Gravity assisted gas displacement of oil in reservoirs is increasingly being considered. Accurate estimates of relative permeabilities are needed to understand and predict fluids motion, especially when very low oil saturations are reached

In our study, gravity drainage experiments under secondary conditions are performed with different core wettabilities. Then, relative permeabilities are determined from the experimental data (oil recovery and saturation profiles measured by gamma-ray attenuation) using an analytical calculation and an identification method based on a numerical model. Our work aims at testing both approaches and efficiencies

The first method results from an analytical treatment of the multiphase flow model, where capillary pressure is taken into account and gas displacement is neglected. Capillary pressure is directly obtained from the last saturation profile when capillary equilibrium is reached. Then, a computer-aided procedure using a numerical finite-difference scheme calculates oil relative permeability from the saturation profiles measured at different times and different positions along the core

Saturation experimental noise due to gamma-ray technique is simulated and its effect on oil relative permeability calculation is tested. Two trends are observed: for high oil saturations, relative permeability curve is correctly described while, for low oil saturations, there is a slope change due to inaccurate values

The second method consists in using an inversion software (CAROPT, developed by TotalFinaElf) based on the minimization between computed and measured data. Inputs are saturation profiles and oil recovery; outputs are relative permeabilities and capillary pressure. Optimization process and final results depend on the initial data set that is considered

Our work suggests that the analytical method provides accurate estimates of relative permeability that are good initial data for the identification method. However, because of the assumptions used in the analytical calculation and its proved inaccuracy for low saturations due to experimental noise, conclusions cannot be drawn about flow regime at these very low saturations and results should be compared to those obtained by the identification method. At last, both approaches give a similar interpretation, which shows they are complementary