反应精馏塔的优化设计外文·文献

1、学校代码： 10128学 号： 201220506019 外文文献及翻译（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 一 六 年 六 月OptimalDesignofaReactiveDistillationColumnEdwinZondervan,MayankShah*andAndrB.deHaanEindhovenUniversityofTechnology,DepartmentofChemistryandChemicalEngineering,P.O.Box513,5600MB,Ei

2、ndhoven,the Netherlands,m.shahtue.nlInthisworkwedevelopaMINLPmodelthatcanbeusedtooptimizethedesignofreactivedistillationcolumn.MINLPmodelisformulatedinGAMSinsuchawaythatitcanbesolvedlocallyandglobally.IntheRDcolumnacomponentAisconvertedintoproductBwhilevapourandliquidareassumedtobeinequilibrium.Theo

3、bjectiveistofindadesignforthisprocessthatminimizesthetotalcosts(consistingofcapitalandoperationalcosts).Thedesignvariablesofinterestarethetotalnumber ofstages,thenumberofreactivestages,thelocationofthereactivestages,thefeedtraylocationandtherefluxratio.Keywords:Reactivedistillation,Design,Optimizati

4、on,MINLP1.IntroductionReactivedistillation(RD)isamaturedtechnologythatcombinesreactionandseparationinasingleprocessingunit.RDhasdistinctadvantages;normallytheequipmentismuchsmallerthanconventionalequipment,theenergyrequirementsarelowerandtheconversionoftheproductishigherastheproductsareimmediatelyre

5、movedbydistillation.Krishnaetal.(2002)giveamorecompleteoverviewofreactivedistillation However, design 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 mathemati

6、cal problem.Althoughtheproblemhasbeenstudiedinthescientificliterature,mostofthetimetheproposedmodelsarestrongsimplificationsofrealityandmostauthorsagreethatthemorecomplexmodelscannotbesolvedtoglobaloptimality.InJacksonandGrossmann(2001)anoptimizationapproachfortheoptimaldesignofareactivedistillation

7、columnisproposed,whichshowsthatdisjunctiveprogrammingcanbeeffectivelyusedtohandletheresultingnonlinearoptimizationproblem.Thedesignofareactivedistillationcolumnisconcernedwithfindingthetotalnumberoftraysofthecolumn,thenumberandlocationofreactivetrays,andthefeedandrefluxlocationsofthecolumn.AlsoSefer

8、lisandGrievink(2001)solveasimilarproblemusingcollocationmodels.Stochasticoptimizationmethodssuchasgeneticalgorithmarealsooftenappliedtodesigntheseprocesses.However,thisapproachiscomputationallyexpensiveandbecauseofaprobabilisticapproach,thereisnoassuranceofglobaloptimality.Thismodelisassociatedwithn

9、onlinearitiesfromreactionkinetics,phaseequilibriumandbilineartermsofthebalanceequations.Gangadwalaetal.(2006)haveformulatedMINLPmodelforRDprocess.However,theycanonlysolvetheproblemlocally.ForglobaloptimalitytheyhaveappliedpolyhedralrelaxationsandconvertedMINLPproblemtoMILPproblem.Theyhaveconcludedth

10、atMINLPproblemforRDprocesscanonlybesolvedlocally.Toovercomethisdesignproblem,inthisworkanRDmodelisformulatedasMINLPinsuchwaythatmodelcanbesolvedglobally.Thismodelcontainscontinuous-aswellasdiscretevariables.Continuousvariablesareusuallyrelatedtooperatingconditionssuchasliquidandvapourflows,feedflows

11、,refluxratio.Discretevariablesarerelatedtonumberandpositionsofreactivestages,refluxlocation,numberandpositionsoffeed,requiredstagestoobtainpureproduct.2.ProblemstatementandproposedmodelInthissectionanMINLPisproposedtooptimizethedesignofareactivedistillationcolumn.Theoptimizationobjectiveistominimize

12、thetotalcostsandtofindoptimalreboilerandcondenserduties,therefluxratio,thenumberofstages,thenumberandlocationofreactivestages,catalystloadingsonreactivestagesandthefeedlocation.InthecolumnareactionAnBtakesplaceforwhichthereactionkinetics,componentbalancesandmaterialbalancesareknown,alsovapourandliqu

13、idareassumedtobeinequilibriumforthesystemofourinterest.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 variables to be determined by solving the MINLP model. The stages

14、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 comp

15、onent and unreacted reactant has to be recycled back completely to the column thus a total reboiler is used, which results RD column 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 to

16、 know whether a stage J is a reactive stage (IREAK (J) =1) or a top stage receiving reflux (IREF (J) =1) or feed stage (ILIN (J) =1). Liquid is not present on the stages above the reflux stage so these stages have no effect on the column performance. Hence, the total number of stages is calculated a

17、s:+-=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 the heat duties:Where NT is the total number of stages, H is the colum

18、n length, D is the column diameter and T are the heat duties. The component balances at each stage n can be given as:Where L are 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 equilibrium we use a relati

