Wettability Stabilizes Fluid Invasion into Porous Media via Nonlocal, Cooperative Pore Filling

We study the impact of the wetting properties on the immiscible displacement of a viscous fluid in disordered porous media. We present a novel pore-scale model that captures wettability and dynamic effects, including the spatiotemporal nonlocality associated with interface readjustments. Our simulations show that increasing the wettability of the invading fluid (the contact angle) promotes cooperative pore filling that stabilizes the invasion and that this effect is suppressed as the flow rate increases, due to viscous instabilities. We use scaling analysis to derive two dimensionless numbers that predict the mode of displacement. By elucidating the underlying mechanisms, we explain classical yet intriguing experimental observations. These insights could be used to improve technologies such as hydraulic fracturing, ${\mathrm{CO}}_2$ geosequestration, and microfluidics.

Figure 1

Model schematic. (a) We simulate radial displacement, tracking the fluid-fluid interface (black line) and fluid pressures (increasing from blue to red). (b) Enlargement showing the lattice of particles and pores. The interface is represented as a sequence of circular menisci, touching particles at contact angle $\theta$, with the curvature set by the local capillary pressures. Menisci can be destabilized by (c) burst, (d) touch, or (e) overlap. Brown arrows indicate the direction of advancement, the destabilized arc as dashed lines.

Figure 2

(a) Simulated invasion patterns, characterized by (b) interface length $L_{\text{inter}}$ and (c) finger width $w$. Rapid injection (high Ca) leads to viscous fingering (VF) with irregular interfaces ($L_{\text{inter}}\approx 1$) and thin fingers ($w\approx 1$). As Ca is decreased, the patterns transition towards capillary fingering (CF) with multiple trapped clusters and relatively long interfaces in drainage (low $\theta$) or compact displacement (CD, $L_{\text{inter}}\ll 1$, $w\gg 1$) in imbibition (high $\theta$). The inset in (c) shows a fit of $w\sim {\mathrm{Ca}}^{-\nu }$ for $\theta =120°$ providing $\nu \approx 0.6$. Error bars show the standard deviation among four realizations.

Figure 3

Occurrence of nonlocal, cooperative pore filling (the number of overlaps out of all instability events) from 208 simulations (gray dots). Increasing $\theta$ enhances overlaps, manifested macroscopically by a more stable displacement. Dashed lines mark the theoretical phase boundaries predicted by scaling (see the text).

Figure 4

Phase diagrams of immiscible displacement: (a) interface length $L_{\text{inter}}$ and (b) finger width $w$. At high flow rates, $N_{\mathrm{Ca}}\gg {N_{\mathrm{Ca}}}^{*}$ predicts VF with long, fractal interfaces and thin fingers ($L_{\text{inter}}\approx 1$, $w\approx 1$). At low rates, $N_{\mathrm{Ca}}\ll {N_{\mathrm{Ca}}}^{*}$, invasion is controlled by the wettability: for drainage, $N_{\mathrm{coop}}<0$ implies CF, whereas for imbibition $N_{\mathrm{coop}}>0$ indicates CD ($L_{\text{inter}}\ll 1$, $w\gg 1$) due to smoothing by cooperative pore filling. Dashed lines show phase boundaries from scaling analysis, $N_{\mathrm{Ca}}={N_{\mathrm{Ca}}}^{*}\approx 4\times 10^{-3}$ and $N_{\mathrm{coop}}=0$. Dots mark data from 208 simulations at various Ca and $\theta$.