Dimension D2 Research Articles

Study on the Pore Structure and Fractal Characteristics of Different Lithofacies of Wufeng-Longmaxi Formation Shale in Southern Sichuan Basin, China.

Gas content and flow characteristics are closely related to shale lithofacies, and significant differences exist in the pore structure and fractal characteristics among lithofacies. In this study, X-ray diffractometer (XRD), field-emission scanning electron microscopy (FE-SEM), gas adsorption (N2 and CO2), and fractal theory were employed to systematically characterize the pore attributes of the marine Wufeng–Longmaxi formation shales. The information of various pores and microfractures among lithofacies was extracted and quantified via high-resolution FE-SEM image stitching technology. Shales were classified into four types based on mineral compositions, and siliceous shales possess the largest SEM-based surface porosity (2.84%) and the largest pore volume (PV) (average 0.0243 cm3/g) as well as specific surface area (SSA) (average 28.06 m2/g). The effect of lithofacies variation on the PV of shale is minor. In contrast, the lithofacies variation has a significant impact on the SSA, and the SSA of siliceous shale is 39.11% higher than that of argillaceous shale. PV and SSA show strong positive correlation with the total organic carbon (TOC) content but negative correlation with clay minerals. Siliceous shales have the greatest fractal dimension D1 (pore surface roughness) (average 2.6821), which is contributed by abundant organic matter pores with more complicated boundaries. The largest fractal dimension D2 (pore structure complexity) (average 2.8263) is found in mixed shales, which is attributed to well-developed intraparticle (intraP) pores associated with carbonate mineral dissolution. This indicates that siliceous shales have the highest methane adsorption capacity and that shale gas desorption, diffusion, and seepage are more difficult in mixed shales.

Chaotic dimension enhancement by optical injection into a semiconductor laser under feedback.

Optical injection into a chaotic laser under feedback is investigated for dimension enhancement. Although injecting a solitary laser is known to be low-dimensional, injecting the laser under feedback is found to enhance the correlation dimension D2 in experiments. Using an exceptionally large data size with a very large reconstruction embedding dimension, efficient computation is enabled by averaging over many short segments to carefully estimate D2. The dimension enhancement can be achieved together with time-delay signature suppression. The enhancement of D2 as a fundamental geometric quantifier of attractors is useful in applications of chaos.

Fractal dimension and area of seismicity in the Baikal Rift System: Implications for modern geodynamics

The fractal geometry and extent of seismicity in the Baikal Rift System (BRS) are estimated from data on 52,700 instrumental events of MLH ≥ 2.5 magnitudes for fifty years (1964–2013). The seismic pattern is characterized by the box-counting Hausdorff dimension D0, multifractal spectra f(α), and surface area S of seismicity at three scales: the rift system as a whole, its three zones, and six subzones. The multifractal spectra record a self-similar hierarchical structure of the BRS seismicity pattern. The space and time variations in the fractal dimension (D0) and area of seismicity (S), which are mapped and plotted as a function of time, show good correlation. The two parameters depend on three related factors: progressive increase in the amount of instrumental data (dataset size), structure of seismogenic fault network, and geodynamic activity. They increase as ever more data appear with time and acquire high local values at increasing extent and density of quakes. Moreover, the obtained D0 estimates reflect statistical self-similarity of earthquake patterns being in the range ≈ 1.45–1.55 over most of BRS, except one zone and one subzone in the rift flanks. They are the highest in the southwest and the lowest in the northeast of the rift system (D0 ≈ 1.60 ± 0.02 and D0 ≈ 1.37 ± 0.02 respectively). This dissimilarity indicates that seismogenic faulting occurs by different mechanisms: distributed failure as a result of superposed global-scale collisional compression and regional rifting in the SW flank and quasi-linear rift propagation in the NE flank. In general, D0 decreases toward the northeastern part of the BRS, where the pattern of earthquakes becomes localized along lineaments instead of being distributed over an area. The space and time variations of D0 and S revealed in the earthquake data are consistent with the location and activity pulses of rifting attractors and provide a realistic explanation of BRS geodynamics and tectonophysics. The global lithospheric compression and the regional pulse-like activity of rifting attractors control the network of seismogenic faults which, in turn, govern the fractal geometry and 2D structure of seismicity in the region. The obtained results confirm the oscillatory dynamics of the regional seismicity at a decadal period correlated with activity pulses of rifting attractors. The oscillations stand out against the background of decreasing global low-frequency secular cycle of the BRS seismicity. The BRS lithospheric geodynamics fits the model of a nonlinear oscillator with dissipation. The suggested analysis of the fractal geometry and extent of seismicity as proxies of the faulting evolution provides insights into modern geodynamics of the Baikal Rift System and its constituents.

