Hierarchical balancing system

The requirement of hierarchicity means that complex balances (of large plants or companies) should be based on lower level balance data sets. Essential is, that the data enter just once and are further easily merged on higher levels and processed by the balance system in the "upward" direction (see Fig. 13-4). 

The previous chapters have concentrated on analyzing the material-balance dynamics of several classes of integrated process systems. We demonstrated that the dynamic behavior of the systems considered exhibits several time scales and described a method for the derivation of reduced-order models describing the dynamics in each time scale. Also, a hierarchical controller design framework was introduced, with distributed control of the fast dynamics and supervisory control of the dynamics at the systems level. 

Chaotic behavior and synchronization in heterogeneous catalysis are closely related. Partial synchronization can lead to a complex time series, generated by superposition of several periodic oscillators, and can in some cases result in deterministically chaotic behavior. In addition to the fact that macroscopically observable oscillations exist (which demonstrates that synchronization occurs in these systems), a number of experiments show the influence of a synchronizing force on all the hierarchical levels mentioned earlier. Sheintuch (294) analyzed on a general level the problem of communication between two cells. He concluded that if the gas-phase concentration is the autocatalytic variable, then synchronization is attained in all cases. However, if the gas-phase concentration were the nonautocatalytic variable, then this would lead to symmetry breaking and the formation of spatial structures. When surface variables are the model variables, the existence of synchrony is dependent upon the size scale. Only two-variable models were analyzed, and no such strict analysis has been provided for models with two or more surface concentrations, mass balances, or heat balances. There are, however, several studies that focused on a certain system and a certain synchronization mechanism. 

The hierarchical patch dynamic paradigm (HPDP) meets the above requirements (Wu and Loucks 1995, Wu and David 2002). It is a model for describing at a fundamental level the interactions and dynamics of ecological systems at landscape and regional scales. The HPDP inherently incorporates and predicts a variety of temporal and spatial scales, heterogeneity, and a wide range of dynamics. The basic tenets of HPDP are listed in Table 2.1. This framework is an alternative to models of ecological systems that incorporate a balance of nature, inherent stability, or multiple equilibriums. 

The chemical reactor has a determinant role on both the material balance and the structure of the whole flowsheet. It is important to stress that the downstream levels in the Hierarchical Approach, as the separation system and heat integration, depend entirely on the composition of the reactor exit stream. However, a comprehensive kinetic model of the reaction network is hardly available at an early conceptual stage. To overcome this shortcoming, in a first attempt we may neglect the interaction between the reactor and the rest of the process, and use an analysis based on stoichiometry. A reliable quantitative relationship between the input and the output molar flow rates of components would be sufficient. This information is usually available from laboratory studies on chemistry. Kinetics requires much more effort, which may be justified only after proving that the process is feasible. Note that the detailed description of stoichiometry, taking into account the formation of sub-products and impurities is not a trivial task. The effort is necessary, because otherwise the separation system will be largely underestimated. 

The key result of the Hierarchical Approach is the development of the basic flowsheet structure, formed by Reactor-Separations-Recycles. This structure defines the material balance envelope. In this respect of highest importance is the behaviour of the reaction system, which should deliver a realistic image of the reaction mixture. Other constraints regarding the reactor operation, as molar ratio of reactants, or safety requirements, are determinant for the structure of recycles. Optimal conversion represents a complex optimisation problem between the valorisation of raw materials and the cost of reactor, separators and recycles. 

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