化工分离过程课件第5章传质分离过程的严格模拟计算.pptx

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1、1传传 质质 分分 离离 过过 程程第五章第五章 传质分离过程的严格模拟计算传质分离过程的严格模拟计算主要内容及要求：主要内容及要求：学习并掌握多组分多级分离过程的平衡学习并掌握多组分多级分离过程的平衡级理论模型的建立及求解。级理论模型的建立及求解。重点：重点：泡点法（泡点法（BP法）、流率加和法（法）、流率加和法（SR法）。法）。2第五章第五章 传质分离过程的严格模拟计算传质分离过程的严格模拟计算 5.1 平衡级的理论模型平衡级的理论模型 5.2 三对角矩阵法三对角矩阵法 5.3 同时校正法同时校正法 5.4 多组分分离非平衡模型多组分分离非平衡模型3p多组分精馏过程简捷计算多组分精馏过程简

2、捷计算精馏简捷计算精馏简捷计算FUG法法FenskeNmUnderwoodRmGillilandR、Np多组分吸收过程简捷计算多组分吸收过程简捷计算4严格计算的必要性严格计算的必要性n简捷算法中引入的假设简捷算法中引入的假设“恒摩尔流和相对挥恒摩尔流和相对挥发度为常数发度为常数”，在高压及塔顶、塔釜温差很，在高压及塔顶、塔釜温差很大的情况下，偏差太大。大的情况下，偏差太大。n简捷计算不能给出各塔板上的浓度、温度等信简捷计算不能给出各塔板上的浓度、温度等信息，也难以处理具有多股进料，多股侧采及有息，也难以处理具有多股进料，多股侧采及有侧线换热等复杂分离过程。侧线换热等复杂分离过程。n特殊精馏，多

3、组分吸收，多组分萃取等过程也特殊精馏，多组分吸收，多组分萃取等过程也以采用严格计算为宜。以采用严格计算为宜。5 Except for simple cases,such as binary distillation,graphical,empirical,and approximate group methods are suitable only for preliminary design studies.Final design of multistage equipment for conducting multicomponent separations requires rigor

4、ous determination of temperatures,pressures,stream flow rates,stream compositions,and heat transfer rates at each stage.However,rigorous calculational procedures may not be justified when multicomponent physical properties or stage efficiencies are not reasonably well known.6严格计算的原则：严格计算的原则：在给定的条件下，

5、对每块塔板同时进行物料衡在给定的条件下，对每块塔板同时进行物料衡算，热量衡算及相平衡和归一化计算。算，热量衡算及相平衡和归一化计算。常用计算软件：常用计算软件：Aspen Plus，HYSIM，Process II等。等。75.1 平衡级的理论模型平衡级的理论模型 UjWjFjLjVjLj-1Vj+1Qjzi,j,HF,j,TF,j,pF,jyi,j+1,Hj+1,Tj+1,pj+1xi,j,hj,Tj,pjxi,j-1,hj-1,Tj-1,pj-1yi,j,Hj,Tj,pj第第j j级级平衡级平衡级General equilibrium stage8Assume that:(1)phase

6、equilibrium is achieved at each stage 各级上达到相平衡各级上达到相平衡(2)no chemical reactions occur 无化学反应无化学反应(3)entrainment of liquid drops in vapor and occlusion of vapor bubbles in liquid are negligible 忽略雾沫夹带假定各级上达到相平衡且无化忽略雾沫夹带假定各级上达到相平衡且无化学反应。学反应。9建模原则：建模原则：M Mass balance 物料衡算；物料衡算；MESH方程方程E Equilibrium relat

