In order to better understand nanopore structure and fractal characteristics of lacustrine shale, nine shale samples from the Da’anzhai Member of Lower Jurassic Ziliujing Formation in the Sichuan Basin, southwestern (SW) China were investigated by total organic carbon (TOC) analysis, X-ray diffraction (XRD) analysis, field emission scanning electron microscopy (FE-SEM), and low-pressure N₂ adsorption. Two fractal dimensions D₁ and D₂ (at the relative pressure of 0–0.5 and 0.5–1, respectively) were calculated from N₂ adsorption isotherms using the Frenkel–Halsey–Hill (FHH) equation. The pore structure of the Lower Jurassic lacustrine shale was characterized, and the fractal characteristics and their controlling factors were investigated. Then the effect of fractal dimensions on shale gas storage and production potential was discussed. The results indicate that: (1) Pore types in shale are mainly organic-matter (OM) and interparticle (interP) pores, along with a small amount of intraparticle (intraP) pores, and that not all grains of OM have the same porosity. The Brunauer–Emmett–Teller (BET) surface areas of shale samples range from 4.10 to 8.38 m²/g, the density-functional-theory (DFT) pore volumes range from 0.0076 to 0.0128 cm³/g, and average pore diameters range from 5.56 to 10.48 nm. (2) The BET surface area shows a positive correlation with clay minerals content and quartz content, but no obvious relationship with TOC content. The DFT pore volume shows a positive correlation with TOC content and clay minerals content, but a negative relationship with quartz content. In addition, the average pore diameter shows a positive correlation with TOC content and a negative relationship with quartz content, but no obvious relationship with clay minerals content. (3) Fractal dimension D₁ is mainly closely associated with the specific surface area of shale, suggesting that D₁ may represent the pore surface fractal dimension. Whereas fractal dimension D₂ is sensitive to multiple parameters including the specific surface area, pore volume, and average pore diameter, suggesting that D₂ may represent the pore structure fractal dimension. (4) Shale with a large fractal dimension D₁ and a moderate fractal dimension D₂ has a strong capacity to store both adsorbed gas and free gas, and it also facilitates the exploitation and production of shale gas.

In the field of fractal theory, the study of permeability in tree-like branching networks has always been rather popular. However, most of the studies have been focused on the permeability models of common fluids. In this study, based on fractal theory and the theory of power-law fluid, a fractal model of the permeability of power-law fluid in a damaged tree-like branching network considering roughness is derived. This study discusses the effects of power-law index, roughness level, damage degree, branching layer number, and length ratio on permeability. The results show that the permeability decreases with an increase in the power-law exponent, roughness, damage degree, bifurcation layer number, and length ratio when the diameter ratio is relatively small; on the contrary, with an increase in the diameter ratio and the power-law exponent, the permeability will increase with an increase in the bifurcation layer number; the permeability will decrease with an increase in the bifurcation layer number when the diameter ratio is large and the power-law exponent is small. The proposed model can be used to analyze the permeability of power-law fluid in a rough damaged tree-like branching network.

The investigation of permeability in tree-like branching networks has attracted widespread attention. However, most studies about fractal models for predicting permeability in tree-like branching networks include empirical constants. This paper investigates the flow characteristics of power-law fluids in the dual porosity model of porous media in embedded tree-like branching networks. Considering the inherent properties of power-law fluids, non-Newtonian behavior effects, and fractal properties of porous media, a power-law fluids rheological equation is introduced based on the fractional-derivative theory and fractal theory. Then, an analytical formula for predicting the effective permeability of power-law fluids in dual porous media is derived. This analytical formula indicates the influences of fractal dimensions and structural parameters on permeability. With increasing length ratio, bifurcation series, and bifurcation angle, as well as decreasing power-law exponent and diameter ratio, the effective permeability decreases to varying degrees. The derived analytical model does not include empirical constants and is consistent with the non-Newtonian properties of power-law fluids, indicating that the model is an effective method for describing the flow process of complex non-Newtonian fluids in porous media in natural systems and engineering. Therefore, this study is of great significance to derive analytical solutions for the permeability of power-law fluids in embedded tree-like bifurcation networks.

Quantitative assessment is still lacking on the pore sizes distribution of micropores and mesopores and the major controlling factors remains enigmatic for the continental Chang 7^th shale reservoirs in Southeastern Ordos Basin. In this study, scanning electron microscopy, organic geochemical analysis, low-temperature gas adsorption, high-pressure mercury injection, and X-ray diffraction analysis were conducted on 29 core samples from representative 8 wells in the Xiasiwan-Yanchang area, yielding a particular investigation on characteristics and controlling factors of pore structure in the Chang 7^th shale. The Chang 7^th shale is mainly characterized by organic and secondary micro- and mesopores, respectively ranging the peaks of pore size from 0.35 to 0.65 nm, 0.75 to 1.00 nm, 1.10 to 1.35 nm, and from 4 to 13 nm. Whole-aperture characterization of pore structure shows that meso- and macropores demonstrate a major contribution to total pore volume and the surface area is mainly provided by micro- and mesopores with pore radii less than 20 nm. A weak positive variation was identified between the pore volume of micro-mesopores and TOC content, implying that micropores are currently in the process of developing. The micro-mesopores specific surface area & volume respectively yield a significant positive and weak variation with the quartz and clay mineral content, suggesting that siliceous minerals are favorable for micro-mesopores development. The infusion of siliceous biogenic debris and silica-replaced carbonate biogenic debris from the northeastern and southwestern source areas, respectively, is likely responsible for development of biogenic siliceous minerals in the Chang 7^th shale. Furthermore, the hollow cavities in siliceous organisms have considerably contributed to the preservation of primary pores owing to their characteristic skeleton-supported framework.