There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

给出了相似维数、容量维数、盒子维数、信息维数、关联维数、广义维数分形维数等6种分形维数的定义方式,并讨论了它们的应用范围.在此基础上,概括出改变粗视化程度求维数、根据测度关系求维数、根据关联函数求维数、根据分布函数求维数、根据波谱求维数等5种测量维数的方法,为不同领域的科研人员应用维数测量提供了有力工具.

分形维数（Fractal dimension）及其测量方法

Characterizing clay textures and their impact on the reservoir using deep learning and Lattice-Boltzmann simulation applied to SEM images

Seismic data and nuclear magnetic resonance (NMR) data are two of the highly trustable kinds of information in hydrocarbon reservoir engineering. Reservoir fluids influence the elastic wave velocity and also determine the NMR response of the reservoir. The current study investigates different pore types, i.e., micro, meso, and macropores’ contribution to the elastic wave velocity using the laboratory NMR and elastic experiments on coal core samples under different fluid saturations. Once a meaningful relationship was observed in the lab, the idea was applied in the field scale and the NMR transverse relaxation time (T2) curves were synthesized artificially. This task was done by dividing the area under the T2 curve into eight porosity bins and estimating each bin’s value from the seismic attributes using neural networks (NN). Moreover, the functionality of two statistical ensembles, i.e., Bag and LSBoost, was investigated as an alternative tool to conventional estimation techniques of the petrophysical characteristics; and the results were compared with those from a deep learning network. Herein, NMR permeability was used as the estimation target and porosity was used as a benchmark to assess the reliability of the models. The final results indicated that by using the incremental porosity under the T2 curve, this curve could be synthesized using the seismic attributes. The results also proved the functionality of the selected statistical ensembles as reliable tools in the petrophysical characterization of the hydrocarbon reservoirs.

NMR-Based Study of the Pore Types’ Contribution to the Elastic Response of the Reservoir Rock

Clay minerals significantly alter the pore size distribution (PSD) of the gas hydrate-bearing sediments and sandstone reservoir rock by adding an intense amount of micropores to the existing intragranular pore space. Therefore, in the present study, the internal pore space of various clay groups is investigated by manually segmenting Scanning Electron Microscopy (SEM) images. We focused on kaolinite, smectite, chlorite, and dissolution holes and characterized their specific pore space using fractal geometry theory and parameters such as pore count, pore size distribution, area, perimeter, circularity, and density. Herein, the fractal properties of different clay groups and dissolution holes were extracted using the box counting technique and were introduced for each group. It was observed that the presence of clays complicates the original PSD of the reservoir by adding about 1.31-61.30 pores/100 μm2 with sizes in the range of 0.003-87.69 μm2. Meanwhile, dissolution holes complicate the pore space by adding 4.88-8.17 extra pores/100 μm2 with sizes in the range of 0.06-119.75 μm2. The fractal dimension ( ) and lacunarity ( ) values of the clays’ internal pore structure fell in the ranges of 1.51-1.85 and 0.18-0.99, respectively. Likewise, and of the dissolution holes were in the ranges of, respectively, 1.63-1.65 and 0.56-0.62. The obtained results of the present study lay the foundation for developing improved fractal models of the reservoir properties which would help to better understand the fluid flow, irreducible fluid saturation, and capillary pressure. These issues are of significant importance for reservoir quality and calculating the accurate amount of producible oil and gas.

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Shanilka Gimhan Fernando

Papers

NMR-Based Study of the Pore Types’ Contribution to the Elastic Response of the Reservoir Rock

Characterizing clay textures and their impact on the reservoir using deep learning and Lattice-Boltzmann simulation applied to SEM images

Fractal Properties of Various Clay Minerals Obtained from SEM Images

Coupling Model of Submarine Deformation Response Prediction during Methane Hydrate Exploitation