A complement to decline curve analysis

Decline curve analysis (DCA) has been the mainstay in unconventional reservoir evaluation. Because of the extremely low matrix permeability, each well is evaluated economically for ultimate recovery as if it were its own reservoir. Classification and normalization of well potential is difficult because of ever-changing stimulation total contact area and a hyperbolic curve fit parameter that is disconnected from any traditional reservoir characterization descriptor. A new discrete fracture model approach allows direct modeling of inflow performance in terms of fracture geometry, drainage volume shape, and matrix permeability. Running such a model with variable geometrical input to match the data in lieu of standard regression techniques allows extraction of a meaningful parameter set for reservoir characterization, an expected outcome from all conventional well testing. Because the entirety of unconventional well operation is in transient mode, the discrete fractured well solution to the diffusivity equation is used to model temporal well performance. The analytical solution to the diffusivity equation for a line source or a 2D fracture operating under constrained bottomhole pressure consists of a sum of terms, each with exponential damping with time. Each of these terms has a relationship with the constant rate, semisteady-state solution for inflow, although the well is not operated with constant rate, nor will this flow regime ever be realized. The new model is compared with known literature models, and sensitivity analyses are presented for variable geometry to illustrate the depiction of different time regimes naturally falling out of the unified diffusivity equation solution for discrete fractures. We demonstrate that apparent hyperbolic character transitioning to exponential decline can be modeled directly with this new methodology without the need to define any crossover point. The mathematical solution to the physical problem captures the rate transient functionality and any and all transitions. Each exponential term in the model is related to the various possible interferences that may develop, each occurring at a different time, thus yielding geometrical information about the drainage pattern or development of fracture interference within the context of ultralow matrix permeability. Previous results analyzed by traditional DCA can be reinterpreted with this model to yield an alternate set of descriptors. The approach can be used to characterize the efficacy of evolving stimulation practices in terms of geometry within the same field and thus contribute to the current type curve analyses subject to binning. It enables the possibility of intermixing of vertical and horizontal well performance information as simply gathering systems of different geometry operating in the same reservoir. The new method will assist in reservoir characterization and evaluation of evolving stimulation technologies in the same field and allow classification of new type curves.