Optimization-based design of reactive distillation columns using a memetic algorithm

The design optimization of reactive distillation columns (RDC) is characterized by complex nonlinear constraints, nonlinear cost functions, and the presence of many local optima. The standard approach is to use MINLP solvers that work on a superstructure formulation where structural decisions are represented by discrete variables and lead to an exponential increase in the computational effort. The mathematical programming (MP) methods which solve the continuous sub-problems provide only one local optimum which depends strongly on the initialization. In this contribution a memetic algorithm (MA) is introduced and applied to the global optimization of four different formulations of a computational demanding real-world design problem. An evolution strategy addresses the global optimization of the design decisions, while continuous sub-problems are efficiently solved by a robust MP solver. The MA is compared to MINLP techniques. It is the only algorithm that finds the global solution in reasonable times for all model formulations.     

Attainable region of reactive distillation—Part IV: Inclusion of multistage units for complex reaction schemes

Reactive distillation (RD) can be advantageously used to improve selectivity of the desired product in a multi-reaction system. Because of the complexity in vapor liquid equilibrium and reaction kinetics, the design methodology is not straightforward and one has to adopt conceptual design and synthesis methods to arrive at the appropriate RD configuration. This paper is continuation of our earlier work (Amte et al., 2011), aimed at extending the concept of attainable region to a larger family of reactors that includes different reactive distillation units. In this work, we incorporate multistage reactive rectification and reactive stripping models with total reflux and total reboil, respectively. We further define the respective vectors, which justify the need of the corresponding units in the RD network. The van de Vusse schemes with both non-azeotropic and azeotropic vapor?liquid equilibria are considered and the attainable regions are constructed. Explanation is provided based on the visualization of selectivity lines in the composition space. In all the cases studied here, the feasible region is significantly broader than the one realized for the network of only conventional reactors.     

Evolutionary design of optimum distillation column sequence

Synthesis of the optimum distillation column sequence (DCS), which incorporates a huge search space composed of both conventional and complex arrangements, is a highly complicated combinatorial problem in the field of chemical process design and optimisation. In this study, a novel procedure for the synthesis of optimum DCS proposed by Boozarjomehry et al. [Boozarjomehry et al., Can. J. Chem. Eng. 87, 477–492 (2009)] is expanded to include the complex distillation arrangements. The method is based on evolutionary algorithms, and the total annual cost (TAC) is the main criterion used to screen alternatives. Efficient procedure has been proposed for encoding mechanism to include and classify various complex arrangements together with conventional distillation columns. All columns existing in each DCS alternative are designed using the most recommended short‐cut methods to estimate the TAC of the DCS. Four standard benchmark case studies are carried out to clearly demonstrate the excellent performance of the proposed method. The produced results for these problems indicate that the proposed method outperforms the other existing approaches in terms of flexibility, accuracy and comprehensiveness. © 2011 Canadian Society for Chemical Engineering     

A linear model predictive control algorithm for nonlinear large‐scale distributed parameter systems

This work provides a framework for linear model predictive control (MPC) of nonlinear distributed parameter systems (DPS), allowing the direct utilization of existing large‐scale simulators. The proposed scheme is adaptive and it is based on successive local linearizations of the nonlinear model of the system at hand around the current state and on the use of the resulting local linear models for MPC. At every timestep, not only the future control moves are updated but also the model of the system itself. A model reduction technique is integrated within this methodology to reduce the computational cost of this procedure. It follows the equation‐free approach (see Kevrekidis et al., Commun Math Sci. 2003;1:715–762; Theodoropoulos et al., Proc Natl Acad Sci USA. 2000;97:9840‐9843), according to which the equations of the model (and consequently of the simulator) need not be given explicitly to the controller. The latter forms a “wrapper” around an existing simulator using it in an input/output fashion. This algorithm is designed for dissipative DPS, dissipativity being a prerequisite for model reduction. The equation‐free approach renders the proposed algorithm appropriate for multiscale systems and enables it to handle large‐scale systems. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Study of heterogeneously catalysed reactive distillation using the D+R tray—A novel type of laboratory equipment

