Phase equilibria composition measurement

The experimental and predicted results for the ternary system carbon dioxide-methanol-water are listed in Table 7. Chang and Rousseau [47] have measured the solubilities of carbon dioxide in methanol-water mixtures at differents pressures and at temperatures below the critical temperature of carbon dioxide while Yoon [51] have measured the liquid and vapor phase equilibrium composition but overestimates shightly these of carbon dioxide in the liquid phase. 

Figure 1 Comparison of measured and model-generated three- phase equilibrium compositions.

Fig. 14.6 Partition coefficient based on mole fractions calculated from measured phase equilibrium compositions at 313, 323, and 333 K, respectively.

Fig. 8. Ternary experimental and predicted points for the Na/Ca/Mg-A system at a normality of 0.4 equiv dm . Measured solution and zeolite phase equilibrium compositions are shown as unfilled stars said filled squares, respectively. The predicted zeolite phase at 0.4 equiv dm is shown as an unfilled circle while the filled circle represents experimental validations at 0.4 equiv dm. Taken from [69]...

As shown in figure 5.72, the equality of potential is satisfied for component a in mixtures a and (5 at the measured compositions. Neglecting the energy information arising from component b, one could deduce that the two phases, with the measured composition (open circles), coexist stably at the estimated F and T of equilibrium. However, as we can see, /x 3 and equilibrium at the de-... 

When mixing two surfactants species in a SOW system, an equilibrium takes place between the oil and water phases and the interface for each species. Since the two species do not necessarily exhibit the same affinity for the interface and the oil and water bulk phases, the compositions of the surfactant mixtures at interface and in the phases might be different. For instance if a very hydrophilic species is mixed with a very lipophihc one, as often recommended in the old formulation literature, then the hydrophihc surfactant has a strong tendency to partition in water, whereas the lipophihc one would partition in the oil. In this case the surfactant mixture in water will contain a large majority of hydrophilic species, i.e., it will be very hydrophilic, whereas the oil phase will predominantly contain the hpophihc species, with the remaining adsorbing at interface. This situation in which each species actuates on its own, more or less independently of the other, has been called non-collective behavior. Since the surfactant mixture composition at interface is often the one that commands the actual property of the system, such as the interfacial tension or the stabihty of the emulsion, it is most important to know how to calculate or measure the characteristics of the mixture present at interface. Such methods will be discussed in the next section. 

Thermodynamic activity coefficients can be determined from the phase equilibrium measurements, and they are a measure of deviations from Raoult s law. Data of the activity coefficients covering the whole range of liquid composition of IL + molecular solvent mixtures have been reported in the literature and discussed in sections 1.6,1.7, and 1.8 as the values obtained from the SLE, LLE, and VLE data. When a strong interaction between the IL and the solvent exists, negative deviations from ideality should be expected with the activity coefficients lower than one. 

In order for a process to be controllable by machine, it must represented by a mathematical model. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as well as the parameters of sensing devices, control valves, and control instruments. The process as a whole then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process models then the computer can be made to optimize the operation continually. 

Equilibrium relations in leaching usually are simpler than in liquid-liquid equilibria, or perhaps only appear so because few measurements have been published. The solution phase normally contains no entrained solids so its composition appears on the hypotenuse of a triangular diagram like that of Example 14.8. Data for the raffinate phase may be measured as the holdup of solution by the solid, K lb solution/lb dry (oil-free) solid, as a function of the concentration of the solution, y lb oil/lb solution. The correspond-... 

A general formulation of the problem of solid-liquid phase equilibrium in quaternary systems was presented and required the evaluation of two thermodynamic quantities, By and Ty. Four methods for calculating Gy from experimental data were suggested. With these methods, reliable values of Gy for most compound semiconductors could be determined. The term Ty involves the deviation of the liquid solution from ideal behavior relative to that in the solid. This term is less important than the individual activity coefficients because of a partial cancellation of the composition and temperature dependence of the individual activity coefficients. The thermodynamic data base available for liquid mixtures is far more extensive than that for solid solutions. Future work aimed at measurement of solid-mixture properties would be helpful in identifying miscibility limits and their relation to LPE as a problem of constrained equilibrium. 

Equilibrium measurements of the solid hydrate phase have been previously avoided due to experimental difficulties such as water occlusion, solid phase inhomogeneity, and measurements of solid phase concentrations. Instead, researchers have traditionally measured fluid phase properties (i.e., pressure, temperature, gas phase composition, and aqueous inhibitor concentrations) and predicted hydrate formation conditions of the solid phase using a modified van der Waals and Platteeuw (1959) theory, specified in Chapter 5. 

Compositions and temperatures corresponding to these points can be used to construct the (fluid + fluid) phase diagram if measurements are made at a sufficiently large number of pressures and temperatures to establish the equilibrium lines. 

