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7.3: Untitled Page 146

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  • Chapter 7

    Material Balances for Complex Systems

    Most recent paradigm shifts in the mathematical analysis of physical systems are due to the use of computers. In Chapter 4 we encountered the application of matrices in the formulation of material balance problems, and for small matrices those problems could be solved easily. For large matrices, solutions are difficult to obtain (see Sec. 4.8) and computer‐aided calculations are necessary. In this chapter we consider the transition from simple and small systems to complex and large systems. We begin with some moderately complex processes involving reactors, separators and recycle streams. These systems can be analyzed without the use of computers. In Sec. 7.4 we introduce sequential analysis using iterative methods that require some programming. This sequential analysis forms the basis for process simulators that will be studied in a senior‐level design course; however, it is absolutely essential to understand the details presented in this chapter prior to using process simulators for computer‐aided design.

    In Chapters 4 and 5 we studied multicomponent, multiphase systems without chemical reactions, and in Chapter 6 we learned how to analyze multiple, independent stoichiometric reactions in a general manner. We are now ready to study more complex systems with chemical reactions such as the one shown in Figure 7‐1. Here we have identified several distinct control volumes, and the Figure 7‐1. Reactor and separator with recycle