The current studies primarily analyze the heterogeneity and complexity of mesopore structures based on low-temperature nitrogen (N₂) adsorption curves and the Frenkel–Halsey–Hill (FHH) fractal model. However, these studies ignore the fact that the low-temperature N₂ desorption curve can also reflect the desorption performance of the mesopore structure. In this research, novel fractal indicators for characterizing the adsorption–desorption performance of mesopores based on the fractal dimension from the N₂ adsorption curves and N₂ desorption curves are proposed. The novel fractal indicators I₁ and I₂ are applied to evaluate the adsorption–desorption performance of mesopores with pore size 2–5 nm and pore size 5–50 nm, respectively. The fractal indicator I₁ shows an increasing trend with coalification, reflecting that the gas adsorption performance of 2–5 nm mesopores is enhanced with coalification. The fractal indicator I₂ exhibits a trend of first increasing and then decreasing with coalification, indicating the gas desorption performance of mesopores with pore size 5–50 nm decreases first and then increases. The proposed indicators provide novel analytical parameters for further understanding the gas adsorption–desorption mechanism of porous coal-based or carbon-based materials.

The traditional Langmuir equation displays drawback in accurately characterizing the methane adsorption behavior in coal, due to it assuming the uniform surface of coal pores. Additionally, the decay law of gas adsorption capacity with an increasing coal reservoir temperature remains unknown. In this study, the fractal adsorption model is proposed based on the fractal dimension (D_f) of coal pores and the attenuation coefficient (n) of the adsorption capacity. The principles and methods of this fractal adsorption model are deduced and summarized in detail. The results show that the pore structures of the two coal samples exhibit obvious fractal characteristics, with the values of fractal dimensions (D_f) being 2.6279 and 2.93. The values of adsorption capacity attenuation coefficients (n) are estimated as −0.006 and −0.004 by the adsorption experiments with different temperatures. The proposed fractal adsorption model presents a greater theoretical significance and higher accuracy than that of the Langmuir equation. The accuracy of the fractal adsorption model with temperature effect dependence is verified, establishing a prediction method for methane adsorption capacity in deep coal reservoirs. This study can serve as a theoretical foundation for coalbed methane exploration and development, as well as provide valuable insights for unconventional natural gas exploitation.

The targeted stimulation of micropores based on the transformation of coal’s molecular structure is proposed due to the chemical properties and difficult-to-transform properties of micropores. Carbon disulfide (CS₂) extraction is used as a targeted stimulation to reveal the internal evolution mechanism of micropore transformation. The variations of microcrystalline structures and micropores of bituminous coal and anthracite extracted by CS₂ were analyzed with X-ray diffraction (XRD), low-temperature carbon dioxide (CO₂) adsorption, and molecular simulation. The results show that CS₂ extraction, with the broken chain effect, swelling effect, and aromatic ring rearrangement effect, can promote micropore generation of bituminous coal by transforming the microcrystalline structure. Furthermore, CS₂ extraction on bituminous coal can decrease the average micropore size and increase the micropore volume and area. The aromatic layer fragmentation effect of CS₂ extraction on anthracite, compared to the micropore generation effect of the broken chain effect and swelling effect, can enlarge micropores more remarkably, as it induces an enhancement in the average micropore size and a decline in the micropore volume and area. The research is expected to provide a theoretical basis for establishing reservoir stimulation technology based on CS₂ extraction.

The pore complexity and heterogeneity in porous media display obvious fractal characteristics, which can be characterized by the fractal dimension for the pore tortuosity (D_T) and the fractal dimension for the pore size (D_f). Correspondingly, a three-dimensional (3D) fractal permeability model for porous media is proposed based on the D_T and D_f. The accuracy of the proposed model is verified by the classical theoretical relation of the permeability versus porosity, the measured permeability, and the previous study. The sensitivity analysis of model parameters (D_f, D_T, λ_min and λ_max) based on elasticity coefficient indicates that the proposed model is much more sensitive to D_f and D_T than λ_min and λ_max, and more sensitive to D_f than D_T. The proposed model is much more sensitive to λ_min than λ_max. Furthermore, the proposed model is compared with the modified Kozeny–Carman equation. The root mean square error (RMSE) analysis shows that the RMSE of the proposed model and the modified Kozeny–Carman equation in predicting permeability are 8.9857 × 10⁻⁴ and 0.5082, exhibiting high prediction accuracy of the proposed model. The proposed fractal permeability model achieves a more accurate characterization of the fluid transport by more comprehensively describing the complexity and tortuosity of pore structure, which can also provide the prospective theoretical significance and method reference for predicting the permeability of 3D porous media.

Fracturing pressure serves as a pivotal parameter governing fracture expansion and permeability improvement, which is essential to enhancing coalbed methane (CBM) production via CO₂ phase transition fracturing (CO₂-PTF). In this study, laboratory CO₂-PTF experiments on coal were performed under fracturing pressures of 120 MPa, 150 MPa and 185 MPa. Combining scanning electron microscopy (SEM), computed tomography (CT) scanning and permeability testing, the fracture evolution characteristics and permeability enhancement effect of coal samples were quantitatively analyzed. The research results show that CO₂-PTF can raise the change rate of total fracture volume fraction by an order of magnitude, with absolute permeability being enhanced by one–two orders of magnitude, which further indicates an exponential-enhancement effect of CO₂-PTF pressure on coal permeability. The exponential-enhancement effect of CO₂-PTF pressure on coal permeability is closely associated with CO₂-PTF processes. The early high-pressure CO₂ jet stage main influences the fracture generation effect, and the subsequent quasi-static high-pressure gas stage induces the fracture expansion–transformation effect; collectively, these processes cause the exponential enhancement in coal permeability. The above analysis can offer theoretical guidance for the technical improvement and field application optimization of CO₂-PTF and efficient enhancement in CBM recovery.

Faults, as a kind of fracture tectonics, play a role in reservoir closure or provide oil and gas transportation channels. The accurate understanding of the distribution characteristics of faults is significant for oil and gas exploration. The traditional fractal dimension for fault number (D_f3) cannot comprehensively characterize the complexity and heterogeneity of fault network distribution. In this paper, a fractal characterization method on three-dimensional (3D) tortuosity of fault tectonics is proposed based on 3D seismic exploration. The methodology is described in detail to establish the model on the fractal dimension for the 3D tortuosity of fault tectonics. The results show the proposed method of estimation of the D_T3 displaying high accuracy and rationality. Compared with the traditional fractal dimension D_f3, the proposed D_T3 can comprehensively characterize the fractal characteristics of faults network systems in the 3D space. This study achieves a breakthrough in the fractal characterization of the 3D tortuosity of fault tectonics. It is worth further study for establishing an analytical fractal equation based on the D_T3 and oil or gas transfer, which can provide the theoretical foundation and technical support for oil and gas exploration.