Quantification of performance targets is essential to identifying the overall merit of a particular process design or operating chemical plant. In order to determine where improvements can be made in terms of energy efficiency, cost-effectiveness, emissions reduction, and overall process sustainability, one must identify realistic benchmarks to compare to. This work here focuses on identifying performance limits for any system of discretely-fed batch reactors. By evaluation of the best possible performance of a batch reactor network under known physical constraints, a designer or decision maker can quantify exactly how good a job their flowsheet or actual reactor network is doing.

I will describe a method [Davis et al. “Identification of the Attainable Region for Batch Reactor Networks” Ind. Eng. Chem. Res., in press] for automatically identifying the set of all points in concentration space that represent outlet compositions of some network of discretely fed batch reactors for a given reaction set with known kinetics. This so-called batch attainable region (BAR) is dependent on the batch network's feed and total operating time, and it is shown to be quantifiable using the Infinite DimEnsionAl State-space (IDEAS) framework. Because a simple batch reactor model possesses the properties that allow application of the IDEAS framework, we can formulate the resulting IDEAS Infinite Linear Program (ILP) whose solution is guaranteed to identify the globally optimal network of batch reactors. A simple transformation of this IDEAS ILP leads to two algorithms that can be used to construct an approximation to the BAR. The first is a “Shrink-Wrap”-like algorithm which creates increasingly accurate approximations of a set guaranteed to contain the true BAR for all network operating times by eliminating infeasible points in concentration space. The second is a breadth-first algorithm that creates increasingly accurate inner approximations to the BAR for a given network operating time. I have implemented these two algorithms and will outline an example where their output converges to the analytically identified BAR.