Lawrence Berkeley National Laboratory

This study develops a mathematical model for the analysis of pressure behavior in fractured lithophysal reservoirs. The lithophysal rock is described as a tri-continuum medium, consisting of fractures, rock matrices, and cavities. In the conceptual model, fractures have homogeneous properties throughout and interact with rock matrices and cavities that have different permeabilities and porosities. Global flow occurs through the fracture network only, while rock matrices and cavities contain the majority of fluid storage and provide fluid drainage to the fractures. Interporosity flows between the triple media are described using a pseudosteady-state concept and the system is characterized by interporosity transmissivity ratios and storativity ratio of each continuum. Pressure behavior is analyzed by examining the pressure drawdown curves, the derivative plots, and the effects of the characteristic parameters. Typical pressure responses from fractures, matrices, and cavities are represented by three semilog straight lines; the transitions by two troughs below the stabilization lines in the derivative plots. The analytical solution to the proposed model is further verified using a numerical simulation. The analytical model has also been applied to a published field-buildup well test and is able to match the pressure buildup data.