• Energy Research

Full Changelog: https://github.com/ChemRxnEngLab/GibbsEnergyMinimizationModel/

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

In process and materials chemistry, digitalization with computational methods has been a long-time continuing process. The methodology based on numerical methods in reaction kinetics as well as for fluid phase thermodynamics applying equations of state has been well established. During the last two decades, however, multiphase technology based on the minimization of Gibbs free energy has made progress in such fields of process and materials chemistry, where the conventional methods have not been applicable. Recent advancements also include introduction of such new Gibbs'ian algorithms, which, in addition to complex equilibrium problems, facilitate modelling of time-dependent dynamic changes in multi-phase systems. Within the said period, VTT has been an active performer in the development of multiphase Gibbs'ian techniques. The research work performed at VTT has led to several new algorithms with practical industrial applications. The particular focus has been the development of the Constrained Gibbs Free energy minimization technique, where instead of material balances and stoichiometric relations derived thereof, also immaterial physical conditions are applied as constraints in the free energy minimizing calculation. In this report, the method of constrained Gibbs energy minimization for calculating chemical equilibria in arbitrary multiphase systems is derived using basic thermodynamic concepts. The method of Lagrange undetermined multipliers is introduced for a simple system of an ideal gas phase and a number of condensed phases, constrained by the number of moles of the system components. The use of additional constraints in the Gibbs energy minimization procedure is facilitated by applying the concept of generalised work-coefficients as the Lagrange multipliers of immaterial components in the system. The thus introduced method of immaterial constraints in Gibbs energy minimization is illustrated with a number of simple practical examples such as electrochemical Donnan equilibria applied for pulp suspensions, surface equilibria and systems constrained by reaction kinetics via the extent of chemical reactions. A few examples of non-equilibrium and parametric phase diagrams calculated with the immaterial constraints are also given. Finally, the applicability of the method for biochemical systems is shortly discussed.

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.