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Transitioning from Discrete to continuous distribution Mathematica vs. Excel —An Example

American Journal of Computational Mathematics 2022年第1期12卷 25-32页

作者： Haiduke Sarafian The Pennsylvania State University University College York USA

Frequencies of the repeated integers of the first n digits of e.g. π utilizing commercial software are listed. The discrete distribution is utilized to evaluate its statistical moments. The distribution is fitted with a polynomial generating a continuous replica of the former. Its statistical moments are evaluated and compared to the former. The procedure clarifies the mechanism transiting from discrete to a continuous domain. Applying Mathematica the fitted polynomial is replaced with an interpolated function with controlled smoothing factor refining the quality of the fit and its corresponding moments. Knowledge learned assists in the understanding of the standard procedure calculating moments of e.g. Maxwell-Boltzmann continuous distribution in kinetic Theory of gases.

关键词： Digits of π Discrete distribution continuous distribution Moments of distribution Excel Mathematica

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Geological theory and exploration & development practice of hydrocarbon accumulation inside continental source kitchens

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Petroleum Exploration and Development 2020年第6期47卷 1147-1159页

作者： JIAO Fangzheng ZOU Caineng YANG Zhi China National Petroleum Corporation Beijing 100007China Research Institute of Petroleum Exploration&Development PetroChinaBeijing 100083China

Continental shale strata in China are rich in petroleum resources and are an important area to strengthen domestic oil exploration and *** on the latest progress in geological research and exploration and development of petroleum inside continental source kitchens of China National Petroleum Corporation exploration areas in recent two years,we have achieved the following results:(1)The geological connotations of continental hydrocarbon accumulation inside source kitchen and"sweet spot"have been *** intra-source petroleum accumulation refers to the accumulation of liquid-rich hydrocarbons retained or captured in the continental organic-rich shale strata,and"sweet spot"refers to the favorable reservoir with higher oil content,better physical properties,easier to stimulate and higher in commercial development value in the overall oil-bearing continental source rock series,they can be divided into three types,interlayer,hybrid sediment and shale.(2)High-quality shale formations in both salt water and freshwater lacustrine basins can generate hydrocarbons on a large scale,shale strata have multiple types of favorable reservoirs with large-scale storage capacity,the intra-source shale strata are overall oil-bearing and large in resource scale,and there are multiple favorable shale series for *** exploration and development practice is propelling the formation of a series of exploration and development key technologies with"sweet spot exploration"and"volume development"as the *** pilot tests of these technologies have provided an important scientific basis for the economic and effective development of hydrocarbon accumulation inside source kitchen,and popularization of these technologies have achieved encouraging results preliminarily.(3)Two types of continental intra-source petroleum resources in China have great potential,including medium-high maturity with liquid-rich hydrocarbons and medium-low maturity with organic-rich matter.

关键词： hydrocarbon accumulation inside source kitchen continental shale oil continuous distribution overall oil-bearing reservoir sweet spot volume development source-reservoir integration

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