An improved permeability evolution model and its application in fractured sorbing media

In this paper, we consider fractured sorbing media (e.g., gas shale and coal bed methane reservoirs) as either dual porosity media comprising matrix-fracture or as triple porosity media comprising separate organic and inorganic matrix components and fractures. We accommodate the combination of mechanical deformation and desorption induced matrix shrinking in conditioning the evolution of fracture aperture and effective stress difference between each medium. These considerations result in an improved permeability evolution model (IPEM) for both dual porosity and triple porosity fractured sorbing media. Then we have simplified the model for triple porosity fractured sorbing media by reducing the geometry configuration from three dimensional to one dimensional, marked as SIPEM1. Specifically, SIPEM1 is a model simplified from the IPEM, and consider that when the size of the REV and the volumetric strain is small, replacing the volume with the side length of each layer medium in defining the model will bring relatively small error. This model is further simplified to SIPEM1-1 by assuming that the effective stress of each medium is the same. Then we have validated the models with field data. Finally, we compared prediction results from these models under different conditions. This study has found that IPEM is the most accurate model, especially for fractured sorbing media with a larger compressibility. SIPEM1-1 does not consider the difference of the effective stress of each medium and thus it is relatively less accurate in describing the evolution of permeability compared with SIPEM1 that considers this difference. This gap increases with the increase of permeability difference between fracture and matrix.