To stop global warming well below 2°C, a rapid decarbonization of our economy, including the industrial sector is required—reaching net-zero GHG emissions in 2050. CO2 mineralization processes, capturing CO2 from industrial point sources and trapping it as carbonate minerals, have the potential to store climate-relevant amounts of CO2. To get there, the potential processes have to be designed and developed, with the help of a process model that can support the process scale-up and optimization. In this work, a process model describing a gas-liquid-solid continuous cristallizer for CO2 absorption into an aqueous ammonium nitrate solution and CaCO3 precipitation has been developed. It consists of the relevant material balances, of a speciation model, and a population balance equation. While several of the model parameters can be obtained from the literature, a few have been estimated by fitting a comprehensive set of experimental data presented earlier. In particular, the process quantities used for parameter estimation are the CO2 mass transfer rate, the calcium carbonate crystallization rate, and the average particle size of the CaCO3 product crystals. The accuracy of the model, particularly in reproducing mass transfer rates and average particle sizes, has been assessed. Interestingly, it has been shown that the dominating mechanism for crystal formation is primary rather than secondary nucleation. The validated model has been used to explore the effect of the different operating conditions on various key performance indicators so as to gain a deeper insight into the process performance and potential. It has been shown that the CO2 absorption efficiency is mainly affected by the feed stoichiometry and the gas feed rate, whereas the CO2 capture and precipitation efficiency are controlled by the liquid phase composition and the residence time; increasing the calcium concentration in the feed is obviously one way to improve the efficiency. Moreover, we could show that the particle size tends to increase with calcium concentration and to decrease with liquid feed rate and supersaturation of the solution.