In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interfa...In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.展开更多
This paper compares the fluid flow phenomena occurring within a fractured reservoir for three different fracture models using computational fluid dynamics.The effect of the fracture-matrix interface condition is studi...This paper compares the fluid flow phenomena occurring within a fractured reservoir for three different fracture models using computational fluid dynamics.The effect of the fracture-matrix interface condition is studied on the pressure and velocity distribution.The fracture models were compared based on the variation in pressure and permeability conditions.The model was developed for isotropic and anisotropic permeability conditions.The results suggest that the fracture aperture can have a drastic effect on fluid flow.The porous fracture-matrix interface condition produces more realistic transport of fluids.By increasing the permeability in the isotropic porous matrix,the pressure drop was significantly higher in both the fracture and reservoir region.Under anisotropic conditions in the 3D fractured reservoir,the effect of the higher longitudinal permeability was found to lower the pressure in the fractured reservoir.Depending on the properties of the fractured reservoir,this study can enhance the understanding of fracture-matrix fluid interaction and provide a method for production optimisation.展开更多
基金This work was supported by the Special Funds for Major State Basic Research Projects (Grant No.2005CB321703)the National Natural Science Foundation of China (Grant Nos. 10476002, 60533020)the Science Foundation of CAEP (Grant No. 20060649)
文摘In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.
文摘This paper compares the fluid flow phenomena occurring within a fractured reservoir for three different fracture models using computational fluid dynamics.The effect of the fracture-matrix interface condition is studied on the pressure and velocity distribution.The fracture models were compared based on the variation in pressure and permeability conditions.The model was developed for isotropic and anisotropic permeability conditions.The results suggest that the fracture aperture can have a drastic effect on fluid flow.The porous fracture-matrix interface condition produces more realistic transport of fluids.By increasing the permeability in the isotropic porous matrix,the pressure drop was significantly higher in both the fracture and reservoir region.Under anisotropic conditions in the 3D fractured reservoir,the effect of the higher longitudinal permeability was found to lower the pressure in the fractured reservoir.Depending on the properties of the fractured reservoir,this study can enhance the understanding of fracture-matrix fluid interaction and provide a method for production optimisation.
