PVT Data

Whereas the fundamental residual property relation derives its usefulness from its direct relation to experimental PVT data and equations of state, the excess property formulation is useful because and are all experimentally accessible. Activity coefficients are found from vapor—Hquid... 

Thermodynamic data on H2, the mixed hydrogen—deuterium molecule [13983-20-5] HD, and D2, including values for entropy, enthalpy, free energy, and specific heat have been tabulated (16). Extensive PVT data are also presented in Reference 16 as are data on the equihbrium—temperature... 

Cluusius-Clupeyron Eijliation. Derived from equation 1, the Clapeyron equation is a fundamental relationship between the latent heat accompanying a phase change and pressure—volume—temperature (PVT data for the system (1) ... 

Vugacity Coefficients. An exact equation that is widely used for the calculation of fugacity coefficients and fugacities from experimental pressure—volume—temperature (PVT) data is... 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

No tables of the coefficients of thermal expansion of gases are given in this edition. The coefficient at constant pressure, l/t)(3 0/3T)p for an ideal gas is merely the reciprocal of the absolute temperature. For a real gas or liquid, both it and the coefficient at constant volume, 1/p (3p/3T),, should be calculated either from the equation of state or from tabulated PVT data. 

Thns, the pressure or vohime dependence of the heat capacities may be determined from PVT data. The temperature dependence of the heat capacities is, however, determined empirically and is often given by equations such as... 

Thns the difference between the two heat capacities may be determined from PVT data. 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

The most satisfactory calciilational procedure for thermodynamic properties of gases and vapors requires PVT data and ideal gas heat capacities. The primary equations are based on the concept of the ideal gas state and the definitions of residual enthalpy anci residual entropy ... 

Values of Z and of (3Z/3T)p come from experimental PVT data, and the integrals in Eqs. (4-158), (4-159), and (4-161) may be evaluated by numerical or graphical methods. Alternatively, the integrals are expressed analytically when Z is given by an equation of state. Residual properties are therefore evaluated from PVT data or from an appropriate equation of state. 

In Eq. (4-215), ky is an empirical interaction parameter specific to an i-J molecular pair. When i = J and for chemically similar species, ky = 0. Otherwise, it is a small (usually) positive number ev uated from minimal PVT data or in the absence of data set equal to zero. 

Shay, R. M., Estimating Linear Shrinkage of Semicrystalline Resins from Pressure-Volume Temperature (pvT) Data, SPE-IMD Newsletter 49, Fall 1998. 

B. One Atmosphere Compressibilities. Most isothermal compressibility (6) measurements are made over extended pressure ranges and very few direct measurements have been made near 1 atm. It is difficult to obtain reliable values of 8 at 1 atm from high pressure PVT data due to the problems of extrapolating the compression [k = (v - v )/v P, where v is the specific volume] to zero applied pressure. If the compressions, volumes, or densities are fit to functions of P, the compressibility... 

Macdonald (144) analyzed several equations of state which had a variety of mathematical forms including the Tammann equation and the secant bulk modulus equation chosen by Hayward. (In his statistical analysis, Macdonald used the PVT data of Kell and Whalley (26) which has been shown to be in error (29) Thus, the conclusions of Macdonald may be questionable.) He disagreed with Hayward and selected the Murnaghan equation to be superior to either the Tammann equation or the linear secant modulus equation chosen by Hayward. If, however, the Tammann equation and the Murnaghan equation were both expanded to second order in pressure, then Macdonald found that the results obtained from both equations would agree. As shown earlier, the expansion of the Tammann equation to second order is equivalent to the bulk modulus form of the original Tait equation. 

Unfortunately, at present, reliable PVT data for electrolytes at high pressures, temperatures and concentrations are not available to further test the applicability of these simple methods to natural waters. Reliable measurements of the speed of sound in aqueous electrolytes as a function of temperature, pressure and concentration should provide the data needed to test the postulation presented above. Since 1 atm measurements of vu and... 