7、ions 相平衡关系；相平衡关系；S Summation equations 组分摩尔分率加和式；组分摩尔分率加和式；H Heat(energy,enthalpy)balance热量衡算。热量衡算。UjWjFjLjVjLj-1Vj+1Qjzi,j,HF,j,TF,j,pF,jyi,j+1,Hj+1,Tj+1,pj+1xi,j,hj,Tj,pjxi,j-1,hj-1,Tj-1,pj-1yi,j,Hj,Tj,pj第第j j级级10对第对第j级：级：（1）物料衡算（）物料衡算（Meq.）：）：01111=+-+-+=+-jijjjijjjijjijjijMjiyWVxULzFyVxLG,)()(i=

8、1,2,CC个个（2）相平衡关系式（）相平衡关系式（Eeq.）：）：0=-=jijijiEjixKyG,i=1,2,CC个个（3）摩尔分率加和式（）摩尔分率加和式（Seq.）：）：2个个 c001=-=.,1=ijiSYjyGi=1,2,C001=-=.,c1=ijiSXjxGi=1,2,C（4）热量衡算式（）热量衡算式（Heq.）：）：01111=-+-+-+=+-jjjjjjjjFjjjjjHjQHWVhULHFHVhLG)()(,1个个 共有共有（2C3）个方程个方程 11将上述将上述N个平衡级按逆流方式串联个平衡级按逆流方式串联:UjWjFjLjVjLj-1Vj+1Qjj jF1V1Q

9、11 1FNLNQNN N普通的普通的N级逆流装置级逆流装置 12UjWjFjLjVjLj-1Vj+1Qjj jF1V1Q11 1FNLNQNN N设计变量分析：设计变量分析：固定设计变量固定设计变量Nx：进料变量数：进料变量数：N（C+2）压力等级数：压力等级数：N可调设计变量可调设计变量Na：N（C+3）串级单元数：串级单元数：侧线采出数：侧线采出数：传热单元数：传热单元数：分配器数：分配器数：12N2N03N-1总设计变量数总设计变量数Ni=Nx+Na=N(C+6)-1 13设计变量的规定：设计变量的规定：设计型：设计型：关键组分的回收率（或浓度）及相关参数关键组分的回收率（或浓度）及相

10、关参数平衡级数，进料位置等平衡级数，进料位置等操作型：操作型：达到的分离程度（回收率或浓度）达到的分离程度（回收率或浓度）平衡级数，进料位置及相关参数平衡级数，进料位置及相关参数14对操作型问题可以指定以下变量：对操作型问题可以指定以下变量：1、进料信息：、进料信息：Fj、zij、TFj、PFj N（C+2）个）个 2、各级压力：、各级压力：Pj N个个 3、各级侧线采出：、各级侧线采出：Uj、Wj 2（N1）个）个 4、各级换热：、各级换热：Qj N个个 5、级数：、级数：N 1个个未知量：未知量：N(C+6)-1 1、液相组成：、液相组成：xi,j NC个个 2、气相组成：、气相组成：yi

11、,j NC个个 3、液相流率：、液相流率：Lj N个个 4、气相流率：、气相流率：Vj N个个 5、各级温度：、各级温度：Tj N个个N（2C+3）个）个有唯一解有唯一解 15 The above relations are nonlinear algebraic equations that interact strongly.Consequently,solution procedures are relatively difficult and tedious.A solution method is required to be programmed for a computer.16

12、5.2 三对角线矩阵法三对角线矩阵法Tridiagonal Matrix Algorithm Equation-tearing Procedures方程解离法（又称配对收敛法）方程解离法（又称配对收敛法）按方程类型分组的多级分离过程的计算方法。按方程类型分组的多级分离过程的计算方法。适合操作型计算。适合操作型计算。5.2.1 5.2.1 方程的解离方法及求解方程的解离方法及求解 5.2.2 5.2.2 泡点法（泡点法（BPBP法）法）5.2.3 5.2.3 流率加和法（流率加和法（SRSR法）法）175.2.1 方程的解离方法及求解方程的解离方法及求解Equation-tearing Proc

13、edures 一、方程的解离：一、方程的解离：MESHME：工作方程：工作方程算组成算组成SH校验方程校验方程（校核方程）（校核方程）算温度、流率算温度、流率求解：求解：液相组成液相组成xi,j，汽相组成，汽相组成yi,j，温度，温度Tj，流率，流率Vj或或Lj。泡点法（泡点法（BP）：用用S检验检验T，用，用H检验检验V。流率加合法（流率加合法（SR）：用）：用S检验检验V，用，用H检验检验T。1801111=+-+-+=+-jijjjijjjijjijjijMjiyWVxULzFyVxLG,)()(i=1,2,CMeq.Eeq.0=-=jijijiEjixKyG,i=1,2,C将相平衡关系

14、（将相平衡关系（E-eq.）代入物料衡算方程（）代入物料衡算方程（M-eq.）：）：011111=+-+-+-jijijjjijjjijjijijjijxKWVxULzFxKVxL,)()(为消去为消去L，从第，从第1级到第级到第j级作总物料衡算：级作总物料衡算：11VWUFVLjmmmjj-+=1m=+)(将上式代入修正的将上式代入修正的M-eq.，整理可得：，整理可得：19jjijjijjijDxCxBxA=+-11,20第第1级无液相采出，第级无液相采出，第N级无汽相采出级无汽相采出:（5-8）21二、三对角线矩阵的托马斯法二、三对角线矩阵的托马斯法 追赶法（托马斯法）求解：追赶法（托马

15、斯法）求解：(1)先假定先假定Tj和和Vj；(2)计算相平衡常数计算相平衡常数Ki,j，得到线性化的，得到线性化的ME方程；方程；(3)高斯消去法，将（高斯消去法，将（5-8）转化为二对角矩阵方程；）转化为二对角矩阵方程；解出解出xi,N，xi,N，xi,1。(4)一般情况下，一般情况下，xi,j不会满足不会满足S-eq.和和H-eq.，用，用S-eq.和和H-eq.作为收敛的校验方程，算出新的作为收敛的校验方程，算出新的Tj和和Vj；(5)以算出的新的以算出的新的Tj和和Vj为迭代值，返回为迭代值，返回(1)；22配对收敛方法的特点：配对收敛方法的特点：将两个校验方程（将两个校验方程（S-e

16、q.和和H-eq.）与两）与两个迭代变量分别配对。个迭代变量分别配对。根据不同的配对方案形成两种不同的根据不同的配对方案形成两种不同的算法算法:泡点法泡点法(BP法法)和流率加和法和流率加和法(SR法法)。23 For separators where the feed(s)contains only components of similar volatility(narrow-boiling case),a bubble-point(BP)method is recommended.For a feed(s)containing components of widely different

17、 volatility(wide-boiling case)or solubility,a sum-rates(SR)method is suggested.245.2.2 泡点法（泡点法（BP法）法）Bubble-point Method BP法法适适用用于于窄窄沸沸程程混混合合物物的的分分离离计计算算，如如一般的精馏过程。一般的精馏过程。在在此此情情况况下下，各各平平衡衡级级上上的的传传质质过过程程主主要要依依赖赖于于两两相相流流体体的的部部分分汽汽化化和和部部分分冷冷凝凝，平平衡衡级级温温度度就就是是泡泡点点温温度度或或露露点点温温度度，它它们们主主要要取取决决于于两两相相组组成成，所所

18、以以用用组组分分的的摩摩尔尔分分数数加加和和式式，即即S-方程来检验平衡级温度方程来检验平衡级温度Tj是否正确。是否正确。精精馏馏系系统统内内的的热热量量传传递递主主要要由由潜潜热热的的变变化化引引起起，由由此此也也引引起起两两相相流流率率的的变变化化，所所以以用用热热量量衡算方程，即衡算方程，即H-方程来检验流率方程来检验流率Vj是否正确。是否正确。25规定：规定：进料：进料：Fj,zi,j,TFj,PFj 压力：压力：pj 侧采：侧采：Uj,Wj 热负荷：热负荷：Qj（除（除Q1和和QN）级数：级数：N 回流量：回流量：L1 气相馏出量：气相馏出量：V1开开 始始设定设定Tj、Vj初值初值

19、解三对角线矩阵方程，求解三对角线矩阵方程，求xi,j归一化归一化xi,j泡点计算，求新的泡点计算，求新的Tj，Vj计算冷凝器和再沸器的热负荷（计算冷凝器和再沸器的热负荷（Q1和和QN）H-eq.计算新的计算新的Vj；计算；计算Lj）调整调整Tj和和Vj结结 束束yesno规定设计变量规定设计变量是否满足迭代收敛准则是否满足迭代收敛准则BP法计算框图法计算框图26StartSpecify conditionsspecify：feed：Fj,zi,j,TFj,PFj pressure：pj side streams：Uj,Wj heat load：Qj No.of stages：N reflux：

20、L1 vapor distillate：V1Initialize tear variables Tj,VjCompute x by Thomas methodNormalize xi,j for each stageCompute new Tj form BP eq and yCompute Q1 and QNCompute new Vj and LjIs 0.01N?ExityesnoconvergedNot convergedAdjust tear variablesAlgorithm for BP Method27一、迭代变量一、迭代变量Tj、Vj初值的给出初值的给出 1、Vj:用指定回

21、流比、馏出量、进料量、侧用指定回流比、馏出量、进料量、侧线采出量，按线采出量，按恒摩尔流恒摩尔流假设给出一组假设给出一组Vj的初的初值。值。Establish an initial set of Vj based on the assumption of constant molar interstage flows using the specified reflux,distillate,feed,and side-stream flow rates.28一、迭代变量一、迭代变量Tj、Vj初值的给出初值的给出 2、Tj:（1）塔顶：）塔顶：气相采出：气相采出：液相采出：液相采出：气、液相混

22、合：气、液相混合：露点温度露点温度泡点温度泡点温度泡、露点之间的温度泡、露点之间的温度（2）塔釜：）塔釜：釜液泡点温度釜液泡点温度线性内插，得到中间各级温度初值。线性内插，得到中间各级温度初值。29二、归一化二、归一化 Normalization 由于求三对角矩阵方程时没有考虑由于求三对角矩阵方程时没有考虑S-eq.的约束，的约束，必须对得到的必须对得到的xi,j归一化。归一化。=Cjijixx=i1jix,三、泡点方程的计算三、泡点方程的计算(实际就是实际就是S-eq.)：001=-=.,c1=ijiSYjyG30四、四、Vj的计算的计算 通过物料衡算和热量衡算得到二对角线矩阵方程：通过物料

23、衡算和热量衡算得到二对角线矩阵方程：先求先求V3，再依次求出，再依次求出V4VN。31五、迭代收敛的标准五、迭代收敛的标准 或更简单的：或更简单的：p186【例【例5-1】泡点法模拟精馏分离轻烃混合物泡点法模拟精馏分离轻烃混合物325.2.3 流率加和法流率加和法Sum-Rates Method SR法适用于宽沸程混合物的分离过程，法适用于宽沸程混合物的分离过程，如吸收、解吸、气提和萃取等过程的计算。如吸收、解吸、气提和萃取等过程的计算。The chemical components present in most absorbers and strippers cover a relativ

24、ely wide range of volatility（组组分分的的挥挥发发度度相相差差大大）.Hence,the BP method of solving the MESH equations will fail because calculation of stage temperature by bubble-point determination is too sensitive to liquid-phase composition（通通过过泡泡点点计计算算的的级级温温度度对对液液相相组组成成的的变变化化太太敏敏感感）and the stage energy balance is

25、much more sensitive to stage temperatures than to interstage flow rates（热量平衡对级温度比对级间流率敏感的多）（热量平衡对级温度比对级间流率敏感的多）.用用S-方程计算流率；用方程计算流率；用H-方程计算级温度。方程计算级温度。33规定：规定：进料：进料：Fj,zi,j,TFj,PFj 压力：压力：pj 侧采：侧采：Uj,Wj 热负荷：热负荷：Qj（除（除Q1和和QN）级数：级数：N 回流量：回流量：L1 气相馏出量：气相馏出量：V1开开 始始设定设定Tj、Vj初值初值解三对角线矩阵方程，求解三对角线矩阵方程，求xi,j归

26、一化归一化xi,j和和yi,j求新的求新的Tj(k+1)=Tj(k)+Tj(k)Tj(k)通过托马斯法求解一偏导数矩阵方程通过托马斯法求解一偏导数矩阵方程(5-18)S-eq.计算计算Lj；物料衡算计算；物料衡算计算Vj）调整调整Tj和和Vj结结 束束yesno规定设计变量规定设计变量是否满足迭代收敛准则是否满足迭代收敛准则SR法计算框图法计算框图34StartSpecify conditionsspecify：feed：Fj,zi,j,TFj,PFj pressure：pj side streams：Uj,Wj heat load：Qj No.of stages：NInitialize te

27、ar variables Tj,VjCompute x by Thomas methodCompute new Lj from sum-rates ralation and new VjNormalize xi,j and calculate corresponding yi,j and normalize yi,jCompute new TjIs 0.01N?ExityesnoconvergedNot convergedAdjust tear variablesAlgorithm for SR Method35(I)Initialization of Tj and Vj Vj:根据气相进料和

28、侧采，按根据气相进料和侧采，按恒摩尔流恒摩尔流假设给假设给出一组出一组Vj的初值。的初值。Assume a set of Vj values based on the assumption of constant molar interstage flows,working up from the bottom of the absorber using specified vapor feeds and any vapor side-stream flows.36一、迭代变量一、迭代变量Tj、Vj初值的给出初值的给出 2、Tj:Generally,an adequate initial se

29、t of Tj values can be provided by computing or assuming both the bubble-point temperature of an estimated bottoms product and the dew-point temperature of an assumed vapor distillate product;or computing or assuming bubble-point temperature if distillage is liquid or a temperature in-between the dew

30、-point and bubble-point temperatures if distillate is mixed,and then determining the other stage temperatures by assuming a linear variation of temperature with stage location.37(II)Calculate new values of Lj and Vj+=CkjkjLL=i 11jix,)()(Lj(k)is calculated from Vj(k)by material balance：Vj(k1)is obtai

31、ned by total material balance for stage jN：()-+-=N=jmmmmNjjWUFLLV1 Values of xi,j obtained by Thomas algorithm are not normalized at this step but are utilized directly to produce new values of Lj by applying the sum-rates equation.38(III)Normalize xi,j and yi,jNormalize xi,j:=Cjijixx=i1jix,Calculat

32、e yi,j by E-eq.:0=-=jijijiEjixKyG,Normalize yi,j:=Cjijiyy=i1jiy,39(IV)Calculate new Tj Since enthalpies are generally nonlinear in temperature,an iterative solution procedure is required,such as the commonly used Newton-Raphson method：This matrix of partial derivatives is called the Jacobian correct

33、ion matrix which can be solve by employing Thomas algorithm to get the set of corrections Tj(k).jkjjkjjkjjDTCTBTA)(1)()(1=D+D+D+-40(V)Convergence criterion Or simply：p190【例【例5-2】流率加和法模拟吸收塔流率加和法模拟吸收塔41Summaryn n1.1.Rigorous methodsRigorous methods are readily available for are readily available for c

34、omputer-solution of equilibrium-based computer-solution of equilibrium-based models for multicomponent,multistage models for multicomponent,multistage absorption,stripping,distillation,and liquid-absorption,stripping,distillation,and liquid-liquid extraction.liquid extraction.n n2.2.The equilibrium-

35、based modelThe equilibrium-based model for a for a countercurrent-flow cascade provides for countercurrent-flow cascade provides for multiple feeds,vapor side streams,liquid side multiple feeds,vapor side streams,liquid side streams,and intermediate heat exchangers.streams,and intermediate heat exch

36、angers.Thus,the model can handle almost any type Thus,the model can handle almost any type of column configuration.of column configuration.42Summaryn n3.3.The model equationsThe model equations include component include component material balances,total material balances,material balances,total mate

37、rial balances,phase equilibria relations,and energy phase equilibria relations,and energy balances.balances.n4.Some or all of the model equations can usually be grouped so as to obtain tridiagonal matrix equations,for which an efficient solution algorithm is available.43Summaryn n5.Widely used metho

38、ds for iteratively solving 5.Widely used methods for iteratively solving all of the model equations are all of the model equations are the bubble-the bubble-point(BP)method,the sum-rates(SR)point(BP)method,the sum-rates(SR)methodmethod,the simultaneous correction(SC),the simultaneous correction(SC)m

39、ethod,and the inside-out method.method,and the inside-out method.n n6.6.The BP methodThe BP method is generally restricted to is generally restricted to distillation problems involving narrow-distillation problems involving narrow-boiling feed mixtures.boiling feed mixtures.n n7.7.The SR methodThe S

40、R method is generally restricted to is generally restricted to absorption and stripping problems involving absorption and stripping problems involving wide-boiling feed mixtures or in the wide-boiling feed mixtures or in the Isothermal Sum-Rates(ISR)form to Isothermal Sum-Rates(ISR)form to extractio

41、n problems.extraction problems.44p1893:Supplements-Development of Equilibrium-based Models The fundamental equations for the equilibrium-based models were first published by Sorel.The equations consisted of material balances around top and bottom sections of equilibrium stages,including a total cond

42、enser and a reboiler,and corresponding energy balances that included provision for heat losses.Graphs of phase-equilibrium data were used instead of equations.Sorels model was not widely applied because of its complexity.45p1921:Supplements-Development of Equilibrium-based Models Sorels model was ad

43、apted to graphical solution techniques for binary systems by Ponchon and Savarit who used an enthalpy-concentration diagram.46p1925:Supplements-Development of Equilibrium-based Models A much simpler,but less rigorous,graphical technique was developed by McCabe and Thiele,who eliminated the energy ba

44、lances by assuming a constant-molar-overflow.McCabe-Thiele graphical method is applied even today for binary distillation because the method gives valuable insight into changes in phase compositions from stage to stage.47p1938:Supplements-Development of Equilibrium-based Models A notable achievement

45、 was made by Smoker for the distillation of a binary mixture by assuming not only constant molar overflow,but also constant relative volatility between the two components.48p1930s1950s:Supplements-Development of Equilibrium-based Models Two iterative,numerical methods were developed for obtaining a

46、general solution to Sorels model for the distillation of multicomponent mixtures.The Thiele-Geddes method requires specification of NT,the feed stage,R,and the distillate flow rate,with the resulting distribution of the components.The Lewis-Matheson method computes the NT and the location of the fee

47、d stage for a specified R and split between two key components.These two methods were widely used for the simulation and design of single-feed multicomponent distillation columns prior to the 1960s.49p1958:Supplements-Development of Equilibrium-based Models Techniques of matrix algebra were applied

48、by Amundson,leading to a number of successful computer-aided design and simulation programs abound for the rigorous,iterative numerical solution of Sorels equilibrium-based model for a wide variety of column configurations and specifications.Although the iterative computations sometimes fail to conv

49、erge,the methods are widely applied and have become more flexible and robust with each passing year.50Limitation of Equilibrium-based Models The equilibrium-based methods assume that equilibrium is achieved,at each stage,with respect to both heat and component mass transfer.Except when temperature c

50、hanges significantly from stage to stage,the assumption of temperature equality for vapor and liquid phases leaving a stage is usually acceptable.However,in most industrial applications,the assumption of equilibrium with respect to exiting phase compositions is not reasonable.In general,exiting vapo