Capillary imbibition is one of the main recovery mechanisms of naturally fractured reservoirs where fracture fluid imbibes, by capillary forces, in the matrix and the matrix fluid is transferred to the fracture. Simulating counter-current imbibition in dual-medium models is a challenging task. The semi-steady state approach has been used in Warren and Root based transfer functions for the past forty years. However, it eliminates the speed of early time recovery and assigns average property values in matrix and fracture. In this paper, we eliminate the semi-steady state approach in matrix capillary imbibition by making the transfer function depend on time, space and two recovery periods (early and late time). We make it depend on space by dividing the invaded face into two equal sub-faces, each with its own capillary pressure, relative permeability and location. Then, the two contributions are summed up to equal one mass conservation equation for each matrix cell. In early time recovery, the saturation front moves laterally in the matrix, until it reaches the no-flux boundary. The distance of invasion is calculated using an integral of the inverse capillary pressure curve, the saturation values of previous time step, and the distance between the invaded face and the no-flux boundary. Then, new capillary pressure, relative permeability and location values are assigned to each sub-face; where the transfer of fluid is calculated. When the saturation front reaches the no-flux boundary, at start of late time, it moves vertically until the Pc at the no-flux boundary equals the Pc at the invaded face. The capillary pressure and relative permeability of the sub-faces are calculated using integral of the inverse of capillary pressure curve and the saturation value of previous time step. Our approach matched the results of fine-grid single-porosity models under various parameters of capillary pressure, matrix shape and mobility. It also outperformed the results of three transfer functions: Gilman & Kazemi, Quandalle & Sabathier, and the General Transfer Function proposed by Hu & Blunt.


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