Phase behavior

Phase Behavior Fundamentals & Review of Thermodynamics - Colombia – Summer 2000

ln (P sat ) = A -

B C+T

(13)

Where A, B, and C are constants specific for each component (i.e propane, cycloheptane, benzene etc.) An even more accurate equation is the Riedel equation (obviously, with more parameters):

ln P sat = A −

B + D ln T + FT T

6

(14)

Two-Phase Properties (SingleComponent)
Properties of mixtures of the two phases are related to the property of each phase and the amount of that phase. Let f be the mole fraction of the gas phase (usually called quality).

ng f = n +n l g
Then for a given saturation point provided by the coordinate pair (P sat, T sat):

(15)

V = f V g + (1 - f )V l

@

P sat, T sat

(16)

Vapor pressures can also be read fromthe COX charts in the following figures.

Author: Dr. Maria Barrufet - Summer, 2000

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Phase Behavior Fundamentals & Review of Thermodynamics - Colombia – Summer 2000

Notice that the temperature scale in the horizontal coordinate in neither linear nor logarithmic. Made up such that, curves are essentially straight.

Author: Dr. Maria Barrufet - Summer, 2000

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Figure 28 - Vapor pressures of normal paraffins. (From Handbook of Natural Gas Engineering by Katz et al.)

Author: Dr. Maria Barrufet - Summer, 2000

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Phase Behavior Fundamentals & Review of Thermodynamics - Colombia – Summer 2000

Figure 29 - Vapor pressures of isomeric paraffins. (From Handbookof Natural Gas Engineering by Katz et al.)

Author: Dr. Maria Barrufet - Summer, 2000

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Phase Behavior Fundamentals & Review of Thermodynamics - Colombia – Summer 2000

Density (mass/volume) is the inverse of specific volume (volume/mass). To see the variation of density (or specific volume) with pressure and temperature another phase diagram must be used. This is thepressure-specific volume diagram. For a pure substance this looks like:

T
Pressure (psia)
CP

Tc

2-phase
VL Vv

Specific Volume (ft3/lbm)
Figure 30 - Pressure-specific volume diagram for a pure substance.

•

The CP is the highest temperature and pressure at which a vapor an a liquid phase can coexist.

• •

Gas and liquid volumes become identical at the critical point. Isotherms aresteeper in the liquid region than in the gas region to reflect lower liquid compressibilities.

Author: Dr. Maria Barrufet - Summer, 2000

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Phase Behavior Fundamentals & Review of Thermodynamics - Colombia – Summer 2000

Phase Behavior of Single and Binary Systems
The following phase diagrams for single and binary mixtures serve to illustrate the behavior of multicomponentfluids at different pressures, temperatures, and compositions.

Left
CP1 P1v T = Ta

Right
Liquid P1v

Pressure

CP2 P2v

rve Cu ble ub B 2-phases
w De
Vapor x1, y1

rve Cu

P2v Ta Temperature

Figure 31 - Vapor pressure curves (left) and (Px)T diagram (right).

The left side of Figure 31 illustrates two vapor pressure curves for component [1] and [2]. At Ta, the vaporpressures are P 1
v

, P2v and component [1] is the most volatile.

Heavier components, in general, exhibit high critical temperatures and lower critical pressures than more volatile components. For example: C2 C10 (ethane) (decane) Tc Tc = 89.92 F = 652.0 F
o o

Pc Pc

= =

706.5 psia 305.2 psia

Author: Dr. Maria Barrufet - Summer, 2000

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Phase Behavior Fundamentals &Review of Thermodynamics - Colombia – Summer 2000

The right hand side of Figure 31 illustrates the phase behavior of all possible mixtures between [1] and [2] at the selected temperature Ta.

By convention the most volatile component is plotted in the x-axis. The two extremes indicate the vapor pressures of the pure components.

The two lines enclosing the two-phase region indicate the bubble...