Vuggy reservoirs are the most common, albeit important heterogeneous carbonate reservoirs in China. However, saturation calculations using logging data are not well developed, whereas Archie method is more common. In ...Vuggy reservoirs are the most common, albeit important heterogeneous carbonate reservoirs in China. However, saturation calculations using logging data are not well developed, whereas Archie method is more common. In this study, electrical conduction in a vuggy reservoir is theoretically analyzed to establish a new saturation equation for vuggy reservoirs. We found that vugs have a greater effect on saturation than resistivity, which causes inflection in the rock-electricity curve. Using single-variable exPeriments, we evaluated the effects of rug size, vug number, and vug distribution on the rock-electricity relation. Based on the general saturation model, a saturation equation for vuggy reservoirs is derived, and the physical significance of the equation parameters is discussed based on the seepage-electricity similarity. The equation parameters depend on the pore structure, and vugs and matrix pore size distribution. Furthermore, a method for calculating the equation parameters is proposed, which uses nuclear magnetic resonance (NMR) data to calculate the capillary pressure curve. Field application of the proposed equation and parameter derivation method shows good match between calculated and experimental results, with an average absolute error of 5.8%.展开更多
Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of theKlein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simulta...Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of theKlein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simultaneously,energy spectrum equations are also obtained. It is shown that the radial equation and angular wave functions areexpressed by confluent hypergeogetric and hypergeogetric functions respectively.展开更多
In the present paper, the effect of variable fluid properties (density, viscosity, thermal conductivity and specific heat) on the convection in the classical Rayleigh-Benard problem is investigated. The investigatio...In the present paper, the effect of variable fluid properties (density, viscosity, thermal conductivity and specific heat) on the convection in the classical Rayleigh-Benard problem is investigated. The investigation concerns water, air, and engine oil by taking into account the variation of fluid properties with temperature. The results are obtained by numerically solving the governing equations, using the SIMPLE algorithm and covering large temperature differences. It is found that the critical Rayleigh number increases as the temperature difference increases considering all fluid properties variable. However, when the fluid properties are kept constant, calculated at the mean temperature, and only density is considered variable, the critical Rayleigh number either decreases or remains constant.展开更多
The Camassa-Holm equation, Degasperis–Procesi equation and Novikov equation are the three typical integrable evolution equations admitting peaked solitons. In this paper, a generalized Novikov equation with cubic and...The Camassa-Holm equation, Degasperis–Procesi equation and Novikov equation are the three typical integrable evolution equations admitting peaked solitons. In this paper, a generalized Novikov equation with cubic and quadratic nonlinearities is studied, which is regarded as a generalization of these three well-known studied equations. It is shown that this equation admits single peaked traveling wave solutions, periodic peaked traveling wave solutions, and multi-peaked traveling wave solutions.展开更多
Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic pot...Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.展开更多
The study of formation and dissociation of CO 2 hydrate in porous media was characterized by magnetic resonance imaging (MRI) system in in situ conditions. This work simulated porous media by using glass beads of unif...The study of formation and dissociation of CO 2 hydrate in porous media was characterized by magnetic resonance imaging (MRI) system in in situ conditions. This work simulated porous media by using glass beads of uniform size. The growth and dissociation habit of CO2 hydrate was observed under different temperature and pressure conditions. The induction time and the hydrate saturation during the growth and dissociation process in different sizes of porous media were obtained by using the MRI signal intensity. The results indicate that hydrate growth rate and the induction time are affected by the size of porous media, pressure, and degree of supercooling. There are three hydrate growth stages, i.e., initial growth stage, rapid growth stage and steady stage. In this study,the CO2 hydrate forms preferentially at the surface of vessel and then gradually grows inward. The hydrate tends to cement the glass beads together and occupies the pore gradually. As the hydrate decomposes gradually, the dissociation rate increases to the maximum and then decreases to zero.展开更多
In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence an...In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of homoclinic solutions. Our results not only solve an open problem proposed by Pankov, but also greatly improve some existing ones even for some special cases.展开更多
This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in ...This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in x and even in t, which are 1-periodic in t, and the function g satisfies g(x,t/x+, as|x| - +. Using the KAM theory for reversible systems, the author proves the existence of invariant tori and thus the boundedness of all the solutions and the existence of quasiperiodic solutions and subharmonic solutions.展开更多
Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It ...Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ*> 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r^(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] .展开更多
基金supported by the National S&T Major Special Project(No.2011ZX05020-008)
文摘Vuggy reservoirs are the most common, albeit important heterogeneous carbonate reservoirs in China. However, saturation calculations using logging data are not well developed, whereas Archie method is more common. In this study, electrical conduction in a vuggy reservoir is theoretically analyzed to establish a new saturation equation for vuggy reservoirs. We found that vugs have a greater effect on saturation than resistivity, which causes inflection in the rock-electricity curve. Using single-variable exPeriments, we evaluated the effects of rug size, vug number, and vug distribution on the rock-electricity relation. Based on the general saturation model, a saturation equation for vuggy reservoirs is derived, and the physical significance of the equation parameters is discussed based on the seepage-electricity similarity. The equation parameters depend on the pore structure, and vugs and matrix pore size distribution. Furthermore, a method for calculating the equation parameters is proposed, which uses nuclear magnetic resonance (NMR) data to calculate the capillary pressure curve. Field application of the proposed equation and parameter derivation method shows good match between calculated and experimental results, with an average absolute error of 5.8%.
