二元提馏式间歇精馏的优化操作与最小汽化总量

理想操作条件下二元提馏式间歇精馏优化操作的汽化总量与最小汽化总量的计算是约束函数优化问题。本文采用罚函数法,将此约束函数优化转变为无约束函数优化,并采用固定双步长因子梯度法数值求解该函数的极值。计算表明:固定双步长因子梯度法具有良好的收敛性,同时,降低分段数较多时,数值截断误差积累对计算结果的影响。二元提馏式间歇精馏优化操作较恒残液组成操作的能耗低的原因如下:在理论板数相对较少(接近二元提馏式间歇精馏恒残液组成操作所需的最少理论板)时,优化操作通过控制再沸比提高了能耗效率;在理论板数相对较多时,优化操作通过控制再沸比,在保证过程的能耗效率较高的同时,可尽可能快地将物料移出系统,减少了精馏过程中塔顶贮槽内液体的混合熵产。通过对计算结果的归纳与外推,得到了理想操作条件下理论板数为无穷多时二元提馏式间歇精馏优化操作再沸比的变化方式以及最小汽化总量的计算公式。

Optimization operation of binary stripping batch distillation and its minimum total evaporation

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.