A new multi-pore fractal model to delineate the effect of various factors on imbibition in shales

Large-scale hydraulic fracturing of horizontal wells is a key technology for shale gas extraction, during which tens of thousands of cubic meters of water could be injected into the formations for hydraulic fracturing. Water is imbibed into the shale pores under the action of capillary force and osmotic pressure. The relevant research has intensively been conducted worldwide on imbibition in porous media, including fractal modeling of the phenomenon. One significant drawback of the imbibition models proposed is their focus solely on the capillary force and pore fractal characteristics, ignoring the self-imbibition of clay pores under osmotic pressure. In this paper, the pore characteristics of shale are analyzed by field emission scanning electron microscopy (FSEM) and fractal analysis. A multi-pore fractal model is then developed for imbibition in shales, honoring capillary forces, osmotic pressure and pore structure. The results show that the morphology of organic and brittle pores tends to resemble an ellipse, while that of clay pores is similar to parallel fractures. It is observed that the imbibition capacity is more influenced by the fractal dimension of pore tortuosity rather than pore volume. In this regard, the effect of the maximum short axis of an elliptic pore on imbibition is more important that of the minimum short axis. The imbibition ability has a direct relationship with fluid viscosity. But there is a critical viscosity value, beyond which the imbibed volume flattens out. In the case of multiple-pore imbibition, clay pores demonstrate the fastest, longest and largest liquid imbibition process.