The sulfur dioxide (SO2) and carbon dioxide (CO2) emissions from fuel combustion in a coal-fired power plant constitute a significant source of damage to the environment. Therefore, SO2 and CO2 should be captured before being released into the atmosphere. However, the competitiveness between SO2 and CO2 for calcium carbonate (CaCO3)/calcium oxide (CaO) solid sorbents is still unclear. In this study, unsteady state computational fluid dynamics simulation in a riser of an industrial scale circulating fluidized bed boiler integrated with heterogeneous combustion, carbonation, calcination, and desulfurization reactions using a mixed feeding of CaCO3/CaO solid sorbents was developed in a two-dimensional model to investigate the competition between SO2 and CO2 capture. Then, the effect of three operating variables, the mixed solid CaCO3/CaO sorbent particle size, feed position, and the proportion of inlet fuel velocity on the SO2 and CO2 capture were evaluated using a 23 factorial experimental design. The CaCO3/CaO solid sorbent particle size had a significant effect on the SO2 capture, while the interaction between CaCO3/CaO solid sorbent particle size and feed position had a significant effect on the CO2 capture. The reaction rate for CO2 capture was higher than that for SO2 capture. For SO2 capture, CaO reacted with SO2 faster than CaCO3 while, for CO2 capture, solid sorbents had higher carbonation rate than calcination rate. In addition, the overall level of SO2 and CO2 capture with a mixed CaCO3/CaO solid sorbent feed was higher than those with the conventional CaO solid sorbent.