It is likely that before long injection/fall-off tests will largely replace the conventional production/build-up sequence used for reservoir appraisal because they eliminate surface emissions and can significantly reduce testing costs. However, the welltest interpretation is complicated because of the presence of two phases. Fluid saturations vary during injection and only for very favourable mobility ratios the displacement can be assumed piston-like; thus effective permeabilities govern the flow. Gravitational and thermal gradients, heterogeneity and anisotropy might also strongly affect the variation on fluid distribution with time. Analytical approaches are invaluable to help capturing the leading effects controlling the pressure transient behaviour. However, only numerical simulation can thoroughly describe the saturation and pressure field in the reservoir as it evolves during injection and subsequent fall-off. Therefore, numerical simulations are needed to evaluate the skin due to the two phases fluid conditions. Together with the permeability-thickness product this skin is essential to calculate the well productivity. A near wellbore, 3D numerical model for the pressure response during non-isothermal water injection test in oil reservoir was developed and implemented with the aim of designing and interpreting injection tests. The model has virtually no limitations because it accounts for all the aspects that can impact on fluid and pressure distribution, such as gravity, capillary forces, heterogeneity and anisotropy. The results are provided in terms of pressure and pressure derivative for subsequent analyses. The model was used to interpret synthetic cases of water injection into a deep aquifer and brine injection into an oil reservoir. The results are presented in the paper

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