(438e) Stochastic Optimal Control of Batch Distillation for Biodiesel Production

Biodiesel can be produced by either a batch or a continuous process. Design and control of biodiesel production is fraught with uncertainties. These uncertainties include feed composition and thermodynamic uncertainties. In batch processes, these static uncertainties result in dynamic uncertainties. Optimal control under these uncertainties is a difficult problem and is the focus of this paper.

Diwekar and Rico-Ramirez [1] have described a new approach to stochastic optimal control problems in which stochastic dynamic programming formulation is converted into a stochastic maximum principle formulation. The significance of this approach is that solution to the partial differential equations involved in the dynamic programming formulation is avoided. This approach combines Ito's Lemma and the dynamic programming formulation to solve a time dependant problem. This usefulness of this approach to batch processes in handling time dependant thermodynamic uncertainties was illustrated in Ulas and Diwekar (2004) [2].

Batch distillation is an important unit operation in biodiesel production. The optimal control problem in batch distillation involves the difficult task of determining time-varying profiles through dynamic optimization. Biodiesel feedstock is a mixture of various triglycerides and fatty ester, and because of their bio-based origin, the triglyceride and fatty ester components vary considerably even when the feedstock is from the same source. This gives rise to inherent uncertainties in the feedstock composition. Thermodynamic parameters such as vapor liquid equilibrium and relative volatilities are variable. Optimal control of bio-diesel batch distillation becomes even more complex because: 1) bio-diesel is a mixture of several components with different relative volatilities and thermodynamic properties, 2) the relative volatilities and thermodynamic properties are time dependant. Stochastic maximum principle will be used for batch distillation optimal control under uncertainty. The results of this investigation will results in capturing the uncertainty effects on the optimal control profiles in batch distillation of bio-diesel.

1.Diweker, U.M. and V.C. Ramirez (2004), Stochastic maximum principle for optimal control under uncertainty, Computers and Chemical Engineering 28 (2004) 2845?2849

2.Ulas S., & Diwekar, U. (2004). Thermodynamic Uncertainties in Batch Processing and Optimal Control. Comp. Chem. Eng., 28(11), 2245?2258.