A detailed model of a capsule containing sodium carbonate solution is developed here to study the microencapsulated carbon capture solvents (MECS). A rigorous vapor-liquid equilibrium model is developed for the Na2CO3-CO2-H2O system, where liquid-phase nonideality is modeled by the electrolyte nonrandom two-liquid model. The data from the experiments conducted at the Lawrence Livermore National Laboratory is used to obtain a maximum likelihood estimate of the initial solvent concentration inside the capsules and the parameters for the capsule model. A nonisothermal, dynamic model of a fixed bed contactor filled with these capsules is then developed. In addition to direct steam injection, indirect heating using an embedded heat exchanger is modeled for desorption. Finally, the model is used to simulate temperature swing absorption and desorption cycles. The results of these studies indicate that there is an optimal residence time or superficial flue gas velocity to minimize the bed volume. However, the total energy requirement for desorption monotonically decreases with increased residence time as the proportion of the sensible heat to the total regeneration heat keeps decreasing. Furthermore, heat recovery from the bed is crucial to keep energy penalty for regeneration low. A techno-economic analysis is conducted, and the equivalent annual operating cost (EAOC) is analyzed for two different reactor materials (concrete and carbon-steel) and compared with a system using a conventional monoethanolamine (MEA) solvent. The minimum EAOC for the MECS fixed bed configuration is approximately 1.8-2.7 times higher than the EAOC for an MEA system with a similar amount of heat recovery (85%). The impact of +/- 50% uncertainty in the capital cost estimate is also evaluated, and the minimum EAOC is 1.5 times higher than the MEA technology for 85% heat recovery. These results using microencapsulated sodium carbonate solution are a starting point that sets an upper limit on the cost of the MECS carbon-capture system. Improvements to the MECS capsules (e.g., using a higher carbonate concentration and lowering the shell mass transfer resistance) and also exploring other contactor technologies are expected to decrease the system cost and make it more competitive.