A novel analytical well test model for fractured vuggy carbonate reservoirs considering the coupling between oil flow and wave propagation

Fractured vuggy carbonate reservoirs consist of matrix, fractures, and vugs. The existence of vugs in fractured vuggy carbonate reservoirs has long been observed. The volume of a vug is an important parameter owing to the large contribution of vugs to oil reserves. However, there are no reliable well test methods to estimate the volume of a vug yet. In this study, a new analytical well test model considering the coupling between oil flow and wave propagation is proposed. First, the mathematical model is established. Then, combined with the seepage equations in the outer formation, the analytical solutions of transient pressure in the wellbore are obtained through Laplace transformation and inversion. Second, based on the above analytical solutions, the standard log-log type curves are plotted to recognize the flow characteristics. It was found that, the flow in the wellbore and large vug can be divided into six distinct flow regimes. The volume of the large vug can be obtained by pressure transient analysis. Considering the coupling between oil flow and wave propagation, there will be one more V-shaped segment than typical triple-continuum pressure derivative curve. Third, a comparison with the triple-continuum model is performed to verify the validity and reliability of the proposed model in this study as well as a reservoir study. Finally, sensitivity analysis of some key parameters on the pressure derivative are carried out. Through the sensitivity analysis of different parameters for the well test type curves, it is found that the change in these well test curves is in accordance with the findings of the theoretical analysis. The curve behaviors are influenced by the friction coefficient, fluctuation coefficient, damping coefficient, storage ratios, and inter-porosity flow coefficients. The depth of the first V-shape segment is mainly affected by the friction, fluctuation, and damping coefficients. The depths and locations of the second and third V-shape segments are mainly influenced by the storage ratios of the fracture and vug, and inter-porosity flow coefficients within the matrix, fracture, and vug.