Equilibriumrelationshipsandequilibriumstageoperation.ppt
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1、1,Chapter 7 Equilibrium relationships and equilibrium stage operation,2,1. Phase Rule,F = C + 2 F = number of degrees of freedom, or variance C= number of components = number of phases 2 only temperature and pressure may affect the equilibrium state. e.g.: In systems of two components, C=2;=2; there
2、fore, F = 2 - 2 + 2 = 2,3,For binary distillation, F=2, there are four variables of interests: pressure, temperature, and the mole fractions of component A in liquid and vapor phases. If the pressure is fixed,only one variable, e.g., liquid phase mole fraction, can be changed independently, and temp
3、erature and vapor-phase mole fraction follow.,2. Equilibrium of Gas and Liquid and equilibrium stage,4,5,P=pA+pB yA+yB=1,xA+xB=1,6,Equilibrium State: No further changes in composition, temperature, or pressure occur. The chemical potential of the vapor and liquid phases are equal. The apparatus is p
4、erforming as if it were an “equilibrium,” or“theoretical,” or “ideal” stage and the vapor and liquid compositions are the equilibrium compositions.,7,7,3. Thermodynamic relationships,1)Equilibrium ratio ( or equilibrium constant or K value).,Where KA=Equilibrium ratio yA=mole fraction of component A
5、 in vapor xA= mole fraction of component A in liquid,8,The more volatile(易挥发) components in a mixture will have the higher values of KA, whereas less volatile components will have lower values of KA. 2)Relative volatility(相对挥发度)-key separation factor in distillation.,(b),9,3)Ideal system Ideal syste
6、ms of vapor and liquid mixtures obey Daltons and Raoults law. Daltons law relates the concentration of a component present in an ideal gas or vapor mixture to its partial pressure.,10,Raoults law,Where pA=partial pressure of component A, force/length2 xA=molar fraction of component A, dimensionless(
7、无因次),(b),11,Therefore,Combining Equation(a) and (b) yields,12,Vapor pressure of pure component i as a function of temperature is correlated by the Antoine equation:,Where are Antoine constants is absolute temperature, or,is less sensitive to changes in temperature than is KA or KB,(当温度变化不大时,可认为是常数,或
8、取平均值),13,since,14,Bubble point equation:,Dew point equation:,15,Though not a strong function of temperature, generally decreases with increasing temperature and increases with decreasing temperature,16,For a binary system, the relative volatility of the two components (A and B) is given by:,The abov
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