Fast synchrotron tomography is used to study the impact of capillary number, $\text{Ca}$, on fluid configurations in steady-state two-phase flow in porous media. Brine and $n$-decane were co-injected at fixed fractional flow, $f_w=0.5$, in a cylindrical Bentheimer sandstone sample for a range of capillary numbers $2.1\times {10}^{-7}\le \text{Ca}\le 4.2\times {10}^{-5}$, while monitoring the pressure differential. As we have demonstrated in Gao et al. [Phys. Rev. Fluids 5, 013801 (2020)], dependent on $\text{Ca}$, different flow regimes have been identified: at low $\text{Ca}$ only fixed flow pathways exist, while after a certain threshold dynamic effects are observed resulting in intermittent fluctuations in fluid distribution which alter fluid connectivity. Additionally, the flow paths, for each capillary number, were imaged multiple times to quantify the less frequent changes in fluid occupancy, happening over timescales longer than the duration of our scans (40 s). In this paper we demonstrate how dynamic connectivity results from the interaction between oil ganglia populations. At low $\text{Ca}$ connected pathways of ganglia are fixed with time-independent small, medium, and large ganglia populations. However, with an increase in $\text{Ca}$ we see fluctuations in the size and numbers of the larger ganglia. With the onset of intermittency, fluctuations occur mainly in pores and throats of intermediate size. When $\text{Ca}$ is further increased, we see rapid changes in occupancy in pores of all size. By combining observations on pressure fluctuations and flow regimes at various capillary numbers, we summarize a phase diagram over a range of capillary numbers for the wetting and nonwetting phases, ${\text{Ca}}_w$ and ${\text{Ca}}_{nw}$, respectively, to quantify the degree of intermittent flow. These different regimes are controlled by a competition between viscous forces on the flowing fluids and the capillary forces acting in the complex pore space. Furthermore, we plot the phase diagrams of the transition from Darcy flow to intermittent flow over a range of Reynolds and Weber numbers for the wetting and nonwetting phases to evaluate the balance among capillary, viscous, and inertial forces, incorporating data from the literature. We demonstrate that pore geometry has a significant control on flow regime.

• Received 27 March 2020
• Revised 29 July 2020
• Accepted 29 December 2020

DOI:https://doi.org/10.1103/PhysRevE.103.013110