Spherical-radius Seepage Analysis Of Fractal Dual-porosity Reservoirs Based On The Similar Structure

Based on the theory of fractal theory in the dual-porosity reservoirs we can betterdescribe the complexity of reservoirs. First of all, this paper was summarized the Similarstructure method. It will be shown that the solutions of the boundary value problem havecontinued fraction product, and the structure of the solution can be got by the coefficients ofthe inner boundary. The similar kern functions are determined by linearly independentsolutions and the coefficients of the outer boundary. Then we establish the differentialequations of the model for dual-porosity spherical with Darcy’s law, conservation of mass andso on. Secondly, without considering the effect of well-bore storage and introducing skinfactor, considering the effect of well-bore storage and skin factor and considering the effect ofwell-bore storage with the effective radius, three models of the fractal dual-porosity reservoirSpherical-radius seepage are established. On account of Laplace transform, it shows that themodel is the especial form of the extended modified Bessel equation boundary value problemin Laplace space. We obtain the exact solutions of the dimensionless reservoir pressure andthe bottom hole pressures under the three outer boundary condition through the similarstructure method. We proposed a new theory to reveal seepage law of the dual-porosityreservoirs through the systematically revealing the fractal dual-porosity reservoirs’ pressuredynamic distribution and extending application of the similar structure theory.