Vapor-liquid equilibrium system

Compare convergence times, using interval halving, Newton-Raphson, and false position, for on ideal, four-component, vapor-liquid equilibrium system. The pure component vapor pressures are ... 

Correlation of Vapor-Liquid Equilibrium Systems Containing Two Solvents and One Salt... 

BEKERMAN and TASSIOS Vapor-Liquid Equilibrium Systems... 

In applying equation 33, Cpsl (the constant-pressure molar heat capacity of the stoichiometric liquid) is usually extrapolated from high-temperature measurements or assumed to be equal to Cpij of the compound, whereas the activity product, afXTjafXT), is estimated by interjection of a solution model with the parameters estimated from phase-equilibrium data involving the liquid phase (e.g., solid-liquid or vapor-liquid equilibrium systems). To relate equation 33 to an available data base, the activity product is expressed... 

The conditions for phase equilibrium dictate that the chemical potential for a given component is the same in all phases. Distillation is a separation method that takes advantage of this fact and the chemical potential s dependency on pressure and composition. To see how this works we consider a vapor-liquid equilibrium system at pressure P. temperature T, and mole fractions x and v in the liquid and vapor phases respectively. Equation ( 6.1) expresses the chemical potential of component i in the vapor phase, provided the system pressure is not too high. 

The flammability limits for a vapor-liquid equilibrium system is depicted in Fig. 2P The vapor concentration at the point at which the LFL line intersects the vapor concentration curve is the LFL and the corresponding temperature is referred to as the lower temperature limit of flammability (LTL), which is identical to flashpoint. However, the reported LTL and flashpoint can be slightly different because of the different methods used in the tests. 

The Wilson equation is widely used for many nonpolar, polar, and associated solutions in vapor-liquid equilibrium systems. It is often best for hydrogen-bonded substances. For multicomponent solutions, it makes effective use of binary-solution parameters to give good results, but it cannot predict the liquid immiscibihty phenomena. 

The illustrations of this section were meant to demonstrate how one can determine activity coefficients from measurements of temperature, pressure, and the mole fractions in both phases of a vapor-liquid equilibrium system. An alternative procedure is at constant temperature, to measure the total equilibrium pressure above liquid mixtures of known (or measured) composition. This replaces time-consuming measurements of vapor-phase compositions with a more detailed analysis of the experimental data and more complicated calculations. ... 

Using the proposed procedure in conjunction with literature values for the density (11) and vapor pressure (12) of solid carbon dioxide, the solid-formation conditions have been determined for a number of mixtures containing carbon dioxide as the solid-forming component. The binary interaction parameters used in Equation 14 were the same as those used previously for two-phase vapor-liquid equilibrium systems (6). The value for methane-carbon dioxide was 0.110 and that for ethane-carbon dioxide was 0.130. Excellent agreement has been obtained between the calculated results and the experimental data found in the literature. As shown in Figure 2, the predicted SLV locus for the methane-carbon... 

One kind of indifference occurs when we have specified too few property values to solve a problem for example, we give an (F-spedfication when we actually need an F"-specification (recall, T < T ). An example occurs when we specify T and P for a one-component vapor-liquid equilibrium system, but we need to determine the fraction of material in the vapor phase. This is an indifferent situation because, at the specified T and P, om system can be at any of an infinite number of points along the tie line between liquid and vapor. 

Chemical engineers have used the concept of vapor-liquid equilibrium for much of their treatment of separation processes such as distillation, absorption, and stripping. In this chapter, we examine the dynamic modeling and numerical solution of typical vapor-liquid equilibrium systems. 

Since Equation 1.30 was derived at constant temperature and pressure, it may be used to correlate vapor-liquid equilibrium data rigorously only if such data were obtained at constant temperature and pressure. A binary vapor-liquid equilibrium system can exist only at one composition at a fixed temperature and pressure since it has only two degrees of freedom. (Degrees of freedom... 

Fig. 10-6. Vapor-liquid equilibrium system, nitric acid-water-sulfuric acid.

Ideal Vapor/Liquid Equilibrium Systems, Nonideal Vapor/Liquid Equilibrium Systems, Vapor/Liquid Equilibrium Relationships,... 

