Computers and Chemical Engineering 24 (2000) 2055 – 2068 Multiperiod reactor network synthesis William C. Rooney, Lorenz T. Biegler * Department of Chemical Engineering, Carnegie Mellon Uniersity, Pittsburgh, PA 15213, USA Abstract 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. © 2000 Elsevier Science Ltd. All rights reserved. Keywords: Reactor network synthesis; Attainable regions; Multiperiod optimization; Uncertainty; Confidence regions www.elsevier.com/locate/compchemeng 1. Introduction The reactor network is the central part of many, chemical plants. Efficient conversion of raw materials to desired products in the reaction section can greatly impact the process energy use, separation requirements, and overall economics. Although not as well developed as other areas of chemical process design, great progress has been made in the past two decades on developing rigorous methods for synthesizing reactor networks. One technique, superstructure optimization, has been proposed to solve the reactor network synthesis prob- lem. Here, a fixed network of reactors is postulated and an optimal subnetwork is found that optimizes a spe- cified objective function. Recent superstructure opti- mization contributions include the work by Kokossis and Floudas (1990, 1991) and Schweiger and Floudas (1999). While powerful mixed-integer nonlinear pro- gramming (MINLP) formulations and solution tech- niques can handle large superstructures this method can lead to suboptimal solutions since the optimal solution is only as good as the initial superstructure. On the other hand, attainable region (AR) theory has tried to answer the question of what exactly can be produced from a steady state reaction system (with mixing), irrespective of the reactor type. AR theory instead looks at geometric interpretations of the various processes in state space, not equipment functionality. Only after a candidate AR has been found is its boundary interpreted in terms of actual equipment. The AR and its properties have been outlined in a number of articles over the past decade (Glasser, Hildebrandt & Crowe, 1987; Hildebrandt & Glasser, 1990; Feinberg & Hildebrandt, 1997; Feinberg, 2000). AR principles work well for small problems, but beyond three dimensions geometric interpretations become difficult, if not impos- sible to decipher. As a result, Lakshmanan and Biegler (1996) combined AR concepts with superstructure opti- mization to overcome the dimensionality difficulties. In their MINLP model, only forward connectivity between the reactors was assumed, leading to a compact mathe- matical representation. In addition, their method was a constructive approach and did not require an initial superstructure. Lakshmanan and Biegler considered only, plug flow (PFR), continuous stirred tank (CSTR), and differential sidestream reactors (DSR) in their MINLP model. However, their DSR model was restricted to predeter- mined sidestream compositions, such as the process feed. In addition, all of the studies cited above solve the reactor network synthesis problem for known quanti- * Corresponding author. E-mail address: biegler@cmu.edu (L.T. Biegler). 0098-1354/00/$ - see front matter © 2000 Elsevier Science Ltd. All rights reserved. PII: S0098-1354(00)00576-7