Search Results (102)

The pore-throat structure is a key factor in the exploration and development of tight sandstone reservoirs. In the present study, 14 tight sandstone samples from the Chang 8 member of the Ordos Basin were analyzed using high-pressure mercury intrusion, cast thin section analysis, scanning electron microscopy and cathodoluminescence imaging techniques. Fractal dimensions, obtained from the slopes of log(S_W) versus log(P_c) double-logarithmic plots, were applied to quantitatively characterize pore-throat structures and classify reservoirs through multifractal analysis, and discuss the diagenetic controlling factors affecting the pore-throat structure of different reservoir types. The results showed that the Chang 14 tight sandstones are characterized as two segments fractal features, which indicated that these samples have complex pore-throat structure and consist of two types of spaces: mesopore-throat spaces and micropore-throat spaces. The mesopore-throat system shows a higher fractal dimension (D1: 2.74–2.99), indicating greater heterogeneity and irregularity, while the micropore-throat system exhibits a lower dimension (D2: 2.28–2.61). D1 exhibits a negative correlation with the porosity and permeability of mesopores, while D2 shows a weak positive correlation with the properties of micropores. The total fractal dimension (D) is weakly correlated with overall reservoir properties, confirming that reservoir storage and flow capacity are primarily governed by the mesopore system rather than the micropore system. By analyzing the contribution of pore throats to sample physical properties, the results indicate that the 14 samples can be classified into two types based on 35% porosity contribution and 60% permeability contribution thresholds. Type 1, reservoirs dominated by microporous throat space (D values ranging from 2.603 to 2.644); Type 2, reservoirs dominated by mesoporous throat space (D values ranging from 2.544 to 2.598). Type 1 is characterized by primary intergranular pores, residual intergranular pores and intergranular dissolution pores, which enhance connectivity and reduce network complexity, thereby improving fluid permeability. In contrast, Type 2 consists mainly of intragranular dissolution pores, intergranular gap pores and micro-dissolution pores in clay minerals, which significantly inhibit fluid mobility. Diagenesis, including compaction, dissolution and cementation, exerts a significant control on the fractal characteristics and pore-throat structure evolution. The fractal characteristics exhibited in the pore-throat structure could provide a desirable analytical method, distinguishing from classification based on scale or size, for the evaluation and classification of tight sandstone reservoirs. Full article

Background: This study analyzed spectral alterations of heart rate variability (HRV) in Williams syndrome (WS) during sleep, taking into account the multi-fractal properties of RR-interval spectra, including effects of aging and sleep structure. Methods: Using ECG recordings of 20 subjects with WS and matched typically developing (TD) controls, fractal and oscillatory spectral components of RR-intervals were computed. The fractal component was parametrized with a piecewise-linear function, allowing a breakpoint and separate slope and intercept values in the lower- and higher-frequency domains. The dominant peak frequency and prominence were extracted from the LF (0.04–0.15 Hz) and HF (0.15–0.4 Hz) bands. Results: Strong WS/TD group differences were found in the breakpoint frequency, high domain slope, intercept and HF peak prominence. The LF peak frequency showed a slight age-dependent decrease only in TD, and reduced values in WS independent of age. Principal component analysis identified a main fractal component describing typical alterations in the spectrum in WS, which exhibited sleep-structure associations. Conclusions: The broken power-law model successfully characterized the fractal component of RR-interval spectra, capturing altered cardiac regulation in WS, while suggesting the fractal parameters as possible biomarkers of the degree of general autonomic deregulation. Full article

