Spontaneous and forced imbibition are recognized as important recovery mechanisms in naturally fractured reservoirs as the capillary force controls the movement of the fluid between the matrix and the fracture. For unconventional reservoirs, imbibition is also important as the capillary pressure is more dominant in these tighter formations, and the theoretical understanding of the flow mechanism for the imbibition process will benefit the understanding of important multiphase flow phenomenons like water blocking. In this paper, a new semi-analytic method is presented to examine the interaction between spontaneous and forced imbibition and to quantitatively represent the transient imbibition process. The methodology solves the partial differential equation of unsteady state immiscible, incompressible flow with arbitrary saturation- dependent functions using the normalized water flux concept, which is very identical to the fractional flow terminology used in traditional Buckley-Leverett analysis. The result gives a universal inherent relationship between time, normalized water flux, saturation profile and the ratio between co-current and total flux. The current analysis also develops a novel stability envelope outside of which the flow becomes unstable due to strong capillary forces, and the characteristic dimensionless parameter shown in the envelope is derived from the intrinsic properties of the rock and fluid system and can describe the relative magnitude of capillary and viscous forces at the continuum scale. This dimensionless parameter is consistently applicable in both capillary dominated and viscous dominated flow conditions.
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