Abstract
AbstractThe co-moving velocity is a new variable in the description of immiscible two-phase flow in porous media. It is the saturation-weighted average over the derivatives of the seepage velocities of the two immiscible fluids with respect to saturation. Based on analysis of relative permeability data and computational modeling, it has been proposed that the co-moving velocity is linear when plotted against the derivative of the average seepage velocity with respect to the saturation, the flow derivative. I show here that it is enough to demand that the co-moving velocity is characterized by an additive parameter in addition to the flow derivative to be linear. This has profound consequences for relative permeability theory as it leads to a differential equation relating the two relative permeabilities describing the flow. I present this equation together with two solutions.
Publisher
Springer Science and Business Media LLC
Reference13 articles.
1. Wyckoff, R., Botset, H.: The flow of gas–liquid mixtures through unconsolidated sands. Physics 7(9), 325 (1936). https://doi.org/10.1063/1.1745402
2. H. Darcy: Les fontaines publiques de la ville de Dijon: exposition et application des principes à suivre et des formules à employer dans les questions de distribution d’eau, vol. 1 (Victor Dalmont, 1856)
3. Tallakstad, K.T., Knudsen, H.A., Ramstad, T., Løvoll, G., Måløy, K.J., Toussaint, R., Flekkøy, E.G.: Steady-state two-phase flow in porous media: statistics and transport properties. Phys. Rev. Lett. 102(7), 074502 (2009). https://doi.org/10.1103/PhysRevLett.102.074502
4. Tallakstad, K.T., Løvoll, G., Knudsen, H.A., Ramstad, T., Flekkøy, E.G., Måløy, K.J.: Steady-state, simultaneous two-phase flow in porous media: an experimental study. Phys. Rev. E 80(3), 036308 (2009). https://doi.org/10.1103/PhysRevE.80.036308
5. Hansen, A., Sinha, S., Bedeaux, D., Kjelstrup, S., Gjennestad, M.A., Vassvik, M.: Relations between seepage velocities in immiscible, incompressible two-phase flow in porous media. Transp. Porous Media 125, 565 (2018). https://doi.org/10.1007/s11242-018-1139-6