A Semianalytical Model for Predicting Transient Pressure Behavior of a Hydraulically Fractured Horizontal Well in a Naturally Fractured Reservoir With Non-Darcy Flow and Stress-Sensitive Permeability Effects

Non-Darcy flow and the stress-sensitivity effect are two fundamental issues that have been widely investigated in transient pressure analysis for fractured wells. The main object of this work is to establish a semianalytical solution to quantify the combined effects of non-Darcy flow and stress sensitivity on the transient pressure behavior for a fractured horizontal well in a naturally fractured reservoir. More specifically, the Barree-Conway model is used to quantify the non-Darcy flow behavior in the hydraulic fractures (HFs), while the permeability modulus is incorporated into mathematical models to take into account the stress-sensitivity effect. In this way, the resulting nonlinearity of the mathematical models is weakened by using Pedrosa's transform formulation. Then a semianalytical method is applied to solve the coupled nonlinear mathematical models by discretizing each HF into small segments. Furthermore, the pressure response and its corresponding derivative type curve are generated to examine the combined effects of non-Darcy flow and stress sensitivity. In particular, stress sensitivity in HF and natural-fracture (NF) subsystems can be respectively analyzed, while the assumption of an equal stress-sensitivity coefficient in the two subsystems is no longer required. It is found that non-Darcy flow mainly affects the early stage bilinear and linear flow regime, leading to an increase in pressure drop and pressure derivative. The stress-sensitivity effect is found to play a significant role in those flow regimes beyond the compound-linear flow regime. The existence of non-Darcy flow makes the effect of stress sensitivity more remarkable, especially for the low-conductivity cases, while the stress sensitivity in fractures has a negligible influence on the early time period, which is dominated by non-Darcy flow behavior. Other parameters such as storage ratio and crossflow coefficient are also analyzed and discussed. It is found from field applications that the coupled model tends to obtain the most-reasonable matching results, and for that model there is an excellent agreement between the measured and simulated pressure response.