Lower Fractal Dimension Research Articles

Rural Morphology and Forces Driving Change in Rapidly Urbanizing Areas: A Case Study in Fujian, China.

Rapid urbanization in China has transformed many rural areas from agriculture-dominated to diverse systems, but studies of rural morphology are limited compared to studies of urban settlement. This paper uses a fractal dimension (FD) value to analyze the change in rural morphology in Fujian Province, a region with a long history of rural settlement and rapid recent urbanization, and to explore the factors that influenced this change. We found that the rural FD value increased from 2000 to 2012 and that rural morphology was spatially heterogeneous. FD was generally lower than in urban areas but very close to a typical urban area value in the southeast coastal region. A structural equation model was used to identify key factors influencing rural morphology, which were natural conditions, rurality and economic development, while historic administration had the smallest positive effect. With a long history and unique administrative system, the spatial morphology of Chinese rural areas has shown characteristics distinct from compact urban or scattered rural areas. The urban planning method adopted by rural planners is not suitable in rural regions, because the planning potential of rural areas with high and low FD values varies. Although rural planning currently uses a very similar approach to urban planning, it should use a local, flexible and adaptive policy based on rural morphological characteristics.

Simulation of coal microstructure characteristics under temperature-pressure coupling based on micro-computer tomography

The distribution of pore-fracture structure in coal directly affects the storage and migration characteristics of fluids. Simultaneously, under the condition of high buried depth, the coal structure is further changed by the temperature-pressure coupling. To study the pore size distribution of coal and the deformation characteristics of different pore-fracture structures under temperature-pressure coupling conditions, six different coal structure models are constructed using three-dimensional computer tomography reconstruction in this work. The box-counting algorithm is used to calculate the fractal dimensions of the pore-fracture structure and pore clusters in different pore sizes of coal. In the meantime, the fractal characteristics of the pore structure in different pore sizes are analyzed. Based on the coal structure model, a linear elastic deformation model under the temperature-pressure coupling is constructed. Moreover, the relationship of porosity and fractal dimension with the deformation of models is studied. The research results show that the porosity positively correlated with fractal dimension. The changes of pore volume fraction and fractal dimension in each pore size distribution range are consistent. Under the temperature-pressure coupling condition, both the model porosity and fractal dimension exhibit a quadratic function relationship with deformation. The deformation analysis of the three-dimensional models and two-dimensional cross-sections show that as the porosity and fractal dimension increase, the coal body deformation exhibits a trend of first decreasing and subsequent increasing. Low fractal dimension and high porosity could increase the model deformation. The research results can afford a theoretical basis for the study of coal structure characteristics under complex conditions.

Spatial Behavior Characteristics of Land Use Based on Fractal Theory: Taking Poyang Lake Area as an Example

Landscape morphology can reflect the spatial behavior of land use. Using the Poyang Lake area as an example, the landscape pattern characteristics in 1995, 2000, 2015, and 2018 are determined by calculating the fractal dimension, fractal stability, patch density, patch shape fragmentation, and landscape isolation, and fractal theory is used to analyze the spatial behavior of land use. The results show that building land was the land use type which consistently had the highest fractal dimension, but the fractal dimension of building land shows a downward trend, indicating that the spatial form of building land gradually developed in an orderly direction under the action of land use spatial behavior. Paddy, dryland, and forested land were the land use types which always had the lowest fractal dimension, and they are in unstable states. The calculation results of patch density, patch shape fragmentation index, and landscape isolation index supported the conclusions of the fractal analysis. One recommendation for realizing the rational layout of the land is to reduce the fractal dimension of building land through scientific and reasonable planning and to guide the orderly development of building land. For natural landscapes such as forested land, shrub forest land, high-coverage grassland, and water area, their fractal dimensions should be increased to reduce human interference and maintain their stability. Finally, the results of this study suggest that the fractal dimension should be introduced into the National Spatial Planning, and used as an index for evaluating the rationality of the regional land use pattern.

