Graphical addition of streams

Since the triangle used in Fig. 7.3-3 is neither equilateral nor isosceles, it follows that graphical addition of streams and the line satio principle are independent of the shape of the triangle. 

The problem specifications will enable points F, Cj, and LiVa )t located in Fig. 7.3>8. Equations (7.3-IS) and (7.3-16) show that Aj lies at the intersection of the extended lines L Gz and AgF, in accordance with the graphical addition of streams principle. It is clear that whether A2 lies above or below the triangle merely depends on the relative positions of points Lz, Gz, F, and Ag. Thus, when A lies above the diagram, Eq. (7.3-16) (together with Eq. (7.3-15)] shows that Ag — F — - A2. If or f.2 contains no A or B the corresponding point coincides with apex C. 

As an illustration of a class of problems in mass integration, let us consider the direct recycle problem. The objective of this problem is to determine the optimal allocation of sources to sinks without the addition of new equipment. Each source is characterized by a flowrate and composition. For each sink there are constraints on the acceptable feed, which are given in terms of lower and upper bounds on flowrate and composition. One approach to solving this problem is through the use of the material recovery/recycle pinch diagram developed by El-Halwagi et al. [14]. Fig. 4.3 is a representation of this graphical tool. First, flowrate and composition data are collected for all the recyclable streams (referred to as sources) and units (referred to as sinks) that can accept the recycle to reduce the consumption of the fresh resources. The flowrate and composition of impurities are used to calculate the load of impurities in each source as follows ... 

Stream at two dams. In addition, samples of unmarked fish were collected from the river in a study to see whether the sample consisted of distinguishable groups of fish. The fish were returned to the laboratory, and the levels of and Zn were measured. A graphic model of the data was developed. Commenting on the model, the authors stated ... 

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