(214b) A Graph Theoretic Approach for Model Reduction and Control of Complex Energy Integrated Process Networks

Complex process networks, consisting of interconnections of numerous reaction-separation units via material recycle and energy integration, represent a key feature of modern chemical plants. The design of such complex networks, motivated by process limitations (such as reaction kinetics/thermodynamics) and economic benefits (reduced material and/or energy consumption), has received significant attention over the past few years. These complex process networks, however, are quite difficult to operate, especially in the context of transitions between different operating points which are fairly common in the current environment of frequent changes in market conditions and economic objectives.  Specifically, a disturbance in one process unit is often propagated over a large portion of the network owing to the coupling between various process units. Though a system specific analysis can prove beneficial for a particular case, a generic network level analysis allows for the identification of characteristic features exhibited by a class of complex networks, thus broadening the range of applicability of the established results.

In our previous research, we have identified several such fundamental structures, such as networks with large material recycle, networks with large energy recycle, networks with large energy throughput, which capture essential features of some of the relatively simpler integrated process networks (for example, reactor-distillation column systems with low per pass conversion, reactor-feed effluent heat exchanger networks, energy integrated distillation columns, etc). Each of these fundamental structures exhibits unique dynamic features and allows for the reduction (in terms of size and complexity) of the underlying process model.

In the case of complex process networks, the need for model reduction becomes more imperative, and at the same time, more challenging to execute. A preliminary analysis of some of the complex networks [1] has revealed that their underlying structure is composed of combinations of one or more fundamental structures (or building blocks) identified previously. However, the interconnection of (a large number of) these building blocks can result in interactions and dynamic phenomena being exhibited by these networks that are more intricate than can be anticipated by considering the mere association of these building blocks.

Graph theory provides a powerful framework to analyze the structural properties of such complex networks, responsible for their ensemble behavior. The modular structure of these complex networks lends themselves naturally to a graph theoretic analysis, whereby in addition to identifying the fundamental structures, one can achieve the reduction of the overall network through successive application of such identification steps.

In this work, we focus on complex energy integrated process networks characterized by a segregation of the energy flows in the network. This is typical in many industrial systems such as networks of integrated distillation columns, cryogenic systems, etc. We have developed a suite of algorithms within a graph-theoretic framework for identifying the time scales exhibited by the network, generating scaled dynamic equations in each time scale and classifying different control objectives and manipulated inputs to be used in the controllers in each time scale. Specifically, a complex network is represented as an energy flow graph with nodes corresponding to the process units and edges corresponding to the energy flows connecting different units. Equivalent representations of the fundamental structures are identified (for example, recycle being represented by a cycle or throughput being represented by a path) and several cycle finding and graph re-writing algorithms are implemented on the energy flow graph to arrive at equivalent (induced subgraph) representations of the original complex network in each time scale. The nodes in each of these subgraphs represent the units evolving in that time scale. Application of graph traversing algorithms (e.g. depth-first search, breadth-first search) provides scaled equations for the underlying dynamic equations as well as the corresponding reduced order models (if any) in each time scale. Furthermore, it also allows for the classification of the various control objectives to be pursued in each time scale and provides a pool of manipulated inputs to be considered for the same. This framework is generic and parallels the mathematically rigorous model reduction using singular perturbations.

The proposed framework presents an efficient tool for the analysis of complex networks, without performing a rigorous dynamic analysis. The analysis results can aid controller design (input-output pairing, controller hierarchies) for plant-wide control problems. The advantages of the proposed framework are illustrated via application to an integrated naphtha reforming example which utilizes a network of process-to-process heat exchangers to recover energy from the hot reformer exit stream and recycle it back to preheat the cold feed, resulting in multiple interconnected energy recycle loops.

[1] S.S. Jogwar and P. Daoutidis. Energy flow patterns and control implications for integrated distillation networks. Ind. Eng. Chem. Res., 49:8048 – 8061, 2010.