Pressure transient analysis of a well penetrating a filled cavity in naturally fractured carbonate reservoirs

Naturally fractured carbonate reservoirs have been discovered in many oilfields around the world and are characteristic of a complex, heterogeneous porosity system. The presence of large-scale cavities will have a noticeable effect on the transient pressure behavior, especially, when a well is drilled through them. The cavities are usually filled with loose materials, such as gravel, sand, and mud, due to the physical or chemical processes. Therefore fluid flow in a filled cavity may range from low-velocity Darcy flow to high-velocity non-Darcy flow. It is necessary to incorporate cavity filling effect in the type curve matching for flow behavior in fractured carbonate reservoirs. The objective of this work is to develop an efficient well testing model to analyze and interpret the transient pressure responses observed in a naturally fractured carbonate reservoir, in which a well is drilled through a filled cavity. To this end, a radial composite reservoir model including the inner and outer regions with different characteristics is proposed. The inner region is a filled cavity with a well drilled into. The outer region, a naturally fractured reservoir, is considered as a dual-porosity model in this work. The Barree-Conway model, initially proposed for a proppant-packed fracture, is applied to simulate the non-Darcy flow in the inner region. The corresponding mathematical model is developed, and a numerical solution is then obtained based on the finite difference method, which is further verified by the analytical solution under simplified flow condition. Several standard log-log type curves are provided to reveal the flow characteristics. The flow process is shown to have six flow stages in general. Subsequently, sensitivity analyses of the type curves are carried out. The calculated results show that the characteristics of the well testing type curves are influenced significantly by non-Darcy coefficients, the size of the filled cavity, and the petrophysic property ratio between inner and outer areas. Finally, the proposed model is applied to analyze and interpret two field testing examples.