The eigenvalues of the adjacency matrix of a graph are called the eigenvalues of the graph. Let the vector <em>e<sub>j</sub></em> =(0, <span style="font-size:12.8px;white-space:normal;&...The eigenvalues of the adjacency matrix of a graph are called the eigenvalues of the graph. Let the vector <em>e<sub>j</sub></em> =(0, <span style="font-size:12.8px;white-space:normal;">…</span> , 1, … , 0)<sup>T</sup> and the all -1 vector <em>j</em> =(1, 1, <span style="font-size:12.8px;white-space:normal;">…</span>,1)<sup>T</sup>, the cosine of the (acute) angle formed by the vector <em>e<sub>j</sub></em> and the eigensubspace is called an angle of the graph. The cosine of the (acute) angle formed by the vector <em>j</em> and the eigensubspace is called a main angle of the graph. The angles and main angles are all important parameters on the graph, and they can be combined with the eigenvalues of the graph to determine the degree sequence of the graph, the number of triangles, quadrilaterals and pentagons on the graph, and the characteristic polynomials of the complement graph, but there is little study on the angles and main angles of the graph. In this paper, we determine the angles and main angles of the complete graph, the cube graph, the Petersen graph, the cycle and the complete bipartite graph.展开更多
This study discussed the division of matrix- and fracture-type shale oils in the Jiyang Depression, and proposed the concept of fracture development coefficient. The fracture development coefficient is defined as the ...This study discussed the division of matrix- and fracture-type shale oils in the Jiyang Depression, and proposed the concept of fracture development coefficient. The fracture development coefficient is defined as the ratio of fault throw to the distance between a shale oil well and the nearest fault. Based on CO_2 content, state of water, oil production and logging response of shale oil formations, the classification of shale oils was established, i.e., a fracture-type shale oil well has a fracture development coefficient greater than 0.2, while a matrix-type one has a fracture development coefficient less than 0.2. Furthermore, the key control factors of matrix- and fracture-type shale oil enrichment were analyzed using typical anatomical and statistical methods. For matrix-type shale oil enrichment, these factors are lithofacies, total organic carbon（TOC）, shale porosity and abnormal pressure; for fracture-type shale oil enrichment, they are lithofacies, extent of fracture development, and abnormal pressure. This study also first described the differences between matrix- and fracture-type shale oils. The results provide reference for the exploration of terrestrial faulted basins in eastern China.展开更多
To identify the type of main flow channels of complex porous media in oil and gas reservoirs,the"main flow channel index"is defined as the ratio of comprehensive permeability obtained from well test to matri...To identify the type of main flow channels of complex porous media in oil and gas reservoirs,the"main flow channel index"is defined as the ratio of comprehensive permeability obtained from well test to matrix permeability obtained from core analysis or well logging.Meanwhile,a mathematical model is established based on equivalent flow assumption,the classification method for main flow channels is put forward,and quantitative characterization of main flow channels is realized.The method has been verified by analysis of typical gas reservoirs.The study results show that the"main flow channel index"can quantitatively classify types of flow channels.If the index is less than 3,the matrix pore is the main flow channel;if the index is between 3 and 20,the fracture is the main flow channel and the matrix pore acts as the supplement one;if the index is more than 20,the fracture is the only seepage channel.The dynamic analysis of typical gas reservoirs shows that the"main flow channel index"can be used to identify the type of flow channel in complex porous media,guiding the classified development of gas reservoirs,and avoiding development risk.展开更多
文摘The eigenvalues of the adjacency matrix of a graph are called the eigenvalues of the graph. Let the vector <em>e<sub>j</sub></em> =(0, <span style="font-size:12.8px;white-space:normal;">…</span> , 1, … , 0)<sup>T</sup> and the all -1 vector <em>j</em> =(1, 1, <span style="font-size:12.8px;white-space:normal;">…</span>,1)<sup>T</sup>, the cosine of the (acute) angle formed by the vector <em>e<sub>j</sub></em> and the eigensubspace is called an angle of the graph. The cosine of the (acute) angle formed by the vector <em>j</em> and the eigensubspace is called a main angle of the graph. The angles and main angles are all important parameters on the graph, and they can be combined with the eigenvalues of the graph to determine the degree sequence of the graph, the number of triangles, quadrilaterals and pentagons on the graph, and the characteristic polynomials of the complement graph, but there is little study on the angles and main angles of the graph. In this paper, we determine the angles and main angles of the complete graph, the cube graph, the Petersen graph, the cycle and the complete bipartite graph.
基金supported by the National Basic Research Program of China(973 Program)(Grant No2014CB239104)
文摘This study discussed the division of matrix- and fracture-type shale oils in the Jiyang Depression, and proposed the concept of fracture development coefficient. The fracture development coefficient is defined as the ratio of fault throw to the distance between a shale oil well and the nearest fault. Based on CO_2 content, state of water, oil production and logging response of shale oil formations, the classification of shale oils was established, i.e., a fracture-type shale oil well has a fracture development coefficient greater than 0.2, while a matrix-type one has a fracture development coefficient less than 0.2. Furthermore, the key control factors of matrix- and fracture-type shale oil enrichment were analyzed using typical anatomical and statistical methods. For matrix-type shale oil enrichment, these factors are lithofacies, total organic carbon（TOC）, shale porosity and abnormal pressure; for fracture-type shale oil enrichment, they are lithofacies, extent of fracture development, and abnormal pressure. This study also first described the differences between matrix- and fracture-type shale oils. The results provide reference for the exploration of terrestrial faulted basins in eastern China.
文摘To identify the type of main flow channels of complex porous media in oil and gas reservoirs,the"main flow channel index"is defined as the ratio of comprehensive permeability obtained from well test to matrix permeability obtained from core analysis or well logging.Meanwhile,a mathematical model is established based on equivalent flow assumption,the classification method for main flow channels is put forward,and quantitative characterization of main flow channels is realized.The method has been verified by analysis of typical gas reservoirs.The study results show that the"main flow channel index"can quantitatively classify types of flow channels.If the index is less than 3,the matrix pore is the main flow channel;if the index is between 3 and 20,the fracture is the main flow channel and the matrix pore acts as the supplement one;if the index is more than 20,the fracture is the only seepage channel.The dynamic analysis of typical gas reservoirs shows that the"main flow channel index"can be used to identify the type of flow channel in complex porous media,guiding the classified development of gas reservoirs,and avoiding development risk.