Recently, novel equipment for heterogeneously catalysed reactive distillation, the D+R tray, has been introduced by Schmitt et al. (2009). The present work reports results of measurements of the separation capacity of D+R trays. Furthermore, results of reactive distillation experiments on two test systems are presented that show that the D+R tray can be used routinely for laboratory studies of heterogeneously catalysed reactive distillation. As test systems, the esterifications yielding butyl acetate and hexyl acetate were chosen. Reactive distillation using catalytic packings was studied previously in detail ( [Parada, 2008], [Schmitt et al., 2004] and [Schmitt et al., 2005]) with the same test system. The experiments of the present work are carried out so that a direct comparison is possible. For both test systems, the most important process parameters such as feed rate and mass of catalyst were systematically varied. High conversions of the reactants and high purities of the products were achieved. The reproducibility of the results is excellent. The study shows that the D+R tray is a novel laboratory equipment that facilitates fast and flexible investigations of heterogeneously catalysed reactive distillation processes and that it can be used for studying process designs of columns equipped with either catalytic packings or trays.     

Reactive column profile map topology: Continuous distillation column with non-reversible kinetics

In this paper we present a topologically based approach to the analysis and synthesis of reactive distillation columns. We extend the definition of Tapp et al. [Tapp, M., Holland, S., Glasser, D., & Hildebrandt, D. (2004). Column profile maps part A: Derivation and interpretation. Industrial and Engineering Chemistry Research, 43, 364–374] of a column section in non-reactive distillation column to a reactive column section (RCS) in a reactive distillation column. A RCS is defined as a section of a reactive distillation column in which there is no addition or removal of material or energy. We introduce the concept of a reactive column profile map (RCPM) in which the profiles in the RCPM correspond to the liquid composition profiles in the RCS. By looking at the singular points in the RCPM, it is demonstrated that for a single chemical reaction with no net change in the total number of moles, the bifurcation of the singular points depends on both the difference point as introduced by Hauan et al. [Hauan, S., Ciric, A. R., Westerberg, A. W., & Lien, K. M. (2000). Difference points in extractive and reactive cascades I-Basic properties and analysis. Chemical Engineering Science, 55, 3145–3159] as well as the direction of the stoichiometric vector. These two vectors combine to define what we call the reactive difference point composition. We show that there only certain feasible topologies of the RCPM and these depend only on the position of the reactive difference point composition. We look at a simple example where the vapour liquid equilibrium (VLE) is ideal and show that we can classify regions of reactive difference point compositions that result in similar topology of the RCPM. Thus, by understanding the feasible topologies of the RCPM, one is able to identify profiles in the RCPM that are desirable and hence one is able to synthesize a reactive distillation column by combining RCS that correspond to the desired profile in the RCPM.We believe that this tool will help understand how and when reaction could introduce unexpected behaviors and this can be used as a complementary tool to existing methods used for synthesis of reactive distillation columns.     

Optimal design of mixed acid esterification and isopropanol dehydration systems via incorporation of dividing-wall columns

This study explores the design of a reactive distillation system and that of a heterogeneous azeotropic system by incorporating dividing-wall column (DWC). The first system involves the esterification of mixed acid (acetic acid and propionic acid) with methanol. Simulation studies are carried out for conventional reactive distillation sequence as well as for reactive dividing-wall distillation system. Both systems are optimized by an iterative optimization procedure. Optimal design results show that the reactive dividing-wall system saves steam consumption by 45.2% and reduces total annual costs (TAC) by 34.5%. The second case investigated is a heterogeneous azeotropic distillation system involving dehydration of crude isopropyl alcohol with cyclohexane as entrainer. Two optimal separation systems are generated, including one with a single-dividing wall column and one with a double-dividing wall column. In comparison with an energy-efficient azeotropic distillation sequence containing two stripping columns by Chang et al. (2012) [1], simulation results show that the former two systems can cut steam usage further by 6.0%. The two systems save about 5.4–6.1% in terms of TAC. DWCs prove to be superior to the convention distillation systems with respect to both cost and energy efficiency.     

