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.反应精馏塔的优化设计埃德温译，Mayank Shah和安德烈éB. 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

48、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，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

49、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，grievink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，

50、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MI

51、NLP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