Two kinds of unconnected double fan graphs with even vertices,(P^((1))_(1)∨(P^((1))_(2n)∪P^((2))_(2n)))∪P_(2n+1)∪(P_(1)^((2))∨K_(2n))and(P_(1)^((1))∨(P^((1))_(2n)∪P^((2))_(2n)))∪(P_(1)^((2))∨K_((1))^(2n))∪(P...Two kinds of unconnected double fan graphs with even vertices,(P^((1))_(1)∨(P^((1))_(2n)∪P^((2))_(2n)))∪P_(2n+1)∪(P_(1)^((2))∨K_(2n))and(P_(1)^((1))∨(P^((1))_(2n)∪P^((2))_(2n)))∪(P_(1)^((2))∨K_((1))^(2n))∪(P^((3))_(1)∨K_((2))^(2n))were presented.For natural number n∈N,n≥1,the two graphs are all graceful graphs,where P^((1))_(2n),P^((2))_(2n)are even-vertices path,P_(2n+1)is odd-vertices path,K_(2n),K^((1))_(2n),K^((2))_(2n)are the complement of graph K_(2 n),G_(1)∨G_(2)is the join graph of G_(1)and G_(2).展开更多
In the paper, we study the gracefulness of several unconnected graphs related to wheel. For natural number p ≥ 1, t ≥ 1 , let n = 2t ＋ 3,2t ＋ 4 , which proved W. U K （1） p,t U K（2） is graceful; for p≥1, t≥1 ...In the paper, we study the gracefulness of several unconnected graphs related to wheel. For natural number p ≥ 1, t ≥ 1 , let n = 2t ＋ 3,2t ＋ 4 , which proved W. U K （1） p,t U K（2） is graceful; for p≥1, t≥1 ,let n=2t＋3,2t＋4, then Wn,2n＋1 U K（1）p,t U K（2） p,t is graceful and for m ≥ 1, r ≥ 1 , let n = 2m ＋ 5, Wn,2n＋1 U （C3 v Km） U St（r） is graceful.展开更多
The unconnected gas-bearing pores in shale gas reservoirs may be transformed into“potential recoverable pores”after large scale hydraulic fracturing.However,the mainstream pore classification methods of shale gas re...The unconnected gas-bearing pores in shale gas reservoirs may be transformed into“potential recoverable pores”after large scale hydraulic fracturing.However,the mainstream pore classification methods of shale gas reservoirs,do not take the unconnected pores into account,which impacts the evaluation accuracy of reservoir pore effectiveness.To solve this problem,this paper took the shale of Lower Silurian Longmaxi Formation in the southern Sichuan Basin as the research object to carry out experiments on core porosity,centrifugal+gradual drying NMR after saturated with brine and NMR freezeethaw using plunger samples and crushed samples to analyze the volume,main development location and main pore size distribution range of unconnected pores.Then,the pore systems were classified,and the lower limit of effective pore size of connected gas-bearing pores was determined.Finally,the total pore effectiveness of shale gas reservoirs was evaluated,and the influence of unconnected pores on the development of shale gas was discussed.And the following research results were obtained.First,there are a large number of unconnected pores in the shale gas reservoirs of the study area,accounting for 30.23%.Most of them are mainly developed in organic matters and a few are developed in clay minerals.The distribution of pore size ranges from 5 nm to 30 nm.Second,T_(2)cut-off value of clay bound water in the shale gas reservoirs of the study area is 0.26 ms,whose corresponding pore size is 5.35 nm,which is the lower limit of the effective pore size.Third,large-scale hydraulic fracturing can improve the unconnected pores with the size more than 5.35 nm,so effective development of shale gas will be realized.Fourth,after hydraulic fracturing stimulation,the unconnected pores can increase the storage space of fracturing fluid in the matrix,absorb the fracturing fluid in the fractures,replace the shale gas in the pores and promote the automatic alleviation of water lock in shale gas reservoirs,so the single-well shale gas production will be increased.In conclusion,fluid occurrence and pore system in shale pores can be quantitatively divided by means of centrifugal+gradual temperature drying method combined with NMR experiments,mobile water and capillary bound water can be determined by the high speed centrifugal+NMR experiments,and capillary bound water and clay bound water can be determined by the gradual drying t NMR experiments.展开更多
基金the National Natural Science Foundation of China(11702094)the Fundamental Research Funds for the Central University(3142015045)。
文摘Two kinds of unconnected double fan graphs with even vertices,(P^((1))_(1)∨(P^((1))_(2n)∪P^((2))_(2n)))∪P_(2n+1)∪(P_(1)^((2))∨K_(2n))and(P_(1)^((1))∨(P^((1))_(2n)∪P^((2))_(2n)))∪(P_(1)^((2))∨K_((1))^(2n))∪(P^((3))_(1)∨K_((2))^(2n))were presented.For natural number n∈N,n≥1,the two graphs are all graceful graphs,where P^((1))_(2n),P^((2))_(2n)are even-vertices path,P_(2n+1)is odd-vertices path,K_(2n),K^((1))_(2n),K^((2))_(2n)are the complement of graph K_(2 n),G_(1)∨G_(2)is the join graph of G_(1)and G_(2).
