Carbonate matrix acidizing is widely used in oil fields as a simple and easy method of production enhancement. However, the dissolution pattern created due to the reaction between the acid and the carbonates is a complex phenomenon. Several experimental and modeling studies have been carried out to simplify this process and design the optimum conditions for acidizing. One approach is to develop continuum models to simulate the dissolution process in the core scale. Conventional modeling approaches typically do not consider the effects of spent acid in the models. However, there are a few studies and observations on the solubility of CO2 in the CaCl2-H2O-CO2 system, which shows the possibility of formation of a separate CO2 phase during acidizing. The presence of CO2 as a separate phase affects the dominant wormhole propagation and also the dissolution regime. Moreover, the acid/rock reaction leads to the change of physical properties of the flowing fluid. Hence, neglecting the alterations in the physical properties of the moving fluid, such as density and viscosity, affects the accuracy of the models. In this study, a basic model previously introduced in the Darcy scale is developed to consider the effect of reaction products on the overall acidizing performance. A thermodynamic model is used to estimate the CO2 solubility in the spent acid. The insoluble CO2 may change the relative permeability of the reactants and influence on the optimum conditions. Furthermore, the physical properties of the fluid are estimated and updated at each step of the modeling. Consideration of the spent acid effects in the modeling can improve the modeling accuracy. The developed model has the ability to consider the effect of pressure and temperature of the medium on the optimum conditions. In addition, the developed model has shown better predictions by considering the physical changes during the dissolution.