Digital core and pore network model reconstruction based on random fractal theory

Microscopic structures of porous media are mainly reconstructed using physical experimental methods and numerical reconstruction methods. However, their accuracy is closely related to the resolution of real rock core images and polishing techniques of core chips amongst others, which significantly limit the development of micro-network flow simulation. In this paper, we proposed a new method for digital reconstruction of rock cores on the basis of the random fractal theory. First, we quantitatively describe and identify the multiple fractal dimension and self-similar interval of CT scanning data of 10 sets of rock cores based on the fractal characteristics of microscopic pore structures. Then, we derive a set of fractal expressions of the random probability density function, mean, and variance based on the random distribution theory, and apply the direct sampling method of continuously distributed random variables to obtain the porous media pore data satisfying multi-fractal characteristics. The results show that the rock core data constructed using our method are in a good agreement with the original experimental data, and better than those obtained from single fractal dimension and other distribution characteristics. Furthermore, we analyzed the size distribution of microscopic pores of 3 real rock cores obtained using mercury intrusion porosimetry based on the multi-fractal theory, and determined the multi-fractal interval and dimension of their microscopic pore distribution. We applied our method to design the pore structure and the throat structure of porous media and established a three-dimensional PNM. At last, the network model simulator, which simulates the oil-water flow through the interconnected pore model, proves to be a powerful investigative tool to study the nature of fluid flow at a pore scale level.