基金Supported by the Natural Science Foundation of Beijing(1102015)University Scientific Research Project of Hebei Province(Z2014032)the Fundamental Research Funds for the Central Universities(HKXJZD201402,2011B019,3142013025,3142014127)
文摘In the paper, we study the gracefulness of several unconnected graphs related to wheel. For natural number p ≥ 1, t ≥ 1 , let n = 2t ＋ 3,2t ＋ 4 , which proved W. U K （1） p,t U K（2） is graceful; for p≥1, t≥1 ,let n=2t＋3,2t＋4, then Wn,2n＋1 U K（1）p,t U K（2） p,t is graceful and for m ≥ 1, r ≥ 1 , let n = 2m ＋ 5, Wn,2n＋1 U （C3 v Km） U St（r） is graceful.
基金supported by the National Natural Science Foundation of China“Research on nanopore structure characterization and seepage mechanism of shale reservoirs”(No.:51674044)Chongqing Key Industry Common Key Technology Innovation Special Project“Exploration and development key technology and its application of shale gas in Chongqing”(No.:cstc2017zdcyzdyfx0040)+1 种基金Sichuan Applied Basic Research Project“Research on intelligent evaluation system of marine shale gas construction and production core area(provincial key project)”(No.:2019YJ0340)Sichuan Promising Key Project“Study on evaluation of the fracturing effect of shale gas reservoirs based on the law of fracturing fluid flow back”(No.:2019JDRC0095).
文摘The unconnected gas-bearing pores in shale gas reservoirs may be transformed into“potential recoverable pores”after large scale hydraulic fracturing.However,the mainstream pore classification methods of shale gas reservoirs,do not take the unconnected pores into account,which impacts the evaluation accuracy of reservoir pore effectiveness.To solve this problem,this paper took the shale of Lower Silurian Longmaxi Formation in the southern Sichuan Basin as the research object to carry out experiments on core porosity,centrifugal+gradual drying NMR after saturated with brine and NMR freezeethaw using plunger samples and crushed samples to analyze the volume,main development location and main pore size distribution range of unconnected pores.Then,the pore systems were classified,and the lower limit of effective pore size of connected gas-bearing pores was determined.Finally,the total pore effectiveness of shale gas reservoirs was evaluated,and the influence of unconnected pores on the development of shale gas was discussed.And the following research results were obtained.First,there are a large number of unconnected pores in the shale gas reservoirs of the study area,accounting for 30.23%.Most of them are mainly developed in organic matters and a few are developed in clay minerals.The distribution of pore size ranges from 5 nm to 30 nm.Second,T_(2)cut-off value of clay bound water in the shale gas reservoirs of the study area is 0.26 ms,whose corresponding pore size is 5.35 nm,which is the lower limit of the effective pore size.Third,large-scale hydraulic fracturing can improve the unconnected pores with the size more than 5.35 nm,so effective development of shale gas will be realized.Fourth,after hydraulic fracturing stimulation,the unconnected pores can increase the storage space of fracturing fluid in the matrix,absorb the fracturing fluid in the fractures,replace the shale gas in the pores and promote the automatic alleviation of water lock in shale gas reservoirs,so the single-well shale gas production will be increased.In conclusion,fluid occurrence and pore system in shale pores can be quantitatively divided by means of centrifugal+gradual temperature drying method combined with NMR experiments,mobile water and capillary bound water can be determined by the high speed centrifugal+NMR experiments,and capillary bound water and clay bound water can be determined by the gradual drying t NMR experiments.
