Fractured reservoirs present a challenge in terms of characterization and modeling. Due to the fact that they consist of two coexisting and interacting media: matrix and fractures, not only we need to characterize the intrinsic properties of each medium but also accurately model how they interact. Dual-porosity models have been the norm in modeling fractures reservoirs. However, these models assume uniform matrix and fractures properties all over that medium. One further step into capturing the reservoir heterogeneity is to subdivide each medium and assign each one different property. In this paper, fractures are considered to have different properties and hence the triple-porosity model is introduced.
The triple-porosity model presented in this paper consists of three contiguous porous media: a matrix, less permeable microfractures and more permeable macrofractures. These media coexist and interact differently in the reservoir. It is assumed that flow is sequential following the direction of increased permeability and only macrofractures provide the conduit for fluids flow. Different solutions were derived based on different assumptions governing the flow between the fractures and matrix systems; i.e., pseudosteady state or transient flow in addition to different flow geometry; i.e., linear and radial. Some of these solutions are original. The model was confirmed mathematically by reducing it to dual-porosity system and numerically with reservoir simulation and applied to field cases. In addition, the solutions were modified to account for gas flow due to changing gas properties and gas adsorption in fractured unconventional reservoirs.