A semianalytical model for transient pressure analysis of a horizontal well with non-uniform fracture geometry and shape-dependent conductivity in tight formations

Abstract

Hydraulic fracture geometry greatly affects production performance of the fractured horizontal wells in a tight formation; however, limited attempts have been made to evaluate the performance of wells with non-uniform fracture geometries which are more close to the reality. In this work, a new slab source function was formulated and employed to accurately and efficiently evaluate the transient flow behaviour of a horizontal well with multiple non-uniform fracture geometries in a tight formation. More specifically, such a slab source function in the Laplace domain can assign a geometrical width for the source, which is usually neglected in the existing studies. Then, a semianalytical method is employed to solve the transient flow problem by dividing the non-uniform fracture into several segments, each of which can be assumed as a uniform-flux slab source. Thus, transient pressure behaviour considering complex fracture geometry can be taken into account with the slab source function using the superposition principle and the Stehfest inverse algorithm. The slab source function was validated with numerical and semianalytical solutions and then extended to field application. Also, effects of both the partially propped fractures and near-wellbore fracture damage are well examined and analyzed. It is found that the width of the fracture only affects the early time transient pressure response, while the pressure response at later time is identical to that of the line source solutions. The fracture geometry imposes a significant impact on the well response at the early and intermediate time period and the fracture with concave geometry results in the lowest pressure response, while the rectangular fracture has the largest pressure response. Both the length of the propped fractures and the damaged fracture zone mainly dominate the intermediate-stage pressure behaviour, while the width of the damaged zone will impose an important impact on the transient pressure response for the early and intermediate time period.