We are developing a novel DAC system (Cryo-DAC system) that directly captures atmospheric CO2 using the cryogenic heat (-162 degrees C) of liquefied natural gas (LNG), and we aim to obtain design and development guidelines for a Cryo-DAC system combining an amine absorption method and a cryo-sublimation pump. In particular, it has been pointed out that when a non-phase-change gas such as N-2 mixes into the sublimation tank from the regeneration tower, it accumulates downstream of the sublimation tank and strongly inhibits dry ice production. Therefore, it is essential to elucidate the changes in the gas distribution in the sublimation tank and how the gas accumulation reduces the dry ice production rate. An unsteady lumped parameter system numerical model consisting of a regeneration tower, a connecting passage, and a sublimation tank divided into three parts was developed and numerically analyzed to investigate the influence of the non-phase-change gas on the temporal change of various quantities in the process and on the formation characteristics of dry ice. In particular, the effects of various analytical parameters on pressure, temperature, CO2 regeneration rate in the regeneration tower, unsteady changes in CO2 solidification rate in the sublimation tank, and the amount and efficiency of dry ice production were clarified. This report presents the temporal changes in process parameters under the reference analysis conditions and elucidates the temperature and material concentration changes among the three sublimation tanks. We also found that the thickness of the dry ice layer increases unsteadily in proportion to the square root of time and that the magnitude of heat transfer to the cooling surface and the bulk gas phase changes, resulting in an unsteady state for the entire sublimation tank.