Stickiness of randomly rough surfaces with high fractal dimension: is there a fractal limit?

Two surfaces are “sticky” if breaking their mutual contact requires a finite tensile force. At low fractal dimensions D, there is consensus stickiness does not depend on the upper truncation frequency of roughness spectrum (or “magnification”). As debate is still open for the case at high D, we exploit BAM theory of Ciavarella and Persson-Tosatti theory, to derive criteria for all fractal dimensions. For high D, we show that stickiness is more influenced by short wavelength roughness with respect to the low D case. BAM converges at high magnifications to a simple criterion which depends only on D, in agreement with theories that includes Lennard-Jones traction-gap law, while Persson-Tosatti disagrees because of its simplifying approximations.

Pore structure characteristics and their influencing factors: A case study from the middle jurassic mixed siliciclastic carbonate rocks, Turpan-Hami basin, Northwest China

The mixed siliciclastic-carbonate rocks of the second member of the Qiketai Formation (J2q2) in the Turpan-Hami Basin are lacustrine tight oil reservoir with vitrinite reflectance values (%, Ro) ranging from 0.64% to 0.81%. X-ray diffraction (XRD), thin sections, field emission scanning electron microscopy (FE-SEM) of argon-milled thin sections, low-temperature N2 adsorption (LNTA), and nuclear magnetic resonance (NMR) analyses were performed to investigate the pore structure characteristics and their influencing factors of the mixed siliciclastic-carbonate reservoirs. The results show that the tight reservoir has a medium-high total organic carbon (TOC) content, and the sedimentary textures include laminated, massive, and intraclasts-rich types. Nanometer scale interparticle pores and microfractures are dominant in the tight reservoirs. The small pores (2–100 nm) make a dominant contribution to the nanoscale storage space according to the comprehensive analysis of the T2 spectra of NMR. Reversed S-shaped isotherms obtained from N2 adsorption are type IV, and hysteresis loops indicate that the shape of pores include slit-or plate-like, ink-bottle-shaped and mixtures of the two. BET surface areas and BJH total pore volume vary from 1.707 m2/g to 8.556 m2/g and 1.13 cm3/100 g to 3.0 cm3/100 g, with an average of 4.31 m2/g and 1.848 cm3/100 g, respectively. The massive and intraclasts-rich rocks have higher NMR porosities, pore sizes and pore volumes than the laminated rocks. Based on the Frenkel-Halsey-Hill model of low-temperature N2 adsorption, the fractal dimensions D1 and D2 are 2.4305–2.7081 and 2.2667–2.6070, respectively. The correlations between the pore structure parameters and the mineralogical composition, TOC content, and fractal dimension reveal that dolomite makes greater contribution to the pore volume and movable fluid saturation than the siliciclastic gains and organic matter, resulting in higher fractal dimensions and more complicated pore structure. In addition, the clay minerals increase pore specific surface area and its complexity in the tight reservoirs. The samples with high silicate mineral and TOC contents tend to contain lower specific surface areas and pore volumes, resulting in lower fractal dimensions and more simplistic pore structure than clay rich samples. Therefore, the complex mineralogical composition, various sedimentary textures and organic matter content all play important roles in the development of pore network.

Study of fractal based oxygen adsorption experiment of porous coal

Coal is China?s main energy source and fuel. Coal spontaneous combustion is one of the most prominent issues that threaten the production safety of coal mining, storage, and transportation. In order to explore the factors affecting coal spontaneous combustion, we investigated the pore structure characteristics of the coal based on the fractal theory, through the low temperature liquid nitrogen adsorption experiment of coal. The fractal dimension of the coal sample was calculated, and the oxygen adsorption quantity of the same coal sample was obtained by using the physical adsorption experiment of coal. Experimental and fitting results showed that coal sample has obvious surface fractal dimension features and pore structure fractal features. Fractal dimension expressed coal oxygen adsorption well. In the meantime, the coal samples with lower fractal dimension, higher temperature, smaller porosity usually have less oxygen adsorption quantity. This research cannot only enrich the study of oxygen adsorption in porous media such as coal, but also help to understand its spontaneous combustion mechanism in depth, thereby reducing the occurrence of spontaneous combustion disasters.

