A method for simulating compositional and/or multiphase transfers between the porous matrix and the fractures of a fractured multilayer porous medium, which are respectively saturated by a distinct liquid phase and gas phase. The method comprises constructing a geologic model representative of the networks of natural fractures of the medium and converting this geologic model into an equivalent double porosity model. Diffusion of the gas phase between the fractures and the matrix is modelled considering that a gas-liquid front exhibiting a quasi-static equilibrium at the interfaces is established from an initial time and progresses at a velocity controlled by the diffusion transfers within each phase. The transfers involve the difference between the concentration within the phase and the concentration of equilibrium between the two phases, as well as a variable exchange distance expressed as a function of the matrix saturation.
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