Evaluation of limits on the performance of reactors and reactor networks is crucial to the economic success of any chemical process. Consequently, the analysis and design of reactors and reactor networks has been one of the primary foci of process systems engineering research in the chemical and environmental engineering fields. The advancement of fundamental research in reactor network performance is an important exercise not only for the improvement of science education but also in the continued economic development of environmentally-friendly processes.

One method of identifying these performance limits for networks of batch reactors is through identification of the batch attainable region (BAR). Identifying BAR will provide us with the opportunity to quantify the fundamental limitations that may be imposed on any batch reactor network design by the underlying reaction kinetics, the provided initial conditions or the batch mode of operation itself. To consider the impact on a variety of objectives we will classify these objectives in two categories. First those whose value is uniquely correlated to each point of the BAR, and second those that do not have such a unique value at each point of the BAR. Characterization of the objectives which belong to one or the other category will be the subject of our research. It should be emphasized that the causal nature of the batch reactor network may play a crucial role in determining the category in which a particular objective belongs.

Synthesis of the batch reactor network that realizes some desirable characteristic will also be the subject of our research. Upon completion of the BAR construction, limits on the performance of all batch reactor network designs are established. Creating networks that can realize these performance limits will be the subject of our research. The forward algorithm may naturally construct networks that lead to particular locations in BAR. If however the desired characteristic is not simply a function of the BAR location, then linear programming approaches may be employed to identify a network with desirable characteristics. Even in this case however, identification of the BAR reduces the complexity of the underlying optimization by eliminating candidate network components whose “inlets” and / or “outlets” do not belong to BAR.

Moreno-Andrade et al. describe in their 2006 work a model for the batch treatment of wastewater containing 175 to 625 milligrams per liter of 4-chlorophenol. They used the dissolved oxygen concentration in the reaction vessel as an indicator of the rate of pollution removal by the biomass and used that control variable to optimize the reactor with respect to reaction time. We propose to incorporate this model in to the proposed batch attainable region formulation and to give performance limits on the operation of an optimal network of these batch treatment reactors.