Minimization, Gibbs free energy

Typically, solving (5.151) to find fc(oo ) is not the best approach. For example, in combusting systems Srp(0 4)1 < 1 so that convergence to the equilibrium state will be very slow. Thus, equilibrium thermodynamic methods based on Gibbs free-energy minimization are preferable for most applications. 

Thermodynamic calculations presented here are based on Gibbs free energy minimization and were carried out using HSC Chemistry. The equilibrium amount of each species that is formed is normalized on the basis of one mole of n-Ci6, a model compound for diesel fuel, fed to the reactor. Carbon formation is a function of both the S/C ratio and reforming temperature. Figure 17 shows the minimum amount of S/C ratio thermodynamically required for carbon-free SR of n-Ci6 at a given temperature. Carbon-free operation of n-Cig is thermodynamically possible above the curve. Higher temperatures and S/C ratios inhibit carbon formation. 

Thermodynamic software packages may be used to find equilibrium compositions at prescribed temperatures and pressures. Such calculations require knowledge of feed components and products and their thermodynamic properties and are based on Gibbs free energy minimization techniques. Examples of thermodynamic packages may be found in Smith and Missen (Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982) and in Walas (Phase Equilibria in Chemical Engineering, Butterworths, 1985). 

In one approach, T is assumed and Gibbs free energy minimized to give compositions. Then T is adjusted to satisfy the specification e.g., H or S. Naphtali (10) suggests this procedure, but does not present an algorithm for adjusting T. 

Gibbs free-energy minimization offers an elegant computational manner without the need to specify the stoichiometry. In addition, phase equilibrium is accounted for. Since occasionally the method fails, considering explicit reactions is safer. 

The study of chemical equilibrium can detect thermodynamic constraints on the achievable conversion and selectivity. In this section we make use of the Gibbs free-energy minimization method available in Aspen Plus [9], We assume that both cyclohexanone and cyclohexanol are products. The curves in Figure 5.2 show the evolution of the phenol equilibrium conversion, yield and selectivity with the ratio hydrogen/phenol at temperatures of 180, 200, 220 °C and a pressure of 3 bar. 

Inside the reactive zone, chemical and phase equilibrium occur simultaneously. The composition of phases can be found by Gibbs free-energy minimization. The UNIQUAC model is adopted for phase equilibrium, for which interaction parameters are available, except the binary fatty-ester/water handled by UNIFAC-Dortmund. 

In this way, the routine Gibbs free energy minimization program can still be used, but thermodynamic data of ordinary graphite should be substituted by thermodynamic data of activated graphite, as listed in Table 1 for the carbon-hydrogen system. The derivation of these data cem be found in our previous papers and books [13-19], and will not be repeated here again. 

Generalized Method of the Gibbs Free Energy Minimization. 

The calculations described in the earlier section gave the incipient point only. At the incipient point, the amount of hydrate formed is infinitesimally small. At conditions that depart from the incipient pressure and temperature, it is possible to estimate the phase fractions (or amounts) of hydrates that have formed. The pioneering work in this field was that of Bishnoi et al., in which solid phases of structure I and II gas hydrates were included in multiphase flash calculations. The multiphase equilibrium calculations are based on a Gibbs free energy minimization methodology... 

RGibbs - rigorous equilibrium and/or multiphase Gibbs free energy minimization RCSTR - continuous stirred-tank reactor, specify volume... 

A complete description of any groundwater system necessitates consideration of reactions between rock forming minerals and the aqueous phase. This cannot be achieved without accurate thermodynamic properties of both the participating aluminosilicate minerals and aqueous aluminum species. Most computer codes used to calculate the distribution of species in the aqueous phase utilize the "reaction constant" approach as opposed to the "Gibbs free energy minimization" approach (3). In the former, aluminosilicate dissolution constants are usually written in terms of the aqueous aluminum species, Al, which is related to other aqueous aluminum species by appropriate dissociation reactions. 

Gibbs free energy minimization provides a practical basis for investigating the fate and removal of alkali species and sour gas components from biomass gasification product gas as a function of temperature and composition of inlet streams. The methane content of the product gas - a result of non-equilibrium conversion - is accounted for in the procedure by setting as inert compounds the corresponding fractions of carbon and hydrogen in the biomass feedstock [42],... 

Example 4.4 Determination of equilibrium conversions of the methanol synthesis reaction by Gibbs free energy minimization... 

The thermodynamic equilibrium compositions can be determined by using an algorithm based on Gibbs free energy minimization, only taking into account the chemical species, that is, reactants and products. Results obtained with a water/ethanol inlet molar ratio of 3, corresponding to the stoichiometry of reaction (24.4), are shown m Figure 24.1. Except carbon, all compounds present in Eqs (24.3)-(24.13) are Included m the thermodynamic calculations. 

In other words, the system Gibbs free energy is optimized in the equilibrium state. 1 leave for the reader to prove that, as a matter of fact, the Gibbs free energy is minimized in the equilibrium. This last result is a consequence of the second law of thermodynamics, which states that the Gibbs free energy minimizes in the equilibrium for systems held at constant pressure and temperature (Planck 1945). 

Tang H, Kitagawa K. 2005. Supercritical water gasification of biomass Thermodynamic analysis with direct Gibbs free energy minimization. Chem Eng J 106 261—267. 

Stoichiometric method Gibbs free energy minimization method... 

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