Theoretical Investigation of Nonlinear-Diffusion Countercurrent Imbibition for Porous Medium with Micro-/Nanopores

Countercurrent imbibition is an important oil recovery mechanism in tight reservoir development. For tight oil reservoirs with hydraulic fractures and natural fractures, the injected fluid imbibes into a tight matrix from the fracture surface while crude oil flows reversely into the fracture during the process of liquid injection and soaking. Based on the traditional imbibition model, this paper proposes a countercurrent imbibition extension model for porous medium with micro-/nanopores, considering the early superdiffusion phenomenon under low water saturation. The reliability of this proposed model is further verified through experimental imbibition data and compared with the classical imbibition model. This model can obtain the dynamic evolution process of the imbibition saturation profile and quantify the countercurrent imbibition distance (imbibition range). The sensitivity analysis is then conducted, including the imbibition time, core length, characteristic parameters of relative permeability, characteristic parameters of capillary pressure, oil viscosity, and permeability. The results demonstrate that the countercurrent imbibition process can be divided into three stages: the superdiffusion stage (faster than t 0.5 ), transition stage, and subdiffusion stage (slower than t 0.5 ). Two key parameters, the critical imbibition saturation and its corresponding critical imbibition time, can be obtained through this model, which are significant to establishing reasonable soaking time for achieving higher oil recovery. This research improves the understanding of the countercurrent imbibition process, which explores the efficient development of water injection for tight oil reservoirs with micro-/nanopores.