Temperature phase diagrams

So far we have considered only a single component. However, reservoir fluids contain a mixture of hundreds of components, which adds to the complexity of the phase behaviour. Now consider the impact of adding one component to the ethane, say n-heptane (C7H.,g). We are now discussing a binary (two component) mixture, and will concentrate on the pressure-temperature phase diagram. 

Figure 5.20 Pressure-temperature phase diagram mixture of ethane and n-heptane...

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

Fig. 3. Typical nonionic amphiphile—oil—water—temperature phase diagram, illustrating (a) the S-shaped curve of T, M, and B compositions, (b) the lines of plait points, (c) the lower and upper critical end points (at and respectively), and (d) the lower and upper critical tielines.

Reactions Between Refractories. In Table 17, the compatibilities of various refractories are given over a range of temperatures. Dissimilar refractories can react vigorously with each other at high temperatures. Phase diagrams are an excellent source of information concerning the reactivity between refractories. 

Water exists in three basic forms vapor, liquid, and solid. The relationship among the three forms of water is described by the pressure-volume-temperature phase diagram (Figure 1.1). 

If we assume that the data of Figs. 22 and 23 can be treated by equilibrium thermodynamics, the discontinuities in the ESP versus temperature phase diagram should indicate the presence of a three-way equilibrium between bulk surfactant and two different film types in both homo- and hetero-chiral systems. The surface heats of transition (U) between the two film types in either system may be obtained by relation (15), where IT is the equilibrium... 

Figure 9.1. Carbon dioxide pressure-temperature phase diagram adapted from McHugh and Krukonis (1994).

Figure 5.5 Phase diagram of a system that sublimes at room temperature phase diagram of carbon dioxide. (Note that the y-axis here is logarithmic)...

Brady et al. [52] have discussed pressure-temperature phase diagrams for carbon dioxide polychlorobiphenyls and examined the rate process of desorption from soils. Supercritical carbon dioxide was used to extract polychlorobiphenyls and DDT and Toxaphene from contaminated soils. 

Figure 5.37. Pressure/temperature phase diagram of carbon.

Schirber JE, Overmyer DL, Carlson KD, Williams JM, Kini AM, Wang HH, Charlier FIA, Love BJ, Watkins DM, Yaconi GA (1991) Pressure-temperature phase diagram, inverse isotope effect, and superconductivity in excess of 13 K in /c-(BEDT-TTF)2Cu[N(CN)2]Cl, where BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene. Phys Rev B44 4666-4669... 

Figure 2, Room temperature phase diagram of the PLZT system illustrating phases present and typical hysteresis loops associated with each phase compositions 1, 2 and 3 are 9565, 7065 and 12040, respectively...

Only for U, Np and Pu sufficient experimental work was carried out so that a pressure-temperature phase diagram can be constructed. 

In fact, iron exhibits all three common metallic crystal structures bcc, fee, and hep within its pressure-temperature phase diagram, as is shown by the inset of Fig. 8.14. The transition from the bcc a phase to the hep e phase... 

Of all the characteristic points in the phase diagram, the composition of the middle phase is most sensitive to temperature. Point M moves in an arc between the composition of the bottom phase (point B) at Tlc and the composition of the top phase (point T) at 7, reaching its maximum surfactant concentration near T = (Tlc + Tuc)/2. (Points B and Tmove by much smaller amounts, also.) The complete nonionic-amphiphile—oil—water—temperature phase diagram is illustrated by Figure 3, including the S-shaped curve of T, M, and B compositions the two lines of plait points, which terminate at the lower and upper critical end points and the lower and upper critical tielines (at Tlc and T respectively). 

Fig. 12. The character of structural modification during catalytic etching is known to be a function of the gas composition and temperature. Phase diagram for the etching of platinum wires heated in ammonia-air mixture for I h. The dashed line indicates the adiabatic wire temperature...

Figure 2.14 Pressure-temperature phase diagram for cyclopropane. (Reproduced from Majid, Y.A., Garg, S.K., Davidson, D.W., Can. J. Chem., 47,4697 (1969). With permission from the National Research Council of Canada.)...

What is a typical pressure-temperature phase diagram for sH hydrates ... 

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. 

Figure 5.12 is the pressure versus temperature phase diagram for the methane+ water system. Note that excess water is present so that, as hydrates form, all gas is incorporated into the hydrate phase. The phase equilibria of methane hydrates is well predicted as can be seen by a comparison of the prediction and data in Figure 5.12 note that the predicted hydrate formation pressure for methane hydrates at 277.6 K is 40.6 bar. 

Figure 5.13 is the equivalent ethane + water pressure versus temperature phase diagram. Note that the Aq-sI-V line intersects the Aq-V-Lhc line at 287.8 K and 35 bar. Due to differences in the volume and enthalpy of the vapor and liquid hydrocarbon, the three-phase hydrate formation line changes slope at high temperature and pressure from Aq-sI-V to Aq-sI-Lhc, due to the intersectiion of Aq-sI-V line with the Aq-V-Lhc line (slightly higher than the ethane vapor pressure). Note that the hydrate formation pressure for ethane hydrates at 277.6 K is predicted to be 8.2 bar. 

Figure 5.14 is the propane + water pressure versus temperature phase diagram. Note that the data are scattered along the Aq-sII-Lhc line due to difficulty... 

To test the predictions, experiments were carried out at the Delft University of Technology (TUD) (Ballard et al., 2001). In CSMGem, the pressure versus temperature phase diagram was generated using the model and then confirmed by experimental data. Figure 5.19 is the pressure versus temperature diagram for a 30/70 mixture of ethane and propane in contact with excess water. 

Under the assumption, that a small deviation from the dimension d = 1 changes only the naive scaling dimensions of the fields, our results can be extended also to d = 1 + e dimensions (For details see appendix [20]). The zero temperature phase diagram is modified and illustrated in Fig. 3. For e < 0 the fixed point at (K = K, u = 0) is shifted to positive u-values (see left inset of Fig. 3), whereas for e > 0, K and u always flow to the... 

Fig. 3. Schematic zero temperature phase diagram in d = 1 and close to d = 1 dimensions (see text), u and K denote the strength of the disorder and quantum fluctuations, respectively.

Fig. 8. Qualitative zero temperature phase diagram for a system with commensurate lattice potential and small disorder. One has to distinguish two cases (i) < A ...

The combined effect of disorder and the lattice potential on the zero temperature phase diagram, i.e., the competition between unpinning (Anderson) and lock-in (Mott) transition, is still controversially discussed [41, 14] and cannot be explained by the RG-results presented here, since both perturbations become relevant for small K. However, using Imry-Ma arguments one finds, that as soon as If is below one of the two critical values (for the unpinning and lock-in transition) the disorder dominates the lattice potential and only two phases exist. This is in contrast to the proposed existence of a so-called intermediate Mott- Glass phase [14]. 

Figure 15.5. Pressure-temperature phase diagram of pure C02 with a superimposed flow diagram for a closed-loop supercritical fluid treatment process.

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