The phase diagram

The phase diagram shows at a glance the properties of the substance melting point, boiling point, transition points, triple points. Every point on the phase diagram represents a state of the system, since it describes values of T and p. 

The lines on the phase diagram divide it into regions, labeled solid, liquid, and gas. If the point that describes the system falls in the sohd region, the substance exists as a solid. If the point falls in the liquid region, the substance exists as a liquid. If the point falls on a line such as 1-g, the substance exists as liquid and vapor in equilibrium. 

The 1-g curve has a definite upper limit at the critical pressure and temperature, since it is not possible to distinguish between liquid and gas above this pressure and temperature. 

The phase diagram for carbon dioxide is shown schematically in Fig. 12.7. The solid-liquid line slopes slightly to the right, since I oiid- Note that liquid CO2 is not stable at pressures below 5 atm. For this reason dry ice is dry under ordinary atmospheric pressure. When carbon dioxide is confined to a cylinder under pressure at 25 °C, the diagram shows that if the pressure reaches 67 atm, liquid CO2 will form. Commercial cylinders of CO2 commonly contain liquid and gas in equilibrium the pressure in the cylinder is about 67 atm at 25 °C. 

In Fig. 12.10(a) there are three triple points. The equilibrium conditions are 

Quality refers to the percentage of the mixture that is a liquid. In order to determine the quality, we can read this value from the chart, following the curve marked x. This is the fraction that is vapor, so the quaUty is 1-x, or 0.3. Alternatively, the overall enthalpy is equal to the fraction liquid times the liquid enthalpy plus the fraction vapor times its enthalpy. In other words, 

From the graph, we find the liquid enthalpy is 38 BTU/lbm, and the vapor enthalpy is 114 BTU/lbm. We require the overall enthalpy to be 90 BTU/lbm. Substituting and solving provides 

We see that the two solutions are the same, within the limits of our abiUty to read the chart. 

There are three distinct lines shown on this diagram. 

The sublimation curve, which separates the solid phase from the vapor phase. At low temperature and low pressure a material can go directly from the solid to the vapor phase. A good example of (Ms is CO, wMch is sold as dry ice (a solid at low temperature and atmospheric pressure). 

Materials can change their phase as a function of a variety of different thermodynamic variables, such as temperature, pressure, volume, or concentration in a mixture. A diagram of this phase behavior, or phase diagram, can be constructed by plotting the parameter ranges over 

Looking at the phase diagram for water, we can identify some interesting points. The solid red lines represent boundaries between the different phases, and as a reference point the boiling point of water at atmospheric pressure 

FIGURE 1.12 The pressure/temperature phase diagram for water indicating the tripie point at point Tand a critical point at C. The phase boundaries are indicated by the solid red lines. 

At point C, we can note another interesting feature of the diagram. The line that defines the transition between liquid and gas is discontinuous and ends at this point. This is a critical point. Below the critical point, the phase transition is discontinuous, with an associated latent heat (first order), but above this line there is no defined phase transition from liquid to gas, and the density of the material varies continuously. 

The lines on a phase diagram represent the boundaries between thermodynamically stable phases, and close to these lines it takes just a very small change in temperature or pressure to go from one phase to another. 

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Table 1 gives the measured data, estimates of the true values corresponding to the measurements, and deviations of the measured values from model predictions. Figure 1 shows the phase diagram corresponding to these parameters, together with the measured data. 

The example of a binary mixture is used to demonstrate the increased complexity of the phase diagram through the introduction of a second component in the system. Typical reservoir fluids contain hundreds of components, which makes the laboratory measurement or mathematical prediction of the phase behaviour more complex still. However, the principles established above will be useful in understanding the differences in phase behaviour for the main types of hydrocarbon identified. 

Figure 5.21 helps to explain how the phase diagrams of the main types of reservoir fluid are used to predict fluid behaviour during production and how this influences field development planning. It should be noted that there are no values on the axes, since in fact the scales will vary for each fluid type. Figure 5.21 shows the relative positions of the phase envelopes for each fluid type. 

A volatile oil contains a relatively large fraction of lighter and intermediate oomponents which vaporise easily. With a small drop in pressure below the bubble point, the relative amount of liquid to gas in the two-phase mixture drops rapidly, as shown in the phase diagram by the wide spacing of the iso-vol lines. At reservoir pressures below the bubble point, gas is released In the reservoir, and Is known as solution gas, since above the bubble point this gas was contained in solution. Some of this liberated gas will flow towards the producing wells, while some will remain in the reservoir and migrate towards the crest of the structure to form a secondary gas cap. 

