Wettability in complex porous materials, the mixed-wet state, and its relationship to surface roughness

Abstract

A quantitative in situ characterization of the impact of surface roughness on wettability in porous media is currently lacking. We use reservoir condition micrometer-resolution X-ray tomography combined with automated methods for the measurement of contact angle, interfacial curvature, and surface roughness to examine fluid/fluid and fluid/solid interfaces inside a porous material. We study oil and water in the pore space of limestone from a giant producing oilfield, acquiring millions of measurements of curvature and contact angle on three millimeter-sized samples. We identify a distinct wetting state with a broad distribution of contact angle at the submillimeter scale with a mix of water-wet and water-repellent regions. Importantly, this state allows both fluid phases to flow simultaneously over a wide range of saturation. We establish that, in media that are largely water wet, the interfacial curvature does not depend on solid surface roughness, quantified as the local deviation from a plane. However, where there has been a significant wettability alteration, rougher surfaces are associated with lower contact angles and higher interfacial curvature. The variation of both contact angle and interfacial curvature increases with the local degree of roughness. We hypothesize that this mixed wettability may also be seen in biological systems to facilitate the simultaneous flow of water and gases; furthermore, wettability-altering agents could be used in both geological systems and material science to design a mixed-wetting state with optimal process performance.

Keywords: complex porous media; contact angle; curvature; in situ reservoir conditions; roughness.

Fig. 1.

A schematic of wettability and length scales in porous media flows. Right shows images of oil retained within the pore space of WW and OW samples. The curvature of the oil/brine interface is indicated by the colors, while the solid surface in contact with brine is shown in gray. In a WW rock, the oil is trapped in quasispherical ganglia with contact angles less than $90^{°}$. For an OW rock, oil is retained in layers that follow the surface roughness with both positive and negative values of the curvature $\kappa$. This allows the oil to flow to low saturation, facilitating recovery at the kilometer scale (Left). Center shows how the samples are selected from centimeter-scale cores extracted from a reservoir.

Fig. 2.

Roughness, contact angle, and oil/brine interface curvature measurements. (A) A 3D view of the raw segmented dataset of the OW sample with a voxel size of 2 $\mathrm{\mu }$m. (B) The oil (black) and brine (blue) phases are shown in a zoomed-in section of the image. (C) The curvature-based roughness measurement ($R_a$) on each vertex belonging to the rock surface after applying uniform-curvature smoothing: the smooth and rough areas are indicated by blue and red, respectively. (D) The smoothed mesh that is found after applying both Gaussian and curvature smoothing: the identified interfaces oil/brine (green) and oil/solid (red). (E) The measured curvature values of all vertices belonging to the oil/brine interface. (F) The extracted three-phase contact line. (G) Normal vectors are defined on both the oil/brine and the brine/rock interfaces at the three-phase contact line: the cosine of the contact angle is calculated from the dot product of these two normals.

Fig. 3.

Distributions of the measurements on pore space images. A–C show point-by-point values, while D–F show pore-averaged values. (A) Histogram of all of the contact angle measurements, where the values measured on a flat surface are indicated by the vertical lines. (B) Histogram of the measured oil/brine interfacial curvature. (C) The distribution of surface roughness. (D) The variation of contact angle and (E) oil/brine interface curvature using the SD per pore. In addition, the pore-averaged (mode) curvature-based roughness, $R_a$ (F) in each pore is shown for the three samples: WW (blue), MW (green), and OW (red). Std. indicates SD.

Fig. 4.

Spatial correlations computed using Eq. 5. (A–C) The spatial correlation of surface roughness ($R_a$). We see a correlation length of approximately a pore size. (D–F) The correlation between surface roughness and contact angle as a function of the distance between the measurements. Here, a value of $\xi >1$ indicates an anticorrelation in that greater roughness is associated with smaller contact angles. (G–I) The correlation between surface roughness and interfacial curvature. Here, rougher surfaces, which tend to be more WW, are more likely to have a higher interfacial curvature ($\xi <1$) for the MW and OW samples, consistent with the results in D–F. The vertical lines indicate the minimum pore diameter (dotted), the average pore diameter (solid), and the maximum pore diameter (dashed).

Fig. 5.

Relationship between the variation in contact angle, interfacial curvature, and surface roughness using Eq. 6. The calculated correlation ($\rho$) of pore-averaged curvature-based roughness ($R_a$) with measured contact angle (A–C) and oil/brine interface curvature variation (G–I) is shown as a function of pore diameter. Where $\rho =$ 1, the two variables are strongly correlated. Also shown in D–F and J–L is the number of data points considered for each pore size: most of the data comes from the larger pores. Std. indicates SD.