第十讲 平衡级分离过程

A ,B
yA xA K A yA xA K B yB x B 1 y A 1 x A
(4-4)
Binary Vapor-Liquid Systems
While P has been specified, T and zi can change freely in single phase regions but xi and yi both are fixed if T is specified in 2phase region. V and L are also determined by the lever rule.
(10)
Flash Calculations
Flash is a single-equilibrium-stage separation process with partial vaporization or condensation of a feed stream. A real flash process is always accompanied by temperature and pressure change and heat exchange. The isothermal and adiabatic flashes are two idealized situations discussed most commonly.
First page 全日制专业硕士研究生学位课程
传递过程 与 分离技术
面向应用的 专业基础课程
第十讲—平衡级分离过程
i10.1
单级分离过程
and
Flash Calculation
Introduction
The separation process by single equilibrium stage is one in which two phase in contact are brought to physical equilibrium and followed by phase separation. The calculations of single stage separation are made by combining material balance and energy balance with phase equilibria relations.
Gibbs Phase Rule
For a system at physical equilibrium, the number of independent intensive variables to describe its thermodynamic state is given by Gibbs phase rule as
(8)
i
1
Azeotropic Systems
In 2-L region, temperature, total pressure, partial pressures, and phase compositions keep constant as the relative amounts of the 2 liquid phases change.
(1)
For a system with feed streams and extensive variables, the phase rule should be extended by an general analysis of degrees of freedom as follows in which V is the number of variables, E the number of independent equations. It should be pointed out that V does not count the thermodynamic functions which can be calculated from the intensive variables.
F C P 2
(4-1)
in which C is the number of components, P the number of phases. For the vapor-liquid equilibrium of a tern源自文库ry system,
F 32 2 3
Degrees-of-Freedom Analysis
(4)
Azeotropic Systems
Maximum boiling points azeotrope. Partial pressures show negative deviation from Raoults’ law.
(5)
i 1
There is a minimum in its
Degrees of Freedom
The variables to describe the physical equilibrium of a system are classified as intensive variables, which are independent of the size of the system, and extensive variables, which depend on system size. Only a few of the variables are independent to determine the state of system. The number of the independent variables is called the degrees of freedom.
V F
1
zH
Azeotropic Systems
(1)
Azeotropes are formed by liquid mixtures exhibiting maximum or minimum boiling points, which represent, respectively, negative or positive deviations from Raoults’ law. If there is only one liquid phase, the mixture forms a homogeneous azeotrope; if more than one liquid phase are present, the azeotrope is heterogeneous.
Azeotropic Systems
Correspondingly, there is a minimum in its T-x-y curve, which stands for the composition of azeotrope.
(3)
Azeotropic Systems
In y-x plot, equilibrium line has an intersection with the y=x line.
P-x curve.
Azeotropic Systems
Correspondingly, there is a maximum in its T-x-y curve, which stands for the composition of azeotrope.
(6)
Azeotropic Systems
Azeotropic Systems
Minimum boiling points azeotrope. Partial pressures show positive deviation from Raoults’ law.
(2)
i 1
There is a maximum in its
P-x curve.
Degrees-of-Freedom Analysis
Therefore,
(3)
V = CP 2 C P 4 P CP + 6
E = P + CP 1 C 1 P CP + 1
(4-4)
F V E = C 5
For example, if variables (zi, TF, PF, F, T, P) are specified, all the remaining variables can be calculated from the equations.
(2)
Binary Vapor-Liquid Systems
For vaporization, the plot in the right figure is more convenient. The equation of q-line is
(3)
V F 1 yH xH V F
Isothermal Flash & Adiabatic Flash
In an isothermal flash, heating or cooling are necessary to keep TV at the specified value. In an adiabatic flash, the pressure is reduced adiabatically that TV will also reduce to provide the heat of vaporization.
F V E
Degrees-of-Freedom Analysis
(2)
For a single equilibrium stage shown in the right figure, there are (CP +2) intensive variables to determine the phase equilibrium, and (C +P +4) additional variables (zi, TF, PF, F, Q, V, L) to describe the process state. And there should be independent equations for P molar normalizations, C(P -1) K-values, C component material balances and 1 energy balance.
In y-x plot, equilibrium line has an intersection with the y=x line.
(7)
Azeotropic Systems
Heterogeneous azeotrope are always minimum boiling mixtures. The activity coefficients must be much greater than 1 to cause liquid phase split.
(9)
Azeotropic Systems
In 2-L region, the compositions of vapor phase keeps constant Though the total composition of liquid phases change. The points a , b represent the compositions of 2 liquid phases.
Binary Vapor-Liquid Systems
(1)
For binary vapor-liquid systems, Gibbs phase rule gives
F C P 2 2 2 2 2
Then if T and P are specified, the phase compositions (xi , yi) should be completely determined. And the relative volatility A,B (separation factor) is also determined .