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The transverse relaxation time (T2) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in petrophysical characterization of petroleum reservoirs. This study focuses on the systematic analysis of T2 spectra and T2 cut-off values in low-permeability reservoir rocks. Analysis of 36 low-permeability cores revealed a wide distribution of T2 cut-off values, ranging from 7 to 50 ms. Additionally, the T2 spectra exhibited multimodal characteristics, predominantly displaying unimodal and bimodal morphologies, with a few trimodal morphologies, which are inherently influenced by different pore types. Fractal characteristics of pore structure in fully water-saturated cores were captured through the T2 spectra, which were calculated using generalized fractal and multifractal theories. To augment the limited dataset of 36 cores, the synthetic minority oversampling technique was employed. Models for evaluating the T2 cut-off value were separately developed based on the classified T2 spectra, considering the number of peaks, and utilizing generalized fractal dimensions at the weight <0 and the singular intensity range. The underlying mechanism is that the singular intensity and generalized fractal dimensions at the weight <0 can detect the T2 spectral shift. However, the T2 spectral shift has negligible effects on multifractal spectrum function difference and generalized fractal dimensions at the weight >0. The primary objective of this work is to gain insights into the relationship between the kurtosis of the T2 spectrum and pore types, as well as to predict the T2 cut-off value of low-permeability rocks using machine learning and data augmentation techniques. [ABSTRACT FROM AUTHOR]

The heterogeneity of reservoir micro-pores and the multifractal nature of their geometric morphology control the migration of oil and gas in porous media and affect the characteristics of oil and gas accumulation and productivity at the macro-scale. In this paper, based on high-resolution x-ray microscope computer tomography (XCT), combined with fractal and multifractal analysis, the microscopic pore-throat characteristics of 12 igneous rocks cylindrical core igneous rocks in the Huanghua Depression, China, were analyzed. A new DW interpretation chart (D = box-counting dimension; W = width of multifractal spectrum) based on fractal and multifractal analysis is presented to characterize the complexity of pore-throats in igneous rocks and to describe the influence of secondary transformation behavior on pore-throat microstructure. We found that microscopic pore-throat structures of different types of igneous rocks have significantly different fractal and multifractal characteristics. In addition, the complexity of pore-throat microstructure is indicative of the evolution dynamics of reservoir performance. The permeability of igneous rocks with simple microscopic pore-throat structures and strong heterogeneity is more sensitive to changes in porosity, and it is beneficial to the formation of high permeability oil–gas reservoirs. These results show the effect of igneous rock microstructure on macro-reservoirs and will provide a new perspective for the in-depth study of complex igneous oil–gas reservoirs. [ABSTRACT FROM AUTHOR]

Abstract Microfractures in the coal matrix have complex spatial structure because of the joint effects of coalification and tectonism. The accurate modeling and characterization of microfractures directly affect mechanism analysis of coal rock fracturing and mining. In this study, taking the high‐rank coal in the north of Qinshui Basin, structural characteristics of microfracture in intact and tectonic coals were analyzed systematically using 2D thin section, 3D micro‐CT modeling and mercury intrusion based on digital image analysis and fractal theory. The result indicates that the response sensitivity of fractal parameters obtained from different methods to microfractures from two types of coal structures is different greatly. Single fractal dimension (Df) in tectonic coal is higher than that of intact coal. Specially, for 2D thin sections, the indicative effect on the Df of manually corrected images is better than that of automatically extracted and linear ones. Df has a positive correlation with the pixel‐based microfracture porosity, as well as generalized fractal parameters. Moreover, microfracture permeability based on the Cubic‐Law increases with the increase of Df. For 3D micro‐CT modeling, the classical Watershed algorithm cannot segment the spatial microfracture network, which, however, can be segmented and characterized by the self‐developed FracSC3D program. Spatial microstructural parameters including volume, surface and length at three‐axis directions meet bifractal characteristics. Specially, for 2D micro‐CT slices, with the increase of porosity, the multifractal spectrum width Δα also increased. Besides, the fractal parameter based on Menger model from mercury intrusion experiment can act as a good indicator for identifying microfractures, flow pores and diffusion pores.

It is of great significance to study the spatial distribution patterns and petrophysical complexity of volcanic vesicles which determine whether the reservoir spaces of the volcanic rocks can accumulate oil and gas and enrich high yields or not. In this paper, the digital images of three different textures of vesicular andesite samples, including spherical vesicular andesite, shear deformation vesicular andesite, and secondary filling vesicular andesite, are obtained by microscopic morphology X-CT imaging technology. The spatial micro-vesicle heterogeneity of vesicular andesite samples with different textures is quantitatively analyzed by fractal and multifractal methods such as box-counting dimension and the moment method. It is found that the shear stress weakens the spatial homogeneity since vesicles rupture are accelerated, elongated directionally, and connected with one another under the strain; the secondary filling breaks the vesicles, which significantly enhances the spatial heterogeneity. In addition, shear stress and secondary filling increase the complexity of vesicle microstructures characterized by different fractal and multifractal parameters. These conclusions will provide important theoretical and practical insights into understanding the degassing of volcanic rocks and prediction of high-quality volcanic reservoirs. [ABSTRACT FROM AUTHOR]

