Summary: In this study, theoretical models have been formulated, validated, and applied to evaluate the transient pressure behavior of a horizontal well with multiple fractures in a tight formation by taking stress-sensitive fracture conductivity into account. On the basis of the superposition principle in the Laplace domain, we propose a coupled matrix/fracture-flow model with consideration of the stress-sensitivity effect in fractures, which strengthens the nonlinearity of the governing equations. More specifically, a new slab-source function in the Laplace domain was developed to describe the transient pressure responses caused by fluid flow from the matrix to the fracture, and a new solution was derived to describe the fluid flow in the fracture under the stress-sensitivity effect. Subsequently, a semianalytical method was applied by discretizing each hydraulic fracture into small segments, and a linearization scheme and an iteration method are adopted to deal with the nonlinear problem in the Laplace domain. Meanwhile, a modified superposition principle was proposed and applied to generate the pressure distributions for buildup tests with consideration of stress-sensitive fracture conductivity. Furthermore, pressure responses and their corresponding derivative type curves were generated to examine the effect of stress-sensitive conductivity. For pressure-drawdown tests, it is found that gradual increases in both pressure drop and pressure derivative occur over time because of the partial closure of the fractures. The stress-sensitivity effect in fractures becomes more evident with a smaller fracture conductivity and a larger fracture-permeability modulus. From the pressure-buildup curves, a one-fourth-slope line characteristic of the bilinear-flow period and constant derivatives of 0.5 representing a pseudoradial-flow regime can be clearly observed. Only fracture conductivity near the wellbore at the shut-in time can be estimated from the buildup pressures obtained in this work, whereas pressure-buildup analysis derived from the traditional superposition principle will result in an erroneous evaluation of the stress-sensitive fracture conductivity. It is also found that the effect of permeability hysteresis in the fractures has a negligible impact on the pressure-buildup responses.

Summary: 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.