Fractal characteristics of pulverized high volatile bituminous coals with different particle size using gas adsorption

To better understand the effect of particle size on fractal characteristics of pores in coal, three high volatile bituminous coals with mean maximum vitrinite reflectance of 0.82–0.90% collected from the Naryksko-Ostashinskaya coalbed methane field in Kuznetskiy Basin in Russia were crushed and sieved to five progressivelydecreasing particle size fractions: 1.0–0.5 mm, 0.50–0.25 mm, 0.250–0.125 mm, 0.125–0.063 mm and 0.063–0.032 mm. For all particle size fractions, particle size distribution measurement, proximate analysis, maceral analysis and low-pressure N2 adsorption and CO2 adsorption analyses were conducted. Fractal dimensions D1 (pore surface roughness) and D2 (pore structural irregularity) were determined from relative pressure intervals of 0–0.45 and 0.45–1 of N2 adsorption isotherm with the application of the fractal Frenkel-Halsey-Hill theory, respectively. The results demonstrate significant differences in fractal dimensions in different particle size fractions. As particle size of coal samples decreases, D1 decreases, while D2 increases. Some constricted mesopores are transformed into non-constricted mesopores during crushing. The non-constricted mesopores increasingly concentrate in smaller pore sizes, which results in smoother pore surface (decreasing D1) and more heterogeneous pore structure (increasing D2). Mesopores with pore width between 2 nm and 5 nm are the key to fractal dimensions. Individual mesopore structure parameters closely associated with particle size have universal correlations with fractal dimensions. The increasing mesopore specific surface area and volume and decreasing average mesopore width lead to a decrease in D1 and an increase in D2, which further confirms the effect of particle size on fractal dimensions.

Self-assembly process under a solid-state reaction of β-Si3N4/austenitic stainless-steel composites: stirring conditions and material texture

In the self-assembly process of β-Si3N4 (SN)/316L stainless-steel (SUS316L) composite materials tailored via sintering of powder mixtures, the formation of a SN agglomerate resulting from condensation–dispersion reactions during the stirring of SN/SUS316L was found to play an important role in improving the thermal conductivity. Moreover, the obtained SN secondary particle groups connected to form a network through diffusion-limited aggregation. In particular, it was shown that the sample prepared at the milling speed of 150 r/min has a similar particle group area (about 1.38 μm2) to that at 120 r/min, but a higher κ (increased from 9.5 W m−1 K−1 to 11.5 W m−1 K−1). To quantitatively evaluate the microstructural morphology of the texture of the self-assembled composite material, global parameters τ( q) and D q and local parameters α( q) and f( α) were determined via multifractal analysis. These characteristics of the anisotropy, dispersion, and cohesiveness of the particle network in the material texture could be analyzed together with the capacity dimension D0, information dimension D1 (configuration entropy), correlation dimension D2, and α( q) (related to internal energy). The results suggest that α( q) reflects the differences in the cohesion of the additive particle agglomeration that constitutes the self-assembly process under the solid-state reaction.

