Condensed Three-Phase Equilibrium

Katz (1972) first noted that hydrates could form from heavy liquids such as crude oils that have dissolved gases suitable for hydrate formation. He suggested that the point of hydrate formation from water and a liquid hydrocarbon phase (no gas present) could be predicted using the vapor-hydrate distribution coefficient Kvsi of Equation 4.1 together with the more common vapor-liquid distribution coefficient Kyu (=yi/xa). In this case Equation 4.3 becomes  

For condensed three-phase (Lw-H-Lhc) hydrate equilibrium, at pressures above the upper quadruple point, the pressure changes extremely rapidly with only a small change in temperature. This is because all three phases are relatively 

However, the condensed three-phase P-T locus is not exactly vertical. Ng and Robinson (1977) measured the Lw-H-Lhc equilibrium for a number of structure II hydrate mixtures and suggested that a better estimation of the slope dP/dT might be obtained through the Clapeyron equation  

For the upper temperature for hydrate formation, Makogon (1981) suggested a better criterion than the location of Q2 is the P-T condition at which the density of the combined hydrocarbon and water is equal to that of the hydrate. He assumed 

AHu = heat of hydrate formation from liquid water and liquid hydrocarbon2 AV = the molar volume of the hydrate less that of the hydrocarbon and liquid water (= Vh - Vlhc - Vlw)- 

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As discussed in Chapter 6, water forms strong hydrogen bonds and these lead to a number of important features of its atmospheric behavior. All three phases of water exist in the atmosphere, and the condensed phases can exist in equilibrium with the gas phase. The equilibria between these phases is summarized by the phase diagram for water. Fig. 7-9. 

In contrast to these we have the equilibrium processes of sublimation, absorption, dissolution, precipitation, evaporation, and condensation, throngh which the physical states of solid, Uqnid, and gas are connected. For example, the common crystallization of salts from sea water involves all three phases. Distillation, which is essential for prodncing organic solvents, is a two-step evaporation (liquid => gas) condensation (gas => Uqnid) process. 

A triple point is a point where three phase boundaries meet. For water, it occurs at 4.6 Torr and 0.01°C (see Fig. 8.5). At the triple point, all three phases (ice, liquid, and vapor) coexist in dynamic equilibrium. Under these conditions, water molecules leave ice to become liquid and return to form ice at the same rate liquid vaporizes and vapor condenses at the same rate and ice sublimes and vapor condenses directly to ice again at the same rate. The location of the triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. The normal freezing point of water is found to lie 0.01 K below the triple point, so 0°C corresponds to 273.15 K. 

The two calculation methods in Section 4.2 enable prediction of the three-phase (Lw-H-V) gas mixture region extending between the two quadruple points Qi and Q2 in Figure 4.1. Section 4.3 provides a method to use the techniques of Section 4.2 to locate both quadruple points on a pressure-temperature plot. Section 4.3 also discusses equilibrium of three condensed phases [aqueous liquid-hydrate-hydrocarbon liquid (Lw-H-Lhc)] Determination of equilibrium from condensed phases provides an answer to the question, Given a liquid... 

A remarkable shape is calculated with Eq. (9.35) for (3 > 4. A region is obtained where the 0-versus-P curve has a negative slope (dotted curve in Fig. 9.7). This is physically nonsense The coverage is supposed to decrease with increasing pressure and for one pressure there are three possible values of 6. In reality this is a region of two-phase equilibrium. Single adsorbed molecules and clusters of adsorbed molecules coexist on the surface. The situation is reminiscent of the three-dimensional van der Waals equation of state which can be used to describe condensation. 

The feasibility of the above setup can be evaluated by simulation with Aspen Plus [19]. The RD column is built-up as a reboiled stripper followed by a condenser and a three-phase flash, with organic phase refluxed to column. The result is that only 3 to 5 reactive equilibrium stages are necessary to achieve over 99% conversion. The stripping zone may be limited at 2-3 stages, while the rectification zone has 1-2 stages. 

Contact angle measurement is probably the most common method for solid surface tension measurement in condensed state. Young [71] described the equilibrium at three-phase boundary in terms of the vectorial sum, as shown in Fig. 3, resulting in the following equation of equilibrium forces balance... 

On the basis of the Saam-Cole-Findenegg approach, we are now able to revise the ideal isotherm for capillary condensation. A more realistic isotherm for the physisorption of a vapour in an assemblage of uniform cylindrical mesopores is shown in Figure 7.5. Here, C represents the limit of metastability of the multilayer (of thickness fc) and M the point at which the three phases (multilayer, condensate and gas) all coexist. Along MC the multilayer and gas are in metastable equilibrium. 

All three phases of water exist in the atmosphere, and the condensed phases can exist in equilibrium with the gas phase. The equilibria between these phases is summarized by the phase diagram for water (Fig. 10-9). We see from Fig. 10-9 that the partial pressures of H2O at ordinary conditions range from very small values to perhaps 30 or 40 mbar. This corresponds to a mass concentration range up to about 25 g water/m . In typical clouds, relatively little of this is in the condensed phase. Liquid water contents in the wettest of cumulus clouds are around a few grams per cubic meter ordinary mid-latitude stratus clouds have 0.3-1 g/m . 

In this paper, the aldol condensation of acetone and the synthesis of ethylene glycol monoethyl ether are used to show the applications of CD technology for organic synthesis. The predictions of product yield and selectivity and the design of a CD process using a non-equilibrium three-phase model developed by our laboratory [6] will also be discussed. 

Three phases are involved in headspace extraction, namely the condensed phase, its headspace and the SPME polymer. In the sampling process, the SPME fibre acts as a chemical pump , forcing compounds out of the headspace of a (liquid or) solid phase into a phase-coated fibre. For headspace sampling of volatiles the vapour phase should be in equilibrium with the sample. Sample/air/fibre partitioning of volatiles depends on many factors, including the nature of the sample matrix, presence of interfering compounds, sample and headspace volumes. 

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