Gibbs energy direct minimization

Complex Clieinical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

Gibbs energy minimization has also predicted negative isobaric expansion coefficients for certain crystalline zeolite framework structures, which subsequently were confirmed experimentally [6], Many solids show negative thermal expansion at very low temperatures, including even some alkali halides (Barron and White (Further reading)). Many other solids on heating expand in some directions and contract in others. 

In a recent paper Shapiro Shapley [4] have considered the problem of the uniqueness of equilibrium of systems of reactions in several phases in great detail. The computation of equilibrium compositions by direct minimization of the Gibbs free energy function has proved a valuable tool in the discussion of very complex systems and it is important to show that this minimum is unique and achieved under the same conditions that satisfy the mass action laws. This is what Shapiro Shapley have done Sellers has suggested some improvements [5]. 

To compute the concentrations of the species in equilibrium, a Newton-Raphson algorithm is applied to the direct minimization of Gibbs Free Energy. Lagrange multipliers are used to incorporate the restrictions of the problem. Its implementation is adapted to problems with high dynamic minerals appearance/disappearance as in the case presented in next section. 

Direct minimization of Gibbs free energy in muitiphase fiash... 

Pan, H and A. Firoozabadi Complex Multiphase Equilibrium Calculations by Direct Minimization of Gibbs Free Energy Using Simulated Annealing, SPE Res. Eval. and Engl., p. 36, Feb. 1998. 

Wax and asphaltene precipitation are old problems, but only recently have attempts been made to develop a thermodynamic description for these processes. The asphaltene thermod3mamic models have just begun to evolve. In this chapter, we will first present the thermodynamics of wax precipitation and discuss the effects of pressure, temperature, and composition. Then we will present a thermodynamic micellization model for asphaltene precipitation, and study the pressure and composition effects. All the calculations for the equilibrium between the precipitated phase and the crude oil will be based on direct minimization of the Gibbs free energy of the total system. 

Solution We will use two approaches to solve the vapor-liquid multisolid phase equlibrium.The first approach will be based on the flash-type calculations, and a second approach from direct minimization of the Gibbs free energy. 

Direct minimization of Gibbs free energy. The Gibbs free energy of the system in Fig. 5.3 is given by... 

As one of the three composition variables becomes zero, this relation simplifies to the expression for binary mixtures (57). The extension of (60) to multicomponent systems is unproblematic and enables the calculation of phase diagrams for such mixtures of great practical importance if one calculates the composition of the coexisting phases by a direct minimization of the Gibbs energy [19]. In this manner, it is possible to evade the laborious and sometimes even impossible calculation of the chemical potential for each component. 

Le Chatelier s principle is a detailed restatement of the fact that natural systems minimize their Gibbs energy. They respond to changes in T and P by moving in the direction that minimizes Gibbs energy. 

Example 12.1 Estimate the chemical equilibrium composition of a gaseous mixture of -butane and isobutane at 298.15 K and 1 bar, based on direct minimization of Gibbs energy. Assume that -butane and isobutane form an ideal solution of ideal gases at this T and P. 

As already stated, chemical reactions proceed spontaneously in the direction of lowering of chemical potentials. Based on equation 2.1, minimization of chemical potentials corresponds to minimization of the Gibbs free energy of the system. 

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