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Applied Geochemistry, 55 ISSN:0883-2927 ISSN:1872-9134

In a forward chemical equilibrium problem (FCEP), the state of minimum Gibbs energy for a chemical system is sought, in which temperature, pressure, elemental amounts, and thermodynamic model parameters are prescribed. We herein present a mathematical framework for characterizing and solving inverse chemical equilibrium problems (ICEP), a class of problems for which one or more of those prescribed conditions in a FCEP are unknown in advance. In an ICEP, complementary conditions must be imposed, which are referred to here as equilibrium constraints. Examples of ICEPs include those in which a certain property is known at equilibrium (e.g., volume is specified instead of pressure; enthalpy is specified instead of temperature; pH is specified instead of the amount of element H). The equilibrium constraints may also be specified by equations that govern the relationship between several equilibrium properties (e.g., the equations relating temperature, pressure, density, energy, and velocity of the gases produced during the detonation of an explosive). Chemical Engineering Science, 252 ISSN:0009-2509

Computational Geosciences, 17 (1) ISSN:1420-0597 ISSN:1573-1499

Computation of chemical equilibria in multiphase systems by Gibbs free energy minimization under constraints set by the material balance has increasing interest in many application fields, including materials technology, metallurgy and chemical engineering. The results are utilised in multi-phase equilibrium studies or as parts of equilibrium-based process simulation. Yet, there exist a number of practical problems where the chemical system is influenced by other constraining factors such as surface energy or electrochemical charge transport. For such systems, an extended Gibbs energy method has been applied. In the new method, the potential energy is introduced to the Gibbs energy calculation as a Legendre transformed work term divided into substance specific contributions. The additional constraint potential is then represented by a supplementary undertermined Lagrange multiplier.In addition, upper bounds on the amounts of products can be set, which then limit the maximum extents of selected spontaneous chemical reactions in terms of affinity. The range of Gibbs energy calculations can then be extended to new intricate systems. Example models based on free energy minimisation have been made e.g. for surface and interfacial systems, where the surface, interfacial or adsorbed atomic or molecular layers are modeled as separate phases. In an analogous fashion the partitioning effect of a semi-permeable membrane in a two-compartment aqueous system can be modeled. In such system the large ions, not permeable through the membrane, cause an uneven charge distribution of ionic species between the two compartments. In this case, the electrochemical potential difference between the two aqueous phases becomes calculated for the multi-component system. The calculated results are consistent with the Donnan equilibrium theory; however the multi-phase system may also include the gas phase and several precipitating phases, which extends the applicability of the new method. Finally, similar constraints can also be set to extents of reaction advancements, allowing usage of Gibbs energy calculations in dynamic reaction rate controlled systems.

Donnan equilibrium based models can be used to predict ion-exchange related phenomena within many application fields. In this paper, a method for doing Donnan equilibrium calculations using Gibbs energy minimization is presented. With this approach, it is possible to solve Donnan equilibrium systems with complex solution or multiphase chemistry using Gibbs energy minimizing programs.

Changes in chemical equilibria are important in handling high-pressure acid gas fluids and natural gas liquids, particularly, when the fluids contain other trace components, such as H2O, COS and CS2. Beyond ideal gas application, high-pressure reaction equilibria require fugacity coefficients which can be calculated with reference equations of state, provided that reliable mixing parameters are available. Densimetric/Volumetric measurements are one way to validate or reoptimize the mixing parameters to be subsequently used for investigating reaction equilibria in a dense fluid. In this thesis, the volumetric properties of the binary systems of CS2, COS and H2S with dense C3H8 alongside impurities of CO2, CS2, and COS dissolved in dense H2S are reported. Additionally, the thesis explores the equilibrium limits for formation of COS and CS2 in high-pressure H2S fluids containing CO2. For the densimetric measurements for a CS2 + C3H8 system, the data were used to calculate the apparent molar volumes, which were assumed to approximate the partial molar volumes at infinite dilution. These partial molar volumes were used to optimize the adjustable parameters in an infinite correlation equation based on the generalized Krichevskii parameter. The measurements of the COS and H2S in C3H8 fluid were used to compare calculations performed with the mixing coefficients from Kunz & Wagner (2012). Calculations for apparent molar volumes showed an agreement within ±0.4% at high-pressures without the need for re-optimization for these systems. The measured densities of the various compositions of (x(CO2) = 0.0982, 0.270, and 0.496) for the CO2 + H2S binary mixtures were used to compare the data from Stouffer et al. and Nazeri et al. The comparison showed an agreement within ±2% at high pressures and up to 4% in the vicinity of the critical point or high compressibility region. Also, the densities were used to calculate excess molar volumes and further used to ascertain the accuracy of the mixing coefficients from Kunz and ...

The surface tension in metallic alloy systems is modelled by applying a direct Gibbs energy minimisation technique to the surface monolayer model. The model results are compared with previously published experimental values for the Bi–Sn system as well as surface tension values determined by the authors using the sessile drop method for the ternary Ag–Au–Cu system.

A thermochemical method is presented by which multiphase processes can be simulated with concurrent calculation of the Gibbs energy of the reactive mixture during a chemical change. Algorithmic constraints are set for the overall reaction kinetics when the Lagrange method of undetermined multipliers is used to minimize the Gibbs energy of the multicomponent system. Consequently, the chemical change is calculated as a series of successive “virtual” states, which follow the extent of the overall reaction. From the Gibbs energy of these intermediate states, other thermodynamic quantities for the changing chemical system can be deduced, and the entropy production of the process can be calculated. A particular process model was developed for two isothermal aqueous systems and for a nonisothermal high-temperature process. The entropy production in the reactive systems is presented, and the validity of the simulation models is assessed in terms of their time-dependent Gibbs energy and entropy profiles.