Novel Trilinear Flow Model for a Fractured Horizontal Well Considering Spatially Linear Decline of Fracture Conductivity

Abstract

Pressure transient analysis (PTA) of a fractured horizontal well often relies on a trilinear flow model, but a conventional trilinear flow model assumes uniform fracture conductivity along the whole fracture length and therefore may overestimate the contribution of less-conductive fracture sections. A novel analytical trilinear flow model is proposed in this work for pressure analysis by considering a linearly declining fracture conductivity distribution from the wellbore toward the fracture tip through a new parameter (conductivity decline coefficient). The new trilinear flow problem was analytically solved in the Laplace domain, yielding a closed form solution expressed with modified Bessel functions; asymptotic limits were derived to ensure numerical stability without discretizing the fracture into multiple segments. The proposed model has been validated by comparing its results with those of the traditional trilinear flow model with uniform fracture conductivity. It is found that the conductivity decline coefficient mainly affects the middle-time transient pressure behavior by increasing the pressure and pressure derivative. Sensitivity results for CfD0 = 10 and 50 show that a decline coefficient with 1 can elevate the middle-time pressure and pressure derivative by up to 13% and 14%, respectively. The maximum fracture conductivity controls the early time pressure response, whereas well spacing and fracture spacing primarily determine the onset of late-time boundary-dominated flow. In dual-porosity SRV systems, the storativity ratio and interporosity-flow coefficient govern the timing and depth of the concave pressure derivative signature. The proposed model can provide a fast and physically interpretable PTA tool for estimating fracture/reservoir parameters, evaluating conductivity degradation, predicting production performance, and assessing spacing-controlled boundary interaction in fractured tight reservoirs.