Vapor phase non-ideality

Equation (1.3-40) is one of ihe fundamental equations Tor the chemical theory of vapor-phase non-idealities. It asserts that the apparent, or observed, compressibility factor Z differs from the true value Z because of differences berwean the apparent, or assumed, mole number n aed the true vaine n . In a chemical theory, such differences are assumed to obtain because of ihe occurrence of one or more chemical reactions. If the reactions are at equilibrium, (hen one finds the following relationship for the apparent fugacity coefficient 0, ... 

The properties of dissolution as gas solubility and enthalpy of solution can be derived from vapor liquid equilibrium models representative of (C02-H20-amine) systems. The developments of such models are based on a system of equations related to phase equilibria and chemical reactions electro-neutrality and mass balance. The non ideality of the system can be taken into account in liquid phase by the expressions of activity coefficients and by fugacity coefficients in vapor phase. Non ideality is represented in activity and fugacity coefficient models through empirical interaction parameters that have to be fitted to experimental data. Development of efficient models will then depend on the quality and diversity of the experimental data. 

The UNIQUAC model [14] was used to account for liquid phase non-idealities. The vapor phase was modeled using the Redlich-Kwong EOS ]15]. The combination of both is implemented in Aspen Plus as the UNIQ-RK property model. UNIQUAC... 

In order to use the W-P criterion successfully, it is important to accurately determine the effective diffusivity of the reactant in a given catalyst system. In the case of liquid-phase reactions, the pores of the catalyst are filled primarily with solvent, if one is used, and the molecular diffusivity of the reactant solute can be several orders of magnitude lower in a liquid-phase system compared to a vapor-phase system. Apart from the decrease in bulk diffusivities, there can also be liquid-phase non-idealities, adsorption phenomena, and other unknown factors influencing the effective diffusivity [24]. If the size of the diffusing molecules is comparable to the pore size, diffusion in the pores is hindered [25-28]. A different situation arises when the diffusing species has a strong affinity for the catalytic surface, which can lead to surface diffusion and migration [2,29] however, this consideration will not be of importance in liquid-phase reactions [30]. 

We can now use the K-value expression to calculate various equilibrium properties and perform typical flash calculations. As with the simple thermodynamic approach, we can use the heat capacities, and heats of vaporization to obtain enthalpy balances for vapor and liquid streams. In addition, since we account for vapor- and liquid-phase non-ideality due to component interactions, and temperature and pressure effects, we can also apply standard thermodynamic relationships to compute excess properties for enthalpies, etc. The excess properties account for deviations from an ideal mixing behavior and the resulting deviations in equilibrium behavior. 

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

The ammonia partial pressures given in Tables 1 and 2 are based on the concentration of ammonia found in the vapor stream times the total pressure. The actual pressures applied at each run condition are summarized in Table 3 where the pressures varied from 15 psia at 80°C to 90 psia at 120°C. Because nitrogen was used as a pressurizing fluid, the partial pressure of water and the total pressure excluding nitrogen have been computed in Tables 1 and 2 based on Raoult s law for water as noted at the bottom of Table 1. Raoult s law applies for the partial pressure of water because the activity coefficient of water is virtually unity at the low levels of ammonia used in the liquid phase. Minor effects due to vapor non- ideality have not been applied. 

Abstract Isotope effects on the PVT properties of non-ideal gases and isotope effects on condensed phase physical properties such as vapor pressure, molar volume, heats of vaporization or solution, solubility, etc., are treated in some thermodynamic detail. Both pure component and mixture properties are considered. Numerous examples of condensed phase isotope effects are employed to illustrate theoretical and practical points of interest. 

There are many chemically reacting flow situations in which a reactive stream flows interior to a channel or duct. Two such examples are illustrated in Figs. 1.4 and 1.6, which consider flow in a catalytic-combustion monolith [28,156,168,259,322] and in the channels of a solid-oxide fuel cell. Other examples include the catalytic converters in automobiles. Certainly there are many industrial chemical processes that involve reactive flow tubular reactors. Innovative new short-contact-time processes use flow in catalytic monoliths to convert raw hydrocarbons to higher-value chemical feedstocks [37,99,100,173,184,436, 447]. Certain types of chemical-vapor-deposition reactors use a channel to direct flow over a wafer where a thin film is grown or deposited [219]. Flow reactors used in the laboratory to study gas-phase chemical kinetics usually strive to achieve plug-flow conditions and to minimize wall-chemistry effects. Nevertheless, boundary-layer simulations can be used to verify the flow condition or to account for non-ideal behavior [147]. 