However, for mixtures of TPP and toluene, a third (liquid) phase forms in the presence of the gas and the solid, at pressures well below the critical pressure of toluene. At higher pressures, gas-liquid and solid-liquid equilibria were observed, rather than gas-solid equilibrium. Thus, phase compositions for gas-liquid equilibrium were measured for this binary mixture to give TPP solubilities in each of the fluid phases. Pressures and temperatures for three-phase, solid-liquid-gas equilibrium were also measured for both binary mixtures. 

Bubble points for gas-liquid equilibrium were measured at constant temperature by observing the pressure at which the equilibrium gas phase disappeared upon injection of small amounts of solvent into the view cell. The equilibrium composition of the liquid phase was obtained from the known composition in the cell. Other pressures and corresponding compositions at this temperature were obtained by repeating the procedure for different porphyrin loadings. 

Tie lines of the system can be generated from the equilibrium compositions for each run and selectivities computed. The results of measurements obtained for the 5% by volume of ammonia/ethylene are represented in the binodal diagram in Fig. 3. Butene is represented as the distributed component between the solvent phase and the butadiene-rich phase. The ammonia-solvent gas mixture was considered to behave as a pseudo-solvent of fixed composition. The ratio of the integrated peaks for butene(i) and butadiene(j) was used to compute the selectivity, B (beta), defined on a solvent-free basis, as ... 

Interpretation of the pressure measurements of Centnerszwer and Pieckielny would therefore need to take into account all the above reactions. In reaction schemes as complicated as the present one, equilibrium pressure measurements alone are likely to be of limited utility, particularly since the partial pressures of the component gases depend not only on the equilibrium constants of the reactions, but also on the composition of the condensed phases. 

To determinate the freezing point under gas pressure the cell is filled with melt of known composition. Then the wanted pressure is adjusted with the used gas. The measuring procedure is started when the phase equilibrium between melt and gas phase at a temperature tight upon expected freezing point is reached. 

The values of measured phase equilibrium data were plotted in P-T diagrams (fig.2) as lines of constant composition (shown for PEG 1500). On the abszisse a... 

A new experimental apparatus was built to measure the clathrate dissociation pressures and equilibrium compositions of liquid phases which coexist with the clathrate phase. The pressure-temperature behavior of the binary phenol-carbon... 

Figure 4 plots equilibrium compositions of the liquid and respectively of the supercritical gas phase of the system a-tocopherol/carbon dioxide as a function of pressure. Compositions at 313 and 343 K were measured by Meier [4], at 333, 353, 373, 398 and 423 K by Hoff-mann-La Roche AG in June 1995. 

At a selected alloy temperature the vapor pressure of cadmium is determined as a function of alloy composition the cerium solvent has a negligible vapor pressure. The alloy, located in one leg of a sealed inverted U-tube, is subjected to various specific pressures of cadmium from a supply of pure cadmium at selected temperatures in the second leg of the tube. The U-tube is freely suspended at its midpoint and connected to a balance, so that the transfer of cadmium from one leg of the tube to the other can be measured. This gives information as to the change in alloy composition and phase equilibrium. 

An additional program took the energy parameters of the binary systems making up ternary mixtures and calculated the boiling point of the ternary and the equilibrium composition of the vapor phase. Comparison of the measured boiling point with the predicted boiling point for the same composition and pressure was used as a criterion of successful performance of the NRTL equation. 

Intercalation reactions of the dichalcogenides with alkali metals are redox reactions in which the host lattice is reduced by electron transfer from the alkali metal. Lithium and sodium intercalation reactions, for example, have been studied using cells of the type Li/LiC104-dioxolane/MX2 andNa/Nal-propylene carbonate/MX2. The reactions proceed spontaneously to form the intercalation compound if the cell is short circuited alternatively, a reverse potential can be apphed to control the composition of the final product. Apart from their application in synthesis, such electrochemical cells can be used to obtain detailed thermodynamic information and to establish phase relations by measuring the dependence of the equilibrium cell voltage on composition (see Figure 4). 

The computer algorithm for determining the compositions of three and four equilibrium phases at a fixed temperature and pressure is based on the successive substitution algorithm described by Heidemann (10). An initial estimate of the phase compositions was obtained from either the measured phase compositions at the temperature and pressure of interest, or from previous calculations at a nearby temperature and pressure. Trivial solutions giving two phases of identical composition would often result when the initial compositions were not close to the actual equilibrium compositions. 

Of the five different multiphase regions depicted in Figure 3, four were observed in our experiments. Phase compositions corresponding to the L1L2L3G equilibrium quadrilateral were measured at 40 C and 7.8 MPa. Phase compositions for L1L2L3 equilibrium were measured at 40 C and 8.4 MPa. Observations of L1L3G equilibrium were made at 40 C and 7.9 MPa, but phase... 

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