CO2 injection is a well-established method for enhanced oil recovery and numerous studies have been dedicated to studying this process at the pore level. An attractive enhanced oil recovery method with much better sweep efficiency, which has received less attention, is carbonated water injection. In this work, a mathematical model was developed, which simulates, at pore level, the dynamic process of swelling of an oil ganglion when it comes in direct contact with carbonated water or is separated from the CO2 source by water layers (indirect contact), a sensitivity analysis of pertinent parameters on the mass transfer process was carried out based on two different evaluation methods. In the first evaluation method, which is beneficial for evaluating the impact of uncertainty of input parameters for simulating the results of an experiment, the time required for the interface to reach a specified position, which was selected as that of a base case, was investigated. In the second evaluation method, which is more independent, the required time for the interface to reach its equilibrium position, which is different for each case under study, was compared with that of the same base case. The impact of some of the pertinent parameters as predicted by the model was linked to results obtained using a new relationship developed based on the dimensional analysis technique. The results suggest practical guidelines on the effect of a water layer and fluid properties in this multi-physics process.