For batch distillation processes separating a binary mixture of benzene and toluene, we develop rigorous mathematical models of various process devices, physical properties and startup procedures, and simulate them dynamically. The mathematical models include about 1200 differential algebraic equations, and the dynamic simulation includes discrete events of startup procedures sequentially. To show the dynamic behaviors of distillation column internal rigorously following the startup speration, the material and energy balances of every tray in distillation column contain lots of correlations such as Francis weir equation, hydraulics and correlations of predicting weeping rate in sieve trays. The dynamic simulation of the target processes starts with the initial condition of zero holdup of liquid phase at every tray and the reflux drum, and it continues until the beginning of normal operation in which the two components start being separated by the reflux. As results, various dynamic behaviors of thermodynamic variables, process variables and surrounding installations are observed, and the non-ideality of column internal is revealed more rigorously with the prediction of the weeping rate of each tray. The numerical data from this study are expected to be applicable to improving the safety and the efficiency of industrial design.