天津大学化工传质分离资料第2章传质分离过程的热力学基础

For a pure ideal gas, fugacity is equal to the pressure, and for a component in an ideal gas mixture, the partial fugacity is equal to its partial pressure, pi yi p . Dalton’s law
Chemical potential cannot be expressed as an absolute quantity, and the numerical values of chemical potential are difficult to relate to more easily understood physical quantities. Furthermore, the chemical potential approaches an infinite negative value as pressure approaches zero. For these reasons, the chemical potential is not favored for phase equilibria calculations. Instead, fugacity, invented by G. N. Lewis in 1901, is employed as a surrogate.
一、相平衡关系
（2）相平衡条件（准则）： 各相的温度相等、压力相等，每个组分的化学位相等。
T T T ......
P P P ......
......
' i '' i ''' i
Chemical potential
（1）什么是相平衡？ 混合物所形成的若干相保持物理平衡而共存的状态。 热力学：整个物系的自由能最小。 At equilibrium, the total Gibbs free energy (G) for all phases is a minimum. 动力学：相间表观传递速率为零。 The apparent rate of mass transfer across the phase interface is zero.
The rate of separation is governed by mass transfer, while the extent of separation is limited by thermodynamics equilibrium. 极限程度------ 热力学 分离速率------ 动力学
yi Ki xi
yi---Concentration of any component in vapor xi---Concentration of any component in liquid
For the liquid-liquid case（eg. Extraction）, the constant is referred to as the distribution coefficient （分配系数）or liquid-liquid equilibrium ratio（液液平衡常数）.
For the liquid-liquid case, relative selectivity is
K Di ij K Dj
分离因子与1的偏离程度表示组分间分离的难易程度。
2.1.1 汽液平衡 Vapor-liquid equilibria
At vapor-liquid equilibrium,
K Di x / x
(1) i
( 2) i
xi(1)---Concentration of any component in extract
xi(2)---Concentration of any component in raffinate
Calculation of Equilibrium Ratio
Extent = Thermodyanmics Rate = Transport
Contents
2.1 Phase Equilibria 2.1 相平衡基础 2.1.1 Vapor-Liquid Equilibrium 2.1.1气液平衡 2.1.2 Liquid-Liquid Equilibrium 2.1.2液液平衡 2.2 多组分物系的泡点和露点计算 2.2 Bubble-point, and Dew-point Calculation for Multicomponent 2.2.1 泡点温度和压力的计算 Mixtures 2.2.2 露点温度和压力的计算 2.2.1 Bubble-point Temperature and 2.3 多组分闪蒸计算 Pressure Calculation 2.3.1 等温闪蒸和部分冷凝过程 2.2.2 Dew-point Temperature and 2.3.2 绝热闪蒸过程 Pressure Calculation 2.4 液液平衡过程的计算 2.3 Flash Calculation 2.5 多相平衡过程 2.3.1 Isothermal Flash and Partial Condensation 2.6共沸系统和剩余曲线 2.3.2 Adiabatic Flash
相平衡关系的表示方法： 1. 相图 yi
0 2. 相平衡常数：
xi
K i yi / xi
Ki ij xi /x j K j yi /y j
3. 分离因子：
二、相平衡常数
相平衡常数（Ki）--- Equilibrium Ratio
K i yi / xi
Equilibrium Ratio is the ratio of mole fractions of a species present in two phases at equilibrium.
i ˆ C exp f i RT
一、相平衡关系
（2）相平衡条件（准则）： 各相的温度相等、压力相等，每个组分的逸度相等。
T T T ......
P P P ......
ˆ ˆ ˆ f i f i f i ......
and
L ˆL ˆ f i i xi p
(2-8)
ˆV f ˆL f i i
Therefore,
L ˆV ˆ y p i i i xi p
(2-10)
a so-called equation-of-stare form of the K-value is obtained:
ˆ iL yi Ki V ˆ xi i
Case 1—纯组分
V L ˆ ˆ fi fi
逸度等于纯组分的逸度
For a pure component, the partial fugacity, the pure-component fugacity, Case 2---理想气体混合物
fˆi , becomes
fi
. 逸度等于组分的分压
平衡分离过程，常采用分离因子表示平衡关系。
For the vapor-liquid case, separation facor is
Ki ij xi /x j K j
yi /y j
relative volatility（相对挥发度） for Distillation
相对挥发度对温度和压力变化不敏感，常视为常数，简化计算。
传 质 分 离 过 程
第二章 传质分离过程的热力学基础
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Chapter 2 Thermodynamics of Separation Operation
For mass transfer separation processes, the separation is achieved by enhancing the rate of mass transfer by diffusion of certain species relative to mass transfer of all species by bulk movement within a particular phase.
yi xi

i f ioL
ˆV i p
应用状态方程计算汽相逸度系数，应用活度系数方程计算活度系数。
2.1.1 汽液平衡 Vapor-liquid equilibria
相平衡常数计算的两种方法： 状态方程法
ˆ iL yi Ki V ˆ xi i
yi Ki xi
Ki的计算： Case 1---理想体系的吸收过程： 亨利定律（Henry’s Law） Case 2---理想体系的精馏过程 拉乌尔定律（Raoult’s Law） Case 3---非理想体系 用气相逸度和液相活度系数来计算。
三、分离因子 Separation Factor
2.1.1 汽液平衡 Vapor-liquid equilibria
Case 3---真实混合物 用逸度系数或活度系数计算逸度
For a real mixture, partial fugacity coefficients are defined by
ˆV ˆV f i i yi p
(2-7)
ˆL f i i 0L ˆ x f
i iห้องสมุดไป่ตู้
Fugacity under standard state
(2-9)
通常取纯组分i的液体在系统温度 和压力下的逸度。
a so-called activity coefficient form of the K-value is obtained:
Ki