Investigation of robust techniques for the design of chemical processes under uncertainty - Dominguez Palomeque, Luis Felipe (University of Ottawa (Canada), 2007)
The design of a chemical process is a complex optimization problem. Process models are used to describe the interrelationship of the variables being analyzed and provide the means for representing the description of the problem in mathematical terms. Traditionally, deterministic optimization has been employed to obtain values of design and control variables which minimize capital and operating costs. Subsequently, over-design or safety factors are applied to design variables to account for the fact that plant operating parameters and input variables are uncertain. This design strategy has some limitations. Over-design factors unnecessarily increase capital costs and do not guarantee that the process will have feasible operation. Moreover, the deterministic optimization fails to explore the benefits of integrating operability issues, such as flexibility and robustness, at the design stage. This work examined integrated robust techniques for the design of chemical processes and employed a rigorous stochastic optimization approach that fully take into account the uncertainty of technical parameters and the inherent variability of input variables. In addition to capital and operating costs, quality costs were considered. The influence of uncertain parameters on the final cost was also studied and sensitivity analyses were performed to determine their impact. It was found that the optimal values of the process variables were affected by the uncertainty of the parameters. That is, they presented considerable sensitivity. The location of the optimal values of these variables was also influenced by the components of the overall cost. It is shown that capital and operating costs tend to increase when quality costs contribute in great extent to the overall cost. The overall cost was also influenced by the desired extent of robustness in quality variables. The stochastic optimization formulation turns the objective function into a probabilistic representation, commonly in form of expectations. Contrary to the common approach, where quadrature or cubature formulas are used, this work employed sampling techniques to estimate the expected value of the objective function of the stochastic optimization problem. It was found that, at a modest computational effort, the Hammersley Sequence Sampling (HSS) provides a more accurate estimate of the objective function than cubatures and Monte Carlo sampling techniques. Three quasi-Monte-Carlo sampling techniques, based on the sequences of Halton, Faure and Sobol, were also examined for their potential used in the solution of stochastic optimization problems. These sampling techniques were implemented in a computer code in MATLAB and tested in two engineering problems. It was found that the proposed sampling techniques, Halton Sequence Sampling (HalSS), Faure Sequence Sampling (FSS) and Sobol Sequence Sampling (SSS), can compete with Hammersley Sequence Sampling (HSS) in terms of their low required sample sizes and number of function evaluations to achieve sufficient accuracy.
Keywords: Engineering, Chemical.