The double porosity model allows to compute the pressure at a macroscopic scale in a fractured porous media, but requires the computation of some exchange coefficient characterizing the passage of the fluid from and to the porous media (the matrix) and the fractures. This coefficient may be numerically computed by some Monte Carlo method, by evaluating the time a Brownian particle spend in the matrix and the fissures. Although we simulate some stochastic process, the approach presented here does not use approximation by random walks, and then does not require any discretiz- ation. In this first part, we are interested only by the particles in the matrix. A first approximation of the exchange coefficient may then be computed.