Abstract: Lime is an important industrial raw material widely used in iron- and steel-making, flue gas desulfurization, construction, and papermaking industries. Lime is generally obtained via calcining limestone in a kiln, i.e., limestone is heated and decomposed to generate lime and carbon dioxide (CO₂). In the conventional lime calcination, the CO₂ released by the limestone decomposition is mixed with the flue gas because the fuel is burned in the shaft kiln, requiring gas separation for CO₂ capture. The new lime calcination process using CO₂ as a circulating carrier gas to heat limestone particles can avoid the above mixing problem, thereby directly capturing the CO₂ generated by limestone decomposition, which is expected to reduce carbon emissions from lime production by approximately 70%. However, the new calcination process based on CO₂ heating is quite different from the conventional calcination process. To understand the new calcination process and accurately design and optimize it, a mathematical model of the lime calcination process based on CO₂ heating was established. Based on the model, a shaft kiln with a capacity of 200 t·d⁻¹ was simulated and calculated. In addition, profiles of key parameters such as the gas-solid temperature difference, gas flow rate, gas temperature, particle surface temperature, reacting interface temperature, and conversion ratio in the shaft kiln were obtained. Besides, the three operating parameters (feed gas temperature, feed gas flow rate, and radius of the feeding limestone particle) on the calcination were analyzed. The following observations were made: (1) the lower the feed gas temperature, the lower are the final conversion ratio, pinch temperature difference, and tail gas temperature of the kiln. In addition, the changing trend of the final conversion ratio and pinch temperature difference conforms to a quadratic polynomial law, and the changing trend of the tail gas temperature conforms to a linear law. (2) The lower the feed gas flow rate, the lower are the final conversion ratio, pinch temperature difference, and tail gas temperature of the kiln. Moreover, the changing trend of each parameter conforms to a quadratic polynomial law. (3) Finally, the larger the radius of the feeding limestone particle, the lower is the final conversion ratio of the kiln, the higher is the tail gas temperature, and the greater is the pinch temperature difference. The changing trends of various parameters conform to cubic polynomial laws. Compared with the feed gas temperature and the feed gas flow rate, the radius of the feeding limestone particle has a greater impact on the pinch temperature difference and the tail gas temperature when the final conversion ratio changes in the same range.