Controlling parameters of co-current and counter-current imbibition in naturally fractured reservoirs

Naturally fractured formations are complex petroleum reservoirs that are poor candidates for waterflooding due to difficulties in controlling sweep. Injected water can readily propagate through the fracture system, bypassing the hydrocarbon stored in the matrix. Instead, such systems rely on spontaneous imbibition (SI) from the matrix into the extensive fracture gathering system. SI is a crucial recovery mechanism that relies on capillary pressure-dominated fluid movement. SI can occur through two modes, co-current (COSI) and counter-current (COUSI), depending on the relative direction of fluid movement in response to prevailing boundary conditions. Analytical solutions that incorporate the diffusivity coefficient, which combines relative permeability and capillary pressure curves, are used to describe co-current and counter-current imbibition mechanisms. The perturbation method is one approach in solving these analytical equations. In-situ water saturation profiles, ascertained through experimental CT scanning, serve as validation benchmarks for both co-current and counter-current models. The understanding of the SI process can give more details about the fracture-matrix interactions and the exchange function. Sensitivity studies with respect to the parameterization of the driving force for imbibition, capillary pressure, and the resistive forces, captured in relative permeability curves, can guide experimental study planning and aid in inverse problem analysis in the characterization of naturally fractured reservoirs. The results of a parametric study show that capillary pressure curve parameters, such as capillary entry pressure and capillary exponent, significantly affect the position of the waterfront which indicates the imbibition rate. In addition, the water relative permeability exponent has greater impact on both shape and position of water profile than other relative permeability parameters. The nonwetting phase parameters, like oil endpoint relative permeability and oil exponent, have the least influence on water saturation profile.