反应精馏塔的优化设计外文文献

1、学校代码：10128 学 号：201220506019题目：dn1800脱丁烷精馏塔设计 学生姓名：袁浩楠 学院：化工学院 系别：过控系专业：过程装备与控制工程 班级：过控12-1班 指导教师：耿清二o 六年六月optima i design of a reactive distillation co iumnedwin zondervan, mayank shah* and andre b. de haan eindhoven university of technology, department of chemistry and chemi cal engineering，p. 0. b

2、ox 513，5600mb，eindhoven, thenetherlands, m. s hahtue.nl in this work we develop a minlp model that can be used to optimize the design of reactive distillation column. minlp model is f ormulated in gams in such a way that it can be solved locally and gio bally. in the rd column a component a is conve

3、rted into product b whi le vapour and liquid are assumed to be in equilibrium. the objective is to find a design for this process that minimizes the total costs ( consisting of capital and operational costs). the design variables ofinterest are the total numberof stages, the number of reactive stage

4、 s， the location of the reactive stages, the feed tray location and the reflux ratio.keywords: reactive distillation, design， optimization, minlp1. introductionreactive distillation (rd) is a matured technology that combines reaction and separation in a single processing unit. rd has distinct advant

5、ages; normally the equipment is much smaller than conventional equipment, the energy requirements are lower and the conversion of th e product is higher as the products are immediately removed by distil lation. krishna et al. (2002) give a more complete overview of reacti ve distillationhowever, des

6、ign and control of rd is a complex process (al-arfaj and luyben (2000) especially the optimal design of such a system requires accurate process models that lead to a computationally demanding mathematical problem.although the problem has been studied in the scientific literature, most of the time th

7、e proposed models are strong simplifications of rea lity and most authors agree that the morccomplcx models cannot be sol ved to global optimality. in jackson and grossmann (2001) an optimizat ion approach for the optimal design of a reactive distillation column is proposed, which shows that disjunc

8、tive programming can be effecti vely used to handle the resulting nonlinear optimization problem. the design of a reactive distillation column is concerned with finding t he total number of trays of the column, the number and location of re active trays, and the feed and reflux locations of the colu

9、mn. also s eferlis and grievink (2001) solve a similar problem using collocation models. stochastic optimization methods such as genetic algorithm ar e also often applied to design these processes. however, this approac h is computationally expensive and because of a probabilistic approach, there is

10、 no assurance of global optimality.this model is associated with nonlinearities from reaction kinetics, phase equilibrium and bilinear terms of the balance equations. ga ngadwala et al. (2006) have formulated mtnlp model for rd process. ho wever, they can only solve the problem locally. for global o

11、ptimality they have applied polyhedral relaxations and converted minlp problem to m1lp problem. they have concluded that minlp problem for rd proce ss can only be solved locally. to overcome this design problem, in th is work an rd model is formulated as mtnlp in such way that model can be solved gl

12、obally. this model contains continuous- as well as discrete variables. continuous variables are usually related to operating conditions such as liquid and vapour flows, feed flows, reflux ratio.discrete variables are related to number and positions of reactive s tages， reflux location, number and po

13、sitions of feed, required stagesto obtain pure product.2. problem statement and proposed modelin this section an m1nlp is proposed to optimize the design of a reactive distillation column. the optimization objective is to minimi ze the total costs and to find optimal reboiler and condenser duties,th

14、e reflux ratio, the number of stages, the number and location of r eactive stages, catalyst loadings on reactive stages and the feed loc ation. in the column a reaction a b takes place for which the rcac tion kinetics, component balances and material balances are known, al so vapour and liquid are a

15、ssumed to be in equilibrium for the systemof our interest.figure 1: a schematic view of rd column and graphical view of discrete binary variablesa schematic view of rd column is shown in figure 1 which also includes all important design variabl es to be determined by solving the mt nlp model. the st

16、ages are numbered from top to bottom. the first stage represents condenser and the last stage represents the reboiler. since there is only one product produced in a column，which is obtained as distillate, a total condenser is used to obtain the distillate at the top of a column. a reactant is heavy

17、component and unreacted reactant has to be recycled back completely to the column thus a total reboiler is used, which results rdcolumn without bottom flow rate. the binary variables such as ireak (j) for reactive stage location, iref (j) for reflux location, ilin(j) for feed location are introduced