Diastolic left ventricular function in relation to the retinal microvascular fractal dimension in a Flemish population

Fractal analysis provides a global assessment of vascular networks (e.g., geometric complexity). We examined the association of diastolic left ventricular (LV) function with the retinal microvascular fractal dimension. A lower fractal dimension signifies a sparser retinal microvascular network. In 628 randomly recruited Flemish individuals (51.3% women; mean age, 50.8 years), we measured diastolic LV function by echocardiography and the retinal microvascular fractal dimension by the box-counting method (Singapore I Vessel Assessment software, version 3.6). The left atrial volume index (LAVI), e′, E/e′ and retinal microvascular fractal dimension averaged (±SD) 24.3 ± 6.2 mL/m2, 10.9 ± 3.6 cm/s, 6.96 ± 2.2, and 1.39 ± 0.05, respectively. The LAVI, E, e′ and E/e′ were associated (P < 0.001) with the retinal microvascular fractal dimension with association sizes (per 1 SD), amounting to −1.49 mL/m2 (95% confidence interval, −1.98 to −1.01), 2.57 cm/s (1.31–3.84), 1.34 cm/s (1.07–1.60), and −0.74 (−0.91 to −0.57), respectively. With adjustments applied for potential covariables, the associations of E peak and E/e′ with the retinal microvascular fractal dimension remained significant (P ≤ 0.020). Over a median follow-up of 5.3 years, 18 deaths occurred. The crude and adjusted hazard ratios expressing the risk of all-cause mortality associated with a 1-SD increment in the retinal microvascular fractal dimension were 0.36 (0.23–0.57; P < 0.001) and 0.57 (0.34–0.96; P = 0.035), respectively. In the general population, a lower retinal microvascular fractal dimension was associated with greater E/e′, a measure of LV filling pressure. These observations can potentially be translated into new strategies for the prevention of diastolic LV dysfunction.

Membrane fouling performance of Fe-based coagulation-ultrafiltration process: Effect of sedimentation time

Pre-coagulation is commonly used with ultrafiltration (UF) to alleviate the membrane fouling. Compared to conventional coagulation-sedimentation-UF (CSUF) processes, the direct coagulation-UF (CUF) processes are widely believed to perform better due to the formation of a looser cake layer. It is however shown in this study that not only the density of a cake layer, but also its thickness as well, can affect the membrane fouling behavior, which therefore are influenced by both the sedimentation time and flocs characteristics. Herein, the membrane fouling performance of Fe-based coagulation-UF process was systematically investigated with different sedimentation times. A critical threshold of 30 min was observed at the lab-scale: if shorter than that, the membrane fouling depended mainly on the cake layer density, and thus CUF outperformed CSUF; but when the sedimentation time was over 30 min, the cake layer thickness turned to be the dominant factor, thereby resulting in CSUF performing better. Furthermore, it was shown that the critical sedimentation time was decided by flocs characteristics. A lower water temperature induced the formation of irregular flocs with a lower fractal dimension, and the corresponding cake layer exhibited an almost identical density with increasing sedimentation time. In this regard, CSUF processes were constantly superior to CUF as the cake layer thickness decreased. On the other hand, a critical sedimentation time reappeared because of the higher floc fractal dimension under acidic conditions. This work showed for the first time that the membrane fouling of CSUF was up to the sedimentation time, and it was possible to outperform CUF if the sedimentation time exceeded a critical threshold. Such a finding is crucial to the future development of coagulation integrated UF processes.