The relationship between pore structure heterogeneity in tight sandstone reservoirs and their fractal characteristics is well documented. However, the impact of differential diagenesis across lithofacies on pore-throat structure and fractal properties remains unclear. In this study, we investigate the Carboniferous Benxi Formation in the Ordos Basin using a suite of experiments to characterize pore-throat structure and multifractal behavior, and to assess the influence of diagenesis. The results reveal significant differences among lithofacies in mineral composition, pore types, pore throat structure, fractal dimensions, and petrophysical properties, primarily attributed to variations in sedimentary environments and diagenesis. Fractal characteristics were quantified by converting the T₂ spectra into pore-throat size distributions. Macropores exhibit the highest fractal dimensions, indicating the greatest structural complexity and heterogeneity, followed by mesopores, whereas micropores show the lowest heterogeneity (D₃ > D₂ > D₁). Quartz content mainly controls the fractal properties of macropores by enhancing structural stability, whereas clay minerals govern the fractal behavior of micropores and mesopores by increasing pore-throat complexity. High-energy depositional conditions promote sediment transportation and sorting, leading to quartzarenite lithofacies (QL) and sublitharenite lithofacies (SL) with lower fractal dimensions, more uniform pore structures, and better connectivity. In contrast, feldspathic litharenite lithofacies (FL) and litharenite lithofacies (LL) exhibit higher fractal dimensions due to stronger compaction, reduced primary porosity, and higher clay content, resulting in poorer reservoir quality. This study improves understanding of pore structure heterogeneity in tight sandstones and provides useful insights for predicting high-quality reservoirs in similar geological settings. Full article

The deep marine shale of the Wufeng–Longmaxi (WF–LMX) Formation in the Sichuan Basin is characterized by laterally continuous thickness, high porosity, and significant gas content, making it a representative shale reservoir with considerable resource potential. This study investigates the heterogeneity of pore structures and their controlling factors using shale samples from three representative wells, based on low-temperature nitrogen adsorption and mercury intrusion data. The reservoir can be classified into three main lithofacies: mixed siliceous shale (MSS), clay-rich siliceous shale (CSS), and siliceous clay mixed shale (SMS). The results show that siliceous shales (MSS and CSS) exhibit higher total organic carbon and quartz contents, with more developed pore systems. Among them, the CSS exhibits the highest specific surface area and the largest mesopore and macropore volumes, indicating a greater development of larger pores and superior reservoir quality. All three shale facies exhibit clear single and multifractal characteristics. The average D₁ and D₂ values (fractal dimensions from nitrogen adsorption at P/P₀ < 0.45 and >0.45, respectively) are higher than D_Hg, (fractal dimension from mercury intrusion), indicating greater pore-surface roughness than internal pore structure complexity and stronger heterogeneity in larger pores. The D(q)–q spectrum shows a left-wide/right-narrow pattern, whereas the α–f(α) spectrum exhibits the opposite trend. The branch-width ratios S_kd and S_ka (indices of pore-size distribution complexity and heterogeneity) are both <0.1, suggesting that heterogeneity is more pronounced in low-probability regions. Fractal and multifractal analyses reveal significant pore structure heterogeneity across different lithofacies, with CSS showing relatively more homogeneous pore structures, whereas MSS exhibits stronger heterogeneity and poorer connectivity. The heterogeneity of shale reservoirs is primarily controlled by pore development, especially micropores and mesopores, and is strongly influenced by total organic carbon and quartz content. Full article

Understanding the multifractal dynamics of carbon and energy markets is essential for capturing complex cross-market interactions and policy-induced volatility. This study investigates China’s carbon and energy markets from 16 July 2021 to 30 January 2026, integrating macro policy interventions with nonlinear market evolution. We first employ a Generalized Autoregressive Conditional Heteroskedasticity-Dynamic Conditional Correlation (GARCH-DCC) model with exogenous policy variables to quantify volatility spillovers and dynamic correlations under policy shocks. Then, a rolling-window multifractal detrended cross-correlation analysis (MF-DCCA) is applied to reveal multiscale dependencies, characteristic periods, and complex fractal structures in cross-market linkages. The results indicate: (1) pronounced spillover effects exist among carbon and energy markets, with policy interventions amplifying short-term contagion; (2) policy shocks exert a “green-squeezing” effect, particularly in the coal market, while endogenous volatility structures exhibit long-term resilience; (3) cross-market linkages display multifractal characteristics, with turning points between the carbon market and electricity, new energy, and coal markets at approximately 6.28, 5.58, and 6.96 months, respectively. These findings provide insights for policymakers in designing differentiated energy regulations and for investors in multiscale risk management and asset allocation. Full article