Pore Structure and Fractal Characteristics of Organic-Rich Lacustrine Shales of the Kongdian Formation, Cangdong Sag, Bohai Bay Basin

In order to examine the pore structure and reveal the fractal geometric nature of shales, a series of laboratory experiments were conducted on lacustrine shale samples cored from the Kongdian Formation. Based on the low temperature nitrogen adsorption, fluorescent thin section and field emission scanning electronic microscope, a comprehensive pore structure classification and evaluation were conducted on shale samples. Fractal dimensions D1 and D2 (with relative pressure of 0–0.45 and 0.45–1.00, respectively) were obtained from the nitrogen adsorption data using the fractal Frenkel-Halsey-Hill (FHH) method. With additional means of X-ray diffraction analysis, total organic carbon content analysis and thermal maturity analysis, the relationships between pore structure parameters, fractal dimensions, TOC content and mineral composition are presented and discussed in this paper. The results show that interparticle pores and microfractures are predominant, whereas organic matter pores are rarely found. The pore morphology is primarily featured with wide-open ends and slit-shaped structures. In terms of pore scale, mesopores and macropores are predominant. The value of fractal dimension D1 representing small pores ranges from 2.0173 to 2.4642 with an average of 2.1735. The value of D2 which represents large pores ranges from 2.3616 to 2.5981 with an average of 2.4960. These low numbers are an indication of few pore types and relatively low heterogeneity. In addition, smaller D1 values reveal that large pores have more complicated spatial structures than smaller ones. The results of correlation analysis show that: 1) D2 is correlated positively with specific surface area but negatively with average pore diameter; 2) D1 and D2 literally show no obvious relationship with mineral composition, TOC content or vitrinite reflectance (Ro); 3) both total Barrett-Joyner-Halenda (BJH) volume and specific surface area show a positive relationship with dolomite content and a negative relationship with felsic minerals content. These results demonstrate that the pore types are relatively few and dominated by mesopores, and the content of brittle minerals such as dolomite and felsic minerals control the pore structure development whilst organic matter and clay minerals have less influence due to low thermal maturity and abundance of clay minerals.

Influence of water on shale pore heterogeneity and the implications for shale gas-bearing property - A case study of marine Longmaxi Formation shale in northern Guizhou

Shale pore heterogeneity (as described by the fractal dimension) may influence the shale gas-bearing property (GBP). Previous studies on the fractal dimension and its influence on shale GBP were mainly focused on the dry shale samples. Our study investigates the pore structure characteristics under both the dry and moist conditions utilizing low-pressure N2/CO2 adsorption experiments, water-bearing property, and GBP on the eleven as-received (moist) marine Longmaxi shale sampled from the XK3 well in northern Guizhou. Moreover, the fractal dimensions D1 (P/P0: 0–0.5) and D2 (P/P0: 0.5–1.0) for the dry and moist shales were determined respectively, using low-pressure N2 adsorption data based on the Frenkel-Halsey-Hill (FHH) method. The results show that the ranges of D1 and D2 for the dry shales are 2.5759–2.7387 and 2.7681–2.8756, respectively, with averages of 2.6970 and 2.8470, while those for the moist shales are 2.0879–2.2215 and 2.6190–2.7252 respectively (averages 2.1591 and 2.6903). Shale water occurs mainly on nonmicropores (>2 nm) surfaces, and part of water fills the micropores (<2 nm), which reduces the nonmicropores BET specific surface area (SBET), micropore volume (Vmic), and pore size distribution (PSD) and increases the average pore size (APS), thus reducing the D1 and D2 (19.94 and 5.50% on average, respectively). The shales have high gas contents with an average of 2.59 m3/t, which is dominated by adsorbed gas (75.21% on average). Compared with D2, D1 is more suitable for indicating the pore heterogeneity (especially nonmicropores surface heterogeneity) and shows stronger positive linear relationships with the shale GBP, implying that a larger pore surface heterogeneity is favorable for gas adsorption. Water mainly occurs in the clay minerals and reduces the D1 of the clay pores, thus the TOC content controls the D1 and shale GBP.

Использование нелинейных параметров вариабельности сердечного ритма для выявления стресса

