The material balance equation for fractured vuggy gas reservoirs with bottom water-drive combining stress and gravity effects

Compared with conventional porous-water-drive gas reservoirs, calculating the reserve of a fractured vuggy with water driving is a more difficult and challenging task because of its complex matrix types (matrix, fracture and cavity) and strong rock compressibility. Based on the principles of mass conservation, the material balance equation (MBE) for a fractured vuggy gas reservoir with bottom-water driving is established, and the effects of stress sensitivity and gravity segregation are both considered in the proposed model. The original gas in place (OGIP) and the distribution of the reserve in matrix, fracture and cavity can be determined with the proposed MBE. To test the validity of the model, a depletion test simulating the depleting process of fractured vuggy water-drive gas reservoirs and permeability stress sensitivity experiments with actual full-diameter cores under reservoir conditions are conducted. Then, validation and analysis of the model are compared with the experimental data. It is observed that the water production rate shows a stepped increasing trend instead of a gradually increasing trend during the depletion test. The reserve calculated with the proposed model has the lowest error (1.68%) compared with the experimental data, in which the reserve in the cavity is dominant. Thus, gravity and stress should not be neglected when calculating the reserve of a fractured vuggy gas reservoir with bottom water driving; otherwise, a lower accuracy would be introduced.