Abstract
Deterioration of induced fractures is common in hydraulically fractured tight or shale reservoirs due to the energy dissipation of the fracturing operation. New models that account for stimulated reservoir heterogeneity are needed for the rate transient analysis of unconventional formations. In this study, we present a practical and straightforward solution for heterogeneous fractured reservoirs by introducing the concept of dynamic average permeability (DAP). An explicit equation of average permeability for linear flow in heterogeneous formation is derived by integrating the solution of the linear flow diffusivity equation and exponential permeability profile function into the Darcy flow model. Methodologies for performance forecast and evaluation of the distance of investigation (DOI) for heterogeneous unconventional reservoirs are proposed based on the DAP concept. Early deviation from the straight line of reciprocal-of-production-rate versus square-root-of-time plot occurs in highly heterogeneous reservoirs, in contrast to the departure caused by the boundary-domination effect. Meanwhile, the study results show that the DOI is significantly reduced in severely permeability-deteriorated unconventional formations. The accuracy and applicability of the new solution have been validated through real examples and synthetic numerical simulations. The analytical solution for transient linear flow in heterogeneous formation with an exponential permeability profile in the Laplace domain is also provided for the verification of the DAP method. The method proposed in this work can be readily applied to rate transient analysis and production forecasting of heterogeneous unconventional reservoirs, avoiding the complex Laplace solution and numerical inversion process.