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The main purpose of this work is to present an interpretation method for injectivity test in a two-layer reservoir that can be extended to a multilayer approach, based on new analytical solutions to the well pressure response. The developed formulation uses a radially composite reservoir approach and considers that the water front propagation may be approximated by a piston-like flow displacement. The reservoir is assumed to be laterally infinite and properties such as permeability and porosity may be different in each layer. The solutions were developed in the Laplace domain and then inverted to real domain using the Stehfest Algorithm. The proposed formulation was then validated by comparison with a numerical flow simulator. Results showed a good agreement between the numerical simulator and the analytical model. Also, a sensitivity study was done by comparing the results of different scenarios varying oil viscosities and injection flow rate to assess how these properties affect the pressure and pressure derivative profiles.

Dual-phase flow in two-layer porous media: a radial composite Laplace domain approximation