Investigation of mandibular fractal dimension on digital panoramic radiographs in bruxist individuals

This study aimed to evaluate changes in mandibular trabecular bone structure in bruxism using fractal analysis on digital panoramic radiographs obtained with automatic dosing. In this prospective study, fractal analysis was performed on radiographs of 126 bruxists and 126 non-bruxists. Eight paired mandibular regions of interest were selected: the bilateral condylar and gonial regions, and the bilateral dentate regions between the apical areas of the first molar and second premolar and between the first premolar and canine. Fractal dimensions (FDs) were calculated at each site. Mean FD values in the bilateral gonial regions of the bruxists were significantly lower than those of controls (P ≤ .049). In both groups, FD values of the right dentate region anterior to the mental foramen were significantly lower than those on the left side (P ≤ .042). Females exhibited significantly lower FD values in both condylar regions in both groups (P ≤ .039) and in the right dentate regions in the controls (P ≤ .022). Correlations between age and FD in all regions were positive but nonsignificant in both groups (P > .05). FD values of mandibular trabecular bone are affected by bruxism in the gonial region and by laterality and sex differences in the condylar and dentate regions.

Particle size distribution of aggregates effects on mesoscopic structural evolution of cemented waste rock backfill.

The most economical, environmental, and friendly method for recycling gangue is filling mining with cemented waste rock backfill (CWRB), which solves the environmental problems caused by gangue discharge and reduces the mining damages. Evaluating the mesoscopic structure of CWRB is of great significance for maximizing the utilization of gangue recycling and improving the economic benefits of filling mining. This paper constructed the particle flow model of cemented waste rock backfill (CWRB) considering particle size distribution (PSD) of aggregates and hydration of cementing material to investigate the effect of the PSD of aggregates on its mesoscopic structural evolution. The strain energy, crack, force chain, and particle fragment of CWRB during the whole loading were discussed. The binary processing and calculation on the crack image were performed to analyze the fractal dimension of crack distribution by compiling program. The influencing mechanism of the PSD of aggregates on the strength of CWRB is revealed from the mesoscopic levels of crack evolution, force chain structure, and particle fragment. The results show that the strain energy increases firstly and then decreases with the PSD fractal dimension, while the crack number decreases firstly and then increases with that. The cracks with less number and more uniform distribution present the smaller fractal dimension, CWRB with a low fractal dimension of crack distribution has higher strength, the fractal dimension of crack distribution exhibits a correlation with the PSD of aggregates. CWRBs with the PSD fractal dimensions of 2.4-2.6 have the largest strain energy and the smallest crack number, performing the superior structural evolution during loading. This study presents the huge potential of optimizing PSD in CWRB application from a new perspective, it is of great significance for strengthening the internal structure of CWRB and reducing engineering cost.

Seismic Hazards Assessment in the Eastern Himalayas Region

Spatial distribution of seismicity and seismic characteristics (fractal dimension, b-value, energy release, reoccurrence period) are assessed for the Himalayan Region (27° – 30°N and 85°– 97°E). The database consists of relocated earthquakes M ≥ 3.8 selected for the period 1964-2017 from the International Seismological Centre (ISC) catalogues (Engdahl, van der Hilst, and Buland (EHB) 2007). The <i>Gutenberg - Richter</i> frequency-magnitude relation (b-value) is calculated by the Maximum Likelihood Method (MLM) and by Least Square Method. The fractal dimension is estimated using the correlation integral method. The entire event set was also used for estimating radiated energy in the region. Four probabilistic models namely, <i>Weibul, Gamma, Lognormal and Exponential</i> have been used to estimate the probability of the occurrence of moderate earthquakes (M ≥ 5.5 and M ≥ 6.5) during a specified interval of time using the Maximum Likelihood Estimates (MLE) for estimating the model parameters. The highly stressed zones in the entire region are indicated by low b-values, low fractal dimension and low radiated energy. The vulnerable zones (Arunachal Himalayas, Mishami thrust zone) have been identified by these maps which are further corroborated with the probabilistic models to assess the seismic hazards in the Himalaya region. These areas are indicative of future probable earthquakes regions.

