Based on the dual fractal dimension in the fractal theory, the linear density of fractures and the equivalent permeability are characterized by the fractal dimensions of the fracture width and the tortuosity. The seepage field around the horizontal well bore is divided into two regions: the inner seepage region and the outer elliptical nonlinear seepage region. A mathematical model for the two-region coupling steady flow is established based on the conservation law of mass and the motion equation, and the productivity equation is obtained. It is shown that the larger the fractal dimension of the fracture width, the greater the linear density of the fractures, and the larger the equivalent permeability. The greater the tortuosity fractal dimension, the lower the equivalent permeability. Increasing the horizontal well length can have a great impact on the productivity improvement. As the power- law exponent increases, the influence on the productivity of the horizontal well grows, when the power-law exponent n is greater than 0.75. The increase of the threshold pressure gradient leads to a larger decrease rate of the productivity.

fractured heavy oil reservoir  /  power-law fluids  /  horizontal well  /  productivity  /  fractal