19、ve volatility relation of the form:Themodelalsoincludeslogicalconstraintstoincorporateonlyonefeedandonerefluxstage:andtheconstrainsfortherefluxstageabovethefeedstage:Furthermore the model includes structural constraints that ensure the operational conditions, e.g. flows cannot exceed certain minimum

20、 and maximum values, or the configuration settings such as the number of reactive stages cannot exceed the totalnumber of stages. To ensure that the product at the outlet has a specified purity we introducewhere xP is the requested product purity. Eqs. 1-7 above form a mixed integer nonlinear progra

21、mming problem (MINLP) and nonlinearities are associated with reaction kinetics, phase equilibrium and bilinear terms of the balance equations and product purity.3. Results and discussions A pure component A is fed to the column and a minimum product purity of 99.5% of component B in distillate is se

22、t as a constraint. The simulation of the reactive distillation model is performed with the characteristic system data given in table 1.Table 1: Modelling dataSince the product is obtained as distillate, it can be seen from figure 2 that the composition of the product is high at the top stage compare

23、d 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 table 2. The optimal design encompasses a reflux ratio of 6.32, and a total of 29 stages

24、are 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

25、USD to produce 800 tons per year. In particular, 1.10e05 USD is the capital cost of a reactive distillation column and 3.06e04 USD is the operating cost of the column.Figure 2: liquid compositions profile of reactant and product along the column Table 2: optimal design variables found from simulatio

26、nThe MINLP formulation of RD model contains 260 equations, 253 continuous variables and 87 binary variables. This resulting MINLP problem is solved using standard optimization tools in GAMS. For local optimization, particularly DICOPT is used with MINOS for the NLP sub problems and CPLEX for the MIP

27、 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 optimization solvers requires upper and lower bounds for variables but the global optimization solver does not require bounds for variables, which

28、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 28 major iterations are required. BARON found the same design as DICOPT and solved the problem to global optimality in 4673 seconds (5361 iteratio

29、ns). BARON requires more iterations compared to DICOPT because variables are not bounded for BARON and thus BARON tries to check all possible combinations in order to ensure the global optimality. The computational results of two different solvers are compared in table 3.Table 3: Solver comparison f

30、or MINLP problem of reactive distillation column4. Conclusions We have developed a MINLP model for the optimal design of a reactive distillation column. Numerical results are presented and the formulated problem is subsequently solved with DICOPT and BARON. DICOPT performs considerably faster than B

31、ARON, while the found objective values are identical; indicating that DICOPT can finds a solution near to global optimalityReferences 1、Al-Arfaj M., Luyben W.L., 2000, Comparison of alternative control structures for an ideal two-product reactive distillation column, Industrial and Engineering Chemi

32、stry Research, 39 (9), 3298-3307. 2、 Gangadwala J., Kienle A., 2006, Global bound and optimal solution for the production of 2,3 dimethylbutene -1, Industrial and Engineering Chemistry Research, 45, 2261-2271. 3、Jackson J.R., Grossmann, I.E. A., 2001, Disjunctive programming approach for the optimal

33、 design of reactive distillation columns, Computers and Chemical Engineering, 25 (11-12), 1661-1673. 4、Krishna R., 2000, Modelling reactive distillation, Chemical Engineering Science, 55, 51835229 5、Seferlis P., 2001, Optimal design and sensitivity analysis of reactive distillation units using collo

34、cation models, Industrial 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

35、德烈B. de Haan埃因霍温科技大学化学与化学工程系，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，它可以在本地和全球范围内制定的解决上。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。目标是要找到一个设计，这个过程，最大限度地减少总成本（包括资本和运营成本）。设计变量的设计变量的总数量的阶段，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。研发具有明显的优点，通常设备比常规设备小得多

36、，能量要求较低，产品的转化率更高，产品立即通过蒸馏除去。奎师那等人。（2002）提供一个更全面的反应精馏的概述。然而，控制研发设计是一个复杂的过程（Al 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，更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，这表明析取规划可以有效地处理非线性优化问题。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、塔的进料和回流位置有关。另外，griev

37、ink塞弗里斯（2001）使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，也没有保证全局最优。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MINLP模型的研发过程。然而，他们只能解决本地问题。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，在这项工作中RD模型中，模型可以解决这样问题的全局。该模型包含连续和离散变量。连续变量通常与操作条件，如液体和蒸汽流量，进料流

38、量，回流比。离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、回流比、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，同时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，还包括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。因为只有一个产品在列

39、中产生的，这是作为馏出物，总电容器是用来获得在一列顶部的馏分。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）回流位置，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（IREF（j）= 1）或饲料级（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有影响。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）给出了反应阶段的总数。反应精馏塔总成本的目标函数是基于柱尺寸和热负荷在不同的阶段，有一个阶段的总数量，氢是柱的长度，并且是柱的直径，而不是热量的职责。在每个阶段的组件结余，可以给予：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：对于汽液平衡，我们使用的形式的相对波动关系：该模型还包括逻辑约束，将只有一个饲料和一个回流阶段：and the constrains for the above the饲料：回流实习实习此外，该模型包括结构约束，确保操作条件，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