反應(yīng)精餾塔的優(yōu)化設(shè)計(jì)外文·文獻(xiàn)

1、學(xué)校代碼： 10128學(xué) 號(hào)： 201220506019 外文文獻(xiàn)及翻譯（題 目：DN1800脫丁烷精餾塔設(shè)計(jì)學(xué)生姓名：袁浩楠學(xué) 院：化工學(xué)院系 別：過控系專 業(yè)：過程裝備與控制工程班 級(jí)：過控12-1班指導(dǎo)教師：耿清 二 一 六 年 六 月Optimal Design of a Reactive Distillation Column Edwin Zondervan, Mayank Shah* and André B. de Haan

2、  Eindhoven University of Technology, Department of Chemistry and Chemical Engineering, P.O. Box 513, 5600MB, Eindhoven, the Netherlands, m.shahtue.nl In this work we develop a

3、0;MINLP model that can be used to optimize the design of reactive distillation column. MINLP model is formulated in GAMS in such a way that it can be solved

4、0;locally and globally. In the RD column a component A is converted into product B while vapour and liquid are assumed to be in equilibrium. The objective is to

5、 find a design for this process that minimizes the total costs (consisting of capital and operational costs). The design variables of interest are the total number of

6、0;stages, the number of reactive stages, the location of the reactive stages, the feed tray location and the reflux ratio.   Keywords: Reactive distillation, Design, Opti

7、mization, MINLP 1. Introduction Reactive distillation (RD) is a matured technology that combines reaction and separation in a single processing unit. RD has distinct advantages;

8、60;normally the equipment is much smaller than conventional equipment, the energy requirements are lower and the conversion of the product is higher as the products are i

9、mmediately removed by distillation. Krishna et al. (2002) give a more complete overview of reactive distillation However, design and control of RD is a complex process (Al-Arfaj and Luyben (2000). Especially the optimal desig

10、n 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 the proposed models&#

11、160;are strong simplifications of reality and most authors agree that the morecomplex models cannot be solved to global optimality.In Jackson and Grossmann (2001) an optimization&#

12、160;approach for the optimal design of a reactive distillation column is proposed, which shows that disjunctive programming can be effectively used to handle the resulting non

13、linear optimization problem. The design of a reactive distillation column is concerned with finding the total number of trays of the column, the number and location of

14、60;reactive trays, and the feed and reflux locations of the column. Also Seferlis and Grievink (2001) solve a similar problem using collocation models. Stochastic optimization 

15、;methods such as genetic algorithm are also often applied to design these processes. However, this approach is computationally expensive and because of a probabilistic approach,

16、60;there is no assurance of global optimality.   This model is associated with nonlinearities from reaction kinetics, phase equilibrium and bilinear terms of the balance 

17、equations. Gangadwala et al. (2006) have formulated MINLP model for RD process. However, they can only solve the problem locally. For global optimality they have applied 

18、polyhedral relaxations and converted MINLP problem to MILP problem. They have concluded that MINLP problem for RD process can only be solved locally. To overcome this des

19、ign problem, in this work an RD model is formulated as MINLP in such way that model can be solved globally. This model contains continuous- as well as discrete&

20、#160;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

21、 and positions of reactive stages, reflux location, number and positions of feed, required stages to obtain pure product. 2. Problem statement and proposed model In this&

22、#160;section an MINLP is proposed to optimize the design of a reactive distillation column. The optimization objective is to minimize the total costs and to find optimal&

23、#160;reboiler and condenser duties, the reflux ratio, the number of stages, the number and location of reactive stages, catalyst loadings on reactive stages and the feed 

24、location. In the column a reaction A n B takes place for which the reaction kinetics, component balances and material balances are known, also vapour and liquid are&

25、#160;assumed to be in equilibrium for the system of 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

26、variables to be determined by solving the MINLP model. The stages 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 obta

27、in the distillate at the top of a column. A reactant is heavy component 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

