The fracturing fluid leak-off in the reservoirs with developed natural fractures had a comparatively great influence on hydraulic fracture structure

proppant distribution and formation contamination. However

the current mathematical model for fracturing fluid leak-off considering natural fractures almost ignored or simplified the clustered distributed natural fractures

which limited the applications of these models. So firstly

by the multiplicative cascade method

we established a two-dimensional fractal discrete fracture networks model which reasonably showed the clustered distribution of natural fractures. Then

the established fracture networks were transformed into homogeneous anisotropic equivalent continuum media through subdividing the fractured porous domain into small elements. Ultimately

a mathematical model of fracturing fluid leak-off in fractured reservoir was established based on the permeability tensor. The results showed that the the strike of fracture rich zone determined the direction of fracturing fluid leak-off and pressure propagation. As the fracturing fluid tended to filtrate along long fractures

it was suggested to seal the natural fractures near hydraulic fractures before fracturing treatments. Moreover

fracturing fluid viscosity had certain influence on leak-off velocity.