Chapter 15 – An Optimization Approach to Direct Recycle

Publisher Summary This chapter provides an optimization-based formulation for the mathematical solution of the direct-recycle problem. Graphical tools may become cumbersome for problems with numerous sources or sinks and for problems with a wide range of flow rate or load scale. Additionally, algebraic techniques cannot easily handle problems with multiple fresh resources. Therefore, it is beneficial to develop a mathematical-programming approach to the targeting of material recycle. Such an approach can also be integrated with other optimization techniques. The first step in the analysis is to represent the problem through a source–sink representation. Each source is split into fractions of unknown flow rates that are allocated to the various sinks. An additional sink is placed to account for unrecycled/unreused material. This sink is referred to as the “waste” sink. The fresh sources are also allowed to split and are allocated to the sinks. The foregoing formulation is a linear program that can be solved globally to identify the minimum cost or flow rate of the fresh streams, an optimum assignment of process sources to sinks, and the discharged waste. The results are consistent with those obtained graphically using the material recycle pinch diagram.

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