Evaluation of the trabecular structure of the mandibular condyles by fractal analysis in patients with different dentofacial skeletal patterns

Abstract Objective: An orthodontic malocclusion may affect the temporomandibular joint structures in susceptible individuals. This study aims to investigate the bone density of the mandibular condyles in patients presenting with different dentofacial skeletal patterns. Methods: Panoramic radiographs of 200 randomly selected patients with a skeletal and dental Class I, Class II division 1, Class II division 2 and Class III malocclusion were evaluated. Bone density of the right and left mandibular condyles was measured using fractal analysis. Results: No significant difference was detected between the right and left condyles in the various malocclusion groups. However, post-hoc tests showed that Class I patients had significantly higher FD values than Class III and Class II division 1 patients in both right and left condyles following intergroup comparisons. The only significant difference between the genders was detected in the left condyle of Class II division 1 patients, as male patients were found to have significantly higher FD values than females. Conclusions: The results of the present study showed that Class II division 1 and Class III patients displayed significantly lower fractal dimension (FD) values in their mandibular condyles when compared to Class I patients. This might be associated with the possible presence of a temporomandibular disorder in Class II division I patients which resulted in changes to condylar structure, and with less bone complexity in the temporomandibular joint of older Class III patients likely due to continued condylar growth.

Fractal distribution of mineral species among the crystallographic point groups

Abstract Crystallographic data from 5289 IMA-approved mineral species in the RRUFF database were used to examine the distribution of species among the 32 crystallographic point groups. It is found that within each crystal system, minerals strongly prefer point groups with higher group orders. Within a crystal system, the abundance of minerals belonging to each point group approximately obeys a power law with respect to group order, the same mathematical formalism that describes objects with fractal geometry. In this framework, each crystal system has its own fractal dimension; crystal systems possessing threefold (or sixfold) symmetry elements (i.e., trigonal, hexagonal, isometric) have significantly lower fractal dimension (&amp;lt;2), while those with only one-, two-, or fourfold symmetry elements (triclinic, monoclinic, orthorhombic, tetragonal) have higher fractal dimension (&amp;gt;2). While higher symmetry is preferred within a crystal system, the opposite trend is observed when comparing between crystal systems, with more species preferring crystals systems with lower order symmetry elements than those with higher order symmetry elements at constant group order. The combination of these two competing trends leads to a complex distribution of minerals among the crystal systems, and to the monoclinic group 2/m, the orthorhombic group 2/m2/m2/m, and the triclinic group 1 being the three most popular point groups, respectively. The fractal behavior of symmetry distribution among minerals points toward universal scaling patterns not just in physical, geometric objects but also in the way that symmetry is incorporated into natural periodic structures.

Effect of the manufacturing process on Fiore Sardo PDO cheese microstructure by multi-frequency NMR relaxometry

The quality of Fiore Sardo cheese, a traditional Italian dairy product, was analyzed by means of Multi-frequency Nuclear Magnetic (NMR) relaxometry. Specifically, ten cheese wheels were purchased from different production chains, either industrial (N = 5) or artisanal (N = 5) samples. The former came from large scale productions and the latter were produced by shepherds in small quantities and in very small dairy factories. A preliminary interlaboratory proficiency testing of Time Domain - NMR (TD-NMR, 20 MHz) relaxometry by five laboratories, consistently showed that product quality is significantly different in terms of molecular mobility according to their production chain (i.e. industrial or artisanal). More detailed information about cheese microstructure was obtained by Multi-frequency Fast Field Cycling NMR (FFC-NMR) at lower magnetic fields (0.01–10 MHz). According to the interpretative model adopted to describe FFC-NMR data, industrially processed cheeses showed a higher para-casein hydration, higher protein protons to water protons ratio and a higher disorder (lower fractal dimension df) than artisanal products. It is suggested that differences between artisanal and industrial cheeses generate from the processing steps preceding cheese maturation, and are clearly reflected in the visual appearance of cheeses.This study shows that NMR relaxometry techniques can successfully discriminate Fiore Sardo cheese from different production chains, and paves the way for their implementation in quality control practices of dairy products.