28、) for reflux location, ILIN(J) for feed location are introduced 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 (ILIN (J) =1). Liquid is not present on the stages above the reflux stage so these stages have no effect on the col

29、umn performance. Hence, the total number of stages is calculated as:å+×-=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 dimensi

30、ons and the heat duties:Where NT is the total number of stages, H is the column 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 reac

31、tion kinetics holds that:And for the vapour-liquid equilibrium we use a relative volatility relation of the form:The model also includes logical constraints to incorporate only one feed and one reflux stage: and the 

32、;constrains for the reflux stage above the feed stage:Furthermore the model includes structural constraints that ensure the operational conditions, e.g. flows cannot exceed certain minimum and maximum values, or the configuration settings such as the number of

33、 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 programming problem (MINLP) and nonlinearities are associated with reaction ki

34、netics, 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 set as a constraint. The simulation of the reactive distillation model is

35、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 compared to composition of reactant. The composition of reactant is high at the

36、 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 are required to produce 99.5% pure product at the top of the column. The

37、 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 USD to produce 800 tons per year. In particular, 1.10e05 USD is the capi

38、tal 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 simulationThe MINLP formulation of RD model contains 260 equations, 253 continuou

39、s 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 sub problems. To evaluate whether DICOPT has found the global optimum,

40、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 indicates that the solution obtained in this case is at its global optim

41、um. 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 iterations). BARON requires more iterations compared to DICOPT because variables

42、 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 for MINLP problem of reactive distillation column4. Conclusions We have d

43、eveloped 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 BARON, while the found objective values are identical; indicating that DI

44、COPT 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 Chemistry Research, 39 (9), 3298-3307. 2、 Gangadwala J., Kienle A., 2006, Glo

45、bal 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 design of reactive distillation columns, Computers and Chemical Enginee

46、ring, 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 collocation models, Industrial and Engineering Chemistry Research, 40 (7), 16

47、73-1685. 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.反應(yīng)精餾塔的優(yōu)化設(shè)計(jì)埃德溫譯，Mayank Shah和安德烈éB. de Haan埃因霍溫科技大學(xué)化學(xué)與化學(xué)工程系，埃因霍溫，荷蘭，在這項(xiàng)工作中，我們開發(fā)了一個(gè)模型，可用于優(yōu)化設(shè)計(jì)的反應(yīng)精餾

48、塔。MINLP模型是以這樣一種方式，它可以在本地和全球范圍內(nèi)制定的解決上。在路的一個(gè)組成部分，一個(gè)組成部分，被轉(zhuǎn)換成產(chǎn)品，而蒸汽和液體被假定為在平衡。目標(biāo)是要找到一個(gè)設(shè)計(jì)，這個(gè)過程，最大限度地減少總成本（包括資本和運(yùn)營成本）。設(shè)計(jì)變量的設(shè)計(jì)變量的總數(shù)量的階段，反應(yīng)階段的數(shù)目，反應(yīng)階段的位置，進(jìn)料盤位置和回流比。關(guān)鍵詞：反應(yīng)精餾，設(shè)計(jì)，優(yōu)化，模型1、簡(jiǎn)介反應(yīng)精餾技術(shù)是一種將反應(yīng)和分離技術(shù)結(jié)合在一個(gè)單一處理單元中的成熟技術(shù)。研發(fā)具有明顯的優(yōu)點(diǎn)，通常設(shè)備比常規(guī)設(shè)備小得多，能量要求較低，產(chǎn)品的轉(zhuǎn)化率更高，產(chǎn)品立即通過蒸餾除去?？鼛熌堑热?。（2002）提供一個(gè)更全面的反應(yīng)精餾的概述。然而，控制研發(fā)設(shè)計(jì)是

