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In this work, we study the ascent dynamics of a liquid Taylor drop formed from a lock-exchange configuration in a closed vertical pipe. We focus on the buoyancy-driven motion of an elongated drop surrounded by a denser fluid when viscous forces dominate over inertial and surface tension effects. While gaseous Taylor bubbles have been studied extensively, a liquid Taylor drop moving in a closed pipe is less well understood. We formulate an analytical model for estimating the ascent speed and drop thickness from first principles. First, we use a lubrication approximation to solve for the velocity profiles in the two fluids. Then, we analyse the mechanical energy balance of the whole system, including the effect of viscous dissipation, to understand how the ascent speed and drop thickness scale with the viscosity ratio. We show that a drop with density ratio $\mathcal {R}$ reaches a stationary state with a uniform dimensionless thickness of $\sqrt {2}/{2}$ in the absence of dissipation and $\sqrt {2\mathcal {R}}/{2}$ in the dissipative regime. Through a comparison with existing experimental data, we demonstrate that our model correctly predicts the ascent speed of a Taylor drop if the material properties of the fluids and the geometry of the conduit are known. Our theoretical framework can be generalized to an isolated Taylor drop rising in a vertical pipe. [ABSTRACT FROM AUTHOR]

Relative permeability measurements are commonly fitted with the Corey and Brooks‐Corey correlations. Despite such correlations fit experimental data generally well, they are mostly of an empirical nature. Here, we propose a semiempirical model to determine relative permeabilities of the wetting and the nonwetting phases in real 3‐D porous media that accounts for pore‐scale flow regimes. The starting point is the homogenization framework proposed by Picchi and Battiato (2018, https://doi.org/10.1029/2018WR023172), where the upscaling is conducted for different spatial distributions of the flowing phases in the capillary tube setting. First, we extend the approach to realistic media by allowing pore‐scale flow regimes to coexist in a complex geometry while accounting for capillary and viscous limits in the dynamics. Then, we discuss the scaling behavior of normalized relative permeabilities in terms of the phases viscosity ratio and identify three classes which govern their scaling. We also derive an analytical expression for the fractional flow. Finally, we provide a detailed validation of the proposed model for both relative permeabilities and fractional flow against data from numerical simulations and experiments available in the literature. The data set used for validation covers a wide range of systems, ranging from brine‐CO2 to oil‐water flows. The equations derived capture well the trend of both numerical and experimental data. Key Points: We propose a relative permeability model based on pore‐scale flow regimesWe identify the scaling of the normalized relative permeability and fractional flowWe validate the proposed model against data collected from the literature [ABSTRACT FROM AUTHOR]