The nuclear criticality safety analysis is crucial for the nuclear safety of spent fuel reprocessing plants. Thus, a set of numerical tools with high accuracy and efficiency to predict the criticality and simulate the hypothetical accidents in the reprocessing procedure is of great importance. Among them, this paper focus on the analysis of the storage tank which is used for dissolution and storage of the spent fuel. According to the characteristics of spent fuel solution system, a parallel 3D critical safety analysis tool for fissile solution system, Hydra-TD, is developed. Generally, it contains the cross-section generation model, the three-dimensional space-time neutron kinetics model, and the R-Z two-dimensional heat conduction and radiolysis gas simulation model. The verifications based on the experiments of the SILENE and TRACY facility are conducted. The results show good accuracy of the prediction of the first fission power peak, multiplication time and total fission energy, indicating the reliability of these numerical models.