Complex biological and medical systems often exhibit irregular and self-similar structures that can be effectively analyzed using fractal and multifractal frameworks. This study aims to provide a comprehensive overview of multifractal analysis as a mathematical tool for characterizing complex biomedical patterns and improving disease diagnosis. The methods discussed include the Wavelet Transform Modulus Maxima (WTMM) and box-counting techniques, which quantify local scaling behaviors and heterogeneity within medical images. A review of recent studies demonstrates that multifractal parameters have successfully differentiated between normal and pathological tissues in diseases such as cancer, cardiac disorders, and Alzheimer’s disease. This paper also examines the integration of artificial intelligence, particularly machine learning algorithms, with multifractal features to enhance diagnostic accuracy and automate image interpretation. The results indicate that this hybrid approach improves the reliability and sensitivity of early disease detection. In conclusion, multifractal analysis, when systematically applied and combined with AI, offers a promising complementary framework for advancing precision medicine and supporting clinical decision-making. Full article

Dew constitutes a component of the near-surface water balance, but its large-scale fractal dynamical properties remain poorly documented across Africa. This study estimates dew amounts and investigates their fractal and multifractal behavior under African climatic conditions using gridded ERA5 datasets from 1993 to 2022. The Rescaled-Range (R/S) method, Multifractal Detrended Fluctuation Analysis (MFDFA), and the Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) algorithm are used. Hurst exponent (Hu) and the multifractal spectrum width (ω) are evaluated at daily and monthly scales over the full period and two sub-periods (1993–2007 and 2008–2022). The results reveal pronounced spatial heterogeneity in dew distribution. Daily mean amounts range between 0 and 0.18 mm, corresponding to annual accumulations reaching up to ~85 mm·yr⁻¹ in humid coastal, equatorial, and sub-equatorial regions, while remaining below 0.5 mm·yr⁻¹ in hyper-arid deserts. The continental mean annual amount is ~35.5 mm·yr⁻¹. The Hurst exponent exhibits values between zero and one, indicating region-dependent persistent and anti-persistent behaviors. This suggests that prediction schemes based on preceding values may be suitable for dew time series prediction in African regions exhibiting persistent characteristics. The multifractal spectrum width (ω), reaching values of up to 10, highlights strong scaling heterogeneity, particularly at the monthly timescale. These findings indicate that African dew dynamics exhibit significant long-range dependence and multifractal variability, providing new insights into the intrinsic temporal structure of dew and into appropriate approaches for its forecasting. Full article

Power system blackouts represent typical manifestations of instability in complex systems, whose evolution often exhibits non-stationarity, long-range correlations, and nonlinear scaling behavior. Most reliability assessment methods widely used in engineering practice are built on the core assumptions of event independence and light-tailed distribution, which will inevitably lead to systematic underestimation of extreme tail risks when blackouts actually present long-range memory and power-law heavy-tailed characteristics. Based on long-cycle historical blackout records of China’s power grid spanning 1981–2025, this paper develops an integrated framework combining Self-Organized Criticality (SOC) theory, Hurst exponent analysis, symbolic time-series methods, and Multifractal Detrended Fluctuation Analysis (MFDFA). This study systematically characterizes the evolution law and inherent dependence structure of blackout events from four dimensions: statistical scaling, temporal correlation, nonlinear structure, and multi-scale fractal spectrum. The results show that both the load-loss magnitudes and inter-event intervals of blackouts follow strict power-law distributions, with the system exhibiting scaling behavior consistent with SOC theory. The blackout event sequence presents significant long-range positive correlation and self-similarity, confirming a persistent long-term memory effect in the system evolution. Symbolic analysis further reveals the nonlinear fluctuation patterns and burst clustering behavior of the blackout process, reflecting the intermittency and complexity of blackout risks. MFDFA results verify that the blackout sequence has a broad-spectrum multifractal structure across different temporal scales, and Monte Carlo shuffle tests demonstrate that this multifractality mainly arises from intrinsic long-range temporal correlations, rather than being driven solely by heavy-tailed distribution. This study confirms that blackouts in China’s power grid are not random independent events, but present fractal statistical characteristics consistent with the self-organized critical mechanism. The findings provide a novel fractal perspective and quantitative framework for the statistical characterization, operational security assessment, and multi-scale early-warning modeling of blackout risks in China’s large-scale power systems. Full article