18、 to know whether a stage j is a reactive stage (ireak (j) =1) or a top stage receiving reflux (iref (j) =1) or feed stage (1l1n (j) =1). liquid is not present on the stages above the reflux stage so these stages have no effect on the column performance. ilcncc, the total number of stages is calculat

19、ed as:0.2) (maxjirefjnn.the summation of binary variable ireak (j) gives total number of reactive stages. the objective function which represents the total cost of reactive distillation column is based on the column dimensions and theheat duties:where nt is the total number of stages, h is the colum

20、n length, d is the column diameter and t arc the heat duties. the component balances at each stage n can be given as:gn(ljxty, r)=0,vwwhere l arc the liquid flows, v the vapour flows and x and y the liquid and vapour compositions. the reaction kinetics holds that:and for the vapour-liquid equilibriu

21、m we use a relative volatilityrelation of the form:y = knx)the model also includes logical constraints to incorporate only one feed and one refluxstage:and the constrains for the reflux stage above the feed stage:yj. ilix(j >vj./r£f(j)furthermore the model includes structural constraints tha

22、t ensure theoperational conditions, e.g. flows cannot exceed certain minimum and maximum values, or the configuration settings such as the number of reactive stages cannot exceed the total number of stages. to ensure that the product at the outlet has a specified purity we introduce> xpwherexp is

23、 the requested product purity. eqs. 17 above form a mixed integer nonlinear programming problem (mixlp) and nonlinearities are associated with reaction kinetics, phase equilibrium and bilinear terms of the balance equations and product purity.3. results and discussionsa pure component a is fed to th

24、e column and a minimum product purity of 99. 5% of component b in distillate is set as a constraint. the simulation of the reactive distillation model is performed with the characteristic system data given in table 1.table 1: modelling dataparametersdescriptionvalueffeed flow rate (kmol hr)1.5kfofor

25、ward reaction rate constant kniol kg hr333e04efoactivation energy for forward re action kj kmol57 69e03kbobackward reaction rate constant kmol kg hr2j4eboactivation energy for backward reaction kj kmol8.47e03ttemperature of column k335ppressure bar1.013c02mwmolecular weight kg kmol84.16hetpheight eq

26、uivalent to theoretical plate0.33atrebtemperature gradient for heat transfer at condenser k35.0atcontemperature gradient for heat transfer at reboiler k】35.0since the product is obtained as distillate, it can be seen from figure2 that the composition of the product is high at the top stage compared

27、to composition of reactant. the composition of reactant is high at the bottom stage because reactant is heavy component and recycled back to bottom of the column. the optimal design variables are tabulated in table2. the optimal design encompasses a reflux ratio of 6. 32，and a total of 29 stages arc

28、 required to produce 99- 5% pure product at the top of the column. the optimal design suggests introducing a feed to the column at 28th stage. in total 18 reactive stages are required and these reactive stages are located at stage 12 to 29 in the column. the total costs of this system are 1. 41e05 u

29、sd to produce 800 tons per year. in particular, 1.10e05 usd is the capital cost of a reactive distillation column and3. 06e04 usd is the operating cost of the column.mo le f racti o ns kmo le/ kmolefigure 2: liquid compositions profile of reactant and product alongthe columntable 2: optimal design v

30、ariables found from simulationvariablesdescriptionsvalueddiameter (m)0.489hheight of column (m)12.91required area for reboiler (ni2)3.185aurequired area for condenser (m2)2.954qrebrequired heat for reboiler (kj hr)3.21e05required heat for condenser (kj hr)2.98e05mcatrequired catalyst loadings per re

31、active stage (kg)9.284rrreflux ratio (kmol kmol)6.32lrreflux rate (kmol hr)9.382vvapour flow rate (kmol hr)10.867lliquid flow rate (kmol hr)9.382the minlp formulation of rd model contains 260 equations, 253 continuous variables and 87 binary variables. this resulting mtnlp problem is solved using st

32、andard optimization tools in gams. for local optimization, particularly dicopt is used with minos for the nlp sub problems and cplex for the mip sub problems. to evaluate whether dicopt has found the global optimum, the minlp model is ran with a global optimization solver called baron. the local opt