Extensive PVT data as well as precise values for critical property IE s are available for 3He/4He, CH4/CD4, H2/D2 and H20/D20 and these isotopomer pairs comprise an excellent reference in formulating EOS analysis of PVT IE s. Critical properties and critical property IE s for these and a few other selected isotopomer... 

Values and expressions for HR and SR are found from equation 134 through use of PVT data and equations of state. 

Oil, gas and watar flow rates and veasel temperature and presaura together with choke sise and upstream cboke pressure at the well pad are monitored by the computer as before. At the end of the test, reports are produced and three point test data In the well file is updated. Because only a single stage separation process at elevated pressure is used, PVT data stored in the computer is used to correct the measured fluid voliones to standard conditions. Production allocation is handled in the same way by using the upstream choke pressure correlation. 

M.L. Japas and E.U. Franck, High Pressure Phase Equilibria and PVT-Data of the Water-oxygen System including Water-air to 673 K. and 25.0 MPa, Ber. Bunsenves. Phys. Chem., 89, (1985), 1268. 

Giuliani, G., Kumar, S., Zazzini, P, Polonara, F. (1995b) Vapor pressure and gas phase PVT data and correlation for 1,1,1-trifluoroethane (R143a). J. Chem. Eng. Data 40, 903-908. 

The hard sphere diameters were then used to calculate the theoretical Enskog coefficients at each density and temperature. The results are shown in Figure 3 as plots of the ratio of the experimental to calculated coefficients vs. the packing fraction, along with the molecular dynamics results (24) for comparison. The agreement between the calculated ratios and the molecular dynamics results is excellent at the intermediate densities, especially for those ratios calculated with diameters determined from PVT data. Discrepancies at the intermediate densities can be easily accounted for by errors in measured diffusion coefficients and calculated diameters. The corrected Enskog theory of hard spheres gives an accurate description of the self-diffusion in dense supercritical ethylene. 

Our previous study (J 6) of self diffusion in compressed supercritical water compared the experimental results to the predictions of the dilute polar gas model of Monchick and Mason (39). The model, using a Stockmayer potential for the evaluation of the collision integrals and a temperature dependent hard sphere diameters, gave a good description of the temperature and pressure dependence of the diffusion. Unfortunately, a similar detailed analysis of the self diffusion of supercritical toluene is prevented by the lack of density data at supercritical conditions. Viscosities of toluene from 320°C to 470°C at constant volumes corresponding to densities from p/pQ - 0.5 to 1.8 have been reported ( 4 ). However, without PVT data, we cannot calculate the corresponding values of the pressure. 

Figure 19. Static structure factor S(q) in the small- region, at T = 297.6 K, for p = 0.95, 1.37, 1.69, and 1.93 nm-3 (from the bottom to the top), calculated with the ODS integral equation. The dotted lines correspond to the calculations with the twobody potential alone and the solid lines correspond to those that combine the two- and three-body interactions. The squares are for the experimental data of Formisano et al. [13] and the filled circles, at zero-q value, for the PVT data of Michels et al. [115]. Taken from Ref. [129].

Figure 20. Fourier transform of the direct correlation function c(r) at T = 297 K for p = 1.52, 1.97, and 2.42 nm-3 calculated with HMSA. The dashed lines correspond to the two-body interaction and the full lines to the two- plus three-body interaction. Open squares are for the experimental data of Formisano et al. [12]. The values of c(0) are taken from the PVT data of Trappeniers et al. [116]. Taken from Ref. [11].

In principle, the right-hand side of Eq. (3.6) is an infinite series. However, in practice a finite number of terms is used. In fact, PVT data show that at low pressures truncation after two terms provides satisfactory results. In general, the greater the pressure range, the larger the number of terms required. 

The proportionality constant R in Eq. (3.7) is called the universal gas constant. Its numerical value is determined by means of Eq. (3.8) from experimental PVT data for gases ... 

Since PVT data cannot in fact be taken at a pressure approaching zero, data taken at finite pressures are extrapolated to the zero-pressure state. The currently accepted value of (PV)f is 22,711.6 cm3 bar mol-1. Figure 3.4 shows how this... 

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