William Rooney - Academia.edu (original) (raw)

Papers by William Rooney

We propose linear programming (LP) models for attainable region (AR) analysis by considering a ra... more We propose linear programming (LP) models for attainable region (AR) analysis by considering a rate vector ÿeld in concentration space with an arbitrarily large number of points. One model provides a method to construct candidate ARs using a fully connected network of continuously stirred tank reactors (CSTRs) of arbitrary volume. More importantly, these methods are extended to derive linear programming conditions that are stronger necessary conditions than have proposed previously by Glasser and Hildebrandt. We state the LP condition as: No combination of nonzero volume CSTRs, operating at discretized points in the complement of the candidate AR, can extend the region. We demonstrate these proposed linear programming techniques on several two-dimensional reaction mechanisms and then apply the LP methods to verify extensions for a previously published three-dimensional candidate AR. ?

Optimal design under unknown information is a key task in process systems engineering. This study... more Optimal design under unknown information is a key task in process systems engineering. This study considers formulations that incorporate two types of unknown input parameters, uncertain model parameters, and ®ariable process parameters. In the former case, a process must be designed that is feasible o®er the entire domain of uncertain parameters, while in the latter case, control ®ariables can be adjusted during process operation to compensate for ®ariable process parameters. To address this problem we extend the two-stage formulation for design under uncertainty and deri®e new formulations for the multiperiod and feasibility problems. Moreo®er, to simplify the feasibility problem in the two-stage algorithm, we also introduce a KS constraint aggregation function and deri®e a single, smooth nonlinear program that approximates the feasibility problem. Three case studies are presented to demonstrate the proposed approach.

A key objective of the integrated reactor network synthesis approach is the development of waste ... more A key objective of the integrated reactor network synthesis approach is the development of waste minimizing process flowsheets (Lakshmanan & Biegler, 1995). With increasing environmental concerns in process design, there is a particularly strong need to maximize conversion to product and avoid generation of wasteful byproducts within the reactor network. This also avoids expensive treatment and separation costs downstream in the process. In this study, we present an application of the mixed integer nonlinear programming (MINLP)-based reactor network synthesis strategy developed by Lakshmanan and Biegler (1996a). Here we focus on applying these reactor network synthesis concepts to the vinyl chloride monomer production process. Vinyl chloride is currently produced by a balanced production process from ethylene, chlorine and oxygen with three separate reaction sections: oxychlorination of ethylene; direct chlorination of ethylene; and pyrolysis of ethylene dichloride. The hydrogen chloride produced in the pyrolysis reactor is used completely in the oxychlorination reactor. Byproducts such as chlorinated hydrocarbons and carbon oxides are generated by these reaction sections. These are studied using reaction kinetic models for the three reaction sections. The case study results in optimal reactor networks that improve the conversion of ethylene to vinyl chloride and minimize the formation of byproducts. These results are used to generate an improved flowsheet for the production of vinyl chloride monomer. Moreover, an overall profit maximization, that includes the effect of heat integration, is presented and a set of recommendations that improve the selectivity of vinyl chloride production are outlined. Finally, the optimal reactor structures, overall conversion and annual profit are shown to be only mildly sensitive with respect to small changes in the kinetic parameters.

This paper develops a systematic procedure for constructing an attainable region (AR). The approa... more This paper develops a systematic procedure for constructing an attainable region (AR). The approach uses two dimensional ARs constructed in orthogonal subspaces to construct higher dimensional ARs. Our technique relies on previous algorithms that provide a practical assurance of the completeness of ARs in two dimensions, using only PFR and CSTR reactors and mixing. Here we build on a modification of this property by constructing 2D projections and their intersections that provide upper and lower bounds of the AR. These bounds are then improved by applying AR constructions sequentially to candidate regions in orthogonal subspaces. The approach is demonstrated on a well-known AR problem in three dimensions. 0

We present a hybrid approach using both mathematical programming methods and attainable region (A... more We present a hybrid approach using both mathematical programming methods and attainable region (AR) concepts to extend reactor network synthesis techniques to include model parameter uncertainty. First, a revised mixed-integer nonlinear programming (MINLP) reactor network synthesis model is presented that allows for more general reactor networks to be constructed. A complicated reactor network synthesis problem is solved using the revised formulation. Next, we combine AR theory with multiperiod optimization concepts to extend the MINLP model to include model parameter uncertainty. By examining the Karush –Kuhn– Tucker optimality conditions together with AR theory, we show that reactor networks designed under uncertainty, in general do not follow AR properties. Thus, more general reactor types may be needed to solve the reactor network synthesis problem under uncertainty. However, AR theory, can be used to find performance bounds on multiperiod reactor network synthesis problems. These bounds are very useful for screening candidate reactor networks and to initialize the 'MINLP problem. Two example problems are presented to demonstrate the proposed multiperiod approach.