Two-phase envelope

The experiment could be repeated at a number of different temperatures and initial pressures to determine the shape of the two-phase envelope defined by the bubble point line and the dew point line. These two lines meet at the critical point, where it is no longer possible to distinguish between a compressed gas and a liquid. 

When the two components are mixed together (say in a mixture of 10% ethane, 90% n-heptane) the bubble point curve and the dew point curve no longer coincide, and a two-phase envelope appears. Within this two-phase region, a mixture of liquid and gas exist, with both components being present in each phase in proportions dictated by the exact temperature and pressure, i.e. the composition of the liquid and gas phases within the two-phase envelope are not constant. The mixture has its own critical point C g. 

The four vertical lines on the diagram show the isothermal depletion loci for the main types of hydrocarbon gas (incorporating dry gas and wet gas), gas condensate, volatile oil and black oil. The starting point, or initial conditions of temperature and pressure, relative to the two-phase envelope are different for each fluid type. 

The initial condition for the dry gas is outside the two-phase envelope, and is to the right of the critical point, confirming that the fluid initially exists as a single phase gas. As the reservoir is produced, the pressure drops under isothermal conditions, as indicated by the vertical line. Since the initial temperature is higher than the maximum temperature of the two-phase envelope (the cricondotherm - typically less than 0°C for a dry gas) the reservoir conditions of temperature and pressure never fall inside the two phase region, indicating that the composition and phase of the fluid in the reservoir remains constant. 

In addition, the separator temperature and pressure of the surface facilities are typically outside the two-phase envelope, so that no liquids form during separation. This makes the prediction of the produced fluids during development very simple, and gas sales contracts can be agreed with the confidence that the fluid composition will remain constant during field life in the case of a dry gas. 

For both volatile oil and blaok oil the initial reservoir temperature is below the critical point, and the fluid is therefore a liquid in the reservoir. As the pressure drops the bubble point is eventually reached, and the first bubble of gas is released from the liquid. The composition of this gas will be made up of the more volatile components of the mixture. Both volatile oils and black oils will liberate gas in the separators, whose conditions of pressure and temperature are well inside the two-phase envelope. 

Figure 5.23 shows the phase envelopes for the different types of hydrocarbons discussed, using the same scale on the axes. The higher the fraction of the heavy components in the mixture, the further to the right the two-phase envelope. Typical separator conditions would be around 50 bara and 15°C. 

A question of practical interest is the amount of electrolyte adsorbed into nanostructures and how this depends on various surface and solution parameters. The equilibrium concentration of ions inside porous structures will affect the applications, such as ion exchange resins and membranes, containment of nuclear wastes [67], and battery materials [68]. Experimental studies of electrosorption studies on a single planar electrode were reported [69]. Studies on porous structures are difficult, since most structures are ill defined with a wide distribution of pore sizes and surface charges. Only rough estimates of the average number of fixed charges and pore sizes were reported [70-73]. Molecular simulations of nonelectrolyte adsorption into nanopores were widely reported [58]. The confinement effect can lead to abnormalities of lowered critical points and compressed two-phase envelope [74]. 

In the P,7-section the two-phase envelope is tangent to the binary critical curve in the critical point. 

No, a straight line from the point 35 mole percent methane, 65 mole percent ethane plus to the apex at pure carbon dioxide passes through the two-phase envelope. 

Methane, a common impurity in acid gas, tends to broaden the phase envelope because it is lighter than the acid gas components. Figure 3.6 shows two phase envelopes. The first is the phase envelope for an equimolar mixture of hydrogen sulfide and carbon dioxide. This is the same phase envelope shown in figure 3.2. The other phase envelope is for a mixture with 2 mol% methane. 

The density effect can also be examined in terms of liquid-liquid phase equilibria thermodynamics Increasing the continuous phase density Increases the entropy of mixing by lowering the free volume difference between the constituents. Thus the various two-phase envelopes (water-oil, oil-surfactant, and water-surfactant) that combine to affect the emulsion stability will shrink upon increasing density (2H) ... 

In Fig. 3.3a, we present the Txy diagram for binary mixtures of cyclohexane and toluene at a pressure of 1 atm, which is below the critical pressure of both pure species. Point A denotes the boiling temperature of pure toluene, and point C is the boiling temperature of pure cyclohexane. Connecting these two points are two curves that form the two-phase envelope. The upper curve (with the open symbols) is the dew point curve, and the lower curve (with the filled symbols) is the bubble point line. 

Above the two-phase envelope, the system is a vapor, and below the envelope, the system is a liquid. Witliin the envelope, the system separates into a coexisting vapor and liquid phase. The composition of tlie phases is given by the dew point curve and the bubble point curve. For example at point E (mole fraction Za), the system splits into a vapor phase with a composition corresponding to point D (mole fraction / ) and a liquid phase with a composition corresponding to point B (mole fraction Xa The ratio of the total moles of the liquid phase to the total moles of the vapor phase is... 

