化工熱力學國際班ch

1、Chapter 6 Phase Equilibrium of Fluids 流體相平衡Phase equilibrium is one of the most important part in thermodynamics and chemical engineering, which consists the fundamental knowledge for many separation processes. Definition:Phase: is the homogeneous part in a mixture. Deferent phase has deferent prope

2、rties. Between 2 phases a clear boundary can be found.Each phase is an open system. Transfer of mass and energy may occur between 2 phasesIf there is no macro transport of mass and energy between 2 phases, the 2 phases reach equilibrium.When equilibrium reaches, properties and compositions of each p

3、hase will not change with time; each phase has the same T, P and fj .Systems always tend to equilibrium.6.1 The Criterion of Phases Equilibrium相平衡的判據(jù)When coexist and 2phases,If component I converts from to phase： At equilibrium, no macro-transportation ： For multi-phase, N components：At equilibrium,

4、 besides T and P, the chemical potentials of a component in all the phases are equal. since：At equilibrium, the fugacities of a component in all the phases are equal.6.2 Vapor-Liquid Equilibrium 汽液平衡vaporgasFor a binary system, the state is determined by T, P and composition.3 coordinatesGas liquid

5、super-critical fluidGasliquid co-existence regionThe upper shellbubble point boundaryThe lower shelldew point boundaryThe critical point linec1-c2 Types of VLE Calculation 汽液平衡計算類型 The purpose of VLE calculation is to calculate dependent variables from independent variables. The common found Types o

6、f VLE Calculations Calculation typeIndependent variablesDependent variablesBubble point PT, x1,x2,xN-1P, y1,y2,yN-1Bubble point TP, x1,x2,xN-1T, y1,y2,yN-1Dew point PT, y1,y2,yN-1P, x1,x2,xN-1Dew point TP, y1,y2,yN-1T, x1,x2,xN-1Flash calcnT, P,z1,z2,zN-1x1,x2,xN-1, y1,y2,yN-1 VLE Calculations for i

7、deal systemsIdeal system: ideal gas -ideal liquid solutionThe common found expression of VLE (1). Pjs (2). kj (3). （1）VLE expressed by Pjs (2) VLE expressed by kjFor perfect ideal system :Binary system:k=f(T), deferent T, we get T-x1-y1(3) VLE expressed by , the relative volatilitythe relative volat

8、ility:For a perfect ideal system： Get a weaker function of TThen we have： VLE Calculations for real systemsThermodynamic treatment of VLE 汽液平衡的熱力學處理方法EOS method 狀態(tài)方程法 For vapor-liquid equilibrium ：Can be calculated with EOS the Gamma/Phi formulation of VLE 活度逸度系數(shù)法 i can be calculated with excess Gib

9、bs energy model Define:Antoine equation:re6.2.1 VLE under low pressures 低壓汽液平衡 Low pressure VLE are frequently encountered in chemical processing, such as low pressure flash and low pressure distillation, where vapor can be taken as ideal gas : Select pure component standard state: At equilibrium ：6

10、.2.1.1 BUB P calculation: given xi and T, calculate yi and pFor Bub P calculation：Ex. 6.1 BUB P calculation for a binary mixture at 30 with x1=0.3. At 30 SolutionIdeal liquid solution, 1=2=1With Margules equation:Ex.6.2 Benzene (1) and cyclohexane (2) form an azeotrope at x1=0.525 , 77.6 and 1.013 b

11、ar. Ps1=0.993 bar, Ps2=0.980 bar. p-x-y plot ?At azeotrope point, Therefore,Finally, x1g1g2y1p(bar)0.000011.13481.00000.00000.98000.11.09971.00160.11000.99260.21.07241.00610.21261.00170.31.05111.01270.31071.00790.41.03481.02130.40631.01160.51.02251.03130.50121.01300.5251.02001.03400.52491.01310.61.0

12、1351.04250.59641.01250.71.00711.05480.69301.01010.81.00301.06780.79201.00610.91.00071.08150.89401.00030.999991.00001.09581.00000.9930 x112P/ barx1, y1p-x-y plots P-x1P-y1-x plots Ex.Calculate liquid activity coefficient of n-pentanol正戊醇(1)n-hexane正己烷(2) solution with Wilson eqn, in which:Assume idea

