Accurate modeling of multiphase flow, matrix saturation distribution, and having a mathematical model to explain matrix to fracture fluid transfer are crucial issues in dual porosity modeling of fractured reservoirs. Most of the proposed shape factors have been derived for single phase
flow under the expansion mechanism. Unfortunately, due to the process and phase sensitivity of the shape factor, these formulas could not describe the matrix-fracture interaction in the countercurrent imbibition process, which occurs within the water-invaded zone. Furthermore, none of the
existing shape factors included the gravity term in their derivation. Thus, this necessitates development of a transient shape factor specifically for the imbibition mechanism. In the current study, the three-dimensional distribution of fluid saturation within a matrix block and time-dependent
matrix-fracture shape factor formulation are derived analytically by solving the saturation diffusion equation in the countercurrent imbibition process. In contrast to previous works, the proposed formulations have the advantage of including both capillary and gravity forces. Meanwhile, the
analytical solution is verified by a fine grid simulation model. Then, it is used to develop an analytical formula for the matrix-fracture shape factor in the countercurrent imbibition process. As opposed to previous works, the new shape factor has the advantage of considering both forces
of capillary and gravity on matrix-fracture coupling.
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