Balancing Flowsheet - Graph Representation

In the plant documentation we can usually meet with process and instrumentation (P I) diagrams which contain the process equipment and the instrumentation and control loops. P I diagrams are usually too much detailed for balancing purposes. We can simplify them by deleting control loops and a part of instrumentation which is not needed for balancing purposes. Very often the flowsheet can be further simplified by ignoring of some parts of equipment or by merging some pieces into one equipment. 

For example, in the case of mass balance, pumps can be neglected because they have only one input and one output and their mass balance is a trivial one. Even in the case of enthalpy balance, pumps are often neglected as the shaft work exerted on the pump is often negligible in comparison with the enthalpy changes of streams. Similarly, if only the multicomponent balance is set up around a distillation column, the column proper is usually merged with the condenser, boiler, or other supporting equipment. 

The resulting flowsheet whose complexness is just sufficient for the purpose of the balance is finally redrawn in the graph form. The graph representation of the flowsheet for the single-component balance shown in Fig. 2-1 is in Fig. 2-5. The graph consists of nodes (circles) and streams (arrows). Every stream is incident either with two nodes or with one node and the environment (which can te viewed also as one of the nodes). 

By comparing Figs. 2-1 and 2-5, we can see that the new stream (13) occurred in Fig. 2-5. This stream represents the artificial (fictitious) stream - the accumulation of mass in the tank (2). We will meet with artificial streams more in the next parts of the book. 

Reactors are nodes where chemical transformation occurs. To maintain the conservation law, the fictitious streams representing sources or sinks of reacting components going to or from the environment can be defined. It is also possible to eliminate the fictitious streams by an algebraic procedure expounded in Chapter 4. 

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