Abstract: The nonlinear flow through porous media mathematic model of deformed dual media fractal reservoir, based on WarrenRoot model and the introduction of fractal parameters and compression coefficient, takes the influence of pressure on permeability and porosity with fractal feature into consideration. The existence of the solution of the differential equation of the model is probed according to discrete functional analysis and the fixed point theory. It is indicated that in correctly recognizing the complex heterogeneous oil reservoirs and stresssensitive formation oilgas reservoirs, fractal geometrical theory and the method are of unique advantage.

Key words: fractal reservoir, unstable flow through porous media model, finite difference, existence analysis, discrete functional analysis