13、l gas, calculate P and y for 20% n-pentanol solution At 30: Solution : ideal gas , real liquid solution: then 6.2.1.2 BUB T calculation: given xi and p, calculate yi and TWith Newton method:untillthenFig 6.6 Block diagram for BUB T calculation for ideal liquid solution at low pressures6.2.1.3 DEW P

14、calculation: given yi and T, calculate xi and pFor ideal liquid solution, 1=2=1, then Eq (6. 12) Reduced tothenIterative calculation is not necessaryEx.6.3 DEW P calculation for a binary mixture of cyclopentane (1) and cyclohexane (2) at 60 with y1=0.3. At 60：幻燈片 15For real solution:6.2.1.4 DEW T ca

15、lculation: given yi and p, calculate xi and Tvapor pressure ratios are weak functions of temperature, Eq.(6. 12)Multiplied by The temperature 幻燈片 156.2.1.5 Flash calculation：given T, p andzi, calculate xi , yi and Fig.6.9 The flash vaporization The flash equationat the bubble point Fig.6.9 The flash

16、 vaporization at the dew point Example 6.4 A preheated stream of a system acetone(1)/acetonitrile(2)/nitromethane(3) , with a composition z1=0.45, z2=0.35, z3=0.2 and a feed flow rate F1=1000moles/h, is released into a flash drum where vapor-liquid two phases are formed in equilibrium at 80 and 110

17、kPa. If the liquid can be assumed as ideal solution and the flash vaporization is operated under steady state, find the flow rates and the compositions of the product streams.Solution: The vapor pressures of the pure components at 80 areideal solution, , =0.7367 6.2.2 VLE under moderate pressures中壓汽

18、液平衡 Define :For a binary system:Kij is the interact parameter correlated from know data. In homeworks, if not specified, take it 0The resultant eqn is available for non or less polar gases.wherereBUBL P Calculation T and x are known, find P and y: reDew P Calculation: T and y are known, find P and x

19、: Bub T calcn P and x are known, find T and y. Dew T calcn P and y are known, find T and x. Example 6.5 Make a BUB P calculation for a methanol(1)-benzene(2) solution with a composition y1=0.4, at 311.65K and 411.65K. Hinted by the procedures shown in Fig.6.13, C programThe liquid activity models Ma

20、rgules , van Laar , Wilson , NRTL and UNIQUAC Parametersmethanol（1）benzene（2）Antoine constant A16.494814.1603Antoine constant B3593.392948.78Antoine constant C-35.2249-44.5633pc / Pa81000004890000Vc / m3mol-10.0001180.000259Tc / K512.6562.1Zc0.2240.2710.5590.212Margules parameters2.18731.6654Van Laa

21、r parameters2.23501.6871Wilson parameters7187.6873823.5087NRTL parameters3351.66474813.034712 0.5011UNIQUAC parameters-310.39634639.0050Surface area parameters q1.43202.4000Volumetric parameters r1.43113.1878Molar volume of liquid Vm / m3.mole-10.000040730.00008941Tab 6.2 Parameters for methanol（1）-

22、 benzene（2）systemWhen, x1=0.4000 and T=311.65K，the calculation results are Results with Margules Eqn.: y1=0.5598, y2=0.4402, p=44532.82 PaResults with van Laar Eqn.: y1=0.5571, y2=0.4429, p =44447.95 P aResults with Wilson Eqn.: y1=0.5548, y2=0.4452, p =44548.76 P aResults with NRTL Method: y1=0.555

23、5, y2=0.4445, p =44493.83 P aResults with UNIQUAC Method: y1=0.5557, y2=0.4443, p =44467.98 P aAt 411.65KResults with Margules Eqn.: y1=0.6651, y2=0.3349, p =1184743.59 P aResults with van Laar Eqn.: y1=0.6626, y2=0.3374, p =1181078.64 P aResults with Wilson Eqn.: y1=0.6668, y2=0.3332, p =1111502.58

