Although the hydraulic fracturing treatment can improve the conductivity of shale reservoirs, the low recovery rate of the fracturing fluid may cause potential environmental and production issues. For an accurate investigation of these issues, an appropriate model of the water imbibition in shales is required. However, the hydraulic parameters related to water imbibition in shales are hard to be measured due to their tiny pores. In this study, an effective method is proposed to estimate the water imbibition volume. The nuclear magnetic resonance method is applied to obtain the related parameters including the capillary curve, the intrinsic and relative permeability of the shale, which can significantly cut down the time and cost needed to get these data. This model is validated by water imbibition experiments. In addition, we compare two empirical equations used to calculate intrinsic permeability in the NMR method and calibrate the corresponding parameter a for shale, which is poorly investigated in literature. Finally, we suggest that the capillary force dominates the early stage of water imbibition process in unsaturated shales, and the late period may be influenced more by other mechanisms such as the osmosis and the surface hydration.

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The verifier-based key exchange protocol for three parties deals with the authenticated key agreement process between two clients with the help of a trusted server who have to store their verifiers in the server for authentication. Recently, Liu et al. proposed a key exchange protocol for three-party based on verifier authentication and claimed that their protocol could resist many familiar attacks. Unfortunately, we find out that the proposed protocol is insecure against off-line guessing attack and impersonation attack. In this paper, we conduct a detailed analysis on the flaws of Liu et al.’s protocol. In addition, a new protocol is presented with security analysis.