A novel pressure and rate transient analysis model for fracture-caved carbonate reservoirs

Abstract Fracture-caved carbonate reservoirs (FCCRs) have been developed worldwide and contribute significantly to world's hydrocarbon reserves. Numerous models for FCCRs were proposed in the previous works. However, with more and more exploitations, some kinds of FCCRs are observed from the field geological information but not reported in the existing literature. In this paper, a novel model for FCCRs is proposed and its corresponding pressure transient analysis (PTA) and rate transient analysis (RTA) solutions are presented. This model has a wider applicability than the previous models proposed by our research team. First, the geological model is established based on the geological information. Sequentially, the simplified physical model and the mathematical model are developed. Through Laplace transformation, Duhamel's principle, and Stehfest numerical inversion, the solutions of dimensionless bottom-hole pressure and dimensionless flow rate integral are derived. Then, the RTA type curves of two-cave model are plotted to recognize the flow characteristics, which can be divided into five regimes comprehensively. In addition, two concaves are observed on the derivative curve. The RTA type curves of three-cave model are also presented. A comparison between the RTA type curves of two-cave model and three-cave model shows that when one more cave exists in the formation, one more concave will be added to the derivative curve. Furthermore, the differences between the proposed model and previous models are presented through comparing the PTA type curves. Next, the effects of key parameters on the RTA curve behavior of two-cave model are demonstrated. Results indicate that the RTA curves are controlled by the friction and fluctuation coefficients, mobility, storage ratio, region radius, and cave storage constant. The friction and fluctuation coefficients influence the depth of first concave, while the storage ratio, region radius, and cave storage constant dominate the middle flow period, and the mobility has an impact on the boundary dominated flow regime. Finally, the application of proposed model on a field well from Shunbei Oilfield, western China is presented to calibrate its accuracy and reliability.