Pvt analysis. Binary system

PVT analysis. Binary system.
If a system consists of more than one component, its state is also a function of composition. In general, the composition is defined by “mole fractions”. The mole fraction is defined as the ratio between the number of moles of a certain component and the sum of moles of all components. A system being composed of k components is defined by the specification of (k - 1) mole fractions because the sum of the mole fractions always equal 1.Considering a 2-component system, every change in state is described by the equation of state F(p, V, T, z) = 0. z may be the mole fraction of one (lighter) component.
The phase behavior of the ethane/n-heptane system is graphically illustrated by the p, T, z-coordinate system in figure 6.8. The volume is equivalent to the mole volume.
In the plane z = 1, the vapor pressure curve of ethane appears, whereas in the plane z = 0 the one of n-heptane appears. Covering all other z-planes, an envelope surface encloses the 2-phase state. This is demonstrated by the example of three additional z-planes. The upper broken line marks the critical points of all compositions that are possible.

Figure 6.7. Combined reduced pressure - reduced Figure 6.8. Phase equilibrium surface of the
volume phase diagram of paraffins with binary system ethane/n-heptane.
low molecular weight
This curve divides the envelope surface into two parts: the bubble point surface and the dew point surface. The region of an undersaturated liquid state is positioned outside the bubble point surface (low temperature). Outside of the dew point surface (high temperature), the state of a dry gas is given.
Analogous to the pure substance, the critical state of binary systems is defined as the state at which the intensive properties of the phases are no more distinguishable. Just as in case of 1-component systems, the critical isotherms have an inflection point according to equation 6.3.
(eq. 6.3)



Figure 6.9. Pressure - temperature phase diagram Figure 6.10. Pressure - temperature phase of the binary system ethane/n-heptane. diagram of the binary system ethane
(z = 0.9683)/n-heptane
Figure 6.9 shows the projection of figure 6.8 into the p, T-plane. At a given pressure, the bubble point temperature of the mixture is always higher than that of the pure lighter component. Physically, it can be explained by the fact that the thermal motion of the lighter molecules is obstructed by the heavier ones which exhibit more inertia.
On the other side, the dew point temperature of the mixture at a given pressure is always lower than that of the pure heavier component. This is due to the fact that lighter molecules partially transfer their higher kinetic energy to the heavier ones by collision. Consequently, the system maintains the state of a gas phase.
If the mixture consists of two homologous compounds with quite different volatility (in consequence of quite different molecular weights), the critical data curve envelopes a very extensive temperature and pressure region. For example, the maximum of the critical pressure of a methane/n-decane system equals 37 MPa. The smaller the difference between the molecular weights and thus between the volatility, the more flat the envelope curve will be.
Figure 6.10 illustrates the phase behavior of a certain ethane/n-heptane system. Besides the critical point, the curve enveloping the 2-phase region possesses two additional characteristic points:
• C’: the point of highest pressure on the curve that is called cricondenbar.
• C”: the point of highest temperature on the curve that is called cricondentherm.
As on figure 6.10, so called “quality lines” are shown on p,T-diagrams. A quality line represents a certain mole percentage being liquid or vapor in the state of phase equilibrium. In figure 6.10, the quality line “20%” represents the states in which 20% of the system account for the liquid phase. The bubble point curve and the dew point curve represent 100% and 0% liquid, respectively. All the quality lines (isochores) converge at the critical point.
Figure 6.10 also shows an isothermal decrease along the path EF where E defines the system to be a dry gas. If the constant temperature is higher than Tc but lower than the cricondentherm - like in case of the path EF -, the path surpasses the dew point line twice.
Consequently, a condensate drops out at the dew point D’. At some point between D’ and D”, the volume of condensate (liquid) will be at its maximum. This maximum is given by the intersection point of the path EF with the dotted line connecting C and C”. If the decrease in pressure will be continued, the condensate will be vaporized again. As soon as the dew point D” has been reached, the condensated phase has been vaporized in total. This process is called a “retrograde condensation”.
Similar phenomena occur when the temperature is changed by an isobaric process where the constant pressure is higher than pc but lower than the cricondenbar of the system. In figure 6.10, the dotted line connecting point C with point C’ marks the states of the system which exhibit the highest volume percentage of condensate dropout.
Example 6.2. Determining the phase composition.
A sealed container (p = 2.86 MPa), T = 150 C) is filled up with 100 kg of a ethane(z = 0.47)/n-heptane mixture. The mole number of ethane in the liquid phase and in the vapor phase, respectively, can be evaluated from figure 6.11. by using the principle of lever.