Abstract
We present an experimental and numerical study of immiscible two-phase flow of Newtonian fluids in three-dimensional (3D) porous media to find the relationship between the volumetric flow rate (Q) and the total pressure difference (Delta P) in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold (P_t), making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium. In this regime, Q depends quadratically on an excess pressure drop (Delta P-P_t). While increasing the flow rate, there is a transition, beyond which the overall flow is Newtonian and the relationship is linear. In our experiments, we build a model porous medium using a column of glass beads transporting two fluids, deionized water and air. For the numerical study, reconstructed 3D pore networks from real core samples are considered and the transport of wetting and non-wetting fluids through the network is modeled by tracking the fluid interfaces with time. We find agreement between our numerical and experimental results. Our results match with the mean-field results reported earlier.
Highlights
The simultaneous flow of two immiscible fluids in porous media, otherwise known as twophase flow (Bear 1972; Dullien 1992), is getting increasing attention of both the scientific and industrial communities
We presented experimental and numerical studies to investigate the relationship between the pressure drop and the volumetric flow rate in the steady-state two-phase flow of immiscible fluids in three-dimensional porous media
Our two-phase flow experiments utilize a three-dimensional porous medium made of glass beads with air and deionized water flowing through it
Summary
The simultaneous flow of two immiscible fluids in porous media, otherwise known as twophase flow (Bear 1972; Dullien 1992), is getting increasing attention of both the scientific and industrial communities. In single-phase flow of Newtonian fluids, the macro-scale pressure gradient ( P) over a porous medium scales linearly with the superficial fluid velocity governed by the Darcy’s law (Darcy 1856; Whitaker 1986). This is true in the case of two-phase flows at high fluid velocities when capillary forces are negligible. In a different experiment of twophase flow in a three-dimensional (3D) porous medium, similar power law scaling between Q and P was observed, but the exponents were found to vary in the range between 0.45 and 0.3 depending on the saturation (Rassi et al 2011).
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