This paper considers nonlinear dynamics of teth- ered three-body formation system with their centre of mass staying on a circular orbit around the Earth, and applies the theory of space manifold dynamics to deal with ...This paper considers nonlinear dynamics of teth- ered three-body formation system with their centre of mass staying on a circular orbit around the Earth, and applies the theory of space manifold dynamics to deal with the nonlinear dynamical behaviors of the equilibrium configurations of the system. Compared with the classical circular restricted three body system, sixteen equilibrium configurations are obtained globally from the geometry of pseudo-potential energy sur- face, four of which were omitted in the previous research. The periodic Lyapunov orbits and their invariant manifolds near the hyperbolic equilibria are presented, and an iteration procedure for identifying Lyapunov orbit is proposed based on the differential correction algorithm. The non-transversal intersections between invariant manifolds are addressed to generate homoclinic and heteroclinic trajectories between the Lyapunov orbits. （3,3）- and （2,1）-heteroclinic trajecto- ries from the neighborhood of one collinear equilibrium to that of another one, and （3,6）- and （2,1）-homoclinic trajecto- ries from and to the neighborhood of the same equilibrium, are obtained based on the Poincar6 mapping technique.展开更多
With estimated shale gas resources greater than those of US and Canada combined, China has been embarking on an ambitious shale development program. However, nearly 30 years of American experience in shale hydrocarbon...With estimated shale gas resources greater than those of US and Canada combined, China has been embarking on an ambitious shale development program. However, nearly 30 years of American experience in shale hydrocarbon exploration and production indicates a low total recovery of shale gas at 12 %-30 % and tight oil at 5 %-10 %. One of the main barriers to sustainable devel- opment of shale resources, namely the pore structure （ge- ometry and connectivity） of the nanopores for storing and transporting hydrocarbons, is rarely investigated. In this study, we collected samples from a variety of leading hydrocarbon-producing shale formations in US and China. These formations have different ages and geologic char- acteristics （e.g., porosity, permeability, mineralogy, total organic content, and thermal maturation）. We studied their pore structure characteristics, imbibition and saturated diffusion, edge-accessible porosity, and wettability with four complementary tests： mercury intrusion porosimetry, fluid and tracer imbibition into initially dry shale, tracer diffusion into fluid-saturated shale, and high-pressure Wood＇s metal intrusion followed with imaging and ele- mental mapping. The imbibition and diffusion tests use tracer-bearing wettability fluids （API brine or n-decane） to examine the association of tracers with mineral or organic matter phases, using a sensitive and micro-scale elemental laser ablation ICP-MS mapping technique. For two molecular tracers in n-decane fluid with the estimated sizes of 1.39 nm x 0.29 nm x 0.18 nm for 1-iododecane and 1.27 nm ~ 0.92 nm ~ 0.78 nm for trichlorooxobis （triph- enylphosphine） rhenium, much less penetration was observed for larger molecules of organic rhenium in shales with median pore-throat sizes of several nanometers. This indicates the probable entanglement of sub-nano-sized molecules in shales with nano-sized pore-throats. Overall findings from the above innovative approaches indicate the limited accessibility （several millimeters from sample edge） and connectivity of tortuous nanopore spaces in shales with spatial wettability, which could lead to the low overall hydrocarbon recovery because of the limited frac- ture-matrix connection and migration of hydrocarbon molecules from the shale matrix to the stimulated fracture network.展开更多
By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation the...By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.展开更多
基金supported by the National Natural Science Foundation of China(11172020)Talent Foundation supported by the Fundamental Research Funds for the Central Universities+1 种基金Aerospace Science and Technology Innovation Foundation of China Aerospace Science Corporationthe National High Technology Research and Development Program of China(863)(2012AA120601)
文摘This paper considers nonlinear dynamics of teth- ered three-body formation system with their centre of mass staying on a circular orbit around the Earth, and applies the theory of space manifold dynamics to deal with the nonlinear dynamical behaviors of the equilibrium configurations of the system. Compared with the classical circular restricted three body system, sixteen equilibrium configurations are obtained globally from the geometry of pseudo-potential energy sur- face, four of which were omitted in the previous research. The periodic Lyapunov orbits and their invariant manifolds near the hyperbolic equilibria are presented, and an iteration procedure for identifying Lyapunov orbit is proposed based on the differential correction algorithm. The non-transversal intersections between invariant manifolds are addressed to generate homoclinic and heteroclinic trajectories between the Lyapunov orbits. （3,3）- and （2,1）-heteroclinic trajecto- ries from the neighborhood of one collinear equilibrium to that of another one, and （3,6）- and （2,1）-homoclinic trajecto- ries from and to the neighborhood of the same equilibrium, are obtained based on the Poincar6 mapping technique.
基金Funding for this project was partially provided by the following three State Key Laboratories in China: State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu (PLC-201301)State Key Laboratory of Organic Geochemistry, Chinese Academy of Sciences, Guangzhou (No. OGL-201402)the Foundation of State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing (No. PRP/open-1403)
文摘With estimated shale gas resources greater than those of US and Canada combined, China has been embarking on an ambitious shale development program. However, nearly 30 years of American experience in shale hydrocarbon exploration and production indicates a low total recovery of shale gas at 12 %-30 % and tight oil at 5 %-10 %. One of the main barriers to sustainable devel- opment of shale resources, namely the pore structure （ge- ometry and connectivity） of the nanopores for storing and transporting hydrocarbons, is rarely investigated. In this study, we collected samples from a variety of leading hydrocarbon-producing shale formations in US and China. These formations have different ages and geologic char- acteristics （e.g., porosity, permeability, mineralogy, total organic content, and thermal maturation）. We studied their pore structure characteristics, imbibition and saturated diffusion, edge-accessible porosity, and wettability with four complementary tests： mercury intrusion porosimetry, fluid and tracer imbibition into initially dry shale, tracer diffusion into fluid-saturated shale, and high-pressure Wood＇s metal intrusion followed with imaging and ele- mental mapping. The imbibition and diffusion tests use tracer-bearing wettability fluids （API brine or n-decane） to examine the association of tracers with mineral or organic matter phases, using a sensitive and micro-scale elemental laser ablation ICP-MS mapping technique. For two molecular tracers in n-decane fluid with the estimated sizes of 1.39 nm x 0.29 nm x 0.18 nm for 1-iododecane and 1.27 nm ~ 0.92 nm ~ 0.78 nm for trichlorooxobis （triph- enylphosphine） rhenium, much less penetration was observed for larger molecules of organic rhenium in shales with median pore-throat sizes of several nanometers. This indicates the probable entanglement of sub-nano-sized molecules in shales with nano-sized pore-throats. Overall findings from the above innovative approaches indicate the limited accessibility （several millimeters from sample edge） and connectivity of tortuous nanopore spaces in shales with spatial wettability, which could lead to the low overall hydrocarbon recovery because of the limited frac- ture-matrix connection and migration of hydrocarbon molecules from the shale matrix to the stimulated fracture network.
基金This work was supported by the National Natural Science Foundation of China and China Postdoctoral Science Foundation(Grant No.10271097,20040350105)Program for New Century Excellent Talents in Xiamen University.
文摘By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.
