Fraction prediction

Although unattached fractions predicted using the kinetic and diffusion theory for high aerosol concentrations, such as mine atmospheres, are comparable, the same cannot be said for unattached fractions predicted at low aerosol concentrations, such as indoor air. For low aerosol concentrations, neither the kinetic nor the diffusion theory predicts unattached fractions close to those predicted by the hybrid theory. Exclusive use of either of these two theories results in large errors. 

The large Fe isotope fractionations predicted to occur between aqueous ferric and ferrous Fe species (Fig. 3) has been investigated experimentally at two temperatures for hexaquo Fe(III) and Fe(II), as well as the effect of CF substitution (Johnson et al. 2002 Welch et al. 2003). The kinetics of isotopic exchange in these experiments was determined using an enriched Te tracer for the ferric Fe phase. The Fe tracer experiments reported in Johnson et al. (2002) and Welch et al. (2003) indicate that 95% isotopic equilibrium between Fellll) and Fe(II)gq occurs within —60 seconds at room temperature (22°C), or within —5 minutes at 0°C. The relatively slower isotopic exchange rates at lower temperatures are expected. 

N (rpm) Average volume fraction Predicted volume fraction... 

If no experimental data arc available, bubble pressures and vapor mole fractions are calculated at liquid mole fractions Xi = 0 to 1 at intervals of 0.1. In this mode no data are entered to, or accessed from, the disk. Instead, the user provides critical temperature, critical pressure, acentric factor, and the PRSV k parameter for each pure component in addition the Wong-Sandler mixing-rule parameter k 2 and a temperature. The program then returns isothermal bubble pressure and vapor mole fraction predictions at the temperature entered. 

Positive predictive value (= precision) a/(a + b) Fraction predicted positives that are actually positive... 

Negative predictive value d/(c + d) Fraction predicted negatives that are actually negative... 

As the first illustration of the use of these equations, consider vapor-liquid equilibrium in the hexane-triethylamine system at 60°C. These species form an essentially ideal mixture. The vapor pressure of hexane af this temperature is 0.7583 bar and that of triethylamine is 0.3843 bar these are so low that the fugacity coefficients at saturation and for the vapor phase can be neglected. Consequently, Eqs. 10.1-3 and 10.1-4 should be applicable to this system. The three solid lines in Fig. 10.1-1 represent the two species partial pressures and the total pressure, which were calculated using these equations and all are linear functions of the of liquid-phase mole fraction the points are the experimental results. The close agreement between the computations and the laboratory data indicates that the hexane-triethylamine mixture is ideal at these conditions. Note that this linear dependence of the partiaLand total pressures on mole fractions predicted by Eqs. 10.1-2 and 10.1-3 is trae only for ideal mixtures it is not true for nonideal mixtures, as we shall see in Sec. 10.2. 

PRKS Vapor Fraction Predictions C02 - cyclvpeaiane mixture... 

Yu et al. [1994] carried out PALS measurements on four PS fractions (4, 9, 25, and 400 kDa, respectively) versus temperature (Figure 10.4). They evaluated the free-volume fractions on the basis of the proportionality between the free-volume fraction as probed by o-Ps and the product of the o-Ps intensity I3 and the mean cavity volume assumed spherical, as sketched previously [Eq. (10.16)]. On this basis they observed agreement with the free-volume fraction predicted as given by the lattice-hole model [Simha and Somcynsky, 1969] over a range of temperatures above Tg, the proportionality constant C being a molar mass-dependent fitting parameter. 

Dong D.W. et al. 2011. The Mine Gas voltime fraction Prediction based on HHT method. China Safety Science Journal 9 100-105. 

The 3-box model considers a fraction of the Freundlich sites to be in instantaneous equilibrium with dissolved Cs. The larger fraction for K-illite (Table I) is consistent with the greater contribution of the planar sites to Cs sorption on this clay. However, the instantaneous-equilibrium fractions predicted by the model are much greater than can be explained by planar sites alone, and suggest that a substantial portion of the frayed edge sites may also reach very rapid (instantaneous) equilibrium with the solution. The reaction rates for the remaining fraction of reversible sites are similar for both the Ca- and K-illite. 

CO mass fraction predicted by the AR is approximately 0.21. This value is achievable for a mass fraction residence time of approximately 0.5m. h/g as predicted by the AR constmction. Figure 9.9(b) compares the size of the AR in relation to the stoichiometric subspace. 

In Fig. 3.9 we present a comparison of the free volume fraction predicted by SPT (3.36) and computer simulations [32] on hard spheres plus penetrable hard spheres for q = 0.5 as a function of . As can be seen the agreement is very good. In the limit of small depletants the 2 and ) terms of (3.30) can be omitted giving ... 

Figure 19 Comparison of axial profiles of solids volume fraction predicted with the EMMS and filtered drag models In 2D and 3D geometries (Hong et al, 2015).

In order to predict natural gas dew point pressures, we used the van der Waals mixing rules and the decay function proposed by Pedersen et al. (1992) for the heavy ends of different natural gas mixtures containing plus fraction. Predicted dew point pressures were in good agreement with experimental data (Elsharkawy, 2002). 

Fig. 1L8 Comparison of the dry hydrogen mole fraction predicted for the SE-SMR process with the pseudo-...

Composition, particularly C3 and C4, is the most important indicator to evaluate the quality of the LPG product Figure 6.59 represents selected model predictions on LPG composition with AAD of each component. For the most important components, C3 and C4, the model shows only 0.021 and 0.058 AADs, respectively, in molar fraction predictions. For other liquid products, the distillation curve is the most popular analysis to indicate the vaporization temperature after a certain amount of oil fraction vaporized. Figures 6.60 and 6.61 illustrate selected model predictions on distillation curves of light naphtha, heavy naphtha, jet fuel, and residue oil. 

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