is yes [1-7]. The aim of this talk is to describe this new theory. I will focus on a new velocity that pops up, namely the co-moving velocity. This velocity has remarkable properties that hints at something deeper which is yet to be uncovered.

References

[1] A. Hansen, S. Sinha, D. Bedeaux, S. Kjelstrup, M. Aa. Gjennestad and M. Vassvik, Relations between seepage velocities in two-phase flow in homogeneous porous media, Transp. Porous Med. 125, 565 (2018) ; doi:10.1007/s11242-018-1139-6.

[2] S. Roy, S. Sinha, and A. Hansen, Flow-area relations in immiscible two-phase flow in porous media, Front. Phys. 8, 4 (2020) ; doi:10.3389/fphy.2020.00004.

[3] S. Roy, H. Pedersen, S. Sinha, and A. Hansen, The co-moving velocity in immiscible two-phase flow in porous media, Transp. in Porous Media, 143, 69 (2022) ; doi:10.1007/s11242-022-01783-7.

[4] A. Hansen, E. G. Flekkøy, S. Sinha, and P. A. Slotte, A statistical mechanics for immiscible and incompressible two-phase flow in porous media, Adv. Water Res., 171, 104336 (2023) ; doi:10.1016/j.advwatres.2022.104336.

[5] H. Pedersen and A. Hansen, Parametrizations of immiscible two-phase flow in porous media, Front. Phys. 11, 1127345 (2023) ; doi:10.3389/fphy.2023.1127345.

[6] F. Alzubaidi, J. E. McClure, H. Pedersen, A. Hansen, C. F. Berg, P. Mostaghimi and R. T. Armstrong, The impact of wettability on the co-moving velocity of two-fluid flow in porous media, arXiv:2309.0036.

[7] J. Feder, E. G. Flekkøy, and A. Hansen, Physics of Flow in Porous Media, (Cambridge University Press, 2022).