Water alternating gas (WAG) technique is used in the petroleum industry to inject carbon dioxide (CO2) into underground formations either for sequestration or enhanced oil recovery (EOR) processes. CO2 injection causes reactions with formation brine or aquifer and produces carbonic acid, the acid dissolves calcite and changes flow behavior significantly. Modeling and investigating effects of CO2 injection into carbonate formations during WAG processes, investigating parameters related to chemical reactions between reservoir rock and injecting fluid and also better understanding of the process theory for future experiments are the most important goals of this paper. To achieve these experimental data were used. Changes of output calcium concentration from a calcite core sample during three WAG cycles have been studied in laboratory works. The sample is modeled as a medium consisting of a set of capillary pipes and two pore size distribution models are used. Plug flow model and mass conservation law are used for modeling and Darcy law and Hagen-Poiseuille equation are also used to determine characteristics of the porous model. The model is built for linear, miscible and one-dimensional flow. The results show that experimental and model data coincide well in the first and second cycles of both porous models however; they are not coincided in the third cycle. It is because of precipitation and dissolution that cause permeability alternations. Results of the two porous models are compared also.