基金Supported by National Natural Science Foundation of China under Grant No.10865003
文摘Under the condition of an equal mixing of vector and scalar potentials, exact solutions of bound states of theKlein-Gordon equation with pseudo-Coulomb potential plus a new ring-shaped potential are presented. Simultaneously,energy spectrum equations are also obtained. It is shown that the radial equation and angular wave functions areexpressed by confluent hypergeogetric and hypergeogetric functions respectively.
文摘In the present paper, the effect of variable fluid properties (density, viscosity, thermal conductivity and specific heat) on the convection in the classical Rayleigh-Benard problem is investigated. The investigation concerns water, air, and engine oil by taking into account the variation of fluid properties with temperature. The results are obtained by numerically solving the governing equations, using the SIMPLE algorithm and covering large temperature differences. It is found that the critical Rayleigh number increases as the temperature difference increases considering all fluid properties variable. However, when the fluid properties are kept constant, calculated at the mean temperature, and only density is considered variable, the critical Rayleigh number either decreases or remains constant.
基金Supported in part by the NSF-China for Distinguished Young Scholars Grant-10925104
文摘The Camassa-Holm equation, Degasperis–Procesi equation and Novikov equation are the three typical integrable evolution equations admitting peaked solitons. In this paper, a generalized Novikov equation with cubic and quadratic nonlinearities is studied, which is regarded as a generalization of these three well-known studied equations. It is shown that this equation admits single peaked traveling wave solutions, periodic peaked traveling wave solutions, and multi-peaked traveling wave solutions.
基金Supported by National Natural Science Foundation of China under Grant Nos.11375030 and 61304133
文摘Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.
基金supported by the State Key Development Program for Basic Research of China (Grant No. 2009CB219507)National Natural Science Foundation of China (Grant Nos. 51006017 & 50736001)National Science and Technology Major Project (Grant No. 2011ZX05026-004)
文摘The study of formation and dissociation of CO 2 hydrate in porous media was characterized by magnetic resonance imaging (MRI) system in in situ conditions. This work simulated porous media by using glass beads of uniform size. The growth and dissociation habit of CO2 hydrate was observed under different temperature and pressure conditions. The induction time and the hydrate saturation during the growth and dissociation process in different sizes of porous media were obtained by using the MRI signal intensity. The results indicate that hydrate growth rate and the induction time are affected by the size of porous media, pressure, and degree of supercooling. There are three hydrate growth stages, i.e., initial growth stage, rapid growth stage and steady stage. In this study,the CO2 hydrate forms preferentially at the surface of vessel and then gradually grows inward. The hydrate tends to cement the glass beads together and occupies the pore gradually. As the hydrate decomposes gradually, the dissociation rate increases to the maximum and then decreases to zero.
基金supported partially by the Specialized Fund for the Doctoral Program of Higher Eduction (Grant No.20071078001)Key Project of National Natural Science Foundation of China (Grant No. 11031002)+1 种基金Natural Science and Engineering Research Council of Canada (NSERC)Project of Scientific Research Innovation Academic Group for the Education System of Guangzhou City
文摘In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of homoclinic solutions. Our results not only solve an open problem proposed by Pankov, but also greatly improve some existing ones even for some special cases.
文摘This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in x and even in t, which are 1-periodic in t, and the function g satisfies g(x,t/x+, as|x| - +. Using the KAM theory for reversible systems, the author proves the existence of invariant tori and thus the boundedness of all the solutions and the existence of quasiperiodic solutions and subharmonic solutions.
基金supported by the National Natural Science Foundation of China(Nos.11201119,11471099)the International Cultivation of Henan Advanced Talents and the Research Foundation of Henan University(No.yqpy20140043)
文摘Let B R^n be the unit ball centered at the origin. The authors consider the following biharmonic equation:{?~2u = λ(1 + u)~p in B,u =?u/?ν= 0 on ?B, where p >n+4/ n-4and ν is the outward unit normal vector. It is well-known that there exists a λ*> 0 such that the biharmonic equation has a solution for λ∈ (0, λ*) and has a unique weak solution u*with parameter λ = λ*, called the extremal solution. It is proved that u* is singular when n ≥ 13 for p large enough and satisfies u*≤ r^(-4/ (p-1)) - 1 on the unit ball, which actually solve a part of the open problem left in [D`avila, J., Flores, I., Guerra, I., Multiplicity of solutions for a fourth order equation with power-type nonlinearity, Math. Ann., 348(1), 2009, 143–193] .