This paper presents a stress detection algorithm using heart rate variability (HRV) parameters. Five-minute electrocardiograms were recorded at rest and under exam stress (252 students were involved). The determined HRV parameters were applied to detect stress by means of several classification algorithms. We analysed linear indices in the time (standard deviation of NN intervals (SDNN) and root mean square of successive RR interval differences (RMSSD)) and frequency domains (low frequency (LF) and high frequency (HF) power as well as LF/HF ratio). To study nonlinear HRV indices, we evaluated approximate entropy (ApEn), sample entropy (SampEn), α1 (DFA1) and α2 (DFA2) scaling exponents, correlation dimension D2, and recurrence plot quantification measures (recurrence rate (REC), mean diagonal line length (Lmean), maximum diagonal line length (Lmax), determinism (DET), and Shannon entropy (ShanEn)). Receiver operating characteristic (ROC) was used to test the performance of the classifiers derived from HRV. The highest area under the ROC curve (AUC), sensitivity, and specificity were found for mean RR-interval, DFA1, DFA2, RMSSD, and Lmax. These parameters were used for stress/rest classification with the help of algorithms that are common in clinical and physiological applications, i.e. logistic regression (LR) and linear discriminant analysis (LDA). Classification performance for stress was quantified using accuracy, sensitivity and specificity measures. The LR achieved an accuracy of 68.25 % at an optimal cutoff value of 0.57. LDA determined stress with 67.46 % accuracy. Thus, HRV parameters can serve as an objective tool for stress detection.

The dependence of the hierarchical distribution of star clusters on galactic environment

ABSTRACT We use the angular two-point correlation function (TPCF) to investigate the hierarchical distribution of young star clusters in 12 local (3–18 Mpc) star-forming galaxies using star cluster catalogs obtained with the Hubble Space Telescope (HST) as part of the Treasury Program Legacy ExtraGalactic UV Survey. The sample spans a range of different morphological types, allowing us to infer how the physical properties of the galaxy affect the spatial distribution of the clusters. We also prepare a range of physically motivated toy models to compare with and interpret the observed features in the TPCFs. We find that, conforming to earlier studies, young clusters ($T \lesssim 10\, \mathrm{Myr}$) have power-law TPCFs that are characteristic of fractal distributions with a fractal dimension D2, and this scale-free nature extends out to a maximum scale lcorr beyond which the distribution becomes Poissonian. However, lcorr, and D2 vary significantly across the sample, and are correlated with a number of host galaxy physical properties, suggesting that there are physical differences in the underlying star cluster distributions. We also find that hierarchical structuring weakens with age, evidenced by flatter TPCFs for older clusters ($T \gtrsim 10\, \mathrm{Myr}$), that eventually converges to the residual correlation expected from a completely random large-scale radial distribution of clusters in the galaxy in $\sim 100 \, \mathrm{Myr}$. Our study demonstrates that the hierarchical distribution of star clusters evolves with age, and is strongly dependent on the properties of the host galaxy environment.

Nanopore Size Distribution Heterogeneity of Organic-Rich Shale Reservoirs Using Multifractal Analysis and Its Influence on Porosity–Permeability Variation

The shale nanopore size (diameter [less than] 100 nm) distribution heterogeneity (SNDH) is one of the important factors affecting gas production. However, quantitative analysis of the SNDH and the applicability of single and multifractal models need to be further studied. Here, based on low-temperature liquid nitrogen and carbon dioxide tests of organic-rich shale in Qinshui Basin, multifractal dimension variation of micropores ([less than] 2 nm) and mesopores (2–100 nm) are studied, and the multifractal factors that affect the distribution of nanopores are determined. Additionally, the differences between single fractal and multifractal results are compared. Based on this, dynamic variation of porosity and permeability under the constraints of the nanopore structure is discussed from the perspective of multifractal variation. The results of this study are as follows: (1) The pore size distribution of micropores and meso–macropores in shale samples exhibit typical multifractal behavior. The overall distribution heterogeneity of meso–macropores is mainly affected by the distribution of pores in the low-value area of pore volume (LAPV), while the overall distribution heterogeneity of micropores is affected by the distribution of the high-value area of the pore volume. The multifractal parameters and influencing factors of micropores and meso–macropores are clearly different. (2) The single fractal dimension D2 calculated using the Frenkel–Halsey–Hill model has a negative correlation with the multifractal parameters, implying that the distribution heterogeneity of the LAPV gradually decreases with the increase of the D2 value, indicating that the physical meaning of the two models is obviously different. (3) The pore distribution heterogeneity affects permeability variation and diffusion process of shale reservoir. With the increase of the multifractal dimension of meso–macropores, the damaging effect of stress on permeability is stronger. The more heterogeneous the micropore size distribution, the smaller is the ″modification effect″ of stress on the diffusion coefficient.

