Phase prediction method

Method f2.i describes the analysis of the trihalomethanes CHCI3, CHBr3, CHChBr, and CHClBr2 in drinking water using a packed column with a nonpolar stationary phase. Predict the order in which these four trihalomethanes will elute. 

Experiment diffusion coefficients are scarce and not highly accurate, especially in the liquid phase, leading to prediction methods with marginal accuracy. However, use of the v ues predicted are generally suit le for engineering calculations. At concentrations above about 10 mole percent, predicted values should be used with caution. Diffu-sivities in liquids are lO -lO times lower than those in gases. 

Generahzed prediction methods for fci and Hi do not apply when chemical reaction occurs in the liqmd phase, and therefore one must use ac tual operating data for the particular system in question. A discussion of the various factors to consider in designing gas absorbers and strippers when chemical reac tious are involved is presented by Astarita, Savage, and Bisio, Gas Treating with Chemical Solvents, Wuey (1983) and by Kohl and Ricseufeld, Gas Purification, 4th ed., Gulf (1985). 

Interfacial Area This consideration in agitated vessels has been reviewed and summarized by Tatterson (op. cit.). Predictive methods for interfacial area are not presented here because correlations are given for the overall volumetric mass transfer coefficient liquid phase controlhng mass transfer. 

Prediction methods attempt to quantify the resistances to mass transfer in terms of the raffinate rate R and the extract rate E, per tower cross-sectional area Af, and the mass-transfer coefficient in the raffinate phase and the extract phase times the interfacial (droplet) mass-transfer area per volume of tower a [Eqs. (15-32) and (15-33)]. 

There are many types of phase diagrams in addition to the two cases presented here these are summarized in detail by Zief and Wilcox (op. cit., p. 21). Solid-liquid phase equilibria must be determined experimentally for most binaiy and multicomponent systems. Predictive methods are based mostly on ideal phase behavior and have limited accuracy near eutectics. A predic tive technique based on extracting liquid-phase activity coefficients from vapor-liquid equilib-... 

Steam-liquid flow. Two-phase flow maps and heat transfer prediction methods which exist for vaporization in macro-channels and are inapplicable in micro-channels. Due to the predominance of surface tension over the gravity forces, the orientation of micro-channel has a negligible influence on the flow pattern. The models of convection boiling should correlate the frequencies, length and velocities of the bubbles and the coalescence processes, which control the flow pattern transitions, with the heat flux and the mass flux. The vapor bubble size distribution must be taken into account. 

The fluorescent lifetime of chlorophyll in vivo was first measured in 1957, independently by Brody and Rabinowitch (62) using pulse methods, and by Dmitrievskyand co-workers (63) using phase modulation methods. Because the measured quantum yield was lower than that predicted from the measured lifetime, it was concluded that much of the chlorophyll molecule was non-fluorescent, suggesting that energy transfer mechanisms were the means of moving absorbed energy to reactive parts of the molecule. 

The difficulties and low-throughput nature of the experimental dual determination, especially in alkane-water systems, the development of other techniques more amenable to automation, as well as more refined computational approaches for octanol-water systems, aU have contributed to Umit the use of the alkane-water system as a second bulk-phase system. However, efforts have been devoted to the development of log (alkane) computational prediction methods by Rekker et al. [13] as well as Caron and Ermondi [14]. 

The octanol-water partition coefficient Kow is widely used as a descriptor of hydrophobicity. Variation in /fow is primarily attributable to variation in activity coefficient in the aqueous phase (Miller et al. 1985) thus, the same correlations used for solubility in water are applicable to /fow. Most widely used is the Hansch-Leo compilation of data (Leo et al. 1971, Hansch and Leo 1979) and related predictive methods. Examples of Kow correlations are ... 

All the methodology just described requires that the solubilities of the analyte and its impurities be totally additive, which implies that the solubility of any given species cannot be affected by the presence of any other dissolved substance. Such a lack of independence is most commonly indicated by the existence of curved lines when the data are plotted in the conventional manner, and it has been discussed in great detail [38]. In the presence of specific molecular interactions, the phase solubility method cannot be used without the benefit of detailed knowledge of the nature and magnitude of the interactions. Such interactions can either increase or decrease the overall solubility, and the outcome is difficult to predict a priori. A thorough investigation is required to deduce the nature of the interactions if the phase solubility method is to be used. 

