Under ideal operation conditions

the calculation for total evaporation and the minimum total evaporation of binary stripping batch distillation under optimal operations is a constrained function optimization problem. In this work

the constrained function optimization problem is transformed to an unconstrained function optimization problem based on the penalty function method and the fixed double step length factor gradient method is used to solve the unconstrained optimization problem. The calculations show that the fixed double step length factor gradient method has good convergence

and the effect of numerical truncation error accumulation on the calculation results is reduced when the number of segments is large. The energy consumption of binary stripping batch distillation under optimal operation is lower than that under constant residual fraction composition operation. It may be attributed to the following reasons: when the theoretical plate number is relatively small (close to the minimum theoretical plate number required for binary stripping batch distillation under constant residual fraction composition operation)

the energy efficiency is improved because of controllable reboil ratio under the optimal operation; when the theoretical plate number is relatively large

the entropy generation in liquid mixing in the top tank is reduced because the material is removed out of the distillation system as soon as possible in the premise of relatively high energy efficiency under the optimal operation because of the controllable reboil ratio. Under ideal operating conditions and infinite number of theoretical plates

the change strategy of the reboil ratio and the calculation formula of the minimum total evaporation of binary stripping batch distillation under optimal operation are obtained by summarizing and extrapolating the above calculation results.