Microfractures in the coal matrix have complex spatial structure because of the joint effects of coalification and tectonism. The accurate modeling and characterization of microfractures directly affect mechanism analysis of coal rock fracturing and mining. In this study, taking the high‐rank coal in the north of Qinshui Basin, structural characteristics of microfracture in intact and tectonic coals were analyzed systematically using 2D thin section, 3D micro‐CT modeling and mercury intrusion based on digital image analysis and fractal theory. The result indicates that the response sensitivity of fractal parameters obtained from different methods to microfractures from two types of coal structures is different greatly. Single fractal dimension (Df) in tectonic coal is higher than that of intact coal. Specially, for 2D thin sections, the indicative effect on the Df of manually corrected images is better than that of automatically extracted and linear ones. Df has a positive correlation with the pixel‐based microfracture porosity, as well as generalized fractal parameters. Moreover, microfracture permeability based on the Cubic‐Law increases with the increase of Df. For 3D micro‐CT modeling, the classical Watershed algorithm cannot segment the spatial microfracture network, which, however, can be segmented and characterized by the self‐developed FracSC3D program. Spatial microstructural parameters including volume, surface and length at three‐axis directions meet bifractal characteristics. Specially, for 2D micro‐CT slices, with the increase of porosity, the multifractal spectrum width Δα also increased. Besides, the fractal parameter based on Menger model from mercury intrusion experiment can act as a good indicator for identifying microfractures, flow pores and diffusion pores. Key Points: 3D microfracture network is segmented and characterized by the developed algorithm FracSC3DClassical watershed algorithm used to segment pore bodies in porous media cannot be used to segment 3D fracture surfaces in fractured media3D microfracture characteristic parameters and mercury intrusion porosimetry meet the dual fractal scaling rather than single fractal law [ABSTRACT FROM AUTHOR]

Abstract: Accessing the cyclicity and persistence of geological records with time series analysis deepens our understanding of Earth's long‐term evolution. In this study, time series from recent global zircon U‐Pb age and δ18O databases are analyzed using wavelet transform from a fractal perspective. Continuous wavelet transform of the local fractal sequences of both zircon records indicates a strong, persistent ~760 million year cycle over the 4.4 billion years of Earth's history. Wavelet coherence analysis shows that the U‐Pb age and δ18O systems are coupled in significant in‐phase coherence for a cycle of ~760 million year, implying synchronization between the two underlying processes. This study also demonstrates that the variation in the time series records manifests as 1/f β scaling behavior that persists β ~ 1.8 over the entire interval. This 1/f fractal scaling nature furnishes evidence for the conjecture that rather than being an equilibrium system, Earth's long‐term evolution follows a self‐organized pattern. [ABSTRACT FROM AUTHOR]

• Perform fractal and multifractal analysis on the asphalt mixture's aggregate skeleton and void structure. • The influence of design and construction indicators on the microstructural features of pavement materials. • The fractal/multifractal parameters' physical sense and role in characterizing the 3D microstructure are clear. The aggregate skeleton and void structure in the asphalt mixture are critical and highly correlated to the mechanical performance of the pavement. However, the extreme heterogeneity and complexity bring devastating difficulties to characterizing and analyzing the mixtures' mesostructure. Therefore, this study aimed to propose a novel depicting scheme accounting for the size distribution and spatial arrangement of the mixtures' components utilizing the fractal and multifractal analysis. Two compaction methods (Marshell and Superpave) and three design indexes (gradation, NMAS, and compaction work) were adjusted to prepare the samples, which were then scanned and digitally reconstructed. The fractal dimension (D) and related multifractal indicators (i.e., Δ α and Δ f (α)) were determined and applied to quantitative assess the structural changes. Finally, the relationships of design indexes to fractal and multifractal behaviors were comprehensively discussed. Results indicate that fractal and multifractal theories are feasible in describing the heterogeneous particle skeleton and void structure in the asphalt mixture. Firstly, the multifractal approach was proven to allow a more informative characterization of 3D systems than simple fractal theory. Moreover, the excellent correlation between the design/construction and fractal/multifractal indicators has been confirmed for asphalt pavement. Overall, the fractal and multifractal indicators enriched the options for microstructural evaluation, which will be conducive to revealing the relationship between the microstructural characteristics and mechanical performance of the asphalt mixture. [ABSTRACT FROM AUTHOR]

Abstract: Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with observable log-periodicity. We perform detailed numerical analyses of lattice multifractals and explain the origin of three different scaling regions found in the moments. A novel numerical approach is proposed to extract the log-frequencies. In the non-lattice case, there is no visible log-periodicity, i.e., no preferred scaling ratio since the set of complex exponents spreads irregularly within the complex plane. A non-lattice multifractal can be approximated by a sequence of lattice multifractals so that the sets of complex exponents of the lattice sequence converge to the set of complex exponents of the non-lattice one. An algorithm for the construction of the lattice sequence is proposed explicitly. [Copyright &y& Elsevier]