A generalized power-law scaling law for a two-phase imbibition in a porous medium

• A generalized power-law scaling law for imbibition in porous media is introduced.
• Both characteristic and injection velocities are used in the proposed law.
• The scaling law has been tested against a set of experimental data.
• Dimensional analysis is provided for the countercurrent imbibition problem.

Dimensionless time is a universal parameter that may be used to predict real field behavior from scaled laboratory experiments in relation to imbibition processes in porous media. Researchers work to nondimensionalize the time has been through the use of parameters that are inherited to the properties of the moving fluids and the porous matrix, which may be applicable to spontaneous imbibition. However, in forced imbibition, the dynamics of the process depends, in addition, on injection velocity. Therefore, we propose the use of scaling velocity in the form of a combination of two velocities, the first of which (the characteristic velocity) is defined by the fluid and the porous medium parameters and the second is the injection velocity, which is a characteristic of the process. A power-law formula is suggested for the scaling velocity such that it may be used as a parameter to nondimensionalize time. This may reduce the complexities in characterizing two-phase imbibition through porous media and works well in both the cases of spontaneous and forced imbibition. The proposed scaling-law is tested against some oil recovery experimental data from the literature. In addition, the governing partial differential equations are nondimensionalized so that the governing dimensionless groups are manifested. An example of a one-dimensional countercurrent imbibition is considered numerically. The calculations are carried out for a wide range of Ca and Da to illustrate their influences on water saturation as well as relative water/oil permeabilities.