The dependence of elastic moduli of shales on the mineralogy and microstructure of shales is important for the prediction of sweet spots and shale gas production. Based on 3D digital images of the microstructure of Lo...The dependence of elastic moduli of shales on the mineralogy and microstructure of shales is important for the prediction of sweet spots and shale gas production. Based on 3D digital images of the microstructure of Longmaxi black shale samples using X-ray CT, we built detailed 3D digital images of cores with porosity properties and mineral contents. Next, we used finite-element （FE） methods to derive the elastic properties of the samples. The FE method can accurately model the shale mineralogy. Particular attention is paid to the derived elastic properties and their dependence on porosity and kerogen. The elastic moduli generally decrease with increasing porosity and kerogen, and there is a critical porosity （0.75） and kerogen content （ca. ≤3%） over which the elastic moduli decrease rapidly and slowly, respectively. The derived elastic moduli of gas- and oil-saturated digital cores differ little probably because of the low porosity （4.5%） of the Longmaxi black shale. Clearly, the numerical experiments demonstrated the feasibility of combining microstructure images of shale samples with elastic moduli calculations to predict shale properties.展开更多
Based on the trivariate reduction technique two different trivariate Bernoulli mixtures of univariate uniform distributions and their associated trivariate copulas with bivariate linear Spearman marginal copulas are c...Based on the trivariate reduction technique two different trivariate Bernoulli mixtures of univariate uniform distributions and their associated trivariate copulas with bivariate linear Spearman marginal copulas are considered. Mathematical characterizations of these Bernoulli mixture models are obtained. Since Bernoulli mixture trivariate reduction copulas are not compatible with all valid grade correlation coefficients, and there exist linear Spearman compatible non-Bernoulli mixture trivariate copulas, one can ask when there exists at all a trivariate copula with given linear Spearman marginal copulas. Based on a known concordance ordering compatibility criterion, a set of grade correlation inequalities, which must necessarily be satisfied for compatibility, is derived. The existence question for trivariate copulas with compatible linear Spearman marginal copulas is settled in the main result, which states that this set of inequalities is also sufficient for compatibility. The constructive proof makes use of two new classes of trivariate copulas that are obtained from the Bernoulli mixture trivariate copulas through a natural parametric extension. Finally, the obtained classes of trivariate copulas are compared with another class that contains as special case some trivariate copulas with linear Spearman marginal copulas. Since the latter class is incompatible with some type of linear Spearman copulas, the new classes of trivariate copulas build a richer class in this respect. Moreover, in contrast to the mentioned class, which requires in general 11 different elementary copulas in the defining convex linear combination, the new classes require at most five of them, which results in a more parsimonious parametric modelling.展开更多
The main technical problems that should be considered in the design of hydro-turbine generating units of Three Gorges Project (TGP) are analyzed;the key technical researches performed are summarized,and the parameters...The main technical problems that should be considered in the design of hydro-turbine generating units of Three Gorges Project (TGP) are analyzed;the key technical researches performed are summarized,and the parameters of hydro-turbine generating units are optimized through the study on key technical problems.The unit operation indicates that the performance of the hydro-turbine generating units is excellent,and the units can operate in a safe,stable and highly efficient mode for a long term.Therefore,it is verified effectively that the general technical design of units is scientific and rational.展开更多
Let A and K be positive integers and ε∈ {-2,-1,1,2}. The main contribution of the paper is a proof that each of the D(ε~2)-triples {K, A^2 K+2εA,(A +1)~2 K + 2ε(A+1)} has uniqui extension to a D(ε~2)-quadruple. ...Let A and K be positive integers and ε∈ {-2,-1,1,2}. The main contribution of the paper is a proof that each of the D(ε~2)-triples {K, A^2 K+2εA,(A +1)~2 K + 2ε(A+1)} has uniqui extension to a D(ε~2)-quadruple. This is used to slightly strengthen the conditions required for the existencc of a D(1)-quintuple whose smallest three elements form a regular triple.展开更多
基金supported by the Chinese Academy of Sciences Strategic Leading Science and Technology projects(Grant No.XDB10010400)the China Postdoctoral Science Foundation(Grant No.2015M570142)
文摘The dependence of elastic moduli of shales on the mineralogy and microstructure of shales is important for the prediction of sweet spots and shale gas production. Based on 3D digital images of the microstructure of Longmaxi black shale samples using X-ray CT, we built detailed 3D digital images of cores with porosity properties and mineral contents. Next, we used finite-element （FE） methods to derive the elastic properties of the samples. The FE method can accurately model the shale mineralogy. Particular attention is paid to the derived elastic properties and their dependence on porosity and kerogen. The elastic moduli generally decrease with increasing porosity and kerogen, and there is a critical porosity （0.75） and kerogen content （ca. ≤3%） over which the elastic moduli decrease rapidly and slowly, respectively. The derived elastic moduli of gas- and oil-saturated digital cores differ little probably because of the low porosity （4.5%） of the Longmaxi black shale. Clearly, the numerical experiments demonstrated the feasibility of combining microstructure images of shale samples with elastic moduli calculations to predict shale properties.
文摘Based on the trivariate reduction technique two different trivariate Bernoulli mixtures of univariate uniform distributions and their associated trivariate copulas with bivariate linear Spearman marginal copulas are considered. Mathematical characterizations of these Bernoulli mixture models are obtained. Since Bernoulli mixture trivariate reduction copulas are not compatible with all valid grade correlation coefficients, and there exist linear Spearman compatible non-Bernoulli mixture trivariate copulas, one can ask when there exists at all a trivariate copula with given linear Spearman marginal copulas. Based on a known concordance ordering compatibility criterion, a set of grade correlation inequalities, which must necessarily be satisfied for compatibility, is derived. The existence question for trivariate copulas with compatible linear Spearman marginal copulas is settled in the main result, which states that this set of inequalities is also sufficient for compatibility. The constructive proof makes use of two new classes of trivariate copulas that are obtained from the Bernoulli mixture trivariate copulas through a natural parametric extension. Finally, the obtained classes of trivariate copulas are compared with another class that contains as special case some trivariate copulas with linear Spearman marginal copulas. Since the latter class is incompatible with some type of linear Spearman copulas, the new classes of trivariate copulas build a richer class in this respect. Moreover, in contrast to the mentioned class, which requires in general 11 different elementary copulas in the defining convex linear combination, the new classes require at most five of them, which results in a more parsimonious parametric modelling.
文摘The main technical problems that should be considered in the design of hydro-turbine generating units of Three Gorges Project (TGP) are analyzed;the key technical researches performed are summarized,and the parameters of hydro-turbine generating units are optimized through the study on key technical problems.The unit operation indicates that the performance of the hydro-turbine generating units is excellent,and the units can operate in a safe,stable and highly efficient mode for a long term.Therefore,it is verified effectively that the general technical design of units is scientific and rational.
基金supported by Grants-in-Aid for Scientific Research(JSPS KAKENHI) (Grant No. 16K05079)
文摘Let A and K be positive integers and ε∈ {-2,-1,1,2}. The main contribution of the paper is a proof that each of the D(ε~2)-triples {K, A^2 K+2εA,(A +1)~2 K + 2ε(A+1)} has uniqui extension to a D(ε~2)-quadruple. This is used to slightly strengthen the conditions required for the existencc of a D(1)-quintuple whose smallest three elements form a regular triple.
