Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Volume Translation

Predictions of saturated liquid densities of pure fluids from the Soave-Redlich-Kwong equation of state and, to a lesser extent, the Peng-Robsinson equation of state deviate from experimental data. This should be expected given the [Pg.59]

In all of the equations of state discussed so far, the repulsive term has remained unchanged and equal to that proposed by van der Waals and given by the first term on the r.h.s. of eq 4.1. Thanks to the development of molecular simulation methods starting in the 1960s, we are able today to quantify the effects of different interactions on the thermodynamic properties of a fluid. A simple comparison of the van der Waals repulsive term against molecular simulation data for hard spheres reveals the inaccuracy of the former. A more accurate simple repulsive term was proposed by Elliott et a/. and was incorporated into a cubic equation of state that also accounts for the shape (non-sphericity) of the molecules. The Elliott-Suresh-Donohue equation of state is given by  [Pg.60]


Zohar. Five volumes, translated by Harry Sperling and Maurice Simon. New York Rebecca Bennet Publications, no date London Socino Press, 1984. [Pg.255]

Fig. 8.1. Stokes and free volume translational diffusion processes. Black circles solute molecules. White circles solvent molecules. Fig. 8.1. Stokes and free volume translational diffusion processes. Black circles solute molecules. White circles solvent molecules.
Peneloux et al. [35] have introduced a clever method of improving the saturated liquid molar volume predictions of a cubic equation of state, by translating the calculated volumes without efffecting the prediction of phase equilibrium. The volume-translation parameter is chosen to give the correct saturated liquid volume at some temperature, usually at a reduced temperature Tr = T/Tc = 0.7, which is near the normal boiling point. It is possible to improve the liquid density predictions further by making the translation parameter temperature dependent. [Pg.43]

FIGURE 6.18 The variation of the molar heat capacity of iodine vapor at constant volume. Translation always contributes rotation contributes except at very low temperature, and vibrations of the molecule contribute at very high temperatures. When the molecules dissociate, the heat capacity becomes very large, but then settles down to a value characteristic of 2 mol I atoms undergoing only translational motion. [Pg.410]

Eganet al (1994) ... it at [sic] seems plausible that small differences in brain volume translate into millions of excess neurones for some individuals, accounting for their higher IQ. ... [Pg.63]

Beyond applications reported in the literature, process simulation is ubiquitous throughout the chemical industry and academia. Every time users select the Soave, or SRK, thermodynamics model, they apply the Soave equation. One motivation for this selection is the long experience with the model and the compilation of correction factors, when the basic model is deficient. For example, binary interaction parameters (ky s) have been compiled for a large number of binary mixtures to improve VLE correlation. It is also possible to compensate for inaccuracies in density through volume translations. ... [Pg.2748]

Wang, L.S. Ahlers, J. Gmehling, J. Development of a universal group contribution equation of state. 4. Prediction of vapor-liquid equilibria of polymer solutions with the volume translated group contribution equation of state. Ind. Eng. Chem. Res. 2003, 42, 6205-6211. [Pg.2752]

Figure 7 Temperature-density plot for water at constant pressure (253.31 bar) calculated from various equations of state. HSVTvdW is the hard-sphere, volume-translated van der Waals equation of state developed by Kutney et al. (Reprinted from Ref. 48). Other equations of state shown PR = Peng-Robinson, VTPR = volume translated PR, RKS = Redlich-Kwong-Soave, VTRKS = volume-translated RKS... Figure 7 Temperature-density plot for water at constant pressure (253.31 bar) calculated from various equations of state. HSVTvdW is the hard-sphere, volume-translated van der Waals equation of state developed by Kutney et al. (Reprinted from Ref. 48). Other equations of state shown PR = Peng-Robinson, VTPR = volume translated PR, RKS = Redlich-Kwong-Soave, VTRKS = volume-translated RKS...
M. C. Kutney, V. S. Dodd, K. A. Smith, H. J. Herzog and J. W. Tester, A Hard-Sphere Volume-Translated van der Waals Equation of State for Supercritical Process Modeling ... [Pg.446]

An improvement can be achieved with the volume translation concept introduced by Peneloux et al [55]. The idea is that the specific volume calculated by the equation of state is corrected by addition of a constant parameter c. The volume translation has no effect on the vapor-liquid equilibrium calculation, as both the liquid and the vapor volume are simultaneously translated by a constant value. The procedure has also little effect on the calculated vapor volumes, as c is in the order of magnitude of a liquid volume far away from the critical temperature. [Pg.56]

For the application to mixtures, the volume translation parameter c can be calculated by a simple linear mixing rule ... [Pg.56]

The volume translation used in the VTPR equation of state (see Eqs. (2.177-2.180)) has no influence on the results of the phase equilibrium calculations, it does not need to be considered in a mixing rule [16]. Equation (2,180) is used as a mixing rule for the volume translation. [Pg.170]

