An analytical model for imbibition mechanism during water injection in fractured reservoirs with an introduced time-dependent shape factor

Fractured reservoirs have a considerable share of total petroleum resources. A substantial amount of fluid in these reserves has been produced so far, and they have reached the second half of their lives; therefore, different enhanced oil recovery methods should be employed. In water-wet fractured reservoirs, water injection is a practical secondary recovery method. Fluid flow simulation and investigation of different production mechanisms are key tools for reservoir management before and during the enhanced oil recovery process. In this paper, an analytical solution for the water injection process is presented by using the governing equation of two-phase flow in a fracture-matrix porous media. Moreover, for the case of viscous force in the fracture and imbibition force in the matrix block, a novel time-dependent shape factor is developed. Also, the effect of different shapes of fluid flow and the distance from the injection well on the shape factor is studied. Finally, by using the produced water data obtained from a monitoring well, a novel method for the calculation of initial water saturation in the matrix block is presented.