Entropy numbers of Besov classes of generalized smoothness on the sphere

Wang, He Ping; Wang, Kai; Wang, Jing

doi:10.1007/s10114-013-3044-9

Cited by 16 publications

(1 citation statement)

References 25 publications

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“…This problem has a long history and some fundamental problems in this area are still open. Estimates for entropy numbers of different operators and embeddings between function spaces of the types Besov and Sobolev with mixed smoothness into Lebesgue have been studied [8,11,12,19,21]. In the papers [10,18] sharp estimates were obtained for entropy numbers of sets of infinitely differentiable functions and of analytic functions, on two-points homogeneous spaces and on the torus, in several cases.…”

Section: Introductionmentioning

confidence: 99%

Estimates for n-widths of multiplier operators of multiple Walsh series

Córdoba

Tozoni

2019

Journal of Mathematical Analysis and Applications

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Section: Introductionmentioning

confidence: 99%

Estimates for n-widths of multiplier operators of multiple Walsh series

Córdoba

Tozoni

2019

Journal of Mathematical Analysis and Applications

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Diagenesis and reservoir quality of sandstones in the Eocene Shahejie Formation, Raoyang Sag (Jizhong Depression), Bohai Bay Basin, China

et al. 2019

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Deeply buried (3.5–4.5 km) fan deltaic and braided deltaic sandstones of the Eocene Shahejie Formation are important hydrocarbon reservoirs in the Raoyang Sag of the Bohai Bay Basin (North China). An integrated approach incorporating petrophysics, thin‐section petrography, scanning electron microscope (SEM), cathodoluminescence (CL), and well log analysis was applied to investigate diagenesis, diagenetic minerals, and their impacts on reservoir quality. The sandstones of the Sha‐3 (the third Member of the Shahejie Formation) are dominated by lithic arkoses and arkoses with a low‐moderate compositional maturity and a moderate textural maturity. The pore systems are dominated by secondary pores resulting from dissolution of framework grains, micropores among authigenic clays, and minor amounts of primary intergranular pores. Chemically unstable framework grains such as feldspar and lithic fragments experienced alteration and resulted in formation of authigenic kaolinite. Dissolution and alteration of feldspars and rock fragments and pressure solution of detrital quartz grains were the main sources for quartz cements. Mechanical compaction and cementation by calcite, dolomite, quartz, kaolinite, and mixed‐layer illite/smectite destroyed primary pores, whereas dissolution of framework grains generated secondary pores. Five types of diagenetic facies are identified based on framework mineralogy, texture, diagenetic minerals, and pore systems. These comprise the following: (a) quartz‐cemented sandstone, (b) tightly compacted sandstone, (c) carbonate‐cemented sandstone, (d) clay‐mineral‐cemented sandstone, and (e) clean dissolved sandstone. Diagenetic processes and evolution sequences for the five diagenetic facies were reconstructed based on textural relationships from thin section, SEM, and CL studies. The reservoir quality evolution of various diagenetic facies is predicted by considering variations in grain size, sorting, shape, and matrix content of sandstones. This work, which investigates the diagenetic sequence of sandstones, will provide insights into reservoir quality prediction for low‐permeability sandstones with similar tectono‐depositional settings.

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Identification of the lower limit of high-quality source rocks and its relation to hydrocarbon accumulation—Taking the Beier Sag in the Hailaer Basin as an example

Chen

et al. 2012

Pet. Sci.

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The theory of "source rock control" has evolved from source-rock-control hydrocarbon accumulation, to effective source-rock-control hydrocarbon accumulation, and to high-quality sourcerock-control hydrocarbon accumulation. However, there are problems, such as whether high-quality source rocks exist or not? What high-quality source rocks are, and how to identify them, are yet to be agreed upon. Aimed at this issue of concern to explorationists, and taking the Beier Sag in the Hailaer Basin as an example, this paper de nes the high-quality source rocks and the lower limit for evaluation of high-quality source rocks, by using the in ection point on the relationship curve of hydrocarbon (oil) expulsion, which is calculated by the material balance principle, versus total organic carbon (TOC). The results show that when TOC is low, all source rocks have limited hydrocarbon expulsion and slow growth rate, thus they cannot be high-quality source rocks. However, when TOC rises to some threshold, hydrocarbon expulsion increases signi cantly with TOC. This in ection point should be the lower limit of high-quality source rocks those with TOC greater than the in ection-point value are high-quality source rocks. In addition, the lower limit of high-quality source rocks is also related to the type and maturity of organic matters in the source rocks, as well as the mineral components of the source rocks affecting the residual hydrocarbons. Theoretically, the lower limit of high-quality source rocks depends on geological conditions rather than being a constant value. However, for the sake of simplicity and practicability, in this paper TOC=2.0% is regarded as the lower limit of high-quality source rocks. The examination of such standard in the work area indicates that the high-quality source rocks in members K 1 n 2 and K 1 n 1 of the Nantun formation contribute 7 % and 82% to oil generation, and 9 % and 91% to oil expulsion , respectively. The distribution of high-quality source rocks is also closely related to the distribution of hydrocarbon reservoirs in the region, demonstrating that high-quality source rocks control hydrocarbon accumulation.

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Entropy numbers of Besov classes of generalized smoothness on the sphere

Cited by 16 publications

References 25 publications

Estimates for n-widths of multiplier operators of multiple Walsh series

Estimates for n-widths of multiplier operators of multiple Walsh series

Diagenesis and reservoir quality of sandstones in the Eocene Shahejie Formation, Raoyang Sag (Jizhong Depression), Bohai Bay Basin, China

Identification of the lower limit of high-quality source rocks and its relation to hydrocarbon accumulation—Taking the Beier Sag in the Hailaer Basin as an example

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