Note that different values of Xn (and the corresponding Xi ) in Figure 4.1.1(c) represent different closed vapor-liquid equilibrium systems at 1 atmosphere but slightly different temperatures. Note further that 0112 in equation (4.1.24) varies slightly with temperature and is not a constant (since both and vary with temperature). 

If we return, for example, to the aforementioned binary vapor-liquid equilibrium system and impose the requirement that an azeotrope (y -X ) is present, then SC = 1 and F = 1. We can no longer specify both T and X], but only one of them. 

American Petroleum Institute, Bibliographies on Hydrocarbons, Vols. 1-4, "Vapor-Liquid Equilibrium Data for Hydrocarbon Systems" (1963), "Vapor Pressure Data for Hydrocarbons" (1964), "Volumetric and Thermodynamic Data for Pure Hydrocarbons and Their Mixtures" (1964), "Vapor-Liquid Equilibrium Data for Hydrocarbon-Nonhydrocarbon Gas Systems" (1964), API, Division of Refining, Washington. 

Bibliography of vapor-liquid equilibrium data, primarily for systems at low temperatures. 

Two additional illustrations are given in Figures 6 and 7 which show fugacity coefficients for two binary systems along the vapor-liquid saturation curve at a total pressure of 1 atm. These results are based on the chemical theory of vapor-phase imperfection and on experimental vapor-liquid equilibrium data for the binary systems. In the system formic acid (1) - acetic acid (2), <() (for y = 1) is lower than formic acid at 100.5°C has a stronger tendency to dimerize than does acetic acid at 118.2°C. Since strong dimerization occurs between all three possible pairs, (fij and not... 

For systems of type II, if the mutual binary solubility (LLE) data are known for the two partially miscible pairs, and if reasonable vapor-liquid equilibrium (VLE) data are known for the miscible pair, it is relatively simple to predict the ternary equilibria. For systems of type I, which has a plait point, reliable calculations are much more difficult. However, sometimes useful quantitative predictions can be obtained for type I systems with binary data alone provided that... 

Figure 15 shows results for a difficult type I system methanol-n-heptane-benzene. In this example, the two-phase region is extremely small. The dashed line (a) shows predictions using the original UNIQUAC equation with q = q. This form of the UNIQUAC equation does not adequately fit the binary vapor-liquid equilibrium data for the methanol-benzene system and therefore the ternary predictions are grossly in error. The ternary prediction is much improved with the modified UNIQUAC equation (b) since this equation fits the methanol-benzene system much better. Further improvement (c) is obtained when a few ternary data are used to fix the binary parameters. 

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

Application of the algorithm for analysis of vapor-liquid equilibrium data can be illustrated with the isobaric data of 0th-mer (1928) for the system acetone(1)-methanol(2). For simplicity, the van Laar equations are used here to express the activity coefficients. 

Vapor-Liquid Equilibrium Data Reduction for Acetone(1)-Methanol(2) System (Othmer, 1928)... 

The computer subroutines for calculation of vapor-liquid equilibrium separations, including determination of bubble-point and dew-point temperatures and pressures, are described and listed in this Appendix. These are source routines written in American National Standard FORTRAN (FORTRAN IV), ANSI X3.9-1978, and, as such, should be compatible with most computer systems with FORTRAN IV compilers. Approximate storage requirements for these subroutines are given in Appendix J their execution times are strongly dependent on the separations being calculated but can be estimated (CDC 6400) from the times given for the thermodynamic subroutines they call (essentially all computation effort is in these thermodynamic subroutines). 

A tabulation of the partial pressures of sulfuric acid, water, and sulfur trioxide for sulfuric acid solutions can be found in Reference 80 from data reported in Reference 81. Figure 13 is a plot of total vapor pressure for 0—100% H2SO4 vs temperature. References 81 and 82 present thermodynamic modeling studies for vapor-phase chemical equilibrium and liquid-phase enthalpy concentration behavior for the sulfuric acid—water system. Vapor pressure, enthalpy, and dew poiat data are iacluded. An excellent study of vapor—liquid equilibrium data are available (79). 

