Vapor pressure calculation methods

This equation is implicit in fly, inasmuch as the saturated volumes are dependent on fly, but the equation can be readily solved, for instance, by the method of repeated substitution. By using the solved value of fly in the eos. Equation (4.162), the vapor pressure calculated by the eos simply reproduces the experimental vapor pressure data. Wilson correlated the fly s that are fitted to vapor pressure data of a number of normal fluids to obtain Equation (4.157), the Wilson eos. Vapor pressure calculated by the Wilson eos is improved over that of the RK eos, but the accuracy still leaves something to be desired. Soave correlated the vapor pressure, fitting fly with Equation (4.164). Even better, the Soave eos is useful for the quantitative calculation of vapor pressure. In addition, the Peng-Robinson and the chain-of-rotators eos s provide quantitative calculations of vapor pressure. 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

If the vapor pressure is of interest, the acentric factor is calculated by the Lee and Kesler formula or by the Soave method, which are given in article 4.5.2. 

The vapor pressure will be calculated according to one of the methods described later. 

For pure hydrocarbons and petroleum fractions the vapor pressure can be calculated by three methods which are ... 

This method is based on the expression proposed by Lee and Kesler in 1975. It applies mainly to light hydrocarbons. The average error is around 2% when the calculated vapor pressure is greater than 0.1 bar. 

Maxwell and Bonnel (1955) proposed a method to calculate the vapor pressure of pure hydrocarbons or petroleum fractions whose normal boiling point and specific gravity are known. It is iterative if the boiling point is greater than 366.5 K ... 

When criticals cannot he estimated with reasonable accuracy, the method of Maxwell and BonnelP is recommended. The normal boiling point and the specific gravity at 60 F (15.5 C) are required inputs. According to what vapor pressure range is expected, the vapor pressure is calculated from Eqs. (2-34), (2-35), or (2-36). If the wrong range is selected, the procedure will need to be repeated. 

Average errors at low pressures for compounds with tabulated m and C are within a few percent. When values of m and C are calculated from only two vapor pressure points, the method should be used only for interpolation and limited extrapolation. The method is usable from about 220 K (so long as it is above the freezing point of the compound) to the critical point of water (about 647 K). 

Single-Effect Evaporators The heat requirements of a singleeffect continuous evaporator can be calculated by the usual methods of stoichiometry. If enthalpy data or specific heat and heat-of-solution data are not available, the heat requirement can be estimated as the sum of the heat needed to raise the feed from feed to product temperature and the heat required to evaporate the water. The latent heat of water is taken at the vapor-head pressure instead of at the product temperature in order to compensate partiaUv for any heat of solution. If sufficient vapor-pressure data are available for the solution, methods are available to calculate the true latent heat from the slope of the Diihriugliue [Othmer, Ind. Eng. Chem., 32, 841 (1940)]. 

The application of information in Figure 6.19 requires some explanation. The decision as to which calculation method to choose should be based upon the phase of the vessel s contents, its boiling point at ambient pressure T its critical temperature Tf, and its actual temperature T. For the purpose of selecting a calculation method, three different phases can be distinguished liquid, vapor or nonideal gas, and ideal gas. Should more than be performed separately for each phase, and the... 

The calculation method can be selected by application of the decision tree in Figure 9.2. The liquid temperature is believed to be about 339 K, which is the temperature equivalent to the relief valve set pressure. The superheat limit temperatures of propane and butane, the constituents of LPG, can be found in Table 6.1. For propane, T, = 326 K, and for butane, T i = 377 K. The figure specifies that, if the liquid is above its critical superheat limit temperature, the explosively flashing liquid method must be chosen. However, because the temperature of the LPG is below the superheat limit temperature (T i) for butane and above it for propane, it is uncertain whether the liquid will flash. Therefore, the calculation will first be performed with the inclusion of vapor energy only, then with the combined energy of vapor and liquid. 

Because flashing steam-condensate lines represent two-phase flow, with the quantity of liquid phase depending on die system conditions, these can be designed following the previously described two-phase flow methods. An alternate by Ruskin [28] uses the concept but assumes a single homogeneous phase of fine liquid droplets dispersed in the flashed vapor. Pressure drop was calculated by the Darcy equation ... 

When tested in accordance with the methods given in Table 20.1 the properties of the commercial butane and commercial propane shall be in accordance with the limiting requirements given in that table. For gauge vapor pressure, either the direct measurements method described in BS 3324 or the calculation procedure described in Appendix C of this standard shall be used. 

General. The methods we have used to calculate the vapor pressures and vapor compositions at high temperatures are the same as those used previously (1-2) for the U/0 system. The total pressure, p(total), In equilibrium with a Pu02 x condensed phase Is... 

