Generalized Analytical Solutions of Vertically Fractured Wells in Commingled Reservoirs: Field Case Study

Abstract

Accurate identification of the individual-layer parameters for vertically fractured wells in commingled reservoirs is essential for development plan design, reservoir numerical simulation, and stimulation measure selection. Different semi-analytical and numerical models are generally applied in multilayer transient testing (MLT) analysis to determine the properties of individual layer. However, these approaches require numerous computations and are complicated to program due to the fracture and reservoir discretization. This work thus presents the generalized analytical solutions of vertically fractured wells in infinite, closed, or constant-pressure commingled reservoirs with both computational and functional simplicity. The fully analytical solutions are derived based on the early-time approximate solutions of infinite-conductivity fracture and trilinear flow models, infinite-conductivity fracture solutions, pressure superposition principle, and Duhamel principle. A systematic verification by employing a standardized well testing software and trilinear flow model is conducted to ensure the general application accuracy of the presented solutions. The results show that the developed analytical solutions are valid when the dimensionless fracture conductivity is more than 2 (FcD > 2) with an average absolute percent deviation (AAD) of ~2% for pressure and that is ~4% for pressure derivative. The developed analytical solutions also exhibit improvements in early-time pressure and derivative calculation. Finally, a field case of a four-layer fractured well is interpreted by the developed solutions and well testing software to illustrate the feasibility. The interpretation results of two methods are nearly identical, with only a minor difference. The developed analytical solutions are computationally accurate while maintaining functional simplicity and can be considered as an alternative to the current semi-analytical and numerical approaches in MLT analysis.