Experimental and practical investigation of the sealing efficiency of cement grouting in tortuous fractures with flowing water

The diffusion of cement slurry in a fracture with flowing water is an important factor ensuring the grouting effect and a key factor influencing the environment, including natural and social traffic. To better understand the influence of the characteristic fracture parameters and the water flow rate on the cement slurry diffusion law, first, diffusion testing of a cement slurry in a simulated tortuous fracture with flowing water is carried out. Then, the results obtained from these tests are applied to an engineering site. The results of the experimental and engineering tests support the following conclusions. 1) At a low water flow rate, the sealing efficiency of test points near the grouting source increases rapidly with time, while the sealing efficiency of test points far from the grouting source exhibits little change with time. 2) Near the grouting source, the sealing efficiency corresponding to a high fractal dimension of fracture tortuosity is higher than that corresponding to a low fractal dimension of fracture tortuosity; far from the grouting source, this pattern is reversed. 3) When the inflection point of the grouting pressure is reached at a test point, the sealing efficiency of the fracture at this test point is the greatest.

The Relationship between Carotid Doppler Ultrasound and EEG Metrics in Healthy Preschoolers and Adults.

Despite widespread using electroencephalography (EEG) and Doppler ultrasound in pediatric neurology clinical practice, there are still no well-known correlations between these methods that could contribute to a better understanding of brain processes and development of neurological pathology. This study aims to reveal relationship between EEG and Doppler ultrasound methods. We compared two cohorts of adults and preschool children with no history of neurological or mental diseases. The data analysis included investigation of EEG and carotid blood flow indexes, which are significant in neurological diagnosis, as well as calculation of linear and non-linear EEG parameters and ratios between the systolic peak velocities of carotid arteries and carotid blood asymmetry. We have found age-dependent correlations between EEG and power Doppler ultrasound imaging (PDUI) data. Carotid blood flow asymmetry correlated with delta-rhythm power spectral density only in preschoolers. The ratios of blood flow velocities in the internal carotid arteries to those in the common carotid arteries correlated with higher peak alpha frequency and lower fractal dimension; moreover, they were associated with lower Epworth sleepiness scale scores. The study revealed significant correlations between EEG and PDUI imaging indexes, which are different for healthy children and adults. Despite the fact that the correlations were associated with non-clinical states such as overwork or stress, we assumed that the investigated parameters could be applicable for clinical trials.

Effects of the long‐term fertilization on pore and physicochemical characteristics of loess soil in Northwest China

AbstractLong‐term applications of inorganic and organic fertilizers have great effects on soil characteristics and crop yields. However, it is limited to quantify the influence of long‐term fertilization on soil micro‐pore structure. In this study, we investigated the effect of long‐term fertilizer application on soil pore characteristics using X‐ray computed tomography. Loess soil cores were collected from four 25‐yr fertilization treatments in Guanzhong Plain, Northwest China, including no fertilization (CK), nitrogen alone (N), nitrogen + phosphorus + potassium (NPK) and organic manure + chemical fertilizer NPK (OMNPK). The results indicated that, compared with other treatments, OMNPK treatment significantly increased winter wheat (Triticum aestivum L.) yield, total porosity, soil organic carbon and total nitrogen, and decreased soil bulk density. Notably, there is greater soil pore connectivity (EuN, Euler number) and lower fractal dimension in OMNPK than other treatments. Pore size distribution showed a significant difference with different diameters in &lt;50, 50–100, 100–1000, and &gt;1000 μm. In contrast, pore shape distribution of soil core differed little among different treatments, while elongated shape pores were appropriately 99.5% at OMNPK with more frequency than other treatments. Co‐application of organic and inorganic fertilizers improved soil pore structure and soil physical‐chemical properties, which is beneficial for preventing soil degradation.