In a molecular crystal, the idealized symmetry of the molecule is often not fully expressed in other words, the molecule occupies a site of lower point symmetry. For example, in the crystal structure of naphthalene, the CsHio molecule (idealized symmetry Z>2h) is located at a site of symmetry I. On the other hand, the hexamethylenetetramine molecule, (CH2)6N4, retains its T symmetry in the crystalline state. Biphenyl, C6H5 —C6H5, which exists in a non-planar conformation with a dihedral angle of 45° (symmetry >2) in the vapor phase, occupies a site of symmetry I in the crystalline state and is therefore completely planar. 

The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels [82] based on the UNIQUAC model is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the non-ideality, as suggested in Ref. [16],... 

In example (a), the gas composition was modeled assuming ideal solution phases and neglecting known complex vapor species, such as K2SO4, K2CO3 and alkali chlorides. These serious limitations resulted from the non-availability of oxide solution-activity data, accurate vapor species thermodynamic functions, and the inability of existing computer codes to handle non-ideal solution multiphase, multicomponent equilibrium computations. 

In the systems that we have examined so far, the bubble point and the dew point of the mixture vary monotonically with the composition. This is the case for ideal systems. However, for very non-ideal systems, there may be a maximum or a minimum in the bubble and dew point curves. This is the case for azeotropic systems. An example of a system that exhibits a low-boiling azeotrope is a mixture of 77-heptane and ethanol, which is shown in Figure 3.5. For this type of system, both the bubble and dew point temperature curves have a local minimum at the same composition. At this composition, these two curves meet. This point is known as the azeotrope. At the azeotrope, the composition of the coexisting liquid and vapor phases are identical. In this case at the azeotrope, the boiling temperature... 

Vapor-liquid equilibrium with a non-ideal vapor phase... 

Huron, M., and Vidal, J., 1979. New mixing rules in simple equations of state for representing vapor-liquid equilibria of strongly non-ideal mixtures. Fluid Phase Eq., 3 255-271. 

A non-ideal binary mixture may exist as a single liquid phase at certain compositions, temperatures, and pressures, or as two liquid phases at other conditions. Also, depending on the conditions, a vapor phase may or may not exist at equilibrium with the liquid. When two immiscible liquid phases coexist at equilibrium, their compositions are different, but the component fugacities are equal in both phases. 

The liquid phase is a non-ideal solution, for which liquid activity coefficients can be predicted with good accuracy by the Wilson equation (Equation 1.36). The vapor phase is assumed to behave as an ideal gas at the relatively low pressure of 35 kPa. Under these conditions, the K-values may be calculated by Equation 1.29a. 

As pointed out in the introduction of this chapter, two liquid phases as well as two liquid phases and a vapor phase can exist at equilibrium. Non-ideal solution conditions can result in the co-existence at equilibrium of two liquid phases having different compositions. This phenomenon is a consequence of the high non-ideality of the mixture giving rise to a strong dependence of the activity coefficients on the composition. LLE will exist if this dependence is such that components at different concentrations in the liquid can have equal fugacities. 

Because of the phase change associated with the process and the non-ideal liquid-phase solutions (i.e., organic/water), the modeling of pervaporation cannot be accomplished using a solution-diffusion approach. Wijmans and Baker [14] express the driving force for permeation in terms of a vapor partial pressure difference. Because pressures on the both sides of the membrane are low, the gas phase follows the ideal gas law. The liquid on the feed side of the membrane is generally non-ideal. 

At equilibrium, the vapor pressure of benzene over each beaker must be the same. Assuming ideal solutions, this means that the mole fraction of benzene in each beaker must be identical at equilibrium. Consequently, the mole fraction of solute is also the same in each beaker, even though the solutes are different in the two solutions. Assuming the solute to be non-volatile, equilibrium is reached by the transfer of benzene, via the vapor phase, from beaker A to beaker B. 

Owing to the non-ideality of binary or multicomponent mixtures, the liquid phase composition is often identical with the vapor phase composition. This point is called an azeotrope and the corresponding composition is called the azeotropic composition. An azeotrope can not be circumvented by conventional distillation since no enrichment of the low-boiHrig component can be achieved in the vapor phase. Separating azeotropic mixtures therefore requires special processes, e.g. azeotropic or extractive distillation or pressure swing distillation. Azeotropic information is available in literature (Gmehling et al., 2004). 

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