Conventional modeling may be inadequate for prediction of fracturing-fluid flowback and leak-off from hydraulically-fractured horizontal wells in organic-rich shale formations. This work investigates the effect of capillary relaxation and nanometer scale transport effects during two-phase flow displacement (load and flowback) in shale reservoir simulation. It provides a model for prediction of hydraulic fluid spreading that is observed during leak-off (water invasion) and clean-up (flowback production). Constant and variable rates of capillarity relaxation processes are considered. Correlation models of relaxation time against saturation are provided. Water and gas are considered as displacement fluids for leak-off and clean-up, respectively. The saturation profiles of water leak-off for both capillary equilibrium and relaxation cases are compared, revealing a region of saturation that effectively is immobile even tough irreducible saturation has not been reached. Phase trapping may explain the occurance of lower flowback during production relative to the applied load.
It is shown in this study that conventional modeling may be inappropriate for estimating the flowback and leak-off in shale-gas wells due to transient behavior of capillary forces. Essentially, the fluid displacement in nanometer scaled capillaries is not instantaneous but takes some time to attain equilibrium saturation. The net force exerted between the wetting and non-wetting phases causes a retardation or relaxation in attaining equilibrium in capillary forces. Transient behavior of capillarity alters the profiles of saturation and relative permeability. The capillary pressure, relative permeability, and saturation are related to each other (Michel et al. 2012). We present a rigorous formulation of non-equilibrium state petrophysics coupled with proper description of non-equilibrium flow of gas/water systems transport in flow paths near the hydraulic fracture. We demonstrate the relevance of incorporating capillary relaxation into the modeling of gas-water flow through nanometer scale flow paths. Flow through capillaries is implemented for proper modeling of fluid motion. The capillary forces are relaxed in various flow paths to describe the behavior of fluid displacement in shale. The transient behavior of the capillary pressure and relative permeability curves are shown.