Gibbs free energy minimisation

According to the principle of Gibbs free energy minimisation the determination of the equilibrium compositions implies obtaining a set of n, values which lead to a minimal value of G/RT in Equation (4.16). Here, , must be a non-negative number. 

Gibbs free energy minimisation. This model does not need the specification of stoichiometry, but only of the species taking part in reactions. Reliable algorithms are available due to the works of W. Seider and co-workers (1979-1981). 

A second possibility to calculate the equilibrium composition is by Gibbs free energy minimisation. The starting point is the system of equations generated by the relation (8.36). Phase equilibrium may be included in analysis. This method is particularly powerful, because it does not imply necessarily the knowledge of the stoichiometry. However, the user should consider only species representative for equilibrium. As in any optimisation technique, this approach might find local optimum. Specifying explicitly the equilibrium reactions is safer. 

A CVD phase diagram provides important information about the equilibrium compositions of the solid phases present under given conditions of pressure, temperature and input concentration. It is usually constructed either by the equilibrium constant method or the minimisation of Gibbs free energy method. The detailed principles are discussed below. 

Modem simulators can calculate the equilibrium of complex reactions by the minimisation of Gibbs free energy of the reaction mixture. Here we present results obtained with the module RGlbbs of Aspen Plus. An appropriate thermodynamic model is a cubic equation of state, as Peng-Robinson. 

A simplified method to find the conversions in the two reactions is available as will be shown below, but a general method which can solve any ehemieal equilibrium problem is preferred. For this purpose two methods may be used. The first is minimisation of the Gibbs free energy [316], whereas the other one is the solution for conversions [468]. The first one may be attractive from a theoretical point of view and it is readily combined with phase equilibrimn, but the last one is preferred in catalysis, since no combination of reactions may proceed in all cases. The set of equations in Table 1.2 may be solved using the Newton-Raphson method with the conversions as independent variables. Some of the components (higher hydrocabons or oxygen) may almost disappear in the final mixture so it is necessary to handle elimination of reactions with almost complete conversion. 

The characteristic reactions of the black liquor burning, except the ones involved in the particulate formation, are described by a technique based on the minimisation of Gibbs free energy. For this purpose, the KPP furnace has been divided in four regions (Figure 1). In each region, different stages of the process are described ... 

The Gibbs free energies of regions 1 and 2 were minimised and the corresponding results are presented in Tables 1 and 2. In this test, different values of T1 and the mean temperature supplied by KPP for region 2 (T2 = 1080°C) were adopted. 

In another test, the Gibbs free energies of regions 1, 2 and 3 were minimised... 

However, small modifications in Ti or T3 affect significantly the calculated concentration of TRS gases. This behaviour is due to the precision of the optimisation problem resolution, since TRS gases are present in a very small amount (ppm) compared to other chemical species. Thus, the minimisation of the Gibbs free energy technique is not robust enough to predict the TRS gases emission. 

A methodology based on the minimisation of Gibbs free energy has been successfully adopted to describe the chemical composition of an industrial black liquor recovery boiler smelt. Moreover, the chemical composition reported in the literature from other industrial sources could also be satisfactorily reproduced using this technique. 

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