Normal-phase liquid chromatography is thus a steric-selective separation method. The molecular properties of steric isomers are not easily obtained and the molecular properties of optical isomers estimated by computational chemical calculation are the same. Therefore, the development of prediction methods for retention times in normal-phase liquid chromatography is difficult compared with reversed-phase liquid chromatography, where the hydrophobicity of the molecule is the predominant determinant of retention differences. When the molecular structure is known, the separation conditions in normal-phase LC can be estimated from Table 1.1, and from the solvent selectivity. A small-scale thin-layer liquid chromatographic separation is often a good tool to find a suitable eluent. When a silica gel column is used, the formation of a monolayer of water on the surface of the silica gel is an important technique. A water-saturated very non-polar solvent should be used as the base solvent, such as water-saturated w-hexane or isooctane. 

Usually, the values of the transport coefficients for a gas phase are extremely sensitive to pressure, and therefore predictive methods specific for high-pressure work are desired. On the other hand, the transport properties of liquids are relatively insensitive to pressure, and their change can safely be disregarded. The basic laws governing transport phenomena in laminar flow are Newton s law, Fourier s law, and Fick s law. Newton s law relates the shear stress in the y-direction with the velocity gradient at right angles to it, as follows ... 

J.A. Warren and W.J. Boettinger. Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method. Acta Metall, 43(2) 689-703, 1995. 

The same reference (standard) state, f is chosen for the two phases, so that it cancels on both sides of equation 39. The products stffi and y" are referred to as activities. Because equation 39 holds for each component of a liquid—liquid system, it is possible to predict liquid—liquid phase splitting when the activity coefficients of the individual components in a multicomponent system are known. These values can come from vapor—liquid equilibrium experiments or from prediction methods developed for phase-equilibrium problems (4,5,10). Some binary systems can be modeled satisfactorily in this manner, but only rough estimations appear to be possible for multicomponent systems because activity coefficient models are not yet sufficiendy developed in this area. 

The initial predictive method by Wilcox et al. (1941) was based on distribution coefficients (sometimes called Kvsi values) for hydrates on a water-free basis. With a substantial degree of intuition, Katz determined that hydrates were solid solutions that might be treated similar to an ideal liquid solution. Establishment of the Kvsj value (defined as the component mole fraction ratio in the gas to the hydrate phase) for each of a number of components enabled the user to determine the pressure and temperature of hydrate formation from mixtures. These Kysi value charts were generated in advance of the determination of hydrate crystal structure. The method is discussed in detail in Section 4.2.2. 

Fundamentals of phase equilibria (i.e., phase diagrams, early predictive methods, etc.) are listed in Chapter 4, while Chapter 5 states the more accurate, extended van der Waals and Platteeuw predictive method. Chapter 6 is an effort to gather most of the thermodynamic data for comparison with the predictive techniques of Chapters 4 and 5. Chapter 7 shows phase equilibria applications to in situ hydrate deposits. Chapter 8 illustrates common applications of these fundamental data and predictions to gas- and oil-dominated pipelines. 

In Figure 4.2c for natural gases without a liquid hydrocarbon (or when liquid hydrocarbons exist below 273 K), the lower portion of the pressure-temperature phase diagram is very similar to that shown in Figure 4.2a. Two changes are (1) the Lw-H-V line would be for a fixed composition mixture of hydrocarbons rather than for pure methane (predictions methods for mixtures are given in Section 4.2 and in Chapter 5) and (2) quadruple point Qi would be at the intersection of the Lw-H-V line and 273 K, at a pressure lower than that for methane. The other three-phase lines of Figure 4.2a (for I-Lw-H and I-H-V) have almost the same slope at Qj. Otherwise, the same points in Section 4.1.1 apply. 

At the three-phase condition, the calculated methane mole fractions in the aqueous, si hydrate, and vapor phases are 0.0014 (Point 6), 0.14 (Point 7), and 0.9997 (Point 8) respectively, illustrating that the aqueous and vapor concentrations shown in Figure 4.3 are expanded for illustration purposes. Note that the isobaric three-phase temperature at Point 2 marks one P-T condition on the three-phase line (Lw-H-V) shown in Figure 4.2a, with prediction methods in Table 4.1 and Section 4.2. In both Figures 4.2a and 4.3, at temperatures above this line, hydrates cannot form at the specified pressure. 

Section 5.2 shows the prediction method of phase diagrams of the major components of natural gas, namely methane, ethane, and propane hydrates and their mixtures at the common deep-ocean temperature of 277 K. Many of the commonly observed phenomena in natural gas systems are illustrated, while the power of the method is shown to go beyond that of Chapter 4, to illustrate future needs. 

While the method of the present chapter may appear comprehensive, the reader is cautioned that the calculation is limited by the available data, as in any prediction method. For each region of phase equilibrium prediction, the limitations on both the accuracy and data availability are discussed. The methods presented are useful for interpolations between available data sets. The reader is urged to use caution for extrapolations beyond the data range. Further experiments may be required in order to appropriately bound the P-T conditions of interest. 

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