Fractal and multifractal analysis of carbonate pore-scale digital images of petroleum reservoirs

The petrophysical evaluation of the reservoir capacity is of great importance in predicting the reserves and productivity of petroleum fields, which may directly affect petroleum exploration. In the past, such kind of evaluation was mainly based on the experimental measurements of the petrophysical porosity and permeability of reservoir rock samples. Assessing quantitatively the microstructures of carbonates, including irregularities of pore shapes and frequency distributions of pore sizes, is becoming one of the most challenging efforts in pore-scale analysis. Based on the digital analyses of the two-dimensional images from thin sections taken under the environmental scanning electron microscope (ESEM) at various magnification scales, the current paper tries to quantify the pore spaces of carbonate samples by fractal and multifractal methods, which have been demonstrated to be effective. The study area is located in the western Hubei and eastern Sichuan, China. As many as 25 carbonate samples from various members in five formations of the Permian-Triassic periods and 132 ESEM images were chosen in this study. All individual pores had been recognized, and their areas and perimeters had been calculated as well. The box-counting fractal dimensions and four major multifractal parameters associated with the multifractal spectra are used. The results show that the values of the petrophysical porosity and permeability are closely related to the box-counting dimensions and the multifractal parameters, which demonstrates that the textural arrangements of the pores control the porosity and permeability to a certain extent. There is also a link between the reservoiring capabilities of different formations and the fractal and multifractal parameters. The reservoiring capability assessment result is in agreement with the field research analysis.