Pressure two-phase

Hosier, E. R., 1968, Flow Patterns in High Pressure Two-Phase (Steam-Water) Flow with Heat Addition, AIChE Chem. Eng. Prog. Symp. Ser. <54(82) 54, AIChE, New York. (3)... 

If two phases of one component are present, only one degree of freedom remains, either temperature or pressure. Two phases in equilibrium are represented by a curve on a T — P diagram, with one independent variable and the other a function of the first. When either temperature or pressure is specified, the other is determined by the Clapeyron Equation (8.9). If three phases of one component are present, no degrees of freedom remain, and the system is invariant. Three phases in equUibiium are represented on a T — P diagram by a point called the triple point. Variation of either temperature or pressure will cause the disappearance of a phase. 

The first method, which is the more flexible, is to use an activity coefficient model, which is common at moderate or low pressures where the liquid phase is incompressible. At high pressures or when any component is close to or above the critical point (above which the liquid and gas phases become indistinguishable), one can use an equation of state that takes into account the effect of pressure. Two phases, denoted a and P, are in equilibrium when the fugacity / (for an ideal gas the fungacity is equal to the pressure) is the same for each component i in both phases ... 

F. Larachi, A. Laurent, N. Midoux and G. Wild, Experimental study of a trickle-bed reactor operating at high pressure two-phase pressure drop and liquid saturation, Chem. Engng. Science, 46 (1991) 1233-1246. 

Figure 5.13. Representation of phase equilibria of a binary system in terms of the Gibbs energy at constant temperature and pressure two-phase equilibrium.

The most stable state (the state of equilibrium) at any temperature is the state of lowest free energy. It can be seen that, at two temperatures (273 and 373 K at standard pressure), two phases have the same free energy and are therefore in equilibrium. These are the freezing point and boiling... 

Another interesting feature can be seen in the fact that the solubility decreases with pressure. This decrease would illustrate that in the hot pressing of two-phase systems reaction between the two phases becomes less important as greater pressures are applied. Under high enough pressures two-phase systems actually are distinctly two-phase and the problem of a third, interfacial phase is minimized. 

FIGURE 4.5 Simple, constant-pressure, two-phase system. 

In vapor-liquid equilibria, it is relatively easy to start the iteration because assumption of ideal behavior (Raoult s law) provides a reasonable zeroth approximation. By contrast, there is no obvious corresponding method to start the iteration calculation for liquid-liquid equilibria. Further, when two liquid phases are present, we must calculate for each component activity coefficients in two phases since these are often strongly nonlinear functions of compositions, liquid-liquid equilibrium calculations are highly sensitive to small changes in composition. In vapor-liquid equilibria at modest pressures, this sensitivity is lower because vapor-phase fugacity coefficients are usually close to unity and only weak functions of composition. For liquid-liquid equilibria, it is therefore more difficult to construct a numerical iteration procedure that converges both rapidly and consistently. 

As discussed in Chapter 3, at moderate pressures, vapor-phase nonideality is usually small in comparison to liquid-phase nonideality. However, when associating carboxylic acids are present, vapor-phase nonideality may dominate. These acids dimerize appreciably in the vapor phase even at low pressures fugacity coefficients are well removed from unity. To illustrate. Figures 8 and 9 show observed and calculated vapor-liquid equilibria for two systems containing an associating component. 

The general problem is to determine at given conditions of temperature and pressure, the quantities and compositions of the two phases in equilibrium starting from an initial quantity of material of known composition and to resolve the system of the following equations ... 

For mixtures, the calculation is more complex because it is necessary to determine the bubble point pressure by calculating the partial fugacities of the components in the two phases at equilibrium. 

The vapor pressure of a crude oil at the wellhead can reach 20 bar. If it were necessary to store and transport it under these conditions, heavy walled equipment would be required. For that, the pressure is reduced (< 1 bar) by separating the high vapor pressure components using a series of pressure reductions (from one to four flash stages) in equipment called separators , which are in fact simple vessels that allow the separation of the two liquid and vapor phases formed downstream of the pressure reduction point. The different components distribute themselves in the two phases in accordance with equilibrium relationships. 

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. 

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. 

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. 

The diagram (Fig. 5.21) shows that as the pressure is reduced below the dew point, the volume of liquid in the two phase mixture initially increases. This contradicts the common observation of the fraction of liquids in a volatile mixture reducing as the pressure is dropped (vaporisation), and explains why the fluids are sometimes referred to as retrograde gas condensates. 

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. 

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. 

Fluid samples may be collected downhole at near-reservoir conditions, or at surface. Subsurface samples are more expensive to collect, since they require downhole sampling tools, but are more likely to capture a representative sample, since they are targeted at collecting a single phase fluid. A surface sample is inevitably a two phase sample which requires recombining to recreate the reservoir fluid. Both sampling techniques face the same problem of trying to capture a representative sample (i.e. the correct proportion of gas to oil) when the pressure falls below the bubble point. 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191]. 

Applied to a two-phase system, this says that the change in pressure with temperature is equal to the change in entropy at constant temperature as the total volume of the system (a + P) is increased, which can only take place if some a is converted to P ... 

When, for a one-component system, one of the two phases in equilibrium is a sufficiently dilute gas, i.e. is at a pressure well below 1 atm, one can obtain a very usefiil approximate equation from equation (A2.1.52). The molar volume of the gas is at least two orders of magnitude larger than that of the liquid or solid, and is very nearly an ideal gas. Then one can write... 

From this equation one concludes that the maximum number of phases that can coexist in a oiie-component system (d = 1) is tliree, at a unique temperature and pressure T = 0). When two phases coexist F= 1), selecting a temperature fixes the pressure. Conclusions for other situations should be obvious. 

Figure A2.5.3. Typical liquid-gas phase diagram (temperature T versus mole fraction v at constant pressure) for a two-component system in which both the liquid and the gas are ideal mixtures. Note the extent of the two-phase liquid-gas region. The dashed vertical line is the direction x = 1/2) along which the fiinctions in figure A2.5.5 are detemiined.

A third kind of phase diagram in a two-eomponent system (as shown in figure A2.5.5(e) is one showing liquid-liquid phase separation below a oritieal-solution point, again at a fixed pressure. (On aT,x diagram, the eritieal point is always an extremum of tire two-phase eoexistenee eurve, but not always a maximum. 

Figure A2.5.6. Constant temperature isothenns of redueed pressure versus redueed volume for a van der Waals fluid. Full eiirves (ineluding the horizontal two-phase tie-lines) represent stable situations. The dashed parts of the smooth eurve are metastable extensions. The dotted eurves are unstable regions.

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].

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