Analytical pressure-transient model for complex reservoir scenarios

Reservoir deposition occurs through long periods of time, thus most reservoirs are heterogeneous in nature. The presence of various zones and layers of different rock and fluid properties is the usual circumstance in petroleum reservoirs. A secondary recovery operation, such as steam-flooding, results in a composite reservoir situation because of the presence of zones of different fluid properties. Because of reservoir heterogeneity and gravity override effects, fluid boundaries separating two zones may have complicated or irregular shapes. The purpose of this paper is to develop a new analytical pressure-transient model which can accommodate complex reservoir scenarios resulting from reservoir heterogeneity and from thermal recovery or other fluid-injection operations. Mathematically, our analytical model considers such complex situations as a generalized eigenvalue system resulting in a system of linear equations. Computational difficulties faced, validation approach of the new model, and an application for complex reservoir scenarios are discussed.