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.

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Injectivity testing is a procedure used by the oil industry whose purpose, when injecting a fluid, is to obtain information about the characteristics of an oil reservoir. Such characteristics can be estimated from the pressure response obtained during the test. This work presents a solution to the well pressure during an injectivity test, considering a piston flow, using a radially composed reservoir model. It is considered that the reservoir may have a two-phase flow with two regions (water and oil) or three regions. In this case it is considered that the region near the well represents a damaged zone (skin zone). From the known analytical solution for pressure in the Laplace space, it is possible to use a matrix representation of the problem the well pressure calculation. With the aid of Stehfest algorithm, it is possible to perform the numerical inversion of the solution to the real field. From this problem, it was possible to develop a code that simulates the injectivity test and the pressure behavior over time.

This work proposes an analytical model to compute the pressure response for radially heterogeneous multilayer reservoirs. The analytical model proposed in this work was developed based on equations that model pressure behavior during multilayer conventional production tests. A system of linear equations in Laplace domain is built, representing all differential equations, boundary and coupling conditions. The solution of this linear system in Laplace domain is inverted to real domain through Stehfest’s Algorithm. Layer properties such as permeability, oil viscosity, and porosity may be different for each layer. The computed pressure may be used to determine the main properties of an equivalent single-layered radial composite system that responds in the same manner as the heterogeneous one.

Summary An injectivity test consists of continuously injecting a phase (water or gas) into an oil-saturated reservoir during a period. According to the analysis of the wellbore pressure behavior, this procedure estimates reservoir parameters, such as permeability and skin factor, and the volume of recoverable oil. In this context, this study proposes an approximate analytical solution for the pressure behavior during a water injectivity test on a multilayer reservoir considering multiple injection flow rates. The accuracy of the proposed solution was evaluated through comparison with a commercial finite-difference-based flow simulator in different scenarios. The results indicate a considerable agreement between the data provided by the numerical simulator and the proposed model. In addition, we successfully estimated the equivalent reservoir permeability using the proposed model with satisfactory results.