This paper shows that most steady state gas-liquid pipe flow pattern representations can be visualized as two directed graphs, one for the macroscopic mass balance and another for the momentum balance. These directed graphs overlap around nodes where hydrodynamic slip is generated.

In order to understand the model structure of complex flow patterns, simple graphs can be reused to compose complex ones. Through this graphical and mathematical composition technique it is possible to find and understand analogies in the meaning of key variables and closures used by the models.

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