We developed a framework for studying dynamics, distributed control, and optimization of complex networks. Our approach allows us to model complex process systems in a modular manner and in particular explore the interconnection structure of these systems. These ideas are applied to different types of process systems such as chemical process plants, supply chains, oil and gas pipeline networks and even reaction mechanisms and metabolic reaction networks. Properties for stability and optimality of the regarded process systems in connection with decentralized controllers can be derived using non-equilibrium thermodynamics and passivity theory.
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A chemical plant as a process network: Process units such as reactors, mixers, distillation columns are coupled through physical flows and lead to nonlinear and complex system dynamics. By generalizing the unit operations into an interconnected process system, we derive properties for stability and optimality of these process networks. We then design an interconnected controller network which we call the IT system and connect it through an interface layer to the physical system to guarantee for stability and optimality for changing operating conditions. |
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Our framework is based on methods from electrical circuit theory and network thermodynamics. We use graphical representations of the networks we analyse and derive a matrix representation which allows us to formulate and prove stability and optimality. A key component of our framework is the definition of the entropy as a storage function. Defining a storage function, we can use passivity theory to investigate input-output properties of the process system and thereby stability.
Being able to formulate the entire process network in a thermodynamical context, we can derive the optimization problem that a given network solves including its complex interconnection structure. The objective function of the network's optimization problem is closely related to the concept of minimum entropy production from irreversible thermodynamics established by Prigogine (Nobel Prize Chemistry, 1977). The basic thinking can be summarized as networks choosing to evolve along a path and into a state in which the entropy dissipation is minimized and therefore the entropy is maximized. An extension of Tellegen's theorem (electrical circuit theory) as a topological property in combination with variational calculus assists us in deriving these optimality results.
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Methodology and framework for stabilization and optimization through decentralized control:
Top left: Definition of interconnection structure through graph representational system. Top right: Derivation of an algebraic topology representation. Bottom right: Formulation of the optimization problem based on the principle of minimum entropy production. Bottom left: Decentralized control with communicating controllers derived from the optimization problem and its adaptation to problem specific constraints and control objectives. |
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We currently apply the developed theory to an oil production optimization problem of an offshore oil platform on a tactical planning horizon (hours to weeks) in the North Sea. We collaborate in a joint research project with our Norwegian partners at the "Center of Integrated Operations in the Petroleum Industry" (IO-Center) at NTNU.
Due to the complex multi-phase flow behavior of water, gas and oil in subsea oil reservoirs and wells, the state of the art for offshore oil production optimization still relies considerably on heuristics. Individual clusters in the pipeline network of the oil platform are optimized but the assignment of cluster capacities which defines the coupling between clusters is still based on past experience and intuition of the platform operators.
In our work, we intend to develop a more systematic way of optimizing offshore oil production. Currently, different strategies are developed by our partners at the IO-Center consisting of piecewise linearization of the multiphase flow and subsequent solution of an MILP problem using Lagrangean decomposition.
Our framework will help identifying the underlying thermodynamic properties of the pipeline flow in the network and
in particular identify the topological structure and its implications for the optimization problem. This can be used to design a decentralized multi-agent controller systems (MAS) for the offshore platform.
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| 3D-computermodel and schematic network structure of the offshore platform Troll C in the North Sea. |
| Contact person: Michael Wartmann, Erik Ydstie |
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