11 - Multiperiod Blending

Summary

In the problems we have considered so far, we have either ignored the actual material consumption/production (sequential environments) or assumed that materials are consumed/produced at fixed proportions (network environments). There are problems, however, where the proportions in which materials are consumed can vary provided that some specifications are satisfied. This problem, which is termed multiperiod blending or simply blending, is fundamentally different from the ones discussed thus far because it leads to nonlinear models. There are two types of blending problems: (1) different streams/inputs are blended before they are processed/converted (process blending); and (2) streams/inputs are blended to produce final products (product blending). In Section 11.1, we introduce some preliminary concepts and a formal problem statement for product blending. In Section 11.2, we present two alternative formulations for product blending, and in Section 11.3, we present two approximate linear reformulations. We close, in Section 11.4, with a discussion of models for process blending. We focus on the equations necessary to account for the key new features of blending problems: (1) the selection of input materials and their blending in variable proportions, and (2) the requirement to satisfy given property specifications.