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The reduction in CO2 emissions is now a very popular topic. According to the International Energy Agency, CO2 emitted in 2021 was 6% more than that emitted in 2020. Carbon capture and storage (CCS) is gaining popularity as a possible solution to climate change. Experts estimate that industry and power plants will be responsible for 19% of total CO2 emissions by 2050. This paper presents the design of a semi-industrial-scale system for CO2 capture based on the moving bed temperature swing adsorption technology. According to the results of laboratory tests conducted by the SINTEF industry, this technology demonstrates high capture efficiency (>85%). The CO2 capture medium involved in adsorption is activated carbon passing through individual sections (cooling, heating, adsorption), where CO2 is bonded and then released. The heat and mass transfer processes are realised on the developed stand. The heat exchangers use steam and water as the heating/cooling medium. The paper reviews the existing solutions and describes the developed in-house design of heat exchangers that will ensure heat transfer conditions being a trade-off between economic and efficiency-related issues of the CO2 capture process. The designed test stand will be installed in a Polish power plant and is expected to meet the method energy intensity target, set at ≤ 2.7 MJ/kg CO2, with a capture efficiency exceeding 85%. The aim of the work was to develop and solve technical problems that would lead to the construction of a CO2 capture station with parameters mentioned above. This stand uses an innovative method where CO2 is captured by contacting the fluid (gases) with solid particles. The heat exchange associated with the heating and cooling of the adsorbent had to be solved. For this purpose, heat exchangers were designed with high thermal efficiency and to prevent the formation of mounds.