One of the key time-dependant mechanisms for wellbore failure in shales is the penetration of drilling mud into the formation. Previous studies attempted to predict mud pressure penetration into shales using single-phase flow approach. This can lead to some errors because it ignores the two-phase flow and capillary effects. In this study, a numerical model has been used to study fluid flow in shales. For modeling of two-phase flow, relative permeability curve was calculated using modified Corey's method, which is based on pore size distribution. The pore size distribution of shales was quantified by using mercury injection tests. It has been observed that the two-phase flow model can predict mud pressure penetration reasonably well when the permeability of shales is relatively high (k is greater than 500 nD). This approach has an application for the prediction of mud pressure penetration in shales with drilling induced or natural fractures, which may significantly enhance shale's permeability. It was also found that the two-phase fluid flow model, even possibly Darcy's law in general, may be inadequate when shale's permeability is low and the pressure differential is high. Possible explanations are that shales have a complex structure, with different types of water present, and predominant surface interactions, which may change shales' permeability significantly, thus making Darcy's law inadequate. Future work is recommended for investigations into fundamental laws governing fluid flow in shales in order to improve the prediction of time-dependent wellbore instability in shales.

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