This work presents results on both pressure and production responses during transient and boundary-dominated flow periods, in naturally fractured reservoirs with vuggy porosity. It is considered that triple-porosity systems may not be treated as dual-porosity reservoirs, mainly because fractures and vugs have different geological origin and therefore their interaction with matrix blocks do not have to be similar. New solutions are presented for the case where there is no primary flow through vugs, an extension of the Warren and Root model, existing an interaction between matrix, vugs, and fracture systems.
The new model assumes a single partially penetrating well producing from an undersaturated system considering several boundary conditions. The inner boundary condition at the wellbore can be considered either a fixed flux or constant pressure boundary. The upper, lower, and outer boundaries can be modeled at constant pressure or prescribed flux. These boundaries can be closed, or the influx can be modeled via a step rate or a ramp rate function. The step rate function could represent a waterflood effect and the ramp rate function a natural waterdrive or gas drive cap effect. The transient pressure response is also analyzed by considering an infinite outer boundary. In transient well tests and decline curve analysis, the effects of triple-porosity for different upper and lower boundaries conditions are analyzed, besides considering closed upper and lower boundaries as it has been done in the literature. It is shown that for triple porosity systems the derivative function may exhibit different behavior to that of double-porosity reservoirs. It is demonstrated that the presence of vugs and caves may have a definitive influence on transient well test and decline curve behaviors. Synthetic and field examples are presented to illustrate the methodology proposed in this work.