Thermodynamics multicomponent mixtures

However, in the study of thermodynamics and transport phenomena, the behavior of ideal gases and gas mixtures has historically provided a norm against which their more unruly brethren could be measured, and a signpost to the systematic treatment of departures from ideality. In view of the complexity of transport phenomena in multicomponent mixtures a thorough understanding of the behavior of ideal mixtures is certainly a prerequisite for any progress in understanding non-ideal systems. 

Vynckier, E., and Froment, G. F., Modeling of the kinetics of complex processes based upon elementary steps , in Kinetic and Thermodynamic Lumping of Multicomponent Mixtures (G. Astaiita and S. I. Sandler, Eds.) Elsevier, Amsterdam (1991) 131-161. 

The criterion for thermodynamic equilibrium between two phases of a multicomponent mixture is that for every component, i ... 

Petlyuk FB, Platonov VM and Slavinskii DM (1965) Thermodynamically Optimal Method for Separating Multicomponent Mixtures, Ini Chem Eng, 5 555. 

This paper reviews the experiences of the oil industry in regard to asphaltene flocculation and presents justifications and a descriptive account for the development of two different models for this phenomenon. In one of the models we consider the asphaltenes to be dissolved in the oil in a true liquid state and dwell upon statistical thermodynamic techniques of multicomponent mixtures to predict their phase behavior. In the other model we consider asphaltenes to exist in oil in a colloidal state, as minute suspended particles, and utilize colloidal science techniques to predict their phase behavior. Experimental work over the last 40 years suggests that asphaltenes possess a wide molecular weight distribution and they may exist in both colloidal and dissolved states in the crude oil. 

Raffaella Ocone and Gianni Astarita, Kinetics and Thermodynamics in Multicomponent Mixtures... 

In classical thermodynamics, there are many ways to express the criteria of a critical phase. (Reid and Beegle (11) have discussed the relationships between many of the various equations which can be used.) There have been three recent studies in which the critical points of multicomponent mixtures described by pressure-explicit equations of state have been calculated. (Peng and Robinson (1 2), Baker and Luks (13), Heidemann and Khalil (14)) In each study, a different statement of the critical criteria and... 

It is the intent of this doeument to define the terms most commonly encountered in the field of polymer blends and eomposites. The scope has been limited to mixtures in which the eomponents differ in ehemical composition or molar mass or both and in which the continuous phase is polymeric. Many of the materials described by the term multiphase are two-phase systems that may show a multitude of finely dispersed phase domains. Hence, incidental thermodynamic descriptions are mainly limited to binary mixtures, although they can be and, in the scientific literature, have been generalized to multicomponent mixtures. Crystalline polymers and liquid-crystal polymers have been considered in other documents [1,2] and are not discussed here. 

Among other approaches, a theory for intermolecular interactions in dilute block copolymer solutions was presented by Kimura and Kurata (1981). They considered the association of diblock and triblock copolymers in solvents of varying quality. The second and third virial coefficients were determined using a mean field potential based on the segmental distribution function for a polymer chain in solution. A model for micellization of block copolymers in solution, based on the thermodynamics of associating multicomponent mixtures, was presented by Gao and Eisenberg (1993). The polydispersity of the block copolymer and its influence on micellization was a particular focus of this work. For block copolymers below the cmc, a collapsed spherical conformation was assumed. Interactions of the collapsed spheres were then described by the Hamaker equation, with an interaction energy proportional to the radius of the spheres. 

In practice, RSPs rarely operate at thermodynamic equilibrium. Therefore, some correlation parameters, such as tray efficiencies or HETS values, have been introduced to adjust the equilibrium-based theoretical description to reality. For multicomponent mixtures, however, this concept often fails, since diffusion interactions of several components result in unusual phenomena such as osmotic or reverse... 

Astarita G, Sandler SI. Kinetic and Thermodynamic Lumping of Multicomponent Mixtures. Amsterdam Elsevier, 1991. 

Petlyuk FB, Platonov VM, Slavinskii DM. Thermodynamically optimal method for separating multicomponent mixtures. Int Chem Eng 1965 5 555. 

