A matrix/fracture exchange model for a fractured reservoir simulator is described. Oil/water imbibition is obtained from a diffusion equation with water saturation as the dependent variable. Gas/oil gravity drainage and imbibition are calculated by taking into account the vertical saturation distribution in the matrix blocks.
Bech, N., Jensen, O. K., & Nielsen, B. (1991). Modeling of gravity-imbibition and gravity-drainage processes: Analytic and numerical solutions. SPE Reservoir Engineering, 6(1), 129-136. https://doi.org/10.2118/18428-PA