Fractal and multifractal characteristics of shale nanopores

Shale pore structure is an important factor in shale adsorption and percolation. To better characterize the pore structure of shales, this paper selects 24 shale core samples for high-pressure mercury intrusion (HPMI) test, and fractal theory and multifractal theory are applied to analyze the pore structures of shale nanopores. The fractal dimensions using different fractal models and the multifractal parameters are calculated from mercury intrusion capillary pressure (MICP). The correlations between fractal/multifractal parameters and shale nanopore structures are analyzed. The study reveals that the fractal dimension calculated from 3D capillary model can be used as an index for evaluating complex of shale nanopores. The fractal dimension increases with the increase of displacement pressure and homogeneity coefficient and decreases with the increase of the permeability and pore-throat radius. The multifractal analysis shows that shale nanopores have multifractal characteristics, and multifractal parameters can reflect the size, concentration, and asymmetry of pore size distribution (PSD). The PSD of shales are similar when they have similar multifractal parameters (Δα,Δf,α0,α1,α2). The information dimension D1 and correlation dimension D2 are positively correlated to the sizes of shale nanopores, and with the decreasing information dimension D1, the pore size distributes more contributed. Besides, the information dimension D1 has a strong and negative correlation with the fractal dimension derived from 3D capillary model.

Pore Structure and Fractal Characteristics of Shale under the Control of Bedding and Size: A Case Study of Shale from the Longmaxi Formation in China

In this study, the pore structure and fractal characteristics of shale samples with different bedding directions and sizes from the Longmaxi Formation of the Changning block in the Sichuan Basin were investigated by using CT imaging and low-temperature nitrogen adsorption experiments. The pore morphology, pore structure characteristics, relationships between the fractal dimensions and pore parameters, and effect of the size and bedding direction on pore morphology and various pore parameters were explored. In terms of pore structure characteristics, we found that the pores of shale samples were well developed and connected, forming a large number of pore clusters. The pores were mainly open pores and mesopores, which contributed the most to the specific surface area of the pores. Two fractal dimensions D1 and D2 were calculated from nitrogen adsorption data at relative pressures of 0–0.45 and 0.45–1, using the FHH method. These fractal dimensions characterized the pore surface and pore structure complexity, respectively. D1 ranged from 2.773 to 2.923, with a mean value of 2.821, and D2 varied from 2.853 to 2.899, with a mean value of 2.874. These variations indicated that there were irregular pore surfaces and sophisticated pore structures in the shale. The sample size and bedding direction had a significant impact on pore morphology and various pore parameters. Several pore characteristics of the vertical samples were superior to those of the horizontal samples. With an increase in size, the pore distribution became more uniform, the number of pore clusters increased, and the connectivity between pore clusters was enhanced. There was a good positive correlation between the fractal dimension D2 and specific surface area and moderate positive correlation between D2 and porosity and between D2 and pore volume. However, the fractal dimension D1 had a weak negative correlation with porosity and specific surface area and moderate negative correlation with pore volume. Moreover, both D1 and D2 tended to decrease with increasing average pore diameter.

Subspace estimation from unbalanced and incomplete data matrices: ℓ2,∞ statistical guarantees

This paper is concerned with estimating the column space of an unknown low-rank matrix A⋆∈Rd1×d2, given noisy and partial observations of its entries. There is no shortage of scenarios where the observations—while being too noisy to support faithful recovery of the entire matrix—still convey sufficient information to enable reliable estimation of the column space of interest. This is particularly evident and crucial for the highly unbalanced case where the column dimension d2 far exceeds the row dimension d1, which is the focal point of the current paper. We investigate an efficient spectral method, which operates upon the sample Gram matrix with diagonal deletion. While this algorithmic idea has been studied before, we establish new statistical guarantees for this method in terms of both ℓ2 and ℓ2,∞ estimation accuracy, which improve upon prior results if d2 is substantially larger than d1. To illustrate the effectiveness of our findings, we derive matching minimax lower bounds with respect to the noise levels, and develop consequences of our general theory for three applications of practical importance: (1) tensor completion from noisy data, (2) covariance estimation/principal component analysis with missing data and (3) community recovery in bipartite graphs. Our theory leads to improved performance guarantees for all three cases.