In Figure 5.37 the experimental and calculated enthalpies of vaporization using the SRK and the volume translated PR equation of state for 11 different compounds in a wide temperature range up to the critical temperature are shown. It can be... [Pg.236]

Figure 5.39 Experimental and calculated liquid densities using the volume translated PR equation of state for six different solvents in the temperature range Tr = 0.5—0.8. Figure 5.39 Experimental and calculated liquid densities using the volume translated PR equation of state for six different solvents in the temperature range Tr = 0.5—0.8.
Equation of state Soave-Redlich-Kwong Volume-translated Peng-Robinson... [Pg.317]

State, such as Predictive Soave-Redlich-Kwong (PSRK) and Volume-Translated Peng-Robinson (VTPR), or electrolyte models (LIQUAC and LIFAC). ... [Pg.491]

Calculate the enthalpy of reaction for the ammonia synthesis at 450 C and a pressure of 600 atm using the value of the standard enthalpy of reaction at 450 °C in the ideal gas state calculated in Example 12.1. For the calculation of the residual enthalpies, the group contribution equation of state volume-translated Peng-Robinson (VTPR) should be applied. The required VTPR parameters are given in Appendix K. [Pg.529]

The required pure component properties Tc, Pc, and co together with the parameters for the Twu a-function are given in Appendices A and K. The volume translation parameter c should be calculated using Eq. (2.179). [Pg.540]

Being a Translation from the Earliest Account of that Country, entitled Rerum Muscoviticarum Commentarii, by the Baron Sigismund von Herberstein, Ambassador from the Court of Germany to the Grand Prince Vasiley Ivanovich, in the years 1517 and 1526. Two Volumes. Translated and Edited by R. II, Major, Esq. Vol. i. (1851.)... [Pg.176]

Improving Accuracy of PR Equation of State for Predicting Gas Condensate Density by a New Volume Translated Model... [Pg.266]

This work presents a temperature-dependent volume translated model for Peng-Robinson equation of state (PR EOS) for calculating liquid densities of pure compounds and mixtures in the saturated region. For pure compounds, the average absolute percent deviation (AAPD) were calculated in the reduced temperature range of (0.3-0.99). Similarly for mixtures, the (AAPD) of different binary, ternary and multicomponent mixtures were determined. The AAPD for 29 pure compounds and different mixtures(binary, ternary and multicomponents) were 1.29 and 1.35 respectively. The accuracy of this model was compared well with three well-known liquid density correlations and other earlier volume translated models. [Pg.266]

Keywords volume translation, liquid density, EOS, natural gas, LNG, NGL, LPG. [Pg.266]

Where and are critical volume translation factor and critical compressibility factor respectively. Equation (11) has two parameters yand that must be determined for each component. These parameters were optimized by minimizing the following objective function ... [Pg.267]

Where N is the number of experimental data points for each component. By using equation (12), the two parameters were determined for all pure components. Now, the volume translation factor, c(T), can be determined therefore, the improved liquid density value was calculated as follows ... [Pg.268]

Like equation (8), the error in calculation of liquid density by this new volume translation model can be determined by comparison with experimental dada points ... [Pg.268]

Table 1. Optimized parameters for temperature-dependent volume translation model to PR EOS... Table 1. Optimized parameters for temperature-dependent volume translation model to PR EOS...
Most of the pervious temperature-dependent volume translation models were programmed beside this new model (VTPR) in order to compare their abilities in liquid density prediction. The absolute percent deviation (APD) for all models are listed in Tables 2 and 3 in addition to three liquid density correlations. As listed in the Tables 2 and 3, this new volume translation model (VTPR) has the (AAPD) about 1.11 and 1.29 for optimized values and generalized form respectively. These errors are less than other volume translation models. Figure 1 presents graphical comparisons between the predicted and experimental liquid density values of methane. [Pg.269]

Where NC and x, are number of components in mixture and mole fraction of component i respectively. Ji and Lempe [7] used an alternative composition factor ) instead of mole fraction. This factor was used in the mixing rule for volume translation factor (c) which was originally introduced by McFarlane et al. [8]. This mixing rule was changed slightly in order to improve accuracy ... [Pg.269]

The results in Table 4 indicate that VTPR presents the least (AAPD) among other volume translation models, and can reduce the (AAPD) of PR EOS from 8.40 to 1.35. [Pg.270]


See other pages where Volume Translation is mentioned: [Pg.53]    [Pg.2749]    [Pg.2750]    [Pg.409]    [Pg.23]    [Pg.132]    [Pg.1430]    [Pg.1430]    [Pg.56]    [Pg.56]    [Pg.58]    [Pg.239]    [Pg.318]    [Pg.154]    [Pg.5]    [Pg.266]    [Pg.267]   
See also in sourсe #XX -- [ Pg.266 ]

See also in sourсe #XX -- [ Pg.145 ]

See also in sourсe #XX -- [ Pg.59 , Pg.453 , Pg.455 ]




SEARCH



Volume-translated Peng-Robinson equation

Volume-translation parameter

© 2024 chempedia.info