The present paper is the first part of a series of papers about a systematical investigation on the application of the K2CO3/Al2O3 sorbent for capturing CO2 in flue gas. It was focused on the carbonation behaviors of K2CO3/Al2O3 in a thermogravimetric analyzer. The effects of the temperature, gas composition, and pressure on the reactions were studied by analyzing the experimental breakthrough data. It was found that K2CO3/Al2O3 shows a high CO2 capture capacity, and its carbonation conversion reaches 68.3-91.8% in 20 min, when the reaction temperature is in the range of 55-75 degrees C, the CO2 concentration is in the range of 5-20%, the H2O concentration is in the range of 12-21%, and the pressure is 0.1 MPa. The total carbonation conversion mainly depends upon the reaction in the first 5 min, and the reaction rate, reaches the maximum in about 2 min. The total carbonation conversion increases with the increase of CO2 and H2O concentrations but decreases with the increase of the temperature and pressure. Among the factors studied, the H2O concentration and pressure were found to have a significant impact on the carbonation. Moreover, water pretreatment of the sorbent plays an important role in the carbonation reaction.