Theoretical Study On Seepage Flow In Anisotropic Reservoirs Based On Elliptical Flow

The Oil reservoirs flow differential equations are based on the Darcy's law,they are assuming that the oil reservoirs permeability are isotropic,in other words,the permeability of oil reservoirs are the same in all directions.In this assumption,the flow differential equations of oil reservoirs describe the isopiestic lines of the fluid are circular and the flow lines of the fluid are straight lines.Reservoir permeability are easy to be anisotropic and directional.Many studies show that in the anisotropic reservoirs,the isopiestic lines of the fluid are elliptic and the flow lines are hyperbolic,moreover the isopietic lines and the flow lines are intersectant.therefor,flow differential equations of the isotropic permeability could not describe the anisotropic reservoirs accurately.In this paper,using the permeability tensor symmetric matrix to describe characteristic of the permeability and the flow of fluid in all directions in the anisotropic reservoirs.By using the fluid motion equation,state equation and continuity equation to establish the differential equations of the anisotropic flow.Through continuous equivalent permeability,dimensionless and coordinate transform,achieving the differential equations of elliptic flow model in the anisotropic homogeneous,double porosity and triple porosity oil reservoir,and then acquired the expression of the bottom hole pressure and the oil well productivity under the Mathieu function forms.By Laplace numerical inversion and Matlab programming,mapped the typical curves of the anisotropic reservoirs of the infinite conditions at the outer boundary.From the degree of anisotropy of pressure derivative logarithmic curves and the influence of oil well production curves can receive the following conclusions:(1)The degree of the anisotropy of reservoirs has a great influence on the early transition stage of fluid flow.And the greater the degree of anisotropy,the smaller convex of the pressure derivative of the flow transition stage.(2)The degree of anisotropy is higher,the time of the flow transition stage is shorter,and the time is earlier of the homogeneous reservoirs to be the radial flow.(3)The degree of anisotropy is higher,the time of the radial flow of the fracture,and the characteristic is more obvious in the double porosity and triple porosity oil reservoirs.(4)The anisotropic degree has obvious influence on the early well capacity,as the degree of anisotropy is greater,the bottom hole pressure drops faster,No-Steaty well capacity is lower.In this article has builted the elliptical flow differential equations of anisotripic reservoirs,the influencing curves of the parameters of anisotropic reservoirs significative to the anisotropic oil reservoirs,such as,carbonate rock,low permeability and artificial fracturing and so on.Only understanding of the anisotropic oil reservoirs accurately,the reservoirs can be developed by more reasonable,efficient and high production.