Raffaella Ocone and Gianni Astarita, Kinetics and Thermodynamics in Multicomponent Mixtures Arvind Varma, Alexander S. Rogachev, Alexandra S. Mukasyan, and Stephen Hwang, Combustion Synthesis of Advanced Materials Principles and Applications J. A. M. Kuipers and W. P. Mo, van Swaaij, Computional Fluid Dynamics Applied to Chemical Reaction Engineering... 

In real reactive absorption processes, the thermodynamic equilibrium can seldom be reached. Therefore, some correlation parameters such as tray efficiencies or HETP-values (Height Equivalent to One Theoretical Plate) are introduced to adjust the equilibrium-based theoretical description to the reality. However, reactive absorption always occurs in multicomponent mixtures, for which this simplified concept often fails [16, 23, 24]. 

Nigam, A., M. Neurock, and M.T. Klein, Reconcilliationof Molecular Detail and Lumping An Asphaltene Thermolysis Example, in Kinetic and Thermodynamic Lumping of Multicomponent Mixtures. G. Astarita and S.I. Sandler, eds., Elsevier Science Publishers B.V., 1991. 

To be useful, this type of simulator must calculate the thermodynamic properties of multicomponent mixtures in both liquid and vapor phases while predicting bubble and dew points or partial vaporizations or condensations. Using this basic information, the simulator must then make calculations for other processes, such as gas cooling by expansion, gas compression, multiple flashes condensations, and separations by absorption... 

From the point of view of traditional thermodynamics, a microemulsion is a multicomponent mixture formed of oil, water, surfactant, cosurfactant, and electrolyte. There is, however, a major difference between a conventional mixture and a microemulsion. In the former case, the components are mixed on a molecular scale, while in the latter, oil or water is dispersed as globules on the order of 10-100 nm in diameter in water or oil. The surfactant and cosurfactant are mostly located at the interface between the two phases but are also distributed at equilibrium between the two media. In conventional mixtures, the sizes of the component species are fixed. In the case of microemulsions, the sizes of the globules are not given but are provided by the condition of thermodynamic equilibrium. 

From the point of view of traditional thermodynamics, a microemulsion is a multicomponent mixture in thermodynamic equilibrium. The change at constant temperature of the Helmholtz free energy of such a system can therefore be written as... 

Equation (15), which is based on a model, must, however, be equivalent to Eq. (12), which is based on the traditional thermodynamics of a multicomponent mixture. For the free energy changes given by Eqs. (12) and (15) to be the same for arbitrary changes in the independent variables V, , r, and Nit the respective coefficients multiplying dV, d, dr, and dNt must be equal. It should be emphasized, however, that depends on the distribution at equilibrium of tire moles Ni of species i between the two media of the microemulsion and their interface,... 

In Chap. 6 we treated the thermodynamic properties of constant-composition fluids. However, many applications of chemical-engineering thermodynamics are to systems wherein multicomponent mixtures of gases or liquids undergo composition changes as the result of mixing or separation processes, the transfer of species from one phase to another, or chemical reaction. The properties of such systems depend on composition as well as on temperature and pressure. Our first task in this chapter is therefore to develop a fundamental property relation for homogeneous fluid mixtures of variable composition. We then derive equations applicable to mixtures of ideal gases and ideal solutions. Finally, we treat in detail a particularly simple description of multicomponent vapor/liquid equilibrium known as Raoult s law. 

Anderko and Lencka find. Eng. Chem. Res. 37, 2878 (1998)] These authors present an analysis of self-diffusion in multicomponent aqueous electrolyte systems. Their model includes contributions of long-range (Coulombic) and short-range (hard-sphere) interactions. Their mixing rule was based on equations of nonequilibrium thermodynamics. The model accurately predicts self-diffusivities of ions and gases in aqueous solutions from dilute to about 30 mol/kg water. It makes it possible to take single-solute data and extend them to multicomponent mixtures. 

The design engineer dealing with polymer solutions must determine if a multicomponent mixture will separate into two or more phases and what the equilibrium compositions of these phases will be. Prausnitz et al. (1986) provides an excellent introduction to the field of phase equilibrium thermodynamics. 

---