For the monomers in the polymerization under consideration the fugacity coefficients were estimated by Redlich-Kwong equation of state and were found to be close to unity. The activity coefficients (8) for the monomers were estimated by Scatchard-Hildebrand s method (5) for the most volatile monomer there was a temperature dependence but none for the other monomer. These were later confirmed by applying the UNIFAC method (6). The saturation vapor pressures were calculated by Antoine coefficients (5). 

Gee ° has applied this method to the determination of the interaction parameters xi for natural rubber in various solvents. Several rubber vulcanizates were used. The effective value of VelV for each was determined by measuring its extension under a fixed load when swollen in petroleum ether. Samples were then swollen to equilibrium in other solvents, and xi was calculated from the swelling ratio in each. The mean values of xi for the several vulcanizates in each solvent are presented in Table XXXVI, where they are compared with the xi s calculated (Eq. XII-30) from vapor pressure measurements on solutions of unvulcanized rubber in some of the same solvents. The agreement is by no means spectacular, though perhaps no worse than the experimental error in the vapor pressure method. 

In the refining of the Group V metals (which are more accurately represented as metal-carbon-oxygen alloys), carbon deoxidation is not the only method by which oxygen is removed, because sacrificial deoxidation also occurs simultaneously. The relative extents to which each of these two deoxidation modes contributes to the overall removal of oxygen can be assessed by calculating the ratio of the vapor pressures of carbon monoxide and the metal monoxide over the M-C-0 alloy. The value of this ratio for vanadium at 2000 K is given by the expression... 

In the multimedia models used in this series of volumes, an air-water partition coefficient KAW or Henry s law constant (H) is required and is calculated from the ratio of the pure substance vapor pressure and aqueous solubility. This method is widely used for hydrophobic chemicals but is inappropriate for water-miscible chemicals for which no solubility can be measured. Examples are the lower alcohols, acids, amines and ketones. There are reported calculated or pseudo-solubilities that have been derived from QSPR correlations with molecular descriptors for alcohols, aldehydes and amines (by Leahy 1986 Kamlet et al. 1987, 1988 and Nirmalakhandan and Speece 1988a,b). The obvious option is to input the H or KAW directly. If the chemical s activity coefficient y in water is known, then H can be estimated as vwyP[>where vw is the molar volume of water and Pf is the liquid vapor pressure. Since H can be regarded as P[IC[, where Cjs is the solubility, it is apparent that (l/vwy) is a pseudo-solubility. Correlations and measurements of y are available in the physical-chemical literature. For example, if y is 5.0, the pseudo-solubility is 11100 mol/m3 since the molar volume of water vw is 18 x 10-6 m3/mol or 18 cm3/mol. Chemicals with y less than about 20 are usually miscible in water. If the liquid vapor pressure in this case is 1000 Pa, H will be 1000/11100 or 0.090 Pa m3/mol and KAW will be H/RT or 3.6 x 10 5 at 25°C. Alternatively, if H or KAW is known, C[ can be calculated. It is possible to apply existing models to hydrophilic chemicals if this pseudo-solubility is calculated from the activity coefficient or from a known H (i.e., Cjs, P[/H or P[ or KAW RT). This approach is used here. In the fugacity model illustrations all pseudo-solubilities are so designated and should not be regarded as real, experimentally accessible quantities. 

A wide variety of solubilities (in units of g/m3 or the equivalent mg/L) have been reported. Experimental data have the method of determination indicated. In other compilations of data the reported value has merely been quoted from another secondary source. In some cases the value has been calculated. The abbreviations are generally self-explanatory and usually include two entries, the method of equilibration followed by the method of determination. From these values a single value is selected for inclusion in the summary data table. Vapor pressures and octanol-water partition coefficients are selected similarly. 

Kim, Y.-H., Woodrow, J. E., Seiber, J. N. (1984) Evaluation of a gas chromatographic method for calculating vapor pressures with organophosphorus pesticides. J. Chromatogr. 314, 37-53. 

Mokbel, I., Rauzy, E., Meille, J.P., Jose, J. (1998) Low vapor pressures of 12 aromatic hydrocarbons. Experimental and calculated data using a group contribution method. Fluid Phase Equil. 147, 271-284. 

In essence, volumetric methods equilibrate a known headspace dosing volume at a given (measured) water vapor pressure, and then they expose the pre-equil-ibrated sample to this water vapor, with subsequent measurement of the water vapor pressure after equilibration. The mass of water sorbed, An (in moles), at the final pressure in the system, Pf, is obtained from the difference, AP, between Pfcalc, the calculated water vapor pressure at equilibrium, and /ylleas, the final measured water vapor pressure ... 

The averaged velocity of the vapor is expressed by Eq. (54). The pressure distribution in the vapor layer can be obtained by solving Eqs. (54) and (73)-(75) by a piecewise integration method. Details of the solving procedure and how to use the vapor pressure in flow field calculation are given in Section IV.A.2. 

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