This paper focuses on the development and evaluation of a mathematical model for 1D miscible displacement across intrinsically heterogeneous porous media. The model, referred to as the total concentration model, is developed based on the convection-dispersion equation considering the interaction between the rock and the fluids. The model is suitable for treating the data obtained from CT scanners where the dopant deposits at the rock surface. Further, this paper presents a methodology to treat and use the vast amount of data rendered by CT scanners. The methodology involves a multiparametric fitting of the model to the lab data through the simulated annealing metaheuristic. As an application, conducted displacement tests are reported for two brines on a carbonate rock. Results show a very good fitting of the model to the experimental data. The procedure allowed determination of the dispersion coefficient, the mass transfer coefficient, the effective porosity of the porous medium, which differs from the medium porosity, and the amount of solute that is deposited on or removed from the porous medium.2016784PETROBRASANP