Vapor-liquid equilibria determination

Table 3. Approximate Costs of Binary Vapor-Liquid Equilibria Determination"...

Momentary mass of a sample may be derived from momentary weight only if the density of the gas, and thus the buoyancy of the sample, are known. Volumetric data of pure gases are calculated from precise equations of state, as they exist for carbon dioxide and other gases, or taken from tables. Cubic equations of state are used to calculate densities of gas mixtures. We have always employed van-der-Waals mixing rules and fitted the interaction parameter to vapor-liquid equilibria determined by ourselves or taken from literature. 

Hiaki, T. Kawai, A. Vapor-liquid equilibria determination for a hydrofluoroether with several alcohols. Fluid Phase Equilib. 1999, 158-160, 979-989. 

Equation (9.11) identifies the three factors that determine the performance of a pervaporation system. The first factor, pevAp, is the vapor-liquid equilibrium, determined mainly by the feed liquid composition and temperature the second is the membrane selectivity, G-men, an intrinsic permeability property of the membrane material and the third includes the feed and permeate vapor pressures, reflecting the effect of operating parameters on membrane performance. This equation is, in fact, the pervaporation equivalent of Equation (8.19) that describes gas separation in Chapter 8. 

Aizawa, K. Kato, M. Vapor-liquid equilibrium determination by total pressure measurements for three binary systems made of 1,2-dimethoxyethane with toluene, methylcyclohexane, or (trifluoromethyl)benzene 7. Chem. Eng. Data 1991,36, 159-161... 

Kato, M. Tanaka, H. Vapor-liquid equilibrium determination with a flow-type ebuUiometer for six binary systems made of alcohol and amine J. Chem. Eng. Data 1989,34, 203-206... 

To illustrate the criterion for parameter estimation, let 1, 2, and 3 represent the three components in a mixture. Components 1 and 2 are only partially miscible components 1 and 3, as well as components 2 and 3 are totally miscible. The two binary parameters for the 1-2 binary are determined from mutual-solubility data and remain fixed. Initial estimates of the four binary parameters for the two completely miscible binaries, 1-3 and 2-3, are determined from sets of binary vapor-liquid equilibrium (VLE) data. The final values of these parameters are then obtained by fitting both sets of binary vapor-liquid equilibrium data simultaneously with the limited ternary tie-line data. 

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... 

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). 

The vapor-liquid equilibrium of the binary mixture is well fitted by Van Laar s equations (228). It was determined from 100 to 760 mm Hg. and the experimental data was correlated by the Antoine equation (289, 290), with P in mm Hg and t in °C ... 

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. 

The design of a distillation column is based on information derived from the VLE diagram describing the mixtures to be separated. The vapor-liquid equilibrium characteristics are indicated by the characteristic shapes of the equilibrium curves. This is what determines the number of stages, and hence the number of trays needed for a separation. Although column designs are often proprietary, the classical method of McCabe-Thiele for binary columns is instructive on the principles of design. 

By using vapor-liquid equilibrium data the above integral can be evaluated numerically. A graphical method is also possible, where a plot of l/(y - xj versus Xr is prepared and the area under the curve over the limits between the initial and fmal mole fraction is determined. However, for special cases the integration can be done analytically. If pressure is constant, the temperature change in the still is small, and the vapor-liquid equilibrium values (K-values, defined as K=y/x for each component) are independent from composition, integration of the Rayleigh equation yields ... 

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. 

The vapor-liquid equilibrium relationship may be determined from... 

Griswold, J., D. Andres and V. A. Klein, Determination of High Pressure Vapor-Liquid Equilibria. The Vapor-Liquid Equilibrium of Benzene-Toluene," Trans. Amer. Inst. Chem. Engrs. 39, 223 (1943). 

These models are semiempirical and are based on the concept that intermolecular forces will cause nonrandom arrangement of molecules in the mixture. The models account for the arrangement of molecules of different sizes and the preferred orientation of molecules. In each case, the models are fitted to experimental binary vapor-liquid equilibrium data. This gives binary interaction parameters that can be used to predict multicomponent vapor-liquid equilibrium. In the case of the UNIQUAC equation, if experimentally determined vapor-liquid equilibrium data are not available, the Universal Quasi-chemical Functional Group Activity Coefficients (UNIFAC) method can be used to estimate UNIQUAC parameters from the molecular structures of the components in the mixture3. 

Since all experimental data for vapor-liquid equilibrium have some experimental uncertainty, it follows that the parameters obtained from data reduction are not unique3. There are many sets of parameters that can represent the experimental data equally well, within experimental uncertainty. The experimental data used in data reduction are not sufficient to fix a unique set of best parameters. Realistic data reduction can determine only a region of parameters2. 

Before an equation of state can be applied to calculate vapor-liquid equilibrium, the fugacity coefficient < />, for each phase needs to be determined. The relationship between the fugacity coefficient and the volumetric properties can be written as ... 

Example 4.5 2-Propanol (isopropanol) and water form an azeotropic mixture at a particular liquid composition that results in the vapor and liquid compositions being equal. Vapor-liquid equilibrium for 2-propanol-water mixtures can be predicted by the Wilson equation. Vapor pressure coefficients in bar with temperature in Kelvin for the Antoine equation are given in Table 4.113. Data for the Wilson equation are given in Table 4.126. Assume the gas constant R = 8.3145 kJ-kmol 1-K 1. Determine the azeotropic composition at 1 atm. 

