Effect of retardation in fluid displacement on transport inside capillary tubes during leak-off and clean-up for hydraulically stimulated reservoirs is investigated by modeling of the relevant phenomena. The effect of wall proximity during the transport in narrow capillaries is formulated. The importance of the critical properties alteration due to confinement is demonstrated by modification of the real gas deviation factor. The relaxation in fluid displacement observed in the fluid transport dynamics is coupled with the bundle of tubes representation of porous media for investigation of the relaxation effects on fluid saturation, capillary pressure, and relative permeability. An analytical formulation of the relaxation time corresponding to water removal during clean-up processes following hydraulic fracture stimulation is presented. The dynamics of advancement of the wetting and non-wetting fluids inside capillary tubes are illustrated by various applications.

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