Fluid-fluid displacement in mixed-wet porous media

It is well known that wettability exerts fundamental control over multiphase flow in porous media, which has been extensively studied in uniform-wet porous media. In contrast, multiphase flow in porous media with heterogeneous wettability (i.e., mixed-wet) is less well understood, despite its common occurrence. Here, we study the displacement of silicone oil by water in a mostly oil-wet porous media patterned with discrete water-wet clusters that have precisely controlled wettability. Surprisingly, the macroscopic displacement pattern varies dramatically depending on the details of wettability alteration—the invading water preferentially fills strongly water-wet clusters but encircles weakly water-wet clusters instead, resulting in significant trapping of the defending oil. We explain this counterintuitive observation with pore-scale simulations, which reveal that the fluid-fluid interfaces at mixed-wet pores resemble an $\mathsf{S}$-shaped saddle with mean curvatures close to zero. We show that incorporation of the capillary entry pressures at mixed-wet pores into a dynamic pore-network model reproduces the experiments. Our work demonstrates the complex nature of wettability control in mixed-wet porous media, and it presents experimental and numerical platforms upon which further insights can be drawn.

Figure 1

We conduct radial fluid-fluid displacement experiments in microfluidic flow cells with spatially heterogeneous wettabilities. (a) The flow cell is made of a photocurable polymer (NOA81) that is oil-wet in nature, but becomes more water-wet after exposure to high-energy UV radiation. We cover the NOA81 surface with a photomask during UV exposure to achieve water-wet clusters. The borders between oil-wet and water-wet regions are delineated by connecting the centers of mixed-wet pores (inset). (b) The top half of the flow cell consists of a flat sheet of NOA81 patterned with the same spatially heterogeneous wettability and it is precision aligned with the bottom half.

Figure 2

Experimental displacement patterns of water (yellow) displacing silicone oil (black) in mixed-wet microfluidic flow cells at three distinct capillary numbers. The bulk of the flow cell is oil-wet (gray posts, $\theta ={120}^{\circ }$), and it is interspersed either with strongly water-wet clusters (blue posts, $\theta ={30}^{\circ }$), or with weakly water-wet clusters (green posts, $\theta ={60}^{\circ }$). The patterns correspond to when the invading water reaches the perimeter of the flow cell and they are oriented in the same way to aid visual comparison. The invading water saturates the strongly water-wet clusters (top row), but encircles the weakly water-wet clusters (bottom row).

Figure 3

(a) Water-wet pore preference index $I_p$ as a function of Ca, where $I_p$ is defined as the ratio between the number of invaded water-wet pore throats and the number of invaded mixed-wet pore throats. Experimental $I_p$ for flow cells with weakly water-wet clusters (green circles connected by solid lines) and strongly water-wet clusters (blue circles connected by dashed lines) are plotted alongside numerical $I_p$ (squares) obtained from our pore-network model (see Fig. 6). The gray dashed line represents the ratio between the total number of water-wet pore throats and the total number of mixed-wet pore throats in the entire flow cell. (b) Water-wet cluster displacement efficiency $E_d$ as a function of Ca, where $E_d$ is defined as the fraction of the defending fluid displaced from the water-wet cluster closest to the injection port. $E_d$ for flow cells with weakly water-wet clusters (green circles connected by solid lines) and strongly water-wet clusters (blue circles connected by dashed lines) are plotted alongside numerical $E_d$ (squares) obtained from our pore-network model (see Fig. 6). In both plots, the solid circles represent additional experiments conducted at the same conditions.

Figure 4

Three-dimensional visualization of the last stable fluid-fluid interface through (a) a uniform-wet pore consisting of a pair of weakly water-wet posts, (b) a mixed-wet pore consisting of an oil-wet post next to a weakly water-wet post, (c) a uniform-wet pore consisting of a pair of strongly water-wet posts, and (d) a mixed-wet pore consisting of an oil-wet post next to a strongly water-wet post. The color map shows the local mean curvature of the meniscus.

Figure 5

In-plane curvature of the fluid-fluid interface at (a) a typical uniform-wet pore and (b) a typical mixed-wet pore. The circles represent simulation results obtained via surface evolver, whereas solid lines represent our analytical solutions [28]. (c) Experimental snapshot of the meniscus at a mixed-wet pore consisting of an oil-wet post next to a weakly water-wet post at $\text{Ca}=6\times {10}^{-4}$.

Figure 6

Numerical displacement patterns simulated by the dynamic pore network model for the same conditions as the experiments. The simulations closely resemble the experiments (Fig. 2), and they capture the contrasting behaviors of water invasion in clusters of weakly water-wet posts vs clusters of strongly water-wet posts.