Fractal models to describe unsaturated flow

Fractals have been successfully used to model a wide range of complex natural phenomena in Biology, Geology and Astronomy. In this seminar I will present two constitutive models to describe unsaturated flow based on a fractal description of porous media. The first model predicts saturation and hydraulic conductivity of unsaturated fractured rocks. The fracture network is modeled using a classical fractal object known as Sierpinski carpet. The second model describes the evolution of porosity, saturation and hydraulic conductivity during rock dissolution. In this case, the porous medium is represented by an ensemble of sinusoidal capillary tubes with a fractal pore size distribution. Closed-form analytical expressions are obtained for saturation and hydraulic conductivity of both models. Model predictions are validated against experimental data from literature and classical models.