Permeability of shaly sands

The permeability of a sand shale mixture is analyzed as a function of shale fraction and the permeability of the two end-members, i.e., the permeability of a clay-free sand and the permeability of a pure shale. First, we develop a model for the permeability of a clay-free sand as a function of the grain diameter, the porosity, and the electrical cementation exponent. We show that the Kozeny-Carman-type relation can be improved by using electrical parameters which separate pore throat from total porosity and effective from total hydraulic radius. The permeability of a pure shale is derived in a similar way but is strongly dependent on clay mineralogy. For the same porosity, there are 5 orders of magnitude of difference between the permeability of pure kaolinite and the permeability of pure smectite. The separate end-members' permeability models are combined by filling the sand pores progressively with shale and then dispersing the sand grains in shale. The permeability of sand shale mixtures is shown to have a minimum at the critical shale content at which shale just fills the sand pores. Pure shale has a slightly higher permeability. Permeability decreases sharply with shale content as the pores of a sand are filled. The permeability of sand shale mixtures thus has a very strong dependence on shale fraction, and available data confirm this distinctive shale-fraction dependence. In addition, there is agreement (within 1 order of magnitude) between the permeabilities predicted from our model and those measured over 11 orders of magnitude from literature sources. Finally, we apply our model to predict the permeabilities of shaly sand formations in the Gulf Coast. The predictions are compared to a data set of permeability determination made on side-wall cores. The agreement between the theoretical predictions and the experimental data is very good.