Fractal characteristics of the micropore throats in the shale oil reservoirs of the Chang 7 Member of the Yanchang Formation, Ordos Basin

With the development of the global shale oil and gas revolution, shale oil became an important replacement field to increase oil and gas reserves and production. The Chang 7 Member of the Yanchang Formation in the Ordos Basin was an important shale oil exploration series in China. To study the micropore-throat structure characteristics of the Chang 7 Member, we launched nuclear magnetic resonance (NMR) and high-pressure mercury injection (HPMI) experiments to analyze the pore-throat structure features of the Chang 7 reservoir, and we considered fractal theory to study the fractal characteristics. The NMR results indicated that the T2 spectral morphology of the Chang 7 reservoir could be characterized by three main patterns encompassing early and late peaks with different amplitudes: the type 1 reservoir contained mostly small pores and few large pores, and the porosities of the small and large pores range from 4.16% to 9.04% and 0.70% to 2.40%, respectively. The type 2 reservoir contained similar amounts of small and large pores, and the type 3 reservoir contained few small pores and mostly large pores, while the porosities of the small and large pores range from 1.81% to 2.74% and 3.32% to 5.64%, respectively. The pore-throat structure parameters were obviously affected by the pore size distribution, which in turn influenced the reservoir seepage characteristics of the reservoir. The micropore-throat structure of the reservoir exhibited obvious piecewise fractal characteristics and mainly included dichotomous and trilateral fractals. The type 1 reservoirs were dominated by dichotomous fractals, and these two fractal types were equally distributed in the type 2 and 3 reservoirs. The fractal dimension of the pore throats of different scales exhibited a negative correlation with the corresponding porosity, but no correlation was observed with the permeability, indicating that the size of the reservoir determined by pore throats imposed a strong controlling effect on their fractal characteristics.

Consensus of Julia Sets

The Julia set is one of the most important sets in fractal theory. The previous studies on Julia sets mainly focused on the properties and graph of a single Julia set. In this paper, activated by the consensus of multi-agent systems, the consensus of Julia sets is introduced. Moreover, two types of the consensus of Julia sets are proposed: one is with a leader and the other is with no leaders. Then, controllers are designed to achieve the consensus of Julia sets. The consensus of Julia sets allows multiple different Julia sets to be coupled. In practical applications, the consensus of Julia sets provides a tool to study the consensus of group behaviors depicted by a Julia set. The simulations illustrate the efficacy of these methods.

Integration of Information Theory, Fractal Theory and Statistical Analyses for Landslide Susceptibility Mapping at Regional Scales

A new model, integrating information theory, fractal theory and statistical model for accurate landslide susceptibility mapping (LSM) at regional scales, has been proposed. In this model, landslide conditional factors are firstly classified with an optimal number of classes, which is determined by maximizing their information coefficients estimated from Shannon’s entropy model. The spatial association between influencing factors and induced landslides has been measured by introducing the variable fractal dimension method (VFDM). The VFDM approach fully considers the characteristics of landslide fractal distribution. Then the fractal dimensions (\(D\)) are calculated to provide multiple factors with various numerical weights. The proposed model eventually combines the landslide frequency ratio (\(fr\)) of each factor with corresponding weight to achieve spatial prediction of landslides, illustrated by an example area in China. In the study area, 500 landslides have been identified by aerial photograph interpretation, extensive field investigations, historical and bibliographical landslide data. In the model, these landslides are randomly split into a training dataset (70 %)and a validating dataset (30 %) Seven factors are recognized and analyzed by frequency ratio (FR) method, including lithology, distance to fault, altitude, slope, aspect, distance to stream and distance to the road. The receiver operating characteristic curve (AUROC) has been adopted to compare and validate the model results. Results show that the proposed landslide model achieved a more accurate prediction with AUROC equal to 0.8467, over-performing than the conventional frequency ratio method (AUROC=0.8088). According to the final prognostic landslide susceptibility map, 16.37 % f the study area shows very high and high susceptibility, accounting for 63.55 % f the entire landslides. Evaluation of relative factor importance based on a one-by-one factor removal test indicates that the lithology factor contributes unique information for landslides. In conclusion, the example demonstrates that the proposed framework is promising for further improvement of LSM.

Research On the Fractal Dimensions of the Organic-Rich Shale Pores Via Different Models

Fractal dimension can be used to the pore surface characterize. For pore structures in different sizes, the calculation models of fractal theory should be distinguished due to the different principles of the gas adsorption experiments. To further study the adaptability of the fractal model for gas adsorption experimental data, the author collected shale samples of Longmaxi formation from Well JY1, then CO2 and N2 adsorption provided the PSD curves. In addition, the fractal dimensions of micropore and mesopore were calculated by the Jaroniec fractal model and Frenkel–Halsey–Hill (FHH) fractal model respectively. The research shows that the Jaroniec model may be suitable to calculate CO2 adsorption data and could characterize the fractal dimension of micropore, while the FHH model may be suitable to calculate N2 adsorption data in the high relative pressure region. It suggests that the micropore and mesopore could have different dimensions and the evaluation of the structure in shale pores should consider both of them.