Advancing Petrophysics: How can Fractal-Based Models Help Predicting Transport Properties in Porous and Fractured Media ?

Since Mandelbrot's paradigmatic revolution, fractals have become powerful tools for comprehending the scaling characteristics of natural phenomena, from the generation of coastlines to plant growth. Research has shown the robustness of fractal-mathematics for characterizing geological properties. In the realm of porous and fractured media, fractal theory has profound implications. Drawing from microscale knowledge, fractal patterns can describe transport properties in porous and fractured media, including size distributions of pores and fractures, and pore irregularities (e.g., tortuosity and constrictivity). In this contribution, we explore transformative advancements in petrophysics, applying fractal models to predict key properties like porosity, permeability, and electrical conductivity. Diverse fractal objects, such as Sierpinski carpets and Menger sponges, play pivotal roles in upscaling procedures. They allow derivations of transport properties for saturated and partially saturated media, above and below freezing temperatures, and considering hysteretic behavior and reactive media processes. The integration of fractal-based relationships into modelling approaches opens new avenues for hydrogeophysics and critical zone geophysics.