Modeling technique in the P-Graph framework for operating units with flexible input ratios

The P-Graph framework is an efficient tool that deals with the solution of Process Network Synthesis (PNS) problems. The model uses a bipartite graph of material and operating unit nodes, with arcs representing material flow. The framework includes combinatorial algorithms to identify solution structures, and an underlying linear model to be solved by the Accelerated Branch and Bound algorithmic method. An operating unit node in a P-Graph consumes its input materials and produces its products in a fixed ratio of operation volume. This makes it inadequate in modeling such real-world operations where input composition may vary, and may also be subject to specific constraints. Recent works address such cases by directly manipulating the generated mathematical model with linear programming constraints. In this work, a new general method is introduced which allows the modeling of operations with flexible input ratios and linear constraints in general, solely by tools provided by the P-Graph framework itself. This includes representing the operation with ordinary nodes and setting up their properties correctly. We also investigate how our method affects the solution structures for the PNS problem which is crucial for the performance of algorithms in the framework. The method is demonstrated in a case study where sustainable energy generation for a plant is present, and the different types of available biomass introduce a high level of flexibility, while consumption limitations may still apply.