Semi-analytical modeling of transient rate behaviour of a horizontal well with multistage fractures in tight formations considering stress-sensitive effect

Abstract

Stress-sensitive permeability imposes a significant impact on production performance in a tight formation; however, the widely used models assume the constant permeability or same stress-sensitive level for different systems, resulting in incorrect prediction of production rate and reservoir properties. In this work, theoretical models have been formulated, validated, and used to characterize the transient rate behaviour of a horizontal well with multistage fractures at constant wellbore pressure in tight formations by taking the different stress-sensitive effects in matrix and fracture subsystems into account. More specifically, a matrix-fracture fluid flow model with considering stress-sensitive effect was developed, during which the resulting nonlinear governing equation caused by stress-sensitive matrix permeability was weakened and linearized by using the Pedrosa's transform formulation and perturbation technique, respectively. Then, a slab source function was developed to obtain the solution for such a linearized problem in the Laplace domain. Meanwhile, a semi-analytical method is applied to solve the matrix-fracture flow models by discretizing each hydraulic fracture into small segments. Furthermore, the Blasingame type curves are generated to examine the stress-sensitive effects. In particular, stress-sensitivity in matrix and hydraulic fracture subsystems can be respectively analyzed. It is found that stress-sensitive permeability in either the matrix subsystem or the fracture subsystem has its negative influence on production rate. Such an influence is increased as the permeability modulus in matrix and fractures is increased. The matrix permeability modulus mainly decreases the production rate in the intermediate and late flow period, while its effect on the early time production rate is relatively small compared with other flow periods. Stress-sensitivity in fractures mainly affects the early time production rate and imposes a negligible impact on production rate during the intermediate and late period. The production rate is increased with an increase in the initial fracture conductivity. The dominant flow which contributes to the majority of the total production gradually shifts from the near-wellbore fracture segments to the near-tip fracture segments for the intermediate and high conductive fracture cases, while, for the low conductive fractures, the near-wellbore fluid flow is dominant for the entire period. Due to the inherent constraints in a tight formation, rate transient analysis is found to be more physically representative for accurately describing performance of a horizontal well with multistage fractures compared to the traditional pressure transient testing.