Generalized Scaling Approach for Spontaneous Imbibition: An Analytical Model

Summary Scaling the experimental data of spontaneous imbibition without serious limitations has been difficult. To this end, a general approach was developed to scale the experimental data of spontaneous imbibition for most systems (gas/liquid/rock and oil/water/ rock systems) in both cocurrent and countercurrent cases. We defined a dimensionless time with almost all the parameters considered. These include porosity, permeability, size, shape, boundary conditions, wetting- and nonwetting-phase relative permeabilities, interfacial tension (IFT), wettability, and gravity. The definition of the dimensionless time was not empirical; instead, it was based on theoretical analysis of the fluid-flow mechanisms that govern spontaneous imbibition. The general scaling method was confirmed against the experimental data from spontaneous water imbibition conducted at different IFTs in oil-saturated rocks with different sizes and permeabilities. A general analytical solution to the relationship between recovery and imbibition time for linear spontaneous imbibition was derived. The analytical solution predicts a linear correlation between the imbibition rate and the reciprocal of the recovery by spontaneous imbibition in most fluid/ fluid/rock systems.