Figure 9.4 shows a schematic diagram of the phase behavior of a semicrystalline polymer having a narrow molecular weight distribution. The two-phase envelopes located beneath the liquid-gas, critical mixture curve represent equilibrium between a molten, polymer-rich phase and a compressed, solvent-rich phase. If the pressure is isothermally increased to a point above the two-phase envelope, the liquid and gas phases merge to form a single homogeneous phase. As described in some detail in chapter 3, the border... 

Using the Peng-Robinson equation-of-state programs or MATHCAD worksheets described in Appendix B, we obtain the results in Table 7.5-1. The vapor pressure as a function of temperature is plotted in Fig. 7.5-3. The specific volumes and molar enthalpies and entropies of the coexisting phases have been added as the two-phase envelopes in Figs. 6.4-3, 6.4-4, and 6.4-5.B... 

Example 4.1. Thermodynamic properties of isobutane were measured at subcritical temperatures from 70°F (294.29°K) to 250°F (394.26°K) over a pressure range of 10 psia (68.95 kPa) to 3000 psia (20.68 MPa) by Sage and Lacey. Figure 4.1 is a log-log graph of pressure (psia) versus molal volume (fP/lbmole) of the experimental two-phase envelope (saturated liquid and saturated vapor) using the tabulated critical conditions from Appendix I to close the curve. Shown also is an experimental isotherm for 190°F (360.93°K). Calculate and plot 190°F isotherms for the R-K equation of state and for the ideal gas law and compare them to the experimental data. 

Within the two-phase envelope, the R-K equation has continuity, but it fails badly to predict an isobaric condition. This has no serious practical implications. If the molal volume for a two-phase mixture is required, it can be computed directly from individual phase volumes. 

Binodal points represent the points of contact of a common tangent to A vs. V at constant temperature and composition when a region of negative curvature exists between two regions of positive curvature. The locus of binodal points, known as the binodal curve or two-phase envelope, represents the experimentally observed phase boundary under normal conditions. For example, saturated liquid and saturated vapor represent states on the binodal curve. The binodal region exists between the binodal and spinodal curves, where p/ V)T,aa jv < 0. 

The determined two-phase envelopes of the DiPA-H20-NaCl and the DMiPA-H20-NaCl systems (saturated with sodium chloride) are also displayed in Figure 5. The LCST s of the DiPA-H20-NaClsat and the DMiPA-H20-NaClsat systems were estimated to be -11.7 °C and 6.6 °C. The LCST of the DiPA-H20-NaCl system deviates from the one presented by Weingartner et al. who estimated the LCST at -7.5 °C. The LCST s of the amine-water systems as well as the mutual solubilities of the water and the amines in the two liquid phase area decreased substantially as a result of the presence of sodium chloride. The dissolved sodium chloride decreases the miscibility of the amine-water mixtures, due to the fact that it prefers to be surrounded by water molecules and not by amine molecules. At lower temperatures however, the amines are sufficiently hydrophilic to be fully miscible with water saturated with sodium chloride. 

Figure 5. The two phase envelopes of the binary DiPA-H20 and DMiPA-H20 systems and of the ternary DiPA-H20-NaClsat and DMiPA-H20-NaClsat systems. Below the phase lines there is one single liquid phase and above there are two liquid phases present.

Generally, it is agreed that two fundamentally different mechanisms of phase separation can occur, as shown in Fig, 20.1-7. The so-called binodal regions in the two-phase envelope mark metastable regimes in which a single phase can exist until a nucleus (homogeneous or heterogeneous) presents itself and initiates a precipitation process. This process is similar in many respects to classical crystallization from... 

An equation of state is an algebraic expression that can represent the phase behavior of the fluid, both in the two-phase envelope (i.e., inside the binodal curve), as was demanded above, on the two-phase envelope, and outside the binodal curve. The equations of state are divided into two main groups cubic and noncubic. Cubic equations have three roots when T and only one root when T > T. At T = T, there are three equal roots. Figure. 3.4 portrays the deficiency with most of the cubic equations of state. In this plot, the solid circles show measured data and the solid line represents the predictions from an EOS. The flatness around the critical point can not be adequately described by most cubic equations. The liquid phase description is also not so good as the description of the gas phase. Later, we will discuss how the volume-... 

A more complete phase diagram is provided by Figure 7.8, in which the pressure is plotted as a function of volume and temperature. Here we see that depending on the temperature, we may either pass through the two-phase region or, if the fluid is above its critical temperature, we avoid a phase separation. The point at the top of the liquid-vapor region is the critical point of the fluid. The region marked LIQUID-VAPOR depicts the two-phase envelope—below this curve two phases exist in equilibrium. 

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