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Calcium looping systems constitute a promising candidate for thermochemical energy storage (TCES) applications, as evidenced by the constantly escalating scientific and industrial interest. However, the technologically feasible transition from the research scale towards industrial and highly competitive markets sets as a prerequisite the optimal design and operation of the process, especially corresponding reactors. The present study investigates for the first time the development of a detailed, one-dimensional mathematical model for the steady-state simulation of a novel drop-tube carbonator reactor as a core equipment unit in a concentrated solar power (CSP)-thermochemical energy storage integration plant. A validated kinetic mathematical model for a carbonation reaction (CaO(s) + CO2(g) → CaCO3(s)) focused on thermochemical energy storage conditions was developed and implemented for different material conditions. The fast gas–solid reaction kinetics conformed with the drop-tube reactor concept, as the latter is suitable for very fast reactions. Reaction kinetics were controlled by the reaction temperature. Varying state profiles were computed across the length of the reactor by using a mathematical model in which reactant conversions, the reaction rate, and the temperature and velocity of gas and solid phases provided crucial information on the carbonator’s performance, among other factors. Through process simulations, the model-based investigation approach revealed respective restrictions on a tailor-made reactor of 10 kWth, pointing out the necessity of detailed models as a provision for design and scale-up studies.