T Wallek

Constraints of Compound Systems: Prerequisites for Thermodynamic Modeling Based on Shannon Entropy

Thermodynamic modeling of extensive systems usually implicitly assumes the additivity of entropy. Furthermore, if this modeling is based on the concept of Shannon entropy, additivity of the latter function must also be guaranteed. In this case, the constituents of a thermodynamic system are treated as subsystems of a compound system, and the Shannon entropy of the compound system must be subjected to constrained maximization. The scope of this paper is to clarify prerequisites for applying the concept of Shannon entropy and the maximum entropy principle to thermodynamic modeling of extensive systems. This is accomplished by investigating how the constraints of the compound system have to depend on mean values of the subsystems in order to ensure additivity. Two examples illustrate the basic ideas behind this approach, comprising the ideal gas model and condensed phase lattice systems as limiting cases of fluid phases. The paper is the first step towards developing a new approach for modeling interacting systems using the concept of Shannon entropy.

Customized detailing of plant simulations with regard to different applications

Abstract This paper emphasizes the use of graphs for model analysis and simplification within industrial flowsheet simulators. A procedure for developing a complexity measure for models based on weighted cycles and paths in attributed graphs is highlighted. This procedure uses an interface to the process simulator for graph generation. The novel complexity measure serves as the basis for a model reduction approach using attributed graphs and is applied to the real industrial example of an ethylene plant model.

Model-based real-time prediction of corrosion in heat exchangers

Abstract In the chemical and process industry a variety of thermal unit operations is applied in which gases or vapor mixtures must be cooled down to temperatures near the water dew point. Such mixtures often contain substances which tend to evolve corrosive characteristics in case the temperature unintentionally falls below the water dew point. In that particular case, depending on the gas composition, acids can be produced and may cause severe damage to heat exchangers. This kind of corrosion is called ‘pitting’ and may remain undetected for a long time, finally leading to a sudden failure of the equipment. One possible strategy to avoid ‘pitting’ is to use corrosion inhibitors, however, such inhibitors imply a significant increase of costs and are also difficult to dispense under varying process conditions. Consequently, most processes operate with a thermal safety distance to the water dew point in terms of pressure and temperature. A considerable drawback of this approach is that the capacity of the heat exchanging equipment is not fully utilized. To overcome such limitations, this paper suggests a process prediction method for the real-time estimation of the lowest possible heat exchanger surface temperature in view of fully utilizing the optimization potential of the process. The key features of the new approach comprise (i) application of rigorous thermodynamics, considering all relevant facility components that are needed for a complete mass and energy balance, and (ii) a rigorous heat exchanger calculation providing surface temperatures and dead zone temperatures for the current thermodynamic state. The thermodynamic calculation provides the theoretical water dew point as a function of the process parameters. Considering that sensitive variables such as the composition of the multicomponent process stream have a significant influence on the water dew point, the accurate thermodynamic description of the complete system poses one challenge of the method. The customized CFD simulation which is integrated into the simulation model provides the complete spatial distribution of the heat exchanger surface temperatures and dead zone temperatures. Both components are combined to a process prediction model, where an interface between the process prediction model and the process control system (PCS) is used for real-time transmission of the current process parameters to the model, and of recommended process parameters generated by the model back to the PCS. These recommendations can either be used as guidelines for the operator or directly be implemented as PCS command variables in view of an automated optimal operation mode. The proposed methodology couples rigorous thermodynamics with CFD simulation into a novel process prediction model which enhances the overall availability of the process significantly, ensures the definite prevention of ‘pitting’ and increases the efficiency of the process by at least one percentage point.