Fluid vapor-liquid equilibrium calculation

If a fluid composed of more than one component (e.g., a solution of ethanol and water, or a crude oil) partially or totally changes phase, the required heat is a combination of sensible and latent heat and must be calculated using more complex thermodynamic relationships, including vapor-liquid equilibrium calculations that reflect the changing compositions as well as mass fractions of the two phases. 

Many modifications of the original Redlich/Kwohg equation that appear in the literature are intended for special-purpose applications. The SRJt equation, developed for vapor/liquid equilibrium calculations, is designed specifically to yield reasonable vapor pressures for pure fluids. Thus, there is no assurance that molar volumes calculated by the SRK equation are more accurate than values given by the original Redlich/Kwong equation. 

The properties of mixtures of ideal gases and of ideal solutions depend solely on the properties of the pure constituent species, and are calculated from them by simple equations, as illustrated in Chap. 10. Although these models approximate the behavior of certain fluid mixtures, they do not adequately represent the -behavior of most solutions of interest to chemical engineers, and Raoult s law is not in general a realistic relation for vapor/liquid equilibrium. However, these models of ideal behavior—the ideal gas, the ideal solution, and Raoult s law— provide convenient references to which the behavior of nonideal solutions may be compared. 

Huron, M.-J., G.-N. Dufour, and J. Vidal. 1978. "Vapor-Liquid Equilibrium and Critical Locus Curve Calculations with the Soave Equation for Hydrocarbon Systems with Carbon Dioxide and Hydrogen Sulphide" Fluid Phase Equil., 1 247-265. 

Now that the fugacity (or equivalently, the molar Gibbs energy) of a pure fluid can be calculated, it is instructive to consider how one can compute the vapor-liquid equilibrium pressure of a pure fluid, that is, the vapor pressure, as a function of temperature, using a volumetric equation of state. Such calculations are straightforward in princi-... 

Here a new parameter jiry, known as the binary interaction parameter, has been introduced to result in more accurate mixture equation-of-state calculations. This parameter is found by fitting the equation of state to mixture data (usually vapor-liquid equilibrium data, as discussed in Chapter 10). Values of the binary interaction parameter k - that have been reported for a number of binary mixtures appear in Table 9.4-1. Equations 9.4-8 and 9.4-9 are referred to as the van der Waals one-fluid mixing rules. The term one-fluid derives from the fact that the mixture is being described by the same equation of state as the pure fluids, but with concentration-dependent parameters. 

VDW one-fluid rules. Comparisons of predicted and experimental vapor-liquid equilibrium for ternary and multicomponent systems are given in Tables V, VI, and VII, for both the semiempirical and VDW one-fluid mixing rules. In these calculations, the unlike interaction parameters for interactions of ethane and heavier components with each other were taken to be unity. This is a reasonable approximation for the unlike interaction parameters for the heavier components for the interaction of ethane and... 

Under the assnmption of equilibrium conditions, and knowing the composition of the fluid stream coming into the separator and the working pressure and temperature conditions, we conld apply our current knowledge of vapor/liquid/equilibrium (flash calculations) and calculate the vapor and liquid fractions at each stage. 

The equation, referred as the SRK eos, gives quantitative fitting of vapor pressure, good representation of the fugacity of liquid, and improved representation of the energy functions of liquid for normal fluids, although liquid density is not well represented. The equation was the first to be widely used for both the gas and liquid phases and, hence, for gas-liquid equilibrium in engineering calculations. 

The (liquid + liquid) equilibria diagram for (cyclohexane + methanol) was taken from D. C. Jones and S. Amstell, The Critical Solution Temperature of the System Methyl Alcohol-Cyclohexane as a Means of Detecting and Estimating Water in Methyl Alcohol , J. Chem. Soc., 1930, 1316-1323 (1930). The Gjj results were calculated from the (vapor + liquid) results of K. Strubl, V. Svoboda, R. Holub, and J. Pick, Liquid-Vapour Equilibrium. XIV. Isothermal Equilibrium and Calculation of Excess Functions in the Systems Methanol-Cyclohexane and Cyclohexane-Propanol , Collect. Czech. Chem. Commun., 35, 3004-3019 (1970). The results are from M. Dai and J.-P.Chao, Studies on Thermodynamic Properties of Binary Systems Containing Alcohols. II. Excess Enthalpies of C to C5 Normal Alcohols 4- 1,4-Dioxane , Fluid Phase Equilib., 23, 321-326 (1985). 

An equation of state, applicable to all fluid phases, is paitiodariy useful for phase-equilibrium calculations where a liquid phase and a vapor phase coexist at high pressures. At such conditions, conventional activity coefficients are not useful because, with rare exceptions, at least one of the mixture s components is supercritical that is, (he system temperature is above (hat component s critical temperature. In that event, one must employ special standard states for the activity coefficients of the supercritical components (see Section 1.5-2). That complication is avoided when ail fugacities are calculated front en equation of state. 

A schematic diagram of the unit cell for a vapor-Uquid-porous catalyst system is shown in Fig. 9.9. Each cell is modeled essentially using the NEQ model for heterogeneous systems described above. The bulk fluid phases are assumed to be completely mixed. Mass-transfer resistances are located in films near the vapor-liquid and liquid-solid interfaces, and the Maxwell-Stefan equations are used for calculation of the mass-transfer rates through each film. Thermodynamic equilibrium is assumed only at the vapor-liquid interface. Mass transfer inside the porous catalyst may be described with the dusty fluid model described above. 

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