Solution for counter-current imbibition of 1D immiscible two-phase flow in tight oil reservoir

Spontaneous imbibition is an important mechanism for fractured reservoir to enhance oil recovery. Wetting phase enters porous media with the force of capillary pressure and gravity and replaces oil in matrix. To investigate the imbibition of tight reservoirs, on the consideration of tight formation characteristics, this paper derived a one dimension, two phases, counter-current imbibition model, after dimensionless of distance and time, Galerkin method for spatial discretization and time integration, solutions were given, comparisons of conventional sandstone and tight formation were made. The results have indicated that: (1) Imbibition can be divided into gravity assisting, gravity opposing and zero gravity in terms of different gravity conditions. (2) Saturation front of tight formation moves faster than sandstone because of high capillary pressure. (3) Capillary pressure plays the dominant role than gravity in imbibition. Influence of gravity is much greater in high-permeability sandstone than in tight reservoirs. (4) Horizontal well multi-stage fracturing and massive fracturing can increase fracture area and fracture volume, and increase the contact area with wetting phases, this will result in a greater imbibition and a great recovery of oil.