Practical infeasibility of cross-transfer in batch plants with complex recipes: S-graph vs MILP methods

Multipurpose batch processes entail various operational policies that have been widely investigated in published literature. In this paper, no-intermediate-storage (NIS), zero-wait (ZW) and common-intermediate-storage (CIS) operational policies are of particular interest. In all these policies, no dedicated storage facility is available between two consecutive units. Unlike the other operational policies, these particular policies bear some subtle practical infeasibility that has gone unnoticed in literature. In essence, this infeasibility has been reported as optimal, thus assumed to be feasible, by various authors using mathematical programming techniques. It pertains to a unit transferring product to one or more units whilst simultaneously receiving feed from another, which is practically infeasible and as such need not be considered as a possible solution. This feature is particularly conspicuous in batch processes with complex recipes wherein production paths can be in opposite directions. This paper presents the unique feature of the S-graph framework to isolate cross-transfer during optimization, whereas the available mathematical programming methods inherently fail neither to detect nor to eliminate this infeasibility. A few examples taken from published literature are presented for demonstration purposes.