Theoretical Insight Into the Empirical Tortuosity‐Connectivity Factor in the Burdine‐Brooks‐Corey Water Relative Permeability Model

Abstract A model commonly applied to the estimation of water relative permeability k rw in porous media is the Burdine‐Brooks‐Corey model, which relies on a simplified picture of pores as a bundle of noninterconnected capillary tubes. In this model, the empirical tortuosity‐connectivity factor is assumed to be a power law function of effective saturation with an exponent ( μ ) commonly set equal to 2 in the literature. Invoking critical path analysis and using percolation theory, we relate the tortuosity‐connectivity exponent μ to the critical scaling exponent t of percolation that characterizes the power law behavior of the saturation‐dependent electrical conductivity of porous media. We also discuss the cause of the nonuniversality of μ in terms of the nonuniversality of t and compare model estimations with water relative permeability from experiments. The comparison supports determining μ from the electrical conductivity scaling exponent t , but also highlights limitations of the model.