Tight sandstone reservoirs are characterized by highly heterogeneous pore structures, in which multiscale pore–throat systems jointly control the shapes of capillary pressure curves and relative permeability, thereby exerting a fundamental influence on water production behavior and the overall development performance of gas reservoirs. The Ordos Basin is generally characterized by the development of tight sandstone. The tight sandstones exhibit porosities of 2–13% and permeabilities of 0.01–10 × 10⁻³ μm². To quantitatively elucidate the controlling mechanisms of multiscale pore structure on capillary pressure curve morphology and relative permeability, this study systematically investigates the fractal and multifractal characteristics of pore structures in tight sandstones based on high-pressure mercury intrusion (MICP) and nuclear magnetic resonance (NMR) experimental data, and establishes a quantitative relationship between fractal parameters and the capillary pressure curve shape parameter λ. First, capillary pressure curves were fitted using the Brooks–Corey model within the effective saturation interval to extract the shape parameter λ, which characterizes the concentration degree of pore-size distribution and the drainage behavior. Subsequently, based on NMR T₂ spectra, the small-pore fractal dimension D₁, large-pore fractal dimension D₂, and the multifractal singularity spectrum width Δα were extracted to quantitatively describe the geometric complexity of pore structures at different scales. On this basis, the correlations between λ and D₁, D₂, and Δα were systematically analyzed, and the predictive performance of λ under different parameter combinations was compared. The results indicate that: (1) the pore structures of tight sandstones exhibit pronounced fractal and multifractal characteristics at the NMR T₂ scale, with significant differences among samples; (2) λ shows an overall negative correlation with fractal parameters, among which the correlations with the large-pore fractal dimension D₂ and the multifractal spectrum width Δα are the most significant; (3) compared with models using a single fractal dimension, the multiparameter model incorporating Δα provides a more comprehensive characterization of multiscale pore heterogeneity, leading to a substantial improvement in the accuracy and stability of λ prediction; and (4) λ exerts a clear control on the shape of relative permeability curves, where a larger λ corresponds to earlier initiation and forward-shifted rising segments of water-phase flow, while a smaller λ results in overall flatter relative permeability curves. From the perspectives of fractal and multifractal theory, this study establishes an intrinsic linkage among pore structure, capillary pressure curve shape parameters, and relative permeability, providing a novel quantitative framework for constraining relative permeability curve morphology in tight sandstones under conditions where systematic relative permeability experiments are unavailable. Full article

Quantifying the heterogeneity of pore-throat structure and evaluating reservoir quality are of great significance in the exploration and development of tight sandstone oil and gas reservoirs. This study focused on 10 samples of tight sandstone from the Benxi Formation in the Ordos Basin of China. Based on nuclear magnetic resonance (NMR) and combined with the theory of multifractal analysis to calculate multifractal parameters, the pore structure and fractal characteristics of tight sandstone reservoirs were characterized. The results showed that the dominant minerals are quartz, clay minerals, rock fragments and calcite, while feldspar content is relatively minor. The NMR T₂ spectra all exhibited bimodal characteristics. The pore size distribution of the reservoir has multifractal characteristics. The multifractal parameters D_min-D_max range from 2.02 to 2.88, D_min/D_max ranges from 3.69 to 5.11, and △α ranges from 2.441 to 3.316. Different mineral components had different effects on the fractal characteristics. The increase in quartz content retained more primary intergranular pores, affecting the fractal dimension of large pores, and weakening the heterogeneity of the pores. The increase in calcite and clay minerals corresponded to the enhancement of micropores and mesopores, increasing the heterogeneity of the pore structure. Based on the reservoir classification using multifractal parameters, the evolution of pore heterogeneity in tight sandstone rocks can be quantified, thereby effectively evaluating reservoir quality. Overall, reservoirs with larger D_min-D_max and D_min/D_max values, smaller △α, weaker porosity heterogeneity, and better connectivity are favorable areas for hydrocarbon exploration and development. The comprehensive fractal characterization of tight sandstone reservoirs demonstrates the applicability of multifractal dimensions in characterizing the heterogeneity of pore structures in tight sandstones, and is a key factor in improving the exploration effectiveness and development benefits of tight sandstone oil and gas reservoirs. Full article

