Optimization of Biodiesel Production under Uncertainty
This work focuses on the optimization of the biodiesel production process under uncertainty using ASPEN Plus and CAPE-OPEN compliant stochastic simulation and the novel Better Optimization of Nonlinear Uncertain Systems (BONUS) algorithm.
Biodiesel is an alternative to conventional diesel. Biodiesel production involves a trans-esterification reaction where long chain triglycerides are converted to methyl esters and glycerol. Out of available biodiesel process technologies, transesterification followed by separation either in batch or continuous process is the most widely used commercial process. The glycerol and esters are separated out in a settling vessel. The alcohol is separated from the glycerol and ester by either evaporation or flashing. The methyl esters are then neutralized by washing with slightly acidic water and stored. The uncreated triglycerides are recycled and the biodiesel (consisting of methyl esters and some free fatty acids) is either sold as is or blended with diesel for use as B20 fuel. 
The production of biodiesel suffers from inherent uncertainties because the biodiesel feedstock is derived from plant and animal matter having a range of components and different distributions. Due to limited availability of feedstock in an area as a result of geographical and weather constraints, biodiesel processing plants must be flexible enough to process feedstock from a variety of sources and locations, which further increases the uncertainties in feedstock triglyceride composition. The common uncertainties in the biodiesel production process are: feedstock compositions, reactor operating conditions, and methanol to oil ratio of feed to the transesterification reactor. These uncertainties can have a significant impact on the process efficiency and product quality. The recent sharp swings in the price of biodiesel and biodiesel feedstocks have demonstrated that for biodiesel to compete with conventional diesel, the biodiesel process must be efficient and cost effective. In addition, quality of fuel must meet the specifications for diesel so that biodiesel can be used in internal combustion engines of cars without the need for blending with diesel. Thus maximization of process efficiency requires optimal operating parameters while adhering to the constraints of meeting diesel fuel specification in terms of viscosity, 90% liquid boiling point and ocetane number.
Studies for the optimization of biodiesel production processes have focused largely on process integration and evaluated the feasibility of different process pathways using a constant feedstock composition and sensitivity analysis .
In their current unpublished work, the authors of this abstract have quantified the uncertainties in the biodiesel production process by representing them in the from a probability distribution curve and applied stochastic modeling to published optimized flow sheets to evaluate its impact on process efficiency and product specifications. Results have indicated that when compared to the deterministic models, stochastic modeling shows that process efficiency varies widely with the feedstock composition and operating parameters. In addition, the biodiesel fuel produced has difficulty meeting product specifications. It is evident that the optimization of biodiesel production through process integration is not a truly optimized process because it does not consider uncertainties in the biodiesel feedstock and operating parameters. Optimization under uncertainty will capture the uncertainties in feedstock components and operating parameters and incorporate them in the optimization scheme. The objective of the optimization scheme will be to maximize process efficiency under tighter product specification constraints.
Application of optimization in the field of process systems often involves dealing with non linearity and uncertainty necessitating the solution of stochastic non linear programming (SNLP) problems. But current algorithms in this area suffer from various limitations. Diwekar and Shastri  have applied L-shaped BONUS algorithm, which is the integration of BONUS (Better Optimization of Nonlinear Uniform Systems) algorithms and sampling based L-shaped method to cases studies and their results confirm the computation efficiency of the L-shaped BONUS algorithm. The sampling based optimization algorithm structure is shown below.
Figure 1 Sampling-based optimization algorithm structure 
Diwekar and Salazar  have applied the algorithm to minimization of water consumption in coal fired power plants. Optimization under uncertainty for such large scale complex process cannot be solved with conventional stochastic programming because of the large computational expense. However, the novel optimization algorithm BONUS when implemented in ASPEN Plus dramatically decreased the computation requirements of stochastic optimization with results which led to minimization of water consumption in coal fired plants.
Biodiesel production process is very complex and the use of ASPEN Plus and BONUS will dramatically decrease the computational requirements of the stochastic optimization. This study will comprise of two main steps: sensitivity analysis to determine the major decision variables and optimization of the process to maximize process efficiency. The characterization of uncertainties in the biodiesel production process has already been accomplished by the authors in their unpublished work.
The result of the study will be the maximization of process efficiency while using product quality specifications as a constraint. The results of this study can be used for the design of a plant which is flexible to accept any feedstock and the finished product does not require additional blending of fuel to meet diesel fuel specifications.
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2. Shastri Y. and U. Diwekar., L-Shaped BONUS algorithm with application to water pollutant trading, (2008), In Industrial and Engineering Chemistry Research, 47, 9417.
3. Salazar J. and U. Diwekar, Minimization of Fresh Water Consumption for Particulate Carbon (PC) Power Plants, Foundations of Computer Aided Process Design 2009:Design for Energy and Environment, Halwagi M. and A. Linninger Eds., 649.
4. Ai-Fu Chang and Y. A. Liu, Integrated Process Modeling and Product Design of Biodiesel Manufacturing, Ind. Eng. Chem. Res. 2010, 49, 1197–1213
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