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The rock cores of low permeability reservoirs have special pore structures, which are the essential factors to determine the seepage capacity and oil displacement efficiency and directly affect oil and gas reserves and oil well productivity. This paper studies 16 digital rock core samples. Based on the fractal theory for porous media, we carried out the fractal characterization of the pore structure of the samples by an approach combined with binarized CT images and fractal theory. The computing software based on the Box-counting method was used to measure and calculate the fractal dimension and porosity of the samples, and the calculated results were compared with the binarized CT data from the laboratory. It was found that among the tested samples, the results of 12 rock core samples were in good agreement with the experimental data, indicating that the fractal theory is effective in the measurement of fractal dimension and in the calculation of porosity of digital rock core samples. For the results with larger errors compared to laboratory data, we also analyzed and elaborated the reasons from the relevant binarized images and pore distribution images of samples. It is also found that the minimum pore size has a significant impact on the results when the fractal theory was applied to analyze the digital rock core samples. Finally, a standard or criterion is established whether the pore/particle size distribution in a digit rock core/porous medium is fractal or non-fractal.

The sandstone micro-structure is one of the most important parameters for quantitative evaluation of groundwater/oil/gas resources and prediction of flow rates of water/oil/gas. In this study, we applied seven low-permeability sandstone samples obtained from North China to study the structures of pore and solid phase based on digital core technology and the fractal theory. In this work, rock images were collected by scanning electron microscopy (SEM), and then image software (image pro plus) was applied to convert the SEM images into binary images and calculated the perimeter and area of pores and particles. Using the fractal medium criterion, we analyzed the fractal characteristics of pore and solid phases, and then we extended the criterion from the pore phase to both pore and solid phases. This paper explores the relationship among the pore and solid phase fractal characteristics, porosity, pore size, particle size and fractal dimensions for pores and particles. The results were compared with the experimental data and showed that the solid phase satisfies the fractal distribution, while the pore phase dissatisfies the fractal distribution. It was also found that the minimum and maximum pore and particle sizes, magnification times have a significant effect on the results. In addition, by introducing the diameter and mean hydraulic radius into Ergun–Wu equation, the permeabilities of the samples were calculated.

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.