Scaling of spontaneous imbibition data with wettability included

Wettability is a dominant parameter governing spontaneous imbibition. However less attention has been paid to the effect of wettability on the scaling of spontaneous imbibition data. Actually few models can include wettability in scaling of spontaneous imbibition data. To this end, a scaling model has been developed for NAPL (oil)-saturated porous media with different wettability based on the fluid flow mechanisms in porous media. Relative permeability, capillary pressure, initial water saturation, and wettability are considered in the scaling model. Theoretically this scaling model is suitable for both cocurrent and countercurrent spontaneous imbibition. The experimental data of countercurrent spontaneous water imbibition at different wettability cannot be scaled using the frequently used scaling model but can be scaled satisfactorily using the scaling model developed in this study. An analytical solution to the relationship between recovery and imbibition time for linear spontaneous imbibition has also been derived in the case in which gravity is ignored. The analytical solution predicts a linear correlation between the recovery by spontaneous water imbibition and the square root of imbibition time, which has been verified against experimental data.