Determining the limits of performance on a process network is important in process synthesis. Within reactor network synthesis, these limits can be quantified by the system's attainable region (AR). The AR can be defined as the set of all possible points in concentration space that are attainable through reaction and mixing from a given feed point. Our group has already adapted the Infinite DimEnsionAl State-space (IDEAS) framework for reactor network design and AR construction [1], and also using the IDEAS framework, we have established a number of properties that the outlets of feasible reactor networks must possess, putting forward necessary and sufficient conditions for a point in concentration space to belong to the attainable region [2]. These properties were subsequently employed in developing the so-called Shrink–Wrap algorithm [2], which can be used to approximate arbitrarily closely the true AR.

The success of the algorithms that we have developed for AR construction has been demonstrated for applications with a single network inlet [1,2]. In an industrial setting, seldom does the feed to the network consist of a single stream. Our group has done preliminary work in solving the two-feed AR problem using the IDEAS ILP formulation [3]. In this work, we extend our Shrink-Wrap algorithm to allow for the construction of the multi-feed attainable region, by further study of the properties of the IDEAS feasible region for multiple-feed reactor networks. Each distinct additional feed to the network results in the increment of the dimension of the “condition” (intensive stream properties and appropriately defined design parameters) space of the IDEAS process operator, and this brings along additional computational memory requirements. On the other hand, any existing linear dependence among participating reaction rates may be used for reduction of the dimensionality of the “condition” space and therefore of the attainable region. We demonstrate its use on the construction of a two-feed attainable region for methane steam reforming, in order to determine maximum feasible hydrogen production with minimum carbon monoxide generation when the feed consists of two separate streams, for example pure methane and pure steam. We identify the minimum dimension of the space in which the two-feed attainable region for this reaction system, represented by the reactions below, can be constructed:

CH4 + H2O = CO + 3H2

CO + H2O = CO2 + H2

CH4 + 2H2O = CO2 + 4H2

[1] Burri J.F., Wilson S.D., Manousiouthakis V.I. Comput. Chem. Eng. 26, 849 (2002).

[2] Manousiouthakis V.I., Justanieah A.M., Taylor L.A. Comput. Chem. Eng. 28, 1563 (2004).

[3] Burri J.F., Ph.D. Dissertation, UCLA (2004).