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The finite volume method has been successfully applied in several engineering fields and has shown outstanding performance in fluid dynamics simulation. In this paper, the general framework for the simulation of near-wellbore systems using the finite volume method is described. The mathematical model and the numerical model developed by the authors are presented and discussed. A radial geometry in the vertical plane was implemented so as to thoroughly describe near-wellbore phenomena. The model was then used to simulate injection tests in an oil reservoir through a horizontal well and proved very powerful to correctly reproduce the transient pressure behavior. The reason for this is the robustness of the method, which is independent of the gridding options because the discretization is performed in the physical space. The model is able to describe the phenomena taking place in the reservoir even in complex situations, i.e. in the presence of heterogeneities and permeability barriers, demonstrating the flexibility of the finite volume method when simulating non-conventional tests. The results are presented in comparison with those obtained with the finite difference numerical approach and with analytical methods, if possible.