Pressure transient analysis for multi-vug composite fractured vuggy carbonate reservoirs

Abstract Vugs usually exist dispersedly in the formation of fractured vuggy carbonate reservoirs. The vug volume is an important parameter, owing to its significant contribution to oil reserves. However, at present, no reliable method is available for estimating the vug volume. This paper presents an analytical multi-zonal composite reservoir well test model that can determine the vug volume. First, the mathematical model is established according to the simplified physical model, and the analytical solution to the mathematical model is derived using Laplace transform. Second, based on the analytical solution, the type curves of dimensionless wellbore pressure and derivative versus dimensionless time, are plotted through numerical inversion. We use the two-vug model as an example to recognize the flow characteristics, and observe that 10 distinct flow regimes exist with two concaves. Furthermore, by comparing the single-vug and multi-vug models, an interesting finding is that one more concave will be added into the derivative curve when one more vug is present in the formation. The vug volume can be obtained by means of the pressure transient analysis. Also, the characteristics of our model are further exhibited by comparing it with the dual porosity model and the conventional composite model. And, a comparison with the conventional composite model and a field case are conducted to verify the validity and reliability of the proposed model in this study. Finally, the effects of each parameter on the pressure and derivative responses are analyzed. The pressure behavior is influenced by the mobility ratio, storage ratio, vug storage constant, and region radius. The mobility and storage ratios mainly affect the vug storage regimes, while the vug storage constant has an important impact on the concave depth and location, and the radial flow regime is dominated by the region radius.