Analytic representative element rate decline models for naturally fractured reservoir depletion.

Representative single anisotropic matrix block 2D Green's function models for depletion through fully-penetrating, vertical fractures through different numbers of fracture faces are constructed that analytically capture both fracture and block depletion with fracture-matrix mass transfer. The 1D Green's function for a fracture system is likewise solved in terms of the time evolution of average fracture pressure. While transient average pressure values are not inherently measurable, they are transformed into cumulative production or instantaneous flowrate values, thus producing new rate decline model functional forms.