根据分形几何学并结合渗流力学，建立了无限圆柱对称有分形结构的油藏的单相微可压缩、具有起始压力梯度非牛顿幂律液径向流的解析压力不稳定模型，导出了描述分形油藏幂律流的新的偏微分方程。利用拉氏变换和格林函数，得出了分形油藏无限大地层中心一口井在定产量生产时及稳态和不稳态条件下的井底压力解和渐近解。 According to the fractal geometry and the seepage mechanics, a single-phase micro-compressible oil reservoir with infinite cylinder symmetry and fractal structure was established, and the analytical pressure instability model with non-Newtonian power law fluid radial flow with initial pressure gradient was established. New partial differential equations of power law flow in fractal reservoir. Using Laplace transform and Green’s function, the bottom hole pressure solution and the asymptotic solution of a well at the center of an infinite reservoir in a fractal reservoir during steady-state and unsteady conditions are obtained.