Study Of The Similarity Construction Method On Solving The Unsteady Seepage Flow Model In The Spherical-shaped Matrix For Dual-porosity Reservoir

Toward the spherical shaped matrix of dual-porosity reservoir, three kinds of unsteadyseepage flow models are established under different inner boundary conditions. Firstly, thesimilar structure for the ideal model of unstable seepage flow model in the spherical shapedmatrix of dual-porosity reservoir can be got, and it can provides a certain theoretical basis forthe next study. Secondly, through the solving process of the unstable seepage flow model forthe spherical shaped matrix of dual-porosity reservoir which takes the wellbore storage andskin effect into consideration, we can sum up the similar constructive method. Finally, byusing the similar constructive, we can obtain the solution of the seepage model that considersthe wellbore storage and introduces the effective wellbore radius. The similar constructivemethod is employing the basic solution of the differential equation and the coefficients of theouter boundary conditions to construct the kernel function, and combine the kernel functionand the similar structure which determined by the coefficients of the inner boundaryconditions, then the solution to the boundary value problem of differential equation can beconstructed. The similar constructive method of the differential equation is a simple andeffective method, and it is convenient for solving and analyzing the seepage flowmathematical model; and it can improve the computational efficiency greatly and in favor ofcompile the well test analysis software. In addition, this paper has the guiding significance toa further research on the fractal dual-porosity composite reservoirs and the fractaldual-porosity multilayer reservoirs etc. that considers the secondary pressure gradient.