Fractal dimensions of shale

• We analyze the fractal properties of different shales.
• We determine the fractal dimensions of the pore space for each shale.
• We present two fractal patterns for the connected path of the pore space at the core scale.

High-resolution images provide detailed information about pores whose characteristic sizes are usually on the order of few nanometers to micrometers in shales, but it remains challenging to relate the acquired information to the transport properties of a sample whose size is usually on the order of centimeters. It is not yet possible to determine the effective connectivity of the pore space at the core scale (∼1 cm) from high-resolution images. With this in mind, we analyze drainage experiments conducted on cores to interpret the topology of the connected path of the pore space at the core scale. Our study for different shales shows that the distance traveled inside the pore space—the length of the pore space—by the nonwetting phase at each capillary pressure is a fractal, unlike the pore volume, which is not necessarily a fractal. We determine the fractal dimensions for different shales and present two fractal models. This study can have major implications for understanding hydrocarbon transport in shales.