An integrated reactive distillation process for biodiesel production

An integrated reactive distillation process for biodiesel production is proposed. The reactive separation process consists of two coupled reactive distillation columns (RDCs) considering the kinetically controlled reactions of esterification of the fatty acids (FFA) and the transesterification of glycerides with methanol, respectively. The conceptual design of the reactive distillation columns was performed through the construction of reactive residue curve maps in terms of elements. The design of the esterification reactive distillation column consisted of one reactive zone loaded with Amberlyst 15 catalyst and for the transesterification reactive column two reactive zones loaded with MgO were used. Intensive simulation of the integrated reactive process considering the complex kinetic expressions and the PC-SAFT EOS was performed using the computational environment of Aspen Plus. The final integrated RD process was able to handle more than 1% wt of fatty acid contents in the vegetable oil. However, results showed that the amount of fatty acids in the vegetable oil feed plays a key role on the performance (energy cost, catalyst load, methanol flow rate) of the integrated esterification–transesterification reactive distillation process.     

Evaluation of a two-temperature control structure for a two-reactant/two-product type of reactive distillation column

Several different control structures have been proposed for reactive distillation columns. The appropriate control structure depends on the flowsheet and on the type of reactions occurring in the column. If two reactants are involved and if it is desirable to operate the process without any excess of reactant, it is necessary to manage the fresh feed streams so that the stoichiometry is exactly balanced. A composition analyzer that measures an internal composition in the column is often required. However, if two products are produced, it is possible to avoid the use of an analyzer by using two temperatures in the column to adjust the two feed streams. This type of structure was proposed by Roat et al. [Roat, S., Downs. J., Vogel, E., Doss, J., 1986. Integration of rigorous dynamic modeling and control system synthesis for distillation columns. In: Chemical Process Control—CPC III. Elsevier, Amsterdam.] for the ideal reaction A+B↔C+D in one of the earliest papers dealing with reactive distillation control.The purpose of this paper is to explore the effectiveness of this two-temperature control structure for various column designs (number of reactive stages) to quantify the impact of design on controllability. We also discuss the issues of the selection of the trays whose temperatures are to be controlled and the tuning of the two interacting temperature controllers. Disturbances in production rate and fresh feed compositions are made to examine the rangeability of this control structure. Both an ideal reaction system and the methyl acetate system are studied. One of the main conclusions is that the locations of the temperature control trays should be made such that the two temperature controllers both have direct action (an increase in temperature increases feed), which requires negative openloop process gains for both loops.     

Design and control of reactive distillation for ethyl and isopropyl acetates production with azeotropic feeds

Reactive distillations for the production of ethyl acetate (EtAc) and isopropyl acetate (IPAc) are classified as the type-II process where the first column consists of a reactive zone and a rectifying section followed by a stripper [Tang et al., 2005. Design of reactive distillations for acetic acid esterification with different alcohols. A.I.Ch.E. Journal 51, 1683-1699]. Instead of using pure alcohols and acetic acid as reactants, this paper studies the effects of reactant purity on the design and control of reactive distillation. This offers significant economical incentives (by reducing raw materials costs), because ethanol forms an azeotrope with water at 90 mol% and isopropanol/water has an azeotrope at 68%. The purities of the acid is set to 95% for acetic acid (industrial grade), 87% for ethanol, and 65% for isopropanol. The results show that the total annual costs (TAC) increase by a factor of 5% for EtAc and 8% for IPAc production using reactive distillation. Next, the operability of the reactive distillations with azeotrope feeds is explored. Three disturbances, feed flow, acid feed purity, and alcohol feed composition, are introduced to assess control performance using dual-temperature control and one-temperature-one-composition control. Simulation results indicate good control performance can be achieved for reactive distillation with azeotropic feeds.     

Analysis of control properties of intensified distillation sequences: Reactive and extractive cