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A Triple-Continuum Pressure-Transient Model for a Naturally Fractured Vuggy

We present an analytical approach for pressure transient test analysis in naturally fractured vuggy reservoirs. This analysis approach relies on a triple-continuum concept, using observed geological data from carbonate oil formations in western China, to describe transient flow behavior in fracture-vug-matrix reservoirs. In the conceptual mathematical model, fractured vuggy rock is considered as a triple-continuum medium, consisting of fractures, rock matrix, and vugs (or cavities). Similar to the classical double-porosity model, the fracture continuum is assumed to be responsible for the occurrence of global flow, while vuggy and matrix continua (providing primary storage space) interact locally with each other as well as with globally connected fractures. Furthermore, the triple continua of fractures, matrix, and vugs are assumed to have uniform and homogeneous properties throughout, and intercontinuum flows between them are at pseudosteady state. With these assumptions, we derive analytical solutions in Laplace space for transient flow toward a well in an infinite and finite reservoir with wellbore storage and skin effects. The analytical solutions reveal typical pressure responses in a fracture-vug-matrix reservoir and can be used for estimating vug properties, in addition to fracture and matrix parameters, through properly designed and conducted well tests. As application examples, actual well test data from a fractured-vuggy reservoir in Western China are analyzed using the triple continuum model.