Post-fracturing well shut-in is traditionally due to the elastic closure of hydraulic fractures and proppant compaction. However, for shale gas wells, the extension of shut-in time may improve the post-fracturing gas production due to formation energy supplements by fracturing-fluid imbibition. This paper presents a methodology using numerical simulation to simulate the hydrodynamic equilibrium phenomenon of a hydraulically fractured shale gas reservoir, including matrix imbibition and fracture network crossflow, and further optimize the post-fracturing shut-in time. A mathematical model, which can describe the fracturing-fluid hydrodynamic transport during the shut-in process, and consider the distinguishing imbibition characteristics of a hydraulically fractured shale reservoir, i.e., hydraulic pressure, capillarity and chemical osmosis, is developed. The key concept, i.e., hydrodynamic equilibrium time, for optimizing the post-fracturing shut-in schedule, is proposed. The fracturing-fluid crossflow and imbibition profiles are simulated, which indicate the water discharging and sucking equilibrium process in the coupled fracture–matrix system. Based on the simulation, the hydrodynamic equilibrium time is calculated. The influences of hydraulic pressure difference, capillarity and chemical osmosis on imbibition volume, and hydrodynamic equilibrium time are also investigated. Finally, the optimal shut-in time is determined if the gas production rate is pursued and the fracturing-fluid loss is allowable. The proposed simulation method for determining the optimal shut-in time is meaningful to the post-fracturing shut-in schedule.

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Fracturing fluid imbibition and retention are treated as a main mechanism for oil production from shale reservoirs. However, the oil–water exchange phenomenon during post-fracturing soaking periods has not been thoroughly studied. In this study, a water–oil flow model is built to investigate the water imbibition and oil drainage phenomenon in hydraulically fractured shale. With the developed numerical simulator, the main characteristics of post-fracturing soaking, that is, pressure diffusion, water imbibition, and especially, the oil–water exchange behavior are simulated. Three key time points, that is, oil–water exchange equilibrium, steady exchange efficiency, and oil breakthrough in fracture are found. The oil–water exchange efficiency and exchange volume are also calculated. Moreover, the proposed model is validated by field wellhead pressure dynamics, indicating a relevance of time between the oil–water exchange efficiency and the wellhead pressure falloff derivatives. Finally, the influences of shale permeability, wettability, fracture complexity, and oil viscosity on the oil–water exchange behavior are investigated. Results indicate that the matrix of oil-wet shale almost does not suck water and discharge oil, and only the oil in natural fractures exchanges with the water in hydraulic fractures. The water-wet shale with low permeability, high oil viscosity, and few natural fractures needs extra soaking time to achieve good oil–water exchange performance. The suitable soaking period for the water-wet base case in this study is from 17.25 to 169 days, among which 64 days is the optimal soaking time.