Computation of pressure depletion and well productivity of multi-fractured wells with variable fracture spacing using fast and accurate solution method

This study presents a fast method that can model the pressure depletion around hydraulically fractured wells accurately. The Gaussian Pressure-Transient (GPT) method has infinite resolution, because no discrete-grid computations are required − the method solves the pressure field using closed-form solutions. After extensive testing on field cases and calibration against other (independent) solution-methods, it appeared that the pressure interference of multiple fractures represented by pressure transients − in the early phases of pressure advance − behaves according to the traditional superposition-method. However, when pressure interference advances, the traditional superposition method gives increasingly unrealistic and inaccurate results. Therefore, the traditional superposition method typically used for steady-state, needs adjustment when applied to transient systems, modeled here with Gaussian pressure-diffusion probability-density functions. The new solutions are valid for the advance of pressure changes both in the early and late stages of the well-life. A second new insight presented here is that the superposition of multiple fractures using Gaussian solutions (together with pressure-gradient computations and application of Darcy's) can accurately forecast the future production rate and cumulative production of the well over the economic well-life, accounting for the impact of fracture-spacing changes. The new method is validated by history-matching of our Gaussian forecasts using real well-data to constrain specific reservoir properties (hydraulic diffusivity) and completion parameters (fracture half-lengths), and then was benchmarked against independent simulations with CMG-IMEX.