Thermodynamic uncertainties in batch processing and optimal control

Abstract Batch distillation is an important separation process for small-scale production especially in pharmaceutical, specialty chemical and biochemical industries. Although batch distillation units require lower capital cost than continuous units, the unsteady state nature of the process, results in higher operating costs. Optimal control in batch distillation is a mode of operation which allows us to optimize the column operating policy by selecting a trajectory for reflux ratio. Due to the uncertainties in thermodynamic models the reflux ratio profile obtained is often suboptimal. Recently a new method was proposed by Rico-Ramirez et al. [Comput. Chem. Eng. 27 (2003) 1867] to include time-dependent uncertainties in current formulations of batch distillation optimal control for ideal systems. In this paper, a general approach is proposed to handle both dynamic and static uncertainties in thermodynamics for more complex non-ideal systems. The static uncertainties result from the inaccuracies associated with predicting vapor–liquid equilibrium using group contribution methods such as UNIFAC. The unsteady state nature of batch distillation translates these static uncertainties into time-dependent uncertainties. A new Ito process representation is proposed for the dynamic behavior of relative volatility for non-ideal mixtures. Numerical case studies are presented to demonstrate the usefulness of this approach for batch as well as bio-processing.

[1]  E. Prescott,et al.  Investment Under Uncertainty , 1971 .

[2]  Urmila M. Diwekar,et al.  Efficient Combinatorial Optimization under Uncertainty. 2. Application to Stochastic Solvent Selection , 2002 .

[3]  Aage Fredenslund,et al.  A modified UNIFAC group-contribution model for prediction of phase equilibria and heats of mixing , 1987 .

[4]  Aage Fredenslund,et al.  Vapor−Liquid Equilibria by UNIFAC Group Contribution. 6. Revision and Extension , 1979 .

[5]  Urmila M. Diwekar,et al.  Uncertainties in parameter estimation and optimal control in batch distillation , 2004, Comput. Chem. Eng..

[6]  Urmila M. Diwekar,et al.  An efficient sampling technique for off-line quality control , 1997 .

[7]  S. Shreve,et al.  Stochastic differential equations , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[8]  Urmila M. Diwekar,et al.  UNIFIED APPROACH TO SOLVING OPTIMAL DESIGN - CONTROL PROBLEMS IN BATCH DISTILLATION , 1992 .

[9]  Urmila M. Diwekar,et al.  Real option theory from finance to batch distillation , 2003, Comput. Chem. Eng..

[10]  Urmila M. Diwekar,et al.  Stochastic maximum principle for optimal control under uncertainty , 2004, Comput. Chem. Eng..

[11]  Robert Buff.  Continuous Time Finance , 2002 .

[12]  Edward S. Rubin,et al.  Stochastic modeling of chemical processes , 1991 .

[13]  K. P. Madhavan,et al.  BATCH-DIST: A comprehensive package for simulation, design, optimization and optimal control of multicomponent, multifraction batch distillation columns , 1991 .

[14]  Aage Fredenslund,et al.  Vapor-liquid equilibriums by UNIFAC group contribution. Revision and extension. 2 , 1982 .

[15]  J. Gmehling.  Vapor-Liquid Equilibrium Data Collection , 1977 .

[16]  K. Itô,et al.  Stochastic differentials , 1975 .

[17]  Urmila M. Diwekar.  Understanding batch distillation process principles with MultiBatchDS , 1996 .