Evaluation of transient pressure responses of a hydraulically fractured horizontal well in a tight reservoir with an arbitrary shape by considering stress-sensitive effect

Abstract

In this study, a semianalytical technique has been developed to examine stress-sensitive effect on the transient pressure responses of a multiple-fractured horizontal well in an unconventional reservoir with an arbitrary-shape. Considering its arbitrary-shaped boundaries, the boundary element method is adopted to simulate flow behaviour by incorporating the permeability modulus (i.e., stress-sensitive effect) into the governing equation to describe the flow behaviour within the hydraulic fractures. To weaken the nonlinearity of such governing equations in a hydraulic fracture subsystem, a semianalytical approach is used to achieve consistent solutions with good accuracy. The convergence skin effect is introduced to represent the radial fluid-flow pattern in the hydraulic fractures near the horizontal wellbore. Not only can the stress-sensitive effects of hydraulic fractures be examined, but also the corresponding pressure responses together with pressure derivative curves are obtained. The mathematical formulations have been verified and then extended for field applications. The stress-sensitive effect of hydraulic fractures in a box-shaped reservoir with closed boundaries is found to be obvious during the intermediate- and late-time periods. Furthermore, the noticeable stress-sensitive effect in hydraulic fractures occurs earlier by taking the convergence-skin effect into account. A hydraulic fracture with a high permeability modulus is found to result in a positive stress-sensitive effect. Also, sensitivity analysis on pressure responses and their corresponding derivative curves have been performed with respect to the convergence skin effect, boundary shape, maximum distance, and minimum fracture conductivity.