The double porosity model allows one 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 spends in the matrix and the fissures. Although we simulate some stochastic processes, the approach presented here does not use approximation by random walks, and then does not require any discretization. We are interested only in the particles in the matrix. A first approximation of the exchange coefficient may then be computed. In a forthcoming paper, we will present the simulation of the particles in the fissures.