Analytical Characterization of In-Situ Wettability in Porous Media Using Oil Displacement Dataset

Wettability has been known to be responsible for multiphase flow in porous materials and is conventionally characterized as the three-phase contact angle to describe its complex interactions of two immiscible fluids and a solid medium. Even though a simple ex-situ measurement of the contact angle on a surface is widely conducted, an in-situ contact angle that cannot be physically measured has increasingly been accepted as a more crucial and meaningful parameter for oil displacement. Since the in-situ contact angle considers a holistic and yet dynamic movement of fluids within porous material, a number of indirect in-situ characterizations have been performed. The current work aimed to examine a new alternative via an analytic method to characterize in-situ wettability. In this study, a correlation on spontaneous imbibition developed by Standnes was used to characterize in-situ contact angle with Lambert’s \(W\) function. The in-situ contact angles of 160 experiments on oil displacement in sand-pack were then determined analytically. Results of the in-situ contact angles from analytic solution performed on the experiment datasets ranging from 80.21° to 83.52° situated on partially water-wet side, confirming the a priori nature of the wetting state of the sand-pack. Consistency of the resulting in-situ contact angles was also examined with other relevant characterizations, including direct tomographic imaging and yet analytic wettability index. The analytic approach is well correlated with other methods, annotating a robust meaning of the proposed characterization. As water-wet contact angles, the results have an inversely proportional function with the oil recovery as reported in literature. The present analytical solution offers an alternative and yet unique approach to characterize in-situ contact angle, which should be used in simulation studies to further predict oil displacement.