A simple algorithmic method and decision tree have been developed that provide insight into the optimal operation of a chemical plant with excess capacity consisting of a perfectly mixed reactor, separation system, and recycle stream. This methodology has large industrial applications for it is applicable to any process chemistry of reversible or irreversible reactions of equal or unequal reaction order.

Current research in the field of plantwide design and operation addresses issues such as the choice of a process configuration, appropriate equipment sizing, capacity-based operation of an already built chemical plant, appropriate control structure (design) for available control degrees of freedom, and controller selection. For a given plant and operating policy one must choose an appropriate control system configuration: a centralized control structure, with perhaps optimal set-point regulation or a decentralized, perhaps self-optimizing one. Several authors have investigated the case of a plant with a reactor, separation system, and recycle stream for the reaction A→B, which has no selectivity issues. Operating policies suggested to handle production rate changes for that reaction include maintaining constant recycle loop flow rates (Luyben 1994), operating the reactor at maximum holdup (Larson & Skogestad, 2000; Larson et al., 2003), or allowing both the reactor holdup and recycle flows to vary (Wu & Yu, 1996; Wu et al., 2003). A more recent and general approach to this problem considers different classes of irreversible process chemistries, using recycle flow rates as design variables and allowing reactor holdup to vary (Ward et. al, 2004). It is found, depending on the specific underlying chemistry, that the plant should be operated either on the reactor volume constraint (bounded chemistry) or with a variable reactor holdup (non-bounded chemistry) subject to production rate changes and system disturbances.

Ward et al. (Ward et. al, 2004) and Griffin et al. (Griffin et. al, 2006) developed a classification procedure for irreversible process chemistries with one or more undesired reactions where all reactions have the same overall reaction order. This paper presents a new classification scheme for process chemistries with reactions of equal or unequal overall reaction order. In the new classification system, the overall reaction order of each reaction and the reaction order of individual reactant species must be inspected and compared in order to classify the process chemistry. The following inequality is an example of how to classify an undesired reaction for the case in which the main reaction has higher overall reaction order than the undesired reaction in question.

ν ₁^T- ν _j^T > ∑ (α _i- α _ij) Side Reaction j is Bounded w. r. t. Main Reaction

Summation ∑ is from i=1 to k

(ν ₁^T - Overall reaction order of desired reaction; ν _j^T - Overall reaction order of j^th undesired reaction; α _i - Reaction order of species i in desired reaction; α _ij - Reaction order of species i in j^th undesired reaction; k total number of reactant species)

Thus, if the difference in overall reaction order is larger than the difference in individual reaction orders summed over all reactant species for a given undesired reaction, then that undesired reaction is classified as bounded with respect to the main reaction. This means that increasing reactor holdup (and reactant conversion) will lower the overall operating costs (selectivity losses and separation costs) associated with the undesired reaction in question. Therefore, if there is only one undesired reaction and it is classified as bounded the reactor should be operated at its maximum volume constraint to maximize conversion and minimize operating costs.

Similar inequalities have been developed for cases where the main reaction has equal or lower overall order than an undesired reaction. Using these inequalities, each side reaction is classified as either bounded or non-bounded and then a decision tree is used to classify the overall process chemistry. This new classification procedure is valid for any process chemistry consisting of irreversible reactions with elementary kinetics. When reaction reversibility is introduced the optimal operating policy can change depending on which reaction(s) is/are reversible. Summarizing, simple inequalities are available that are evaluated for each side reaction of a process chemistry; based on these evaluations, insight into the economic optimal operation of a plant can be determined.

Griffin, D. W., J. D. Ward, M. F. Doherty, and D. A. Mellichamp, “A Relook at Optimal Operating Policies and Concepts of Bounded and Non-Bounded Chemistries,” Submitted to Ind. Eng. Chem. Res., (December 2005).

Larsson, T., M. S. Govatsmark, S. Skogestad and C.-C. Yu, “Control Structure Selection for Reactor, Separator and Recycle Processes,” Ind. Eng. Chem. Res., 42, 1225 (2003).

Larsson, T. and S. Skogestad. “Plantwide Control---A Review and a New Design Procedure,” Model Ident. Control, 21, 209 (2000).

Luyben, W. L., “Snowball Effects in Reactor/Separator Processes with Recycle,” Ind. Eng. Chem. Res., 33, 299 (1994).

Ward, J. D., D. A. Mellichamp and M. F. Doherty. “The Importance of Process Chemistry in Selecting the Operating Policy for Plants with Recycle,” Ind. Eng. Chem. Res., 43, 3957 (2004).

Wu, K.-L. and C.-C. Yu, “Reactor/Separator Processes with Recycle---1. Candidate Control Structures for Operability,” Comput. Chem. Eng., 20, 1291 (1996).

Wu, K.-L. C.-C. Yu, W. L. Luyben, and S. Skogestad, “Reactor/Separator Processes with Recycle---2. Design for Composition Control,” Comput. Chem. Eng., 27, 401 (2003).