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Relative permeability theory for immiscible two-phase flow in porous media assumes a linear dependency of the seepage velocity of each fluid on the pressure gradient. This implies that the average fluid velocity also exhibits such a linear dependence. Recent experimental, computational and theoretical work, however, show that the average flow velocity follows a power law in the the pressure gradient with an exponent in the range larger than one up to two over a wide range of parameters. Such a behavior is incompatible with relative permeability theory. A recent theory based on Euler homogeneity of the volumetric flow rates of the fluids generalizes relative permeability theory in such a way that it is capable of handling this non-linear behavior. A central quantity in this theory is the co-moving velocity which is related to, but not equal to the difference between the seepage velocities of the fluids. In order to close the equation set that ensues from the theory, a constitutive equation has to be supplied for the co-moving velocity. We construct this constitutive equation from relative permeability data in the literature. It turns out to exhibit a remarkably simple form when expressed in the right variables. We follow this analysis up by simulating immiscible two-phase flow using a dynamic pore network model finding the same results as those based on the relative permeability data.
We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section tr
We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier-Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution. In this model, the materia
Immiscible fluid displacement in porous media is fundamental for many environmental processes, including infiltration of water in soils, groundwater remediation, enhanced recovery of hydrocarbons and carbon geosequestration. Microstructural heterogen
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Diverse processes rely on the viscous flow of polymer solutions through porous media. In many cases, the macroscopic flow resistance abruptly increases above a threshold flow rate in a porous medium---but not in bulk solution. The reason why has been