TABLE OF CONTENTS Chapter Three presented the material recycle pinch diagram as a graphical tool to identify targets for direct recycle problems. In spite of the usefulness and insights of the graphical methods, it is beneficial to develop an algebraic procedure which is particularly useful in the following cases:
Numerous sources and sinks: As the number of sources and sinks increase, it becomes more convenient to use spreadsheets or algebraic calculations to handle the targeting.
Scaling problems: If there is a significant difference in values of flowrates and/or loads for some of the sources and/or sinks, the graphical representation becomes inaccurate since the larger flows/loads will skew the scale for the other streams.
If the targeting is tied with a broader design task that is handled through algebraic computations, it is desirable to use consistent algebraic tools for all the tasks.
This chapter presents the algebraic analogue to the material recycle pinch diagram.
The problem can be expressed as follows:
Given a process with a number ( N sources) of process sources (e.g., process streams, wastes) that may be considered for possible recycle and replacement of the fresh material and/or reduction of waste discharge. Each source, i, has a given flowrate, W i, and a given composition of a targeted species, y i. Available for service is a fresh (external) resource that can be purchased to supplement the use of process sources in sinks. The sinks are N sinks process units...