Vapor/liquid equilibrium (XT E) relationships (as well as other interphase equihbrium relationships) are needed in the solution of many engineering problems. The required data can be found by experiment, but such measurements are seldom easy, even for binaiy systems, and they become rapidly more difficult as the number of constituent species increases. This is the incentive for application of thermodynamics to the calculation of phase-equilibrium relationships. 

For mixtures containing more than two species, an additional degree of freedom is available for each additional component. Thus, for a four-component system, the equihbrium vapor and liquid compositions are only fixed if the pressure, temperature, and mole fractious of two components are set. Representation of multicomponent vapor-hquid equihbrium data in tabular or graphical form of the type shown earlier for biuaiy systems is either difficult or impossible. Instead, such data, as well as biuaiy-system data, are commonly represented in terms of ivapor-liquid equilibrium ratios), which are defined by... 

The phase-distribution restrictions reflect the requirement that ff =ff at equilibrium where/is the fugacity. This may be expressed by Eq. (13-1). In vapor-hquid systems, it should always be recognized that all components appear in both phases to some extent and there will be such a restriction for each component in the system. In vapor-liquid-hquid systems, each component will have three such restrictions, but only two are independent. In general, when all components exist in all phases, the uumDer of restricting relationships due to the distribution phenomenon will be C(Np — 1), where Np is the number of phases present. 

Data on the gas-liquid or vapor-liquid equilibrium for the system at hand. If absorption, stripping, and distillation operations are considered equilibrium-limited processes, which is the usual approach, these data are critical for determining the maximum possible separation. In some cases, the operations are are considerea rate-based (see Sec. 13) but require knowledge of eqmlibrium at the phase interface. Other data required include physical properties such as viscosity and density and thermodynamic properties such as enthalpy. Section 2 deals with sources of such data. 

It is essential to calculate, predict or experimentally determine vapor-liquid equilibrium data in order to adequately perform distillation calculations. These data need to relate composition, temperature, and system pressure. 

K-factors for vapor-liquid equilibrium ratios are usually associated with various hydrocarbons and some common impurities as nitrogen, carbon dioxide, and hydrogen sulfide [48]. The K-factor is the equilibrium ratio of the mole fraction of a component in the vapor phase divided by the mole fraction of the same component in the liquid phase. K is generally considered a function of the mixture composition in which a specific component occurs, plus the temperature and pressure of the system at equilibrium. 

Multicomponent distillations are more complicated than binary systems due primarily to the actual or potential involvement or interaction of one or more components of the multicomponent system on other components of the mixture. These interactions may be in the form of vapor-liquid equilibriums such as azeotrope formation, or chemical reaction, etc., any of which may affect the activity relations, and hence deviations from ideal relationships. For example, some systems are known to have two azeotrope combinations in the distillation column. Sometimes these, one or all, can be broken or changed in the vapor pressure relationships by addition of a third chemical or hydrocarbon. 

Fig. 14. Vapor-liquid equilibrium constants for the //-pentane (l)-propane(2)-methane (3) system at 220°F.

To simulate the RD system, the MESH model is used, which is assumed that each plate is in vapor-liquid equilibrium. The MESH equations are as follows ... 

Both liquid and vapor phases are totally miscible. Conventional vapor/liquid equilibrium. Neither phase is pure. Separation factors are moderate and decrease as purity increases. Ultrahigh purity is difficult to achieve. No theoretical limit on recovery. Liquid phases are totally miscible solid phases are not. Eutectic system. Solid phase is pure, except at eutectic point. Partition coefficients are very high (theoretically, they can be infinite). Ultrahigh purity is easy to achieve. Recovery is limited by eutectic composition. 

Figure 14.1 Vapor-liquid equilibrium data and calcidated values for the n-pentane-acetone system, x andy are the mole fractions in the liquid and vapor phase respectively [reproduced with permission from Canadian Journal of Chemical Engineering].

Figure 14.2 Vapor-liquid equilibrium data and calculated values for the nitrogen-ethane system [reprinted from the Canadian Journal of Chemical Engineering with permission].

---