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 () 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 (), making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium. In this regime, Q depends quadratically on an excess pressure drop (). 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.Electronic supplementary materialThe online version of this article (doi:10.1007/s11242-017-0874-4) contains supplementary material, which is available to authorized users.

Nuclear magnetic resonance (NMR) techniques were used to study the capillary trapping mechanisms relevant to carbon sequestration. Capillary trapping is an important mechanism in the initial trapping of supercritical CO2 in the pore structures of deep underground rock formations during the sequestration process. Capillary trapping is considered the most promising trapping option for carbon sequestration. NMR techniques noninvasively monitor the drainage and imbibition of air, CO2, and supercritical CO2 with DI H2O at low capillary numbers in a Berea sandstone rock core under conditions representative of a deep underground saline aquifer. Supercritical CO2 was found to have a lower residual nonwetting (NW) phase saturation than that of air and CO2. Supercritical CO2 behaves differently than gas phase air or CO2 and leads to a reduction in capillary trapping. NMR relaxometry data suggest that the NW phase, i.e., air, CO2, or supercritical CO2, is preferentially trapped in larger pores. This is consistent with snap‐off conditions being more favorable in macroscale pores, as NW fluids minimize their contact area with the solid and hence prefer larger pores.

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