Volume prediction

This parameter is equal to one when the perfect gas law applies. When the pressure is increased to 10 atm, the predicted perfect gas volume is reduced to 2.24 L and the average distance between the molecules shrinks to 15.5 A when the pressure is increased to 100 atm, the predicted volume is reduced to 0.224 L and the average distance shrinks further to 7.2 A when the pressure is further increased to 1000 atm, the volume predicted by the perfect gas law is 0.0224 L and the average distance shrinks further to 3.3 A. By then, the intermolecular distance is roughly equal to the molecular diameters. As the molecules come together, the attractive forces are first felt, which manifests itself by a drop from the ideal gas volume, which is represented by Z < 1. With further compression, the molecules begin to touch, and the repulsive forces become dominant, which manifests itself as a resistance to further volume reduction and Z > 1. 

For intravenous dosing simulations 60% of the clearance and volume predictions were vfithin twofold of the observed values and the ranking of compounds by predicted versus observed parameters showed correlation coefficients of 0.8 and 0.6 for clearance and volume respectively. For oral dosing simulations, 40% of the predicted AU C values were within twofold of observed values and the mean fold error was 4.1. For compounds with measured solubility less than 0.012 mg/mLonly 10% of predictions were within twofold, while for compounds vfith higher solubility 70% were within twofold [7] (see Figure 10.5). 

Dimensionless bubble volumes predicted by solving Eq. (12-11) numerically and adding the second stage increment are plotted in Fig. 12.1 as functions of the dimensionless flow rate Q, with ju as parameter. It is important to note that ju is constant for a given orifice in a given gas-liquid system. Hence, Fig. 12.1 or Eqs. (12-10) to (12-12) give a convenient means of predicting bubble formation in any liquid-gas system whose properties are known. Over most of... 

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. 

At moderate pressures, the molecules are close enough to exert some attraction between molecules. This attraction causes the actual volume to be somewhat less than the volume predicted by the ideal gas equation, that is, the z-factor will be less than 1.0. 

Dubois, J. E., and M. Loukianoff, DARC Logic Method for Molal Volume Prediction. SAR QSAR Environ. Res., 1993 1, 63-75. 

At 51° and 31.1°, there is only one volume for each pressure. At 12.1°, there are two different values of Vcorresponding to points B and C for the same pressure. However, the third volume predicted by equation (1) is missing. 

Theoretical approaches to total energy as a function of volume predict a phase transition to the rock salt structure under high pressure [11,12], The transition is calculated to occur at a pressure of about 245 GPa and an experimental value of 230 GPa [13] has been quoted [9], but other workers quote 10 -14 GPa [14]. The critical volume ratio [11] is V/V0 = 0.83, equivalent to a molecular volume reduction from 31 to 27 A3. 

For the field-scale projects that have been initiated, calculated optimum CO2 injection volumes ranged from 20 to 50 percent of the hydrocarbon pore volume. Predicted carbon dioxide utilization factors ranged from 5 to 15 Mcf C02/bbl of recovered oil. Projected ultimate enhanced oil recoveries ranged from 5 to 30 percent of the original oil-in-place (Soc. Petrol. Engrs. Forum Series, "Monitoring Performance of Full-Scale CO2 Projects," August 17-21, 1987). 

Boyle P, Gould AL, Roehrborn CG. Prostate volume predicts outcome of treatment of benign prostatic hyperplasia with finasteride Meta-analysis of randomized clinical trials. Urology 1996 48 398 05. 

Dubois, J.-E. and LoukianofF, M. (1993) DARC logic method for molal volume prediction. SAR ei QSAR Environ. Res., 1, 63—75. 

Table 3.4. The connectivity indices and the correction index used, and the van der Waals volumes predicted in units of cc/mole, for 18 polymers whose Vw could not be calculated reliably and consistently by using the group contribution tables available when this work was completed. The values of °% are listed in Table 2.2. The values used for %v are listed in Table 2.3 for silicon-containing polymers and in Table 2.2 for all other polymers. NvdW is determined...

Figure 9.5. Comparison of the molar polarization according to Lorentz and Lorenz (Pll) calculated from measured dielectric constants and molar volumes, with the molar polarization calculated from dielectric constants and molar volumes predicted by using the new correlations developed in this book, for 55 polymers. 

Excess volume predictions are extremely sensitive to the value used for the unlike-molecule size parameter. Small deviations must be allowed from the commonly used arithmetic mean mixing rule for size parameters if quantitative results are to be obtained for VE simultaneously with other measurable excess thermodynamic functions (GE and HE). It should be noted that similar conclusions have been drawn for mixtures of globular molecules (8). 

Campbell, B.C., et al.. Regional very low cerebral blood volume predicts hemorrhagic transformation better than diffusion-weighted imaging volume and thresholded apparent diffusion coefficient in acute ischemic stroke. Stroke, 2010. 41 p. 82-8. 

The discrepancy between prediction and observation in Figure 4.5 starts with the volume predicted right at the beginning of recovery at T, after stepping from Ti. This is particularly noticeable with the two lower Tj values, of experiments 2 and 3. The volumes predicted are too low and too far from the eventual equilibrium volume at T. This then seems to cause the maxima calculated to deviate from experiment in... 

In a typical new product development scenario, we self-evidently would not have the Inxury of actual sales data prior to launch. To complete the picture we used an Eskin-type trial and repeat volumetric model to predict sales volumes for the same 15 products, as would typically be done at the end of the new product development process. The sales volume predictions were then modelled against the corresponding values for our derived index of fit-to-brand. The exponential function shown in Fig. 5.14 fits very well. 

Fig. 2 Comparison of formula unit volumes of 34 high-nitrogen ionic crystals (g/cc) using experimental volume, predicted volumes using the experimental structures, predicted uncorrected volumes using optimized structures, and predicted volumes using optimized structures, corrected for the number of hydrogens (see text)...

The application of the conventional volume-translation technique generally improves the volume predictions away from the critical region, although the improvement is not guaranteed. In the retrograde and near-critical regions, both volumetric and modified volumetric translations may fail to predict volumetric behavior accurately (Bjorlykke and Firoozabadi, 1992). 

The standard state of a pure gas is the hypothetical state in which the gas is at pressure p° and the temperature of interest, and the gas behaves as an ideal gas. The molar volume of a gas at 1 bar may have a measurable deviation from the molar volume predicted by the ideal gas equation due to intermolecular forces. We must imagine the standard state in this case to consist of the gas with the intermolecular forces magically turned off and the molar volume adjusted to the ideal-gas value RT/p°. 

There is very little information available specifically addressing wave-by-wave overtopping volumes at composite structures. The guidance offered by Besley remains the best available. No new formulae or Wei bull a, b values are known so, for the purposes of maximum overtopping volume prediction, the methods for plain vertical walls (Sec. 16.4.2) are used. The key discriminator is that composite structures whose mound is sufficiently small to play little role in the overtopping process are treated as plain vertical, non-impulsive, whereas those with large mounds are treated as plain vertical, impulsive. 

---