Semi-analytical modeling of transient pressure behaviour for a fractured vertical well with hydraulic/natural fracture networks by considering stress-sensitive effect

Abstract

In this study, theoretical models have been formulated, validated, and applied to examine transient pressure behaviour of a fractured vertical well with complex hydraulic and natural fracture networks by taking stress-sensitive effect into account. More specifically, a coupled matrix-fracture flow model is proposed and solved in the Laplace domain with consideration of stress-sensitive effect which escalates the nonlinearity of the governing equations. Such resulting nonlinear mathematical models are weakened and linearized by using the Pedrosa's transform formulation and perturbation technique, respectively. Then, a semi-analytical method is applied to solve the coupled nonlinear fluid flow problems by discretizing the complex fractures into several fracture segments. Furthermore, the pressure response and its corresponding derivative type curves are generated to investigate the stress-sensitive effect. It should be noted that different stress-sensitivities in different subsystems (i.e., matrix, fully propped hydraulic fractures, partially propped hydraulic fractures, and natural fractures) can be considered and analyzed from the newly developed methods, respectively. Five flow regimes may be developed for the fractured vertical wells with complex hydraulic and natural fracture networks. A gradual increase in both pressure and its derivative curves occurs over time due to the stress-sensitive effect, while the stress-sensitive effect in matrix subsystem mainly affects the transient pressure behaviour in the late time period, especially the pseudo-radial flow period. The inherent stress-sensitivity in fully propped fractures mainly increases the pressure response for the early and intermediate time periods, while it has a negligible influence on the late time pseudo-radial flow period. The stress-sensitivity in discrete natural fractures can greatly affect the transient pressure for the transient flow period, while the stress-sensitive effect in partially propped fractures is less significant than those of other subsystems. Also, it is found from field applications that considering different stress-sensitive effects in different subsystems tends to reproduce pressure transient responses in a more reasonable and accurate manner.