Countercurrent imbibition is an important oil recovery mechanism in fractured reservoirs. The imbibition process can be described by a nonlinear diffusion equation that has self-similar solutions. In this paper, we use the diffusion equation to conduct numerical experiments of countercurrent imbibition in a single matrix block to identify flow characteristics. The result demonstrates that the widely-used Aronofsky et al.1  exponential relationship is only valid for cases where diffusion coefficients are constant. The nonlinear diffusion equations in one and two-dimensions are analytically solved using a relative flow rate concept to simplify the analysis. The result is a new understanding regarding the effects of various parameters such as capillary pressure, relative permeability, mobility ratio, and fractional flow on countercurrent imbibition.

The solutions can be directly used to modify an existing single porosity model to a dual porosity model for simulating fractured reservoirs. Results show that our approach provides fairly good accuracy compared to a full-scale dual porosity model with little increase in computation time over single porosity modeling.

You can access this article if you purchase or spend a download.