A novel pressure transient analysis model for fracturing wells in fracture–cavity carbonate reservoirs

Large-scale karst caves are the principal storage spaces for hydrocarbon resources in fracture–cavity carbonate reservoirs. Drilling directly into these caves is considered the ideal mode of development, but many wells do not effectively penetrate karst caves. Therefore, acid fracturing is employed to generate artificial fractures that can connect with these caves. However, there are no appropriate well test methods for fracturing wells in fracture–cavity reservoirs. This study establishes a novel pressure transient analysis model for such wells. A new mathematical model is proposed that couples linear flow in acid fracturing cracks with radial flow in the oil drainage area. The Laplace transform and Stehfest numerical inversion provided analytical solutions for the bottomhole pressure. Typical log–log well testing curves were plotted to analyze oil flow, which occurs in ten stages. During the flow stage in fracturing cracks, the pressure and pressure derivative curves are parallel lines with a slope of 0.5. In the stage of karst cave storage, the pressure derivative curve is a straight line with a slope of 1. A comparison with previous models confirmed the validity of the proposed model. The influence of key parameters on the behavior of typical curves is analyzed. A field case study of the proposed model was carried out. Parameters related to fracturing cracks and karst caves, such as the crack length and cave radius, were successfully estimated. The proposed model has great potential for determining formation parameters of fracture–cavity reservoirs.