Unique fractal characteristics are significantly controlled by shale lithofacies, mineralogical characteristics, and OM features, which in turn determine reservoir properties and gas-bearing capacity. However, a comprehensive understanding of fractal features has remained insufficient. This study presents a systematic investigation into the full-scale pore size distribution for the Wufeng–Longmaxi shales in Sichuan Basin which employed low-pressure CO₂ adsorption (CO₂GA), N₂ adsorption (N₂GA), and mercury injection capillary pressure (MICP), as well as field emission scanning electron microscope (FE-SEM) techniques. The fractal dimensions of pores across different pressure ranges were revealed by different fractal models. The results demonstrate that the shale pores are dominated by micro- to mesopores and partial extremely larger pores, contributed primarily by organic matter (OM) pores and microcracks, respectively. Fractal dimensions follow a consistent increasing order: D_C < D_N1 < D_N2 < D_M or D_C < D_N1 < D_M < D_N2, suggesting that larger pores with diameters lager than 5 nm are more heterogeneous and complex compared to the pores less than 5 nm (smaller pores). This is because smaller pores are predominantly composed of OM pores, while larger pores comprise a mixture of OM pores, mineral-related pores, and microcracks. Different fractal dimensions, in turn, are influenced by distinct factors. The D_C value exhibits a positive correlation with micropore volume. D_N1 and D_N2 values are positively correlated with the content of brittle minerals and TOC, while they show negative correlations with the content of clay minerals. Notably, D_M values do not demonstrate a significant correlation with shale compositions, primarily owing to the development of microcracks. Fractal dimensions, particularly D_N1 and D_N2, are significantly controlled by the lithofacies of shale. The highest D_N1 and D_N2 values occur in the siliceous shale lithofacies, and the mixed shale lithofacies exhibit moderate D_N1 and D_N2 values, whereas the lowest D_N1 and D_N2 values primarily occur in clay-rich shale lithofacies. Different fractal dimensions show various correlations with shale gas content. The Langmuir volume as well as total gas content exhibit significant correlations with D_N1 and D_N2 values, while they exhibit no obvious correlations with D_C and D_M values. This implies that pores with diameters of 1.8–55 nm serve as primary storage sites for both adsorbed and free gas. The findings can significantly improve the cognition of adsorbed gas and free gas behavior in shale reservoirs. Full article

Cementitious composites are heterogeneous porous materials whose pore structure plays a critical role in resistance to chloride-ion penetration. A waterborne nano-silicate-based densifier (CF-S5) was used to examine its influence on the pore structure and resistance to the chloride ion penetration of mortar. We investigated the resistance to the chloride ion penetration of mortar with added CF-S5 admixture through the Rapid Chloride Permeability Test (RCPT). We investigated the pore structure characteristics of mortar by mercury intrusion porosimetry (MIP) coupled with fractal theory and investigated the degree of hydration of the cement paste by thermogravimetric analysis (TG). Ultimately, the degree of correlation between multifractal parameters and the chloride ion migration coefficient of mortar was examined using gray relational analysis (GRA). Results indicate that the CF-S5 admixture reduces mortar porosity and the content of harmful pores while increasing pore tortuosity, thus improving the resistance to the chloride ion penetration of mortar. Multifractal analysis indicated that the CF-S5 admixture decreased the connectivity and increased the complexity of the mortar pore structure. The CF-S5 admixture did not reduce the hydration degree of cement paste at 28 d. Additionally, the multifractal parameters show a high gray relational degree with the chloride migration coefficient; therefore, they may serve as potential indicators to reflect the resistance to the chloride ion penetration of mortar. Full article

