Modeling the diffusion flux between matrix and fissure in a fissured reservoir

Numerical simulation of recovery in fractured reservoirs by simulators requires determination of transfer parameters between fracture and matrix. These large-scale transfer parameters accounts for capillary, diffusive or gravity effects and can be derived by up-scaling the local physical mechanisms. The transfer driven by capillary or gravity forces is easy to model, but there is no simple model for diffusion. Our study was aimed to calculate the transfer of a component by diffusion as a function of fracture geometry, fluid velocity in the fracture, and fluid compositions in fracture and matrix. The diffusion flux is calculated assuming a uniform fluid saturation at the interface between matrix and fracture and a laminar flow in the fracture. The coupled flow and concentration equations are solved along the width of the fracture and then integrated over its length. The resulting diffusion flux is given by a simple analytical formula. Calculations were then compared to experiments performed at reservoir conditions with pure methane injected in the fracture and binary mixtures in the matrix (C1,C5). The results were in very good agreement, without any adjustable parameters. Finally, it is shown how the calculations can be implemented in a reservoir simulator. The fracture is considered as a porous block but then cannot directly account for the diffusion flux as a boundary condition. The only way to model the diffusion transfer is to calculate an effective diffusion coefficient which accounts for the diffusion transfer but also the grid discretization. A good agreement is obtained without any adjustable parameters between numerical simulations and experiments.