Haemodynamic activity characterization of resting state networks by fractal analysis and thalamocortical morphofunctional integrity in chronic migraine

BackgroundChronic migraine (CM) can be associated with aberrant long-range connectivity of MRI-derived resting-state networks (RSNs). Here, we investigated how the fractal dimension (FD) of blood oxygenation level dependent (BOLD) activity may be used to estimate the complexity of RSNs, reflecting flexibility and/or efficiency in information processing in CM patients respect to healthy controls (HC).MethodsResting-state MRI data were collected from 20 untreated CM without history of medication overuse and 20 HC. On both groups, we estimated the Higuchi’s FD. On the same subjects, fractional anisotropy (FA) and mean diffusivity (MD) values of bilateral thalami were retrieved from diffusion tensor imaging and correlated with the FD values.ResultsCM showed higher FD values within dorsal attention system (DAS) and the anterior part of default-mode network (DMN), and lower FD values within the posterior DMN compared to HC. Although FA and MD were within the range of normality, both correlated with the FD values of DAS.ConclusionsFD of DAS and DMN may reflect disruption of cognitive control of pain in CM. Since the normal microstructure of the thalamus and its positive connectivity with the cortical networking found in our CM patients reminds similar results obtained assessing the same structures but with the methods of neurophysiology, in episodic migraine during an attack, this may be yet another evidence in supporting CM as a never-ending migraine attack.

Identification and Delineation of the Earth’s Large-Scale Closed Terrain Depressions and Their Fractal Size Distribution

Closed terrain depressions are geomorphic features that show scale invariance over the wide range of scales on which they occur, from metres to thousands of kilometres. They are also global features that are present on all continents. Morphometric analyses of these depressions are now possible because of the availability of global digital elevation models and advances in methods for mapping closed depressions. Here, a simple and automatic but efficient method is proposed for mapping closed terrain depressions. The GTOPO30 global digital elevation model, with a spatial resolution of around 1 km, was used to map the closed depressions of eight large test sites sampled from all inhabited continents. The identified and delineated terrain depressions include lake watersheds together with many other terrain depressions including deserts, karst terrains and rift valleys. A fractal analysis shows that South America and Central Africa have similar, and also the largest, fractal dimensions; Central Europe and North Africa have intermediate fractal dimensions; and North America, Central Asia, the Near East and Australia have similar, low fractal dimensions. The methodology proposed in this paper can be used to identify areas of interest for which a more exhaustive analysis, using digital elevation models with better spatial resolution, can be conducted.

An investigation into pore structure fractal characteristics in tight oil reservoirs: a case study of the Triassic tight sandstone with ultra-low permeability in the Ordos Basin, China

Pore structure, which not only determines the microscopic characteristics of reservoirs but also controls the macroscopic physical properties of reservoirs, has been difficult to study in reservoir research. Fractal theory is an effective method for quantitative analysis of the irregular and complex pore structures of rocks. On the basis of high-pressure mercury intrusion experiments, the fractal dimensions of tight sandstones in the Yanchang Formation of the Triassic in the Ordos Basin are calculated by two methods (the water saturation method and mercury saturation method), and the fractal characteristics of the pore structures in this tight sandstone reservoir are also analyzed. The results show that the pore structures of tight sandstone reservoirs are heterogeneous and can be divided into four types. The fractal dimensions calculated by the water saturation method are poorly correlated with reservoir quality, while the fractal dimensions calculated by the mercury saturation method have good correlation with reservoir quality, that is, reservoirs with low fractal dimensions have high reservoir permeability and large pore-throat radii, while reservoirs with high fractal dimensions have low reservoir permeability and small pore-throat radii. Therefore, the fractal dimensions calculated by the mercury saturation method are presented to characterize tight sandstone reservoirs. The pore structures with large pore-throat sizes (radius>rtr) and small pore-throat sizes (radius<rtr) are relatively independent, and this results in clear turning points on the fractal curves of most samples. More importantly, samples with different fractal characteristics can represent reservoirs with different physical properties and pore structures. In conclusion, fractal dimensions can be used as an effective parameter for the quantitative characterization of tight sandstone reservoir with ultra-low permeability.