Abstract: Based on the structured packing PACK-13C, an ultra-high purity cryogenic distillation system was designed to remove krypton from commercially available xenon to satisfy the needs of low-background and high-sensitivity dark matter detection experiment. The distillation tower had a total height of 6 meters, with an internal packing height of 4 meters. Within the packing, the rectification section was 1.9 meters, and the stripping section was 2.1 meters. The inner diameter of the tower was 80 millimeters. The experiment result of cryogenic distillation system demonstrated that during total-reflux stage, it maintained vacuum of 6\times 10⁻³ Pa between the inner and outer tower, the temperature of the distillation column is 178 K, the pressure of the top reboiler was approximately 221 kPa. and the krypton concentration in xenon could be reduced from 3×10⁻⁹ mol/mol to 3×10⁻¹² mol/mol. According to the characteristic unit of structured packing PACK-13C which used in the cryogenic distillation system, this article constructs a Computational Fluid Dynamics （CFD） model incorporating multi-physics coupling, which can perform coupled calculations of flow field, temperature field, and concentration field, and the mass transfer coefficient is calculated from the Delft model. This CFD model could be utilized to simulate the gas-liquid separation process on structured packing unit during total-reflux stage. Compared to the experimental result, the simulation results show the acceptable error and indicate appropriate hole diameter could form a trail with a significant concentration gradient downstream of the holes. The gas-liquid exchange channel between two pieces of packing could effectively increase the local flow velocity, which was able to enhance the mass transfer between cryogenic gas and liquid. The peak height and wave distance are negatively correlated with separation efficiency, as the peak height and wave distance increase, the concentration of the liquid at the outlet rises, the purification efficiency decreases, and the peak height have a more significant impact.