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.
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