The conventional dual-porosity model (Warren and Root 1963) may not apply to naturally fractured reservoirs which have poorly connected fractures. To narrow this gap, a discrete fracture model based numerical well testing (NWT) model is developed for pressure transient analysis in vertical wells interacting with natural fractures.
The accuracy and practicality of the proposed model have been demonstrated by model verifications. The results show that the flow regimes of the vertical well interacting with natural fractures can be divided into wellbore storage and skin effects, bilinear flow, linear flow, radial flow, natural-fracture (NF) effect, and boundary-dominated flow. This radial flow is the radial flow of the formation before pressure propagates to natural fractures, which is virtually quite different from that in the conventional dual-porosity model (Warren and Root 1963). However, there are no bilinear and linear flow stages in the vertical well interacting with no natural fractures. It is found that the vertical well interacting with natural fractures has a lower pressure depletion. It is also found that the "V-shape" caused by the NF effect in the pressure derivative curve becomes deeper when there are more natural fractures, longer natural fractures, and higher fracture conductivity. Furthermore, the "V-shape" appears earlier and the duration of the NF effect is longer as the number of natural fractures increases. Besides, with the decrease of the distance between the fracture and well, the impacts of natural fractures on pressure transient behaviors of the vertical well are more significant. This work provides a meaningful way to understand the pressure transient behaviors of discrete natural fractures.