A three-parameter Kozeny–Carman generalized equation for fractal porous media

The Kozeny–Carman equation is a traditional permeability–porosity relationship which has been used in many models of real problems related to flows in porous media. In spite of this, some limitations of this well-known equation has motivated the conception of different versions, specialized for particular applications. In the present article, we deduce a three-parameter Kozeny–Carman equation obtained from a fractal structure involving the specific surface and the tortuosity of the porous medium. Here, a theoretical analysis indicates that the new equation is capable to generalize several models existent in the literature. Besides, parameter estimations fitting experimental data of different materials show that the present model can be used to describe the relationship between permeability and porosity of many materials, such as sandstones, sisal fiber mat and glass fiber fabrics.