24、 P aResults with NRTL Method: y1=0.6596, y2=0.3404, p =1102959.42 P aResults with UNIQUAC Method: y1=0.6692, y2=0.3308, p =1108413.53 P a6.2.2.5 Bubble point and dew point calculations with ExcelRead after class 6.2.3 VLE at High Pressures 高壓汽液平衡 If the pressure is not much too high, the gamma-fi me

25、thod may be still available, with the following considerations. the two-term virial equation should be substituted by available EOS, for ex. the P-R eqn.the pointing factor should be taken accounted for liquid fugacity calculation.Suitable eqn for vapor pressure calculation should be adopted. For ex

26、ample the Ridal equation:For vapor：For liquid：In the calculation, EOS should be combined with mixing rules properly.If the pressure is much too high, g will influenced evidently by p , EOS Method is preferredThe calculation is commonly complex6.3 Gas-Liquid EquilibriumIn VLE, if some of the componen

27、ts exist as gas, i.e. the system temperature exceeds the critical temperatures of those components; the mixture is at gas-liquid equilibrium (GLE). Fig.6.22 .Liquid-phase fugacity of soluteFor the solute For solvent:At equilibriumHome Work6.1, 6.2, 6.46.4 Liquid -Liquid Equilibrium 液液平衡gases are mut

28、ually soluble in all proportions,Liquids not. two stable liquid phases the LL extraction.6.4.1 LLE phase diagrams液液平衡相圖 2 liquid components mix, the mixture may appears in 1 or 2 phases.For a binary system, the maximum No of freedom is 3. if P effect is negligible, the freedom No es 2. Then the stat

29、e of the mixture can be expressed on Tx1 graph.（1）system with UCST (upper critical solution temperature)（the water-benzoamide system）At low T, the 2 components partially dissolved, forming a aqueous phase at left and a oily phase at the right.When T, the solubility of benzoamide in water increases a

30、long DAU. At the same time, the solubility of water in benzoamide increases along EBU. Eventually, the 2 curves meet at point U, the mixture es a homogeneous phase. DE兩相區(qū)單相區(qū)Binary system（2） System with LCST (lower critical solution temperature)如水-三乙基胺等。兩相區(qū)單相區(qū)At T，the horizontal line goes across the

31、solubility lines at A and B which show the composition of the 2 phases respectively. Point L, TL is the lower critical solution temperature (LCST) （3） System with UCST and LCST 如水和煙堿等。The island is 2 phase region. UAL is solubility of component 1 in 2; and UBL is 2 in 1.（4）complete soluble system.兩相

32、區(qū)單相區(qū)The normal triangle coordinate：the sum of the distances of any point in the triangle to the 3 margins equals the height of the triangle. If we set the height is 1, the mole fraction constraint is satisfied.The 3 acmes: pure componentSolubility line AEPFBTurbidity methodthe phase graph for C6H6(A

33、)H2O(B) CH3COOH(C) systemC6H6(A)H2O(B)CH3COOH(C)a1a2a3a4a5b1b2b3b4b5kd1d2d3d4d5dx(B)x(A)x(C)Ternary System2 pairs of mutual partially dissolved system 3 pairs of mutual partially dissolved system6.4.2 Solution stability 溶液的穩(wěn)定性 A spontaneous process： The curve plump up, unstable, phase splitThe curve

34、 sinks. stableFig.6.25 The stability of a binary solutionthe mixture is in stable homogenous single phase solutionthe solution will split into 2 phasethe mixture is at the border line of the island, much likely to undergo phase change.Ex. 6.9 Prove that an ideal solution is stable. Solution : if the

35、 the solution would to split into 2 phases, The G for an ideal solution as function of composition is： Ideal solution is stable, can not split into 2 or more phases At phase equilibrium For ponent system: If the mixture forms ideal solution, it can only be present as a homogeneous solution, say, one phase only 6.4.3 L-L Equilibrium Calculations 液液平衡計算 (1) LLE calculation for binary system 二元液液平衡的計算 The unknowns： x1、x1、 x2、x2 The eqns : a. Select an activity model，solve the eqns，and th