Today modern plants are to a large extent equipped with on-line data acquisition systems, which not only are used for control on the plant level, but which are also used for capacity assessment, planning and scheduling. Given access to such a data acquisition system, one first intrinsically assumes that one knows what is flowing in the pipes at all times, but if one looks a little more carefully, one though finds that by far not all streams are connected to the data-acquisition system. In the case of a well-equipped refinery or a gas plant, for example, one finds that really only about half of the main streams are equipped with measurements. If one wants to profile the plant in terms of energy and mass, one thus faces the problem of first computing those streams that can be computed with the given information. If for a given stream this is not the case, one has to reduce the granularity of the plant description by locally extending the system boundary until one meets the basic algebraic conditions for solving the balance equations. Thus, whilst there is often a flood of information available in the time domain, information is rather limited in space – meaning number and location of measurements in the plant. Graphs, where the nodes represent primitive capacities connected by arcs depicting mass and energy flows, are a powerful tool for representing any plant. Such networks can be constructed on any level of detail where “level” is often characterised by the term granularity of the model. The level of granularity can be adjusted by, on one hand refining a node into a sub-graph or sub-network or, on the other hand, by coalescing adjacent parts of the plant, thus forming larger system agglomerations within the given plant representation. The later is a model reduction method.

For calculating the streams one closes the steady-state balances of mass, component mass and energy for each node (capacity). The respective balances require increasing amounts of information: for mass one only requires the total mass flows, for the component mass one requires in addition concentration information and for the energy the respective properties must be known as well as the heat and mechanical work flows. The graph thus can also be interpreted as a network of equations and known and unknown variables. With the nodes being described by the respective conservation equations, the coalescing of nodes is based on the linearity of the balances, thus on the Euler-one property of the conserved quantities.

The paper describes the method for finding the reduced model resulting in three different kind of subsystems: (i) well defined ones, where the missing streams can be calculated (ii) over-determined nodes, where one has too much information and which either are intrinsically dynamic element, such as tanks or one has to use data re-conciliation (iii) domains where one can not close the balances, one of the common reasons being that this section includes infinite capacities as they are used to model sources systems and sink systems.

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