Shale gas production from reservoirs with hierarchical multiscale structural heterogeneities

Hydrofractured shale reservoirs exhibit a complex hierarchy of heterogeneous structures. Although the importance of hierarchical structures has long been recognised, the full control of scale-dependent heterogeneities on gas production remains ill-defined. We characterize reservoir structural heterogeneity at four hierarchical levels: (1) heterogeneous nanopore structure of the OM (Organic Matrix/Kerogen); (2) heterogeneous micro-structure of the IOM (Inorganic Matrix); (3) discrete structure of the NFNs (Natural Fracture Networks); and (4) discrete structure of the HFs (Hydraulic Fractures). A fractal approach is applied to characterize these internal structural heterogeneities for both the OM and IOM. These characterisations are incorporated into the constitutive relations defining transport within the OM and IOM. NFNs are generated by the Monte Carlo method while HFs are represented by a fractal tree-like network. A constitutive law for flow within a fracture is applied to both NFNs and HFs. Overall mechanical equilibrium and continuity of deformations are applied across these hierarchical systems comprising the shale reservoir while separate field equations for transport are derived for each structural system. The mass exchange between the individual structural systems is satisfied through source/sink terms compatibility of deformation enforced through boundary conditions and internal controls. The resulting multi-scale heterogeneous model is verified against the analysis of an idealised shale reservoir. Simulation results honor the ultimate recovery fractions and demonstrate the significant impacts of both hydraulic fracture and natural fracture heterogeneities on the evolution of recovery. The verified model is applied to a field case. The modelled gas production rate curve agrees well with field data for a reservoir in Barnett shale. Sensitivity studies confirm that heterogeneities at all scales are important but that their respective roles evolve separately during the history of gas production.