Scaling Group for Spontaneous Imbibition Including Gravity

Abstract

Spontaneous imbibition of water into the matrix blocks due to capillary forces is an important recovery mechanism for recovery of oil from fractured water-wet reservoirs. Scaling groups is one important way to estimate oil recovery from such types of reservoirs. This paper describes a new scaling group for the estimation of oil recovery from single matrix blocks which also accounts for gravity effects. The group is derived on the basis of the analytical solution of the Washburn equation accounting for gravity effects using the Lambert’s W function. The new scaling law was tested using numerical simulation varying the core permeability and the size of the core sample. The new scaling law was able to perfectly scale these data into one unique single curve describing oil recovery as a fraction of recoverable oil versus a new dimensionless time introduced in this research.