Black oils are a common category of reservoir fluids, and are similar to volatile oils in behaviour, except that they contain a lower fraction of volatile components and therefore require a much larger pressure drop below the bubble point before significant volumes of gas are released from solution. This is reflected by the position of the iso-vol lines in the phase diagram, where the lines of low liquid percentage are grouped around the dew point line. 

After having proved the principles a dynamic test facility has been constructed. In this facility it is possible to inject 3 tracers in a flownng liquid consisting of air, oil and water. By changing the relative amounts of the different components it is possible to explore the phase diagram and asses the limits for the measurement principle. Experiments have confirmed the accuracy in parameter estimation to be below 10%, which is considered quite satisfactorily for practical applications. The method will be tested on site at an offshore installation this summer. 

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].

Syimnetrical tricritical points are also found in the phase diagrams of some systems fomiing liquid crystals. 

Figure B3.6.5. Phase diagram of a ternary polymer blend consisting of two homopolymers, A and B, and a synnnetric AB diblock copolymer as calculated by self-consistent field theory. All species have the same chain length A and the figure displays a cut tlirough the phase prism at%N= 11 (which corresponds to weak segregation). The phase diagram contains two homopolymer-rich phases A and B, a synnnetric lamellar phase L and asynnnetric lamellar phases, which are rich in the A component or rich in the B component ig, respectively. From Janert and Schick [68].

Lattice models have been studied in mean field approximation, by transfer matrix methods and Monte Carlo simulations. Much interest has focused on the occurrence of a microemulsion. Its location in the phase diagram between the oil-rich and the water-rich phases, its structure and its wetting properties have been explored [76]. Lattice models reproduce the reduction of the surface tension upon adsorption of the amphiphiles and the progression of phase equilibria upon increasmg the amphiphile concentration. Spatially periodic (lamellar) phases are also describable by lattice models. Flowever, the structure of the lattice can interfere with the properties of the periodic structures. 

Charged particles in polar solvents have soft-repulsive interactions (see section C2.6.4). Just as hard spheres, such particles also undergo an ordering transition. Important differences, however, are that tire transition takes place at (much) lower particle volume fractions, and at low ionic strengtli (low k) tire solid phase may be body centred cubic (bee), ratlier tlian tire more compact fee stmcture (see [69, 73, 84]). For tire interactions, a Yukawa potential (equation (C2.6.11)1 is often used. The phase diagram for the Yukawa potential was calculated using computer simulations by Robbins et al [851. 

The accompanying sketch qualitatively describes the phase diagram for the system nylon-6,6, water, phenol for T > 70°C.f In this figure the broken lines are the lines whose terminals indicate the concentrations of the three components in the two equilibrium phases. Consult a physical chemistry textbook for the information as to how such concentrations are read. In the two-phase region, both phases contain nylon, but the water-rich phase contains the nylon at a lower concentration. On this phase diagram or a facsimile, draw arrows which trace the following procedure ... 

The locations of the tietriangle and biaodal curves ia the phase diagram depead oa the molecular stmctures of the amphiphile and oil, on the concentration of cosurfactant and/or electrolyte if either of these components is added, and on the temperature (and, especially for compressible oils such as propane or carbon dioxide, on the pressure (29,30)). Unfortunately for the laboratory worker, only by measuriag (or correcdy estimatiag) the compositions of T, Af, and B can one be certain whether a certain pair of Hquid layers are a microemulsion and conjugate aqueous phase, a microemulsion and oleic phase, or simply a pair of aqueous and oleic phases. 

Fig. 2. The phase diagrams and terminology of a microemulsion system close to its two critical end points, where the middle phase and one of the binodals...

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 and the composition of the top phase (point T) at reaching its maximum surfactant concentration near T = - -T )/2. (Points B and Tmove by much smaller amounts, also.) The complete nonionic-amphiphile—oh—water—temperature... 

Nevertheless, possibiUties for confusion abound. From the definitions of microemulsions and macroemulsions and from Figure 1, it immediately follows that in many macroemulsions one of the two or three phases is a microemulsion. Until recentiy (49), it was thought that all nonmultiple emulsions were either oil-in-water (O/W) or water-in-oil (W/O). However, the phase diagram of Figure 1 makes clear that there are six nonmultiple, two-phase morphologies, of which four contain a microemulsion phase. These six two-phase morphologies are oleic-in-aqueous (OL/AQ, or O/W) and aqueous-in-oleic (AQ/OL, or W/O), but also, oleic-in-microemulsion (OL/MI), microemulsion-in-oleic (MI/OL), aqueous-in-microemulsion (AQ/MI), and microemulsion-in-aqueous (MI/AQ) (49). 

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