(586a) A Graph Theoretic Approach to Time Scale Analysis of Energy Integrated Networks

Energy integration, motivated by the high cost of energy and the rapidly diminishing sources of energy, is a rule rather than exception in modern process industries. It involves coupling of energy sources and sinks (via process-to-process heat exchangers), thereby minimizing the net consumption of energy. The design of energy integrated networks has been an area of rich research activity, resulting in configurations such as heat integrated reactors, thermally coupled distillation, multi-effect evaporators, etc. These networks offer significant cost benefits, but are also challenging to operate and control, owing to the strong interactions among the individual units. These interactions give rise to slowly evolving network dynamics, in addition to the dynamics of the individual units, which evolve at a faster rate.

In our previous work [1], we have identified a generic class of energy integrated networks where significant energy flows (arising from energy recycling or of external origin) result in dynamic models with a multi-time scale structure. This class captures structural properties of numerous integrated configurations with single integration loop. In the present work, we analyze the properties of complex networks (with multiple integration loops). We show that these complex networks are, in fact, composed of combinations of two fundamental configurations (networks with large energy recycle and networks with large energy throughput) of the generic class. We also identify that, if a process network is represented as a graph (where nodes represent process units and edges the energy flow between two units) then the two fundamental configurations have topological equivalents ? recycles are equivalent to circuits and trails imply throughputs. Motivated by this equivalence, we use graph theoretical formalisms to reduce a complex process network into these fundamental configurations, and subsequently predict the corresponding time scale properties. The proposed algorithm identifies the trails and circuits (of a particular magnitude) in a process graph, and provides insights about dynamics in each time scale (e.g. dimensionality, available manipulated inputs, etc) in a systematic manner.

The proposed framework presents a simple and effective tool for the analysis of complex networks, without performing rigorous dynamic analysis. The analysis results can aid controller design (input-output pairing, controller hierarchies) for plant-wide control problems. The effectiveness of the proposed framework is demonstrated through an industrially relevant example network.

[1] SS Jogwar, M Baldea and P. Daoutidis. Tight energy integration: Dynamic impact and control advantages. Comput. Chem. Eng. (2010) doi:10.1016/j.compchemeng.2010.02.005 (Article in press).