Determinations of the multifractal characteristics of the pore structures of low-, middle-, and high-rank coal using high-pressure mercury injection

The multifractal characteristics of pore structures of low-, middle-, and high-rank coals were analyzed in this study based on the results of high-pressure mercury injection analysis and multifractal theories. The results showed that coal pore structures exhibit multifractal behavior, and were much affected by coalification degrees. For example, it was observed that the Hurst Index (H), information dimension D1, and correlation dimension D2 decreased with increases in the coalification degree. Also, the spectrum width increased, indicating greater local fluctuations of the pore size distributions (PSDs), narrower distribution intervals, enhanced heterogeneity, and reduced pore connectivity. Micropores and mesopores have opposing effects on the multifractal characteristics of pore structures. It has been found that increases in the percentage of mesopores lead to better pore connectivity and more homogeneous pore structures. In addition, increases in mineral content and Mad lead to better connectivity and more uniform pore structures. However, increases in vitrinite content results in decreased pore connectivity, and the complexity of pore structures tends to increase. Also, increases in inertinite content reduce the heterogeneity of the low value regions of the pore volumes, resulting in decreases in the complexity of the overall pore structures.

Effects of composition changes of coal treated with hydrochloric acid on pore structure and fractal characteristics

In order to investigate the influence of coal compositions on the pore structure, low temperature gas adsorption (LTGA) method was used to analyze the pore evolution of coal samples treated with hydrochloric acid. The results demonstrate that hydrochloric acid treatment significantly reduced the content of minerals and volatile matter in coal, which could increase the porosity and the pore connectivity of coal. The removal of volatile matter has an obvious reaming effect on supermicropores, but ultramicropores remained unchanged. The role of minerals in pores of different pore widths is different, which are the fillers in macropores, the skeletons of some large mesopores and the blockage in some small mesopores. With the decrease of minerals, the macropore volume increased, and the large mesopore volume first decreased and then increased. In addition, the opening of many closed small mesopores increased the fractal dimension D2 of pore structure complexity, and provides an increase in specific surface area, but it has no significant relationship with the fractal dimension D1 of pore surface roughness.

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.

Distribution characteristics of soil particle size in alpine steppe and alpine meadow in the source region of the Yangtze River, China.

To explore the heterogeneity of spatial distribution and particle size distribution (PSD) in the main underlying surface soil in the source area of the Yangtze River, we used the fractal theory to describe the soil particle size distribution of alpine steppe and alpine meadow, and analyzed the difference of fractal dimension characteristics of soil of two different underlying surface and its relationship with soil particle composition. The results showed that soil particle size in the study area was mainly concentrated in 100-800 μm. The single fractal dimension (DV) of alpine steppe soil was 2.429-2.508, and that of alpine meadow soil was 2.697-2.743. The soil texture of alpine steppe was coarse, while that of alpine meadow soil was fine. Soil texture was the finest in the 20-30 cm depth, and the coarsest in the 0-10 cm layer. The multi-fractal dimension (capacity dimension D0, information entropy dimension D1, correlation dimension D2) of alpine steppe (0.896-0.961, 0.828-0.887, 0.725-0.819) was higher than that of alpine meadow (0.890-0.914, 0.693-0.744, 0.540-0.603). Compared with the alpine meadow, the alpine steppe had wider soil PSD, more complex soil structure, and higher soil heterogeneity. DV was positively correlated to clay and silt contents, and negatively correlated to sand content. D1 and D2 were negatively correlated with clay and silt contents, and positively correlated with sand content. Sand content was the main factor accounting for the non-uniform distribution of PSD and the changes of fractal dimension.

