A Contrast Analysis Of The Draft Tube’s Flow Of Francis Turbine

As the percolation model in dual-porosity reservoir takes a large proportion in the process ofoil and gas reservoir development, a further development research for the percolation modelin dual-porosity reservoir will be studied on the basis of predecessors’ researches in thispaper.Above all, this paper presents the Similar Constructive Method for solving the boundaryvalue problem of second order homogenous linear ordinary differential equation and gives theproof about it.Then, for the nonlinear spherical percolation problem in dual-porosity reservoirconsidering the quadratic-gradient term, there are12percolation models established asmathematical method and percolation theory with four inner boundary conditions, thatare,ignoring both the wellbore storage and the effective radius, considering the wellborestorage，considering the effective radius, considering both the wellbore storage and theeffective radius; and three types of outer boundary conditions: closed, constant pressure andinfinity.In addition, these models can be linearized by the substitution of variables and aboundary value problem（BVP） of ordinary differential equation is obtained by the Laplacetransformation. And the BVP can be solved as the new method: Similar Constructive Methodpresented above. Then a uniform solution of the model on different boundary conditions isobtained, namely the Similar Structure of the solution.As the Similar Constructive Method, the solution of such BVP can be constructed as twoindependent solutions of the basic equation and coefficients of boundary conditions. Whencoefficients of boundary conditions changed, the new solution could be constructed bysubstituted into the new coefficients of boundary conditions. The Similar ConstructiveMethod avoids the complex process of common solving of the BVP and provides greatconvenience to the programming of well test analysis software for oil workers.Achievements in the present research not only further interpret the percolation law ofdual-porosity reservoir but also complements and perfects the nonlinear percolation theory.