In the petroleum industry, well testing is a common practice that consists of wellbore pressure, temperature and flow rates data acquisition to estimate parameters that govern the flow in porous media. Injection-falloff testing is particularly important for offshore reservoirs, especially for the oil reserves that contain high carbon dioxide and sulfur content. In this environment, a conventional well test in an exploratory well should not be run in order to avoid discarding high concentrations of these gases to the atmosphere. Therefore, there is a need for developing techniques for analyzing pressure data from injection-falloff tests. In this work, we have developed an approximate semi-analytical solution for wellbore pressure response during gas injection and falloff well tests in reservoirs containing oil and gas with complex composition by applying the Thompson and Reynolds steady-state theory. For the injection period, we first determine the overall concentrations distributions from a system of hyperbolic conservation equations using the method of characteristics (MOC), assuming a one-dimensional homogeneous reservoir with incompressible fluids and constant molar density, and neglecting capillary, gravity effects, volume changing on mixing and diffusion. During the falloff stage, it is assumed that there is no phase nor concentration movement in the reservoir, which is reasonable as we neglect capillary pressure, diffusion, gravity force and fluid compressibilities. Once we have the concentration profiles in the reservoir, we can calculate the total mobility distributions and then integrate the pressure gradient given by Darcy's law to find the wellbore pressure response. The semi-analytical approximate solution obtained was validated against the commercial numerical simulator STARS from CMG. After validation, the developed model was used as a forward model to estimate absolute permeability and skin factor by history matching noisy data obtained from the numerical simulator mentioned.

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