The influence of long-time water intrusion on the mineral and pore structure of coal

The formation water intruding into the coal seam through cross-layer seriously reduces the gas extraction efficiency. In this work, a series of experiments were carried out to investigate the influence of long-time pressure water on the mineral content and pore structure of coal. Results show that, the water intrusion makes a decrease in the types and contents of mineral in coal. Furthermore, full-scale pore size was analyzed by using low-temperature N2 adsorption and CO2 adsorption experiment, indicating that the macropore shows a different change trend before and after water intrusion. For TY and YZ sample, the macropore volume decreased by 18.56% and 0.98%, respectively. For QC sample, the macropore volume increased by 3.20%, while the micropore volume, mesopore volume and total volume of three samples increase in different extent, which are 16.67%–30.77%, 11.56%–17.59%, and 16.10%–125.00%, respectively. Then, the fractal dimension of coal before and after water intrusion was calculated by using FHH model, showing that the fractal dimension D1 decreases while the fractal dimension D2 increases after water intrusion because the water intrusion is able to create and expand pore of coal but it can reduce the roughness of the pore surface. Finally, the influence mechanism of water intrusion on the pore structure of coal is analyzed based on clay mineral collapse, mineral dissolution and coal swelling. The clay minerals in coal is a key factor impacting the pore structure during water intrusion process due to its poor water stability. In addition, the mineral dissolution and coal swelling also play the significant roles in pore structure. This work is significant for the gas control and prevention of coal mine in rich-water coal strata.

Fractal Characteristics of the Middle-Upper Ordovician Marine Shale Nano-Scale Porous Structure from the Ordos Basin, Northeast China.

The fractal characteristics of marine shale from the Middle-Upper Ordovician Wulalike Formation (O₂w) in the southwest margin of the Ordos Basin are studied. Based on low-temperature nitrogen adsorption experiments, the FHH (Frenkel-Halsey-Hill) model was employed to investigate the relationship between the marine shale composition, such as TOC, mineral content and shale gas content, and pore structure parameters, such as BET specific surface area, average pore diameter, porosity and fractal dimension. The results show that the pore size distribution curve of shale slowly decreased after the pore size was greater than 50 nm, the pore size distribution showed multiple peaks, and the peak value was mainly in the range of 2-10 nm. Most pores are nanopores, although the pore type and shape are different. Two different fractal dimensions D1 and D₂ are obtained from the two segments with relative pressures of 0-0.5 and 0.5-1.0, respectively: the D1 range is 2.77-2.82, and the D₂ range is 2.63-2.66. As D1 is larger than D₂, the pore structure of small pores is more uniform than that of large pores in the shale samples. The relationship between the fractal dimensions D1 and D₂ and the total organic carbon (TOC) content is a convex curve. Fractal dimension D reaches its maximum when TOC is 0.53 wt.%. Fractal dimension D decreases with increasing specific surface area, porosity and average pore size. The fractal dimension has a different influence on the gas storage and migration in shale; the larger the fractal dimension is, the stronger the heterogeneity and the more complex the pore structure, and this outcome is conducive to the storage of gas in shale but not beneficial to the permeability and production of gas.

Fractal Characteristics and Its Controlling Factors of Nanopore of Coal from Shanxi Province, North China.

Much attention has been recently paid to the Carboniferous-Permian coal-bearing strata in Shanxi Province, now the largest producing coalbed methane field in China. In this study, a comprehensive approach of mercury injection, low-temperature liquid nitrogen adsorption, and permeability experiments was adopted to investigate the structure and fractal characteristics of nanopores in the Carboniferous-Permian coal (with 0.77%˜3.04% Ro,ran). Based on the fractal model, two fractal dimensions D1 and D₂ corresponding to diffusion pore (<65 nm) and seepage pore (pore size ≥65 nm), respectively, were calculated, and the relationships between the fractal dimensions with the pore structure parameters and permeability are discussed here. The results indicate that the studied coal samples have good fractal characteristics and that the calculated linear correlation coefficients are higher than 0.80. The fractal dimension D1 of the diffusion pores ranges from 2.3777 to 2.4624, with an average of 2.4173, while the fractal dimension D₂ of the seepage pores is between 2.5844 and 2.6256, with an average of 2.5990. The fractal dimensions D1 of the diffusion pores increases with an increase in the BET specific surface area, vitrinite content, and Ro,ran while it decreases with an increase in the permeability, and has a weak correlation with the total pore volume. The correlation coefficients R² for the fractal dimension D₂ of the seepage pores, pore parameters, permeability, and maceral composition ranges from 0.0357 to 0.2551. These results indicate that uncertain relationships exist among these parameters.