The vapor-liquid x-y diagram in Figures 4.6c and d can be calculated by setting a liquid composition and calculating the corresponding vapor composition in a bubble point calculation. Alternatively, vapor composition can be set and the liquid composition determined by a dew point calculation. If the mixture forms two-liquid phases, the vapor-liquid equilibrium calculation predicts a maximum in the x-y diagram, as shown in Figures 4.6c and d. Note that such a maximum cannot appear with the Wilson equation. 

Care should be exercised in using the coefficients from Table 4.14 to predict two-liquid phase behavior under subcooled conditions. The coefficients in Table 4.14 were determined from vapor-liquid equilibrium data at saturated conditions. 

In contrast to the Gibbs ensemble discussed later in this chapter, a number of simulations are required per coexistence point, but the number can be quite small, especially for vapor-liquid equilibrium calculations away from the critical point. For example, for a one-component system near the triple point, the density of the dense liquid can be obtained from a single NPT simulation at zero pressure. The chemical potential of the liquid, in turn, determines the density of the (near-ideal) vapor phase so that only one simulation is required. The method has been extended to mixtures [12, 13]. Significantly lower statistical uncertainties were obtained in [13] compared to earlier Gibbs ensemble calculations of the same Lennard-Jones binary mixtures, but the NPT + test particle method calculations were based on longer simulations. 

The solution requires the concentration of the heptane and toluene in the vapor phase. Assuming that the composition of the liquid does not change as it evaporates (the quantity is large), the vapor composition is computed using standard vapor-liquid equilibrium calculations. Assuming that Raoult s and Dalton s laws apply to this system under these conditions, the vapor composition is determined directly from the saturation vapor pressures of the pure components. Himmelblau6 provided the following data at the specified temperature ... 

Several techniques are available for measuring values of interaction second virial coefficients. The primary methods are reduction of mixture virial coefficients determined from PpT data reduction of vapor-liquid equilibrium data the differential pressure technique of Knobler et al.(1959) the Bumett-isochoric method of Hall and Eubank (1973) and reduction of gas chromatography data as originally proposed by Desty et al.(1962). The latter procedure is by far the most rapid, although it is probably the least accurate. 

Stoeck, S. and Roscher, T. Determination of the vapor-liquid equilibrium in the system cyclopentadiene-norbomene, Leuna... 

The proper design of distillation and absorption columns depends on knowledge of vapor—liquid equilibrium, as do flash calculations used to determine the physical state of streams at given conditions of temperature, pressure, and composition. Detailed treatments of vapor—liquid equilibria are available (6,7). 

A procedure is presented for correlating the effect of non-volatile salts on the vapor-liquid equilibrium properties of binary solvents. The procedure is based on estimating the influence of salt concentration on the infinite dilution activity coefficients of both components in a pseudo-binary solution. The procedure is tested on experimental data for five different salts in methanol-water solutions. With this technique and Wilson parameters determined from the infinite dilution activity coefficients, precise estimates of bubble point temperatures and vapor phase compositions may be obtained over a range of salt and solvent compositions. 

On examination of Equations 14 and 16, it is clear that estimates of vapor pressure lowering and ks are all that are required to determine the influence of a given salt on the vapor-liquid equilibrium behavior of a binary solvent mixture. 

Vapor-liquid equilibrium experiments were performed with an improved Othmer recirculation still as modified by Johnson and Furter (2). Temperatures were measured with Fisher thermometers calibrated against boiling points of known solutions. Equilibrium compositions were determined with a vapor fractometer using a type W column and a thermal conductivity detector. The liquid samples were distilled to remove the salt before analysis with the gas chromatograph the amount of salt present was calculated from the molality and the amount of solvent 2 present. Temperature measurements were accurate to 0.2°C while compositions were found to be accurate to 1% over most of the composition range. The system pressure was maintained at 1 atm. 1 mm... 

A method of prediction of the salt effect of vapor-liquid equilibrium relationships in the methanol-ethyl acetate-calcium chloride system at atmospheric pressure is described. From the determined solubilities it is assumed that methanol forms a preferential solvate of CaCl296CH OH. The preferential solvation number was calculated from the observed values of the salt effect in 14 systems, as a result of which the solvation number showed a linear relationship with respect to the concentration of solvent. With the use of the linear relation the salt effect can be determined from the solvation number of pure solvent and the vapor-liquid equilibrium relations obtained without adding a salt. 

Therefore, the solvation number can be calculated by determining xia from the measured values using the vapor-liquid equilibrium relation obtained without... 

Prediction of salt effect. The procedure for calculation of the preferential solvation number S has been described above. By reversing this procedure, that is, by determining xia from S, we can estimate the salt effect using the vapor-liquid equilibrium without a salt. When the salt concentration is below saturation, the preferential solvation number S can be expressed as follows in cases where the solvation is formed with the first component. 

The salt effects of potassium bromide and a series office symmetrical tetraalkylammonium bromides on vapor-liquid equilibrium at constant pressure in various ethanol-water mixtures were determined. For these systems, the composition of the binary solvent was held constant while the dependence of the equilibrium vapor composition on salt concentration was investigated these studies were done at various fixed compositions of the mixed solvent. Good agreement with the equation of Furter and Johnson was observed for the salts exhibiting either mainly electrostrictive or mainly hydrophobic behavior however, the correlation was unsatisfactory in the case of the one salt (tetraethylammonium bromide) where these two types of solute-solvent interactions were in close competition. The transition from salting out of the ethanol to salting in, observed as the tetraalkylammonium salt series is ascended, was interpreted in terms of the solute-solvent interactions as related to physical properties of the system components, particularly solubilities and surface tensions. 

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