Enthalpies Mixtures

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. ... 

The computation of pure-component and mixture enthalpies is implemented by FORTRAN IV subroutine ENTH, which evaluates the liquid- or vapor-phase molar enthalpy for a system of up to 20 components at specified temperature, pressure, and composition. The enthalpies calculated are in J/mol referred to the ideal gas at 300°K. Liquid enthalpies can be determined either with... 

The steam used in this process is generated by the turbine exhaust gas. Typically, water at 14.7 psia (1 Bar) and 80 °F (26.7 °C) enters the pump and regenerator, where it is brought up to 60 psia (4 Bar) above the compressor discharge and the same temperature as the compressor discharged air. The steam is injected after the compressor but far upstream of the burner to create a proper mixture which helps to reduce the primary zone temperature in the combustor and the NO output. The enthalpy of State 3 hi,) is the mixture enthalpy of air and steam. The following relationship describes the flow at that point ... 

Temperature rc) Humidity kg HjO/kg dry air) Water vapor partial pressure (kPa) Water v K>r partial density (kg/m ) Water vaporization heat M/kg) Mixture enthalpy (kj/kg dry air) Dry air partial density (lKinematic viscosity (I0< mJ/s) Specific heat (kJ/K kg) Heat conductivity (W/m K) Diffusion factor water air (1 O mJ/s) Temperature rc)... 

Some data comparisons were made of several predictive methods with steam mixture enthalpy data obtained by Professor Wormald (3). To provide a basis of comparison, Figure 6 illustrates how three methods currently in vogue in the thermodynamics world perform in predicting the enthalpy departures from ideality of methane. The predictions of the Lee-Kesler equation-of-state seem to best replicate the data, with a maximum error of 1.2 kJ/kg. 

Figure 9 provides a comparison of the predictions of empirical methods with Wormald s data for a 50/50 mole percent mixture of steam and methane. As can be seen, the frequently used artifices of calculating mixture enthalpies by blending the pure component enthalpies at either total or partial pressures are very inaccurate. Likewise, the assumption of ideal gas enthalpy for the real gas mixture, equivalent to a zero enthalpy departure on the diagram, is an equally poor method. 

Professor Wormald, in a paper presented at this conference, has provided additional steam mixture enthalpy data and some correlation work he has done on the data using an association model. 

Example For hydrocarbon mixture enthalpy interpolation The enthalpy of a mixture as a liquid at 100°F is to be calculated. The enthalpy of the same mixture is to be determined at 1 atm and 500°F. The mixture analysis is as follows ... 

Next, using RefFlsh, determine the dew point temperature of the debutanizer flashed feed problem at the 85-psig pressure. The answer found is a 396°F dew point. A rapid reading with a quick mental interpolation of Table 2.1 shows we have a mixture enthalpy of 431 Btu/lb at this dew point temperature. The following calculations derive the cooler/condenser duty. 

Thermodynamic properties (i.e., fugacities, entropies, and enthalpies) are required by this simulating program in the calculations of vapor/liquid phase equilibrium, compression/ expansion paths, and heat balances. Fugacities are required for the individual components of the existing vapor and liquid mixtures. Enthalpies and entropies are required for the vapor mixture or the liquid mixture. Also, mixture densities are required for both phases. 

Off to the left of the 100% relative humidity line you will observe scales showing the enthalpy per mass of dry air of a saturated air-water vapor mixture. Enthalpy... 

For gas-liquid systems involving phase change the mixture enthalpy consists of a sensible heat and a latent heat of vaporization. The corresponding heat jump condition (3.173) can be expressed as E + hg + Ef + hf O, or alternatively [138] ... 

In a set of introductory steps, the mixture composition and the temperature are calculated. A set of scalar transport equations on the form (12.183) is generally solved for the species mass densities and the mixture enthalpy at the next time level n - - 1. However, in reactor simulations, the enthalpy balance is frequently expressed in terms of temperature. The discrete form of the governing equations is thus written as ... 

Gibbs free energy expressed in terms of mass (J) total mixture enthalpy (or enthalpy) expressed in terms of temperature, pressure and the masses of the various species in the mixture (J) or enthalpy expressed in terms of temperature, pressure and the mole numbers of the various species in the mixture (J) total mixture enthalpy (or enthalpy) expressed in terms of temperature, pressure and the masses of the various species in the mixture, a fluid dynamic quantity (J) or enthalpy expressed in terms of temperature, pressure and the mole numbers of the various species in the mixture, a fluid dynamic quantity (J) non-dimensional temperature (—)... 

If a petroleum mixture is represented by pseudocomponents corresponding to its TBP curve, its properties can be estimated by the same methods that apply to mixtures of chemical species. For instance, the mixture enthalpy and phase behavior can be predicted by the methods discussed in this chapter. 

Another graphical design method for binary systems is that of Ponchon" and Savarit. This method includes an energy balance on each stage and is totally rigorous for binary systems. However, it requires mixture enthalpy data, often unavailable, and is cumbersome in application. 

Differentiating (4-94), substituting the result into (4-97), and summing yields a working equation for vapor mixture enthalpy. 

Replacing Pf by (4-83)— the Antoine vapor pressure relation, vlv by (4-91) with P,. evaluated at saturation, and vu by (4-79) differentiating the resulting equation for inffi solving for the species liquid enthalpy and summing, yields the following expression for the ideal liquid mixture enthalpy... 

Other thermodynamic properties can be computed in a consistent manner with the C-S X-value correlation. For the vapor, the R-K equation of state is used to determine vapor mixture density from (4-38), as illustrated in Example 4.2 and vapor mixture enthalpy from (4-64). 

Liquid mixture enthalpy is computed from the vfL and y,x equations used in the C-S correlation by classical procedures, as shown by Edmister, Persyn, and Erbar. The starting equation is a combination of (4-55) and (4-57) with (4-62). 

The liquid mixture enthalpy relative to an ideal vapor at 400°F and 0 psia is obtained from the following equation, which is equivalent to (5-14). 

Jain, R. K., Simha, R., Balik, C. M Statistical thermodynamics of fluid mixtures-enthalpies and equations of state, Indian Journal of Pure Applied Physics, 22(ll),pp. 651-657(1984). 

Before energy balances can be used in the analysis or design of multicomponent flow processes, we must have data or correlations for mixture enthalpies as functions of composition. Such correlations can be developed from models for volumetric equations of state or from models for g in the latter case, we would need a form for the temperature-dependence of the parameters in the g model. In this section we discuss how an equation of state can be used to compute an enthalpy-concentration diagram for a two-phase equilibrium situation such diagrams contribute to the analysis or design of distillation columns. 

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