The present study presents the development and application of a mathematical model for the 1-D miscible displacement in an intrinsically heterogeneous porous media. The model, referred to as total concentration model (TCM), is developed based on the convection-dispersion equation considering the interaction between the rock and the flowing fluids. The parameters involved in TCM are the dispersion coefficient, the mass transfer coefficient, the effective porosity of the porous medium at the time of the displacement and the amount of solute that is deposited or removed from the porous medium. These parameters are determined in the application of the model through multiparametric matching to the data obtained in the laboratory. In order to evaluate the developed model, two sets of experiments (A and B) were carried out. The tests consisted of displacing two brines across carbonate rock samples. The evolution of salt concentration distribution along the porous medium sample was monitored by X-Ray Computed Tomography (CT).
The great sum of data pertaining to the concentration profiles determined from the CT images in experiment A was analyzed and matched to the TCM model through the simulated annealing metaheuristic method (Simulated Annealing, SA). A dispersion coefficient of 0.01cm2/s for a 1 cm3/min flow rate; and of 0.05 cm2/s for a 5 cm3/min flow rate was determined. The parameters of mass transfer between the fluid and the rock were also evaluated.
Experiment B was carried out in order to double check solute deposition while flowing through the rock sample. Within the TCM model, the phenomenon was quantified by the fr parameter. The concentration profiles were measured at the inlet position, along the rock sample and at the output end. A mass balance calculation was carried out with the obtained data in order to evaluate the fraction of solute deposited (fr) during the experiment. The values determined for fr were 0.2 to 0.4, figures that are consistent with the results obtained with the TCM matching procedure.
The proposed model (TCM) is appropriate for treating data obtained with CT scanners in miscible displacement experiments with relevant interaction between the rock and the fluids. The global matching procedure, considering all curves in the concentration evolution, was used to determine the governing parameters in the model. The amount of data used and the robustness of the method allowed a very good matching of the model to the experimental data.