49、一個(gè)復(fù)雜的過程（Al arfaj和Luyben（2000）。特別是這樣一個(gè)系統(tǒng)的優(yōu)化設(shè)計(jì)，需要精確的過程模型，導(dǎo)致一個(gè)計(jì)算要求苛刻的數(shù)學(xué)問題。雖然這個(gè)問題已經(jīng)被研究的科學(xué)文獻(xiàn)，所提出的模型是現(xiàn)實(shí)的強(qiáng)烈的簡(jiǎn)化和大多數(shù)作者同意，更復(fù)雜的模型不能解決全局最優(yōu)的時(shí)間。在杰克遜和格羅斯曼（2001）提出了對(duì)反應(yīng)精餾塔的優(yōu)化設(shè)計(jì)的優(yōu)化方法，這表明析取規(guī)劃可以有效地處理非線性優(yōu)化問題。反應(yīng)精餾塔的設(shè)計(jì)與發(fā)現(xiàn)塔的總數(shù)量、反應(yīng)塔的數(shù)量和位置、塔的進(jìn)料和回流位置有關(guān)。另外，grievink塞弗里斯（2001）使用配置模型解決類似問題。隨機(jī)優(yōu)化方法，如遺傳算法也經(jīng)常被應(yīng)用到設(shè)計(jì)這些過程。然而，這種方法是計(jì)算昂貴的，

50、因?yàn)橐粋€(gè)概率的方法，也沒有保證全局最優(yōu)。此模型與非線性反應(yīng)動(dòng)力學(xué)，相平衡和雙線性項(xiàng)的平衡方程。gangadwala等人。（2006）制定的MINLP模型的研發(fā)過程。然而，他們只能解決本地問題。全局最優(yōu)性他們應(yīng)用多面體的松弛和MINLP問題轉(zhuǎn)化為混合整數(shù)線性規(guī)劃問題。他們的結(jié)論是，研發(fā)過程的MINLP問題的解決只能局部。為了克服這個(gè)設(shè)計(jì)問題，在這項(xiàng)工作中RD模型中，模型可以解決這樣問題的全局。該模型包含連續(xù)和離散變量。連續(xù)變量通常與操作條件，如液體和蒸汽流量，進(jìn)料流量，回流比。離散變量的數(shù)目和位置的反應(yīng)階段，回流位置，數(shù)量和位置的飼料，所需的階段，以獲得純產(chǎn)品。2、問題陳述和模型在這一部分的MI

51、NLP優(yōu)化了反應(yīng)精餾塔的設(shè)計(jì)。優(yōu)化目標(biāo)是最小化總成本，找到最佳的再沸器和冷凝器的職責(zé)、回流比、若干階段，反應(yīng)階段的數(shù)量和位置、催化劑用量對(duì)反應(yīng)階段和進(jìn)料位置。在列B發(fā)生反應(yīng)的反應(yīng)動(dòng)力學(xué)，成份平衡和物料平衡是已知的，同時(shí)蒸汽和液體被假定是平衡我們的利益制度。圖1：離散二進(jìn)制變量的第三列和圖形視圖的示意圖一個(gè)RD柱示意圖在圖1中，還包括所有重要的設(shè)計(jì)變量是通過求解MINLP模型確定出。階段被編號(hào)從頂部到底部。第一階段是冷凝器和再沸器的最后階段代表。因?yàn)橹挥幸粋€(gè)產(chǎn)品在列中產(chǎn)生的，這是作為餾出物，總電容器是用來獲得在一列頂部的餾分。一個(gè)反應(yīng)是沉重的分量和未反應(yīng)的反應(yīng)物必須回收完全列因此總再沸器的使用，其結(jié)果RD柱無底流速。二進(jìn)制變量如ireak（J）反應(yīng)階段的位置，IREF（J）回流位置，吉林（J）對(duì)進(jìn)料位置介紹知道一期J是一個(gè)反應(yīng)階段（ireak（j）= 1）或頂尖級(jí)接收回流（IREF（j）= 1）或飼料級(jí)（吉林（j）= 1）。液體不存在于回流階段的階段，所以這些階段對(duì)柱的性能沒