Deep coalbed methane (CBM) development in the Eastern Ordos Basin indicates that strong vertical heterogeneity within the Benxi Formation No. 8 thick coal seam can severely constrain well productivity. Here, twelve coal samples from two typical wells (W1: upper coal seams; W2: lower coal seams) were analyzed to quantify vertical variability in pore structure and its controls. Proximate and maceral analyses were combined with low-temperature N₂ adsorption (2–100 nm) and CO₂ adsorption (<2 nm) to characterize mesopores and micropores, respectively; mono-fractal and multifractal approaches were further applied to quantify pore-system heterogeneity. The results indicate that upper coal seams (W1) exhibit more developed micropores and stronger adsorption capacity, while the lower coal seams (W2) display more significant heterogeneity in pore structure, particularly at the micropore scale. Ash content is identified as the dominant control factor for vertical variations in pore characteristics, showing a negative correlation with both micropore and mesopore volumes, while coal rank and maceral composition exert secondary influences. A vertical zoning model has been established based on multiple parameters: the upper section is classified as a high-quality sweet-spot interval, whereas only localized layers in the lower section retain development potential. These findings can serve as a geological basis for optimizing target layer selection and fracturing design in deep coalbed methane wells. Full article

This work presents a lightweight and interpretable framework for the early warning of voltage stability degradation in distribution networks, based on fractal and spectral features from flow measurements. We propose a Fast Voltage Stability Index (FVSI), which combines four independent indicators: the Detrended Fluctuation Analysis (DFA) exponent α (a proxy for long-term correlation), the width of the multifractal spectrum Δα, the slope of the spectral density β in the low-frequency range, and the $c_2$ curvature of multiscale structure functions. The indicators are calculated in sliding windows on per-node series of voltage in per unit Vpu and reactive power Q, standardized against an adaptive rolling/first-N baseline, and anomalies over time are accumulated using the Exponentially Weighted Moving Average (EWMA) and Cumulative SUM (CUSUM). A full online pipeline is implemented with robust preprocessing, automatic scaling, thresholding, and visualizations at the system level with an overview and heat maps and at the node level and panel graphs. Based on the standard IEEE 13-node scheme, we demonstrate that the Fractal Voltage Stability Index (FVSI_Fr) responds sensitively before reaching limit states by increasing α, widening Δα, a more negative $c_2$, and increasing β, locating the most vulnerable nodes and intervals. The approach is of low computational complexity, robust to noise and gaps, and compatible with real-time Phasor Measurement Unit (PMU)/Supervisory Control and Data Acquisition (SCADA) streams. The results suggest that FVSI_Fr is a useful operational signal for preventive actions (Q-support, load management/Photovoltaic System (PV)). Future work includes the calibration of weights and thresholds based on data and validation based on long field series. Full article

River discharge scaling is fundamental to the global hydrological cycle and to water resource assessment. This study investigates the existence of multiple scaling regimes and introduces a novel framework for clustering river discharge using multiscale fractal characteristics. We analyzed daily discharge data from 38 stations across continental Canada over an 80-year period. Multifractal characterization was performed at decadal and long-term scales using three key parameters: the singularity exponent (${\alpha }_0$), multifractal strength ($\alpha$), and asymmetry index (r). K-means clustering in the $\alpha -r$, ${\alpha }_0-r$, and $\alpha -{\alpha }_0$ planes revealed distinct clusters, with the asymmetric parameter (r) emerging as the strongest distinguishing factor. These clusters represent groups of rivers with similar dynamical structures: the $\alpha -r$ clusters categorize discharge based on scaling strength and fluctuation influence. Analysis of the generalized Hurst exponent revealed anti-persistent behavior at most stations, with exceptions at five specific locations. This multifractal clustering approach provides a powerful method for classifying river regimes based on intrinsic characteristics and identifying the physical drivers of discharge fluctuations. Full article