33、imization solvers requires upper and lower bounds for variables but the global optimization solver does not require bounds for variables, which indicates that the solution obtained in this case is at its global optimum. we found the optimal design of rd column with dicopt in 0. 28 seconds and only 2

34、8 major iterations arc required. baron found the same design as dtcopt and solved the problem to global optimality in 4673 seconds (5361 iterations). baron requires more iterations compared to dicopt because variables are not bounded for baron and thus baron tries to check all possible combinations

35、in order to ensurcthe global optimality. the computational results of two different solvers are compared in table 3.table 3: solver comparison for minlp problem of reactive distillationcolumndicoptbaronobjective value1.41e+051.41e05cpu time (sec)0.2814673total number of iteration28 (major iterations

36、)5361best solution found at node35834. conclusionswe have developed a m1nlp model for the optimal design of a reactive distillation column. numerical results arc presented and the formulated problem is subsequently solved with dtcopt and baron. dtcopt perforins considerably faster than baron, while

37、the found objective values are identical; indicating that dicopt can finds a solution near to global optimalityreferences1、al-arfaj m. , luyben w. l，2000，comparison of alternative control structures for an ideal two-product reactive distillation column, industrial and engineering chemistry research,

38、 39 (9)， 3298-3307.2、gangadwala j.，kicnlc a., 2006，global bound and optimal solution for the production of 2,3dimethylbutene 1， industrial and engineering chemistry research, 45, 2261-2271.3、jackson j. r., grossmann, i. e. a. , 2001，disjunctive programming approach for the optimal design of reactive

39、 distillation columns, computers and chemical engineering, 25 (11-12)， 1661-1673.4、krishna r.，2000，modelling reactive distillation, chemicalengineering science, 55，5183 - 52295、seferlis p., 2001, optimal designand sensitivity analysis of reactive distillation units using collocation models, industri

40、al and engineering chemistry research, 40(7)，1673-1685.6、viswanathan j.，grossmann i. e.，1993，optimal feed locations and number of trays for distillation columns with multiple feeds, industrial and engineering chemistry research, 32， 2942-2949.反应精馏塔的优化设计埃德温译，mayank shah和安德烈6b. dehaan埃因霍温科技大学化学与化学工程系，

41、埃因霍温，荷兰，在这项工作中，我 们开发了一个模型，可用于优化设计的反应精馏塔。minlp模型是以这样一种方 式，它吋以在本地和全球范围a制定的解决上。在路的一个组成部分，一个组成 部分，被转换成产品，而蒸汽和液体被假定为在平衡。标是要找到一个设计， 这个过程，最大限度地减少总成本（ti拈资本和运营成本）。设计变量的设计变 景的总数景的阶段，反应阶段的数目，反应阶段的位置，进料盘位置和回流比。关键词：反应精馏，设计，优化，模型1、简介反应精馏技术是一种将反应和分离技术结合在一个单一处理单元中的成熟 技术。研发具冇明显的优点，通常设备比常规设备小得多，能量要求较低，产品 的转化率更高，产品立即通

42、过蒸馏除去。奎师那等人。（2002）提供一个更全面 的反应精簡的概述。然而，控制研发设计是一个复杂的过程（a1 arfaj和luyben （2000）。特别是这样一个系统的优化设计，需要精确的过程模型，导致一个计 算要求苛刻的数学问题。虽然这个问题已经被研究的科学文献，所提出的模型是 现实的强烈的简化和大多数作者同意，史复杂的模型不能解决全局最优的时间。 在杰克逊和格罗斯曼（2001）提出了对反应精馏塔的优化设计的优化方法，这表 明析取规划吋以冇效地处理非线性优化叫题。反应精馏塔的设计与发现塔的总数 量、反应塔的数量和位置、塔的进料和冋流位置有关。另外，grievink塞弗里 斯（2001）使

43、用配置模型解决类似问题。随机优化方法，如遗传算法也经常被应 用到设计这些过程。然而，这种方法是计算昂贵的，因为一个概率的方法，也没 宥保证全局最优。此模型与非线性反应动力学，相平衡和双线性项的平衡方程。 gangadwala等人。（2006）制定的mtnlp模型的研发过程。然而，他们只能解决 木地问题。全局最优性他们应用多面体的松弛和minlp问题转化为混合整数线性 规划问题。他们的结论是，研发过程的minlp问题的解决只能局部。为了克服这 个设计问题，在这项工作屮kd模型屮，模型可以解决这样问题的全局。该模型 包贪连续和离散变量。连续变量通常与操作条件,如液体和蒸汽流量,进料流量，回流比。离

44、散变量的数目和位置的反应阶段，回流位置，数量和位置的饲料，所 需的阶段，以获得纯产品。2、问题陈述和模型在这一部分的minlp优化了反应精馏塔的设计。优化目标是最小化总成本， 找到最佳的再沸器和冷凝器的职责、凹流比、若干阶段，反应阶段的数量和位置、 催化剂用量对反应阶段和进料位置。在列b发生反应的反应动力学，成份平衡和 物料平衡是已知的，m吋蒸汽和液体被假定是平衡我们的利益制度。图1:离散二进制变量的第三列和图形视图的示意图一个rd柱示意图在图1中，还拈所有重要的设计变量是通过求解minlp 模型确定出。阶段被编号从顶部到底部。第一阶段是冷凝器和再沸器的最后阶段 代表。因为只宥一个产品在列中产

45、生的，这是作为馏出物，总电容器是用来获得 在一列顶部的榴分。一个反应是沉重的分量和未反应的反应物必须回收完全列因 此总再沸器的使用，其结果rd柱无底流速。二进制变量如ireak （j）反应阶段 的位置，iref （j）冋流位置，吉林（j）对进料位置介绍知道一期j是一个反应 阶段（ireak （j） =1）或顶尖级接收回流（1ree （j） = 1）或例料级（吉林（j）=1）。液体不存在于回流阶段的阶段，所以这些阶段对柱的性能没宥影响。因此， 阶段总人数的计算方法为：（0.2） maxjirefjnn。ireak二进制变量的总和（j） 给出y反应阶段的总数。反应精馏塔总成木的标函数是基于柱尺、?

46、和热负荷min/gvr,7/.z)?ar)在不同的阶段，有一个阶段的总数量，氢是柱的k度，并且是柱的直径，而 不是热景的职责。在每个阶段的组件结余，可以给予：gn(ljxty,r)=qyn在那里我是液体流动，五蒸汽流和*和液体和蒸汽组成。反应动力学认为： r” =(x:lvw对于汽液平衡，我们使用的形式的相对波动关系：y = kk(x)该模型还包括逻辑约束，将只冇一个饲料和一个回流阶段：z(«7)=lz(«)=land the constrains for the above the 饲料：回流实实jyj->zj-iref(j)此外，该模型包括结构约束，确保操作条件，

47、如流量不能超过某一最大值和 最小值，或配置设置，如反应阶段的数量不能超过总数的阶段。为确保该产品在 出口处有一个指定的纯度，我们将介绍xd>xp在xp是要求产品纯度。情商。1-7在上面形成一个混合整数非线性规划问 题(minlp)和非线性反应动力学相关的平衡方程和相平衡的产品纯度和双线性 条款。3、结果与讨论一个纯组分的一个列和一个最小的产品纯度为99. 5%的组件乙在馏出物被 设置为约束。釆用表1给出的特征系统数据进行反应精馏模型的仿真。表1:模拟数据parametersdescriptionvalueffeed flow rate (kmol hr)1.5kfoforward rea

48、ction rate constant kmol kg hr3.33e04efoacti ation energy for forward reaction kjkmol57.69e03kbobackward reaction rate constant kmol kg hr2.24eboactivation energy for backward reaction kj kmol8.47e03ttemperature of column k335ppressure barl.0l3e02mwmolecular weight kg kmol84.16hetpheight equivalent

49、to theoretical plate0.33atrebtemperature gradient for heat transfer at condenser k35.0atcontemperature gradient for heat transfer at reboiler k35.0由于产品的馏分，可以看出，从阁2屮的组合物的产品是在顶部阶段相比， 组合物的反皮物。反极物的组成很高，因为反极物是重组分，并将其回收到柱底。 优化的设计变量表中表2。的最佳设计包括回流比为6. 32,和29个阶段所需的 个阶段，以产生99. 5%个纯产品的顶部的列。优化设计建议在第二十八级引入一 个进料柱。在总的18个反应阶段是必需的，这些反应阶段在12至29的列在第。 该系统的总成本1. 41e05美元生产800吨