The productivity of the batch distillation columns is affected by the design and operation parameters. While the batch distillation design problem considers the determination of the vapor load, number of stages and column structure (regular or unconventional), the column operation problem deals with the calculation of the reflux ratio as constant optimal value or optimal profile. The batch time is fixed or is an additional optimization variable. Previous works have analyzed the influence of the vapor rate on the batch distillation columns and have concluded that for the unlimited market demand the vapor rate should be as high as possible.
During the operation of the distillation columns at low pressure conditions (depending on the reboiler volume and rectification column diameter) the maximum vapor rate may induce reboiler liquid swelling before causing rectification column flooding. Liquid swelling occurs when the vessel content level rises due to a vapor stream which passes through the liquid. A practical solution to avoid reboiler swelling related problems is to decrease the batch size (filling level) to a safe value; however, the batch size decreases as well. Since the distillation productivity is determined by the batch size and batch time, one should attempt to find an optimum between a large batch size (high filling degree) and fast operation (large vapor rate).
This contribution addresses the optimal design (determination of the batch size) and operation (optimal reflux ratio and vapor load profile) of batch distillation columns under the reboiler liquid swelling and column flooding constraints. To our knowledge the batch distillation design and operation optimization with regard to reboiler liquid swelling has not been tackled previously in the literature.
The batch distillation column is modeled using a tray-by-tray model based on mass balances (differential equations), the true liquid level in the reboiler and the rectification column flooding are calculated using hydrodynamic equations. The design optimization problem is implemented in the outer loop, whereas the optimal control problem which gives the optimal operation is solved in the inner loop. The manipulated variables are the batch size (outer loop), the reflux ratio and vapor flow rate profiles (inner loop). The constraints of the optimization problem are posed by the batch distillation model and the algebraic equations which describe the hydrodynamic conditions. The outer optimization is solved by enumeration since it is one variable and the range of the optimal value is approximately known. The inner optimal control problem, which is computationally much more demanding, is based on the SQP algorithm. The SQP method is implemented in a user-friendly software environment, OptCon, which provides a Matlab interface for easy problem setup. The optimization approach is based on a large-scale nonlinear optimization solver (HQP), which offers a very efficient technique, based on a multiple shooting algorithm. The integrator is the DASPK and the multiple-shooting optimal control algorithm is implemented and compiled as C language library. The model equations are implemented in a Simulink C file.
The OptCon software package solves in about 1-2 seconds the optimal control problem of several hundreds of variables. Therefore, the control profile with large number of discretization intervals can assure a detailed solution and several scenarios can be quickly and efficiently evaluated. The OptCon software is hosted at the Loughborough University, U.K., by Zoltan K. Nagy (http://www-staff.lboro.ac.uk/~cgzkn/).
The optimizations are performed for industrial scale batch distillation reboilers and rectification columns. Furthermore, we analyze the sensitivity of the optimal solution towards the light component ratio in the mixture and towards the start-up time.