New approaches for model parameter uncertainty in process and reactor network synthesis.

摘要

Mathematical programming and optimization have become important tools in process systems engineering. This thesis develops new optimization formulations to accurately include model parameter uncertainty into process design and reactor network synthesis problems.; The first part of this thesis develops new mathematical models for reactor network synthesis. A revision is made to a previous mixed-integer nonlinear programming (MINLP) model to include a more general description of differential sidestream reactors (DSR). Next, novel linear programming (LP) formulations for reactor network synthesis are proposed. By considering a rate vector field in concentration space at an arbitrarily large number of points, we derive LP models for reactor network synthesis and attainable region (AR) analysis. The methods are extended to derive strong necessary conditions for AR analysis. We demonstrate the proposed LP techniques on several example problems.; The thesis then addresses model parameter uncertainty in process and reactor network synthesis. Elliptical confidence regions for model parameters are used to capture their uncertainty. This is in contrast to previous approaches which often used simple lower and upper bounds for the model parameters. A two-stage solution algorithm is used to solve several design problems under model parameter uncertainty.; Next, multiperiod formulations are developed to include model parameter uncertainty in reactor network synthesis problems. A novel approach is taken where the constraints in the multiperiod problem are formulated in terms of candidate ARs in composition space. AR analysis is used to derive upper and lower bounds for the multiperiod problems. Two examples problems are solved showing the effectiveness of using a hybrid approach combining AR analysis with mathematical programming.; The elliptical confidence regions used earlier to describe the model parameters may be inaccurate for nonlinear systems. Thus, they are replaced with confidence regions derived from the likelihood ratio test. Several process synthesis problems are solved and the effect of using different confidence regions for the model parameters is readily apparent.; Finally, this thesis looks at treating process variability and model parameter uncertainty differently in process synthesis. We assume the continuous fluctuations normally associated with several process quantities (temperature, flowrates, etc.) can be measured accurately and control variables are then used to minimize their effect. However, the true values of the uncertain model parameters are unknown, and thus we assume control variables cannot be used to compensate for their uncertainty. Multiperiod problems are solved for discretized values of the process variability and model parameter uncertainty. The feasibility of the designs from these multiperiod optimization problems is checked with a new feasibility test problem. An approximate solution strategy is proposed to solve the nested optimization problems in the feasibility test using an aggregation of the inequality constraints. Two examples are solved to demonstrate the proposed approach.