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Summary The conventional dual-porosity model (Warren and Root 1963) may not apply to naturally fractured reservoirs (NFRs), which have poorly connected fractures. To narrow this gap, a new discrete fracture model (DFM)-based numerical well-testing model is developed for pressure transient analysis in vertical wells interacting with natural fractures (NFs). The numerical model is based on a DFM and unstructured perpendicular bisector (PEBI) grid system. The accuracy and practicality of the proposed model have been demonstrated by model verifications with a commercial numerical software. The results show that the flow regimes of the vertical well interacting with NFs can be divided into wellbore storage and skin effects, bilinear flow, linear flow, radial flow, NF effect, and boundary-dominated flow. This is the radial flow of the formation before pressure propagates to NFs, which is virtually quite different from that in the conventional dual-porosity model. However, there are no bilinear and linear flow stages in the vertical well interacting with no NFs. It is found that the vertical well interacting with NFs 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 NFs, longer NFs, and higher fracture conductivity. Furthermore, the “V-shape” appears earlier, and the duration of the NF effect is longer as the number of NFs increases. Besides, with the decrease of the distance between the fracture and the well, the impacts of NFs 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 NFs.

Fractured carbonate reservoirs are different from conventional reservoirs and generally develop fractures. Conventional reservoir well test performance analysis can only obtain the formation parameters and discharge radius around a single well. For vertical wells in fractured carbonate reservoirs, we can establish a dual-porosity composite reservoir model for well testing interpretation and analysis based on the actual conditions of the reservoir and combined with geological knowledge. The model can be applied to formations with different reservoir properties in the near-well and far-well areas around a single well to analyze the fracture parameters (elastic reserve ratio and channeling coefficient) and the effective flow capacity of formation fluids in the two areas. On this basis, we use the interpretation of actual production wells to verify the accuracy of the model and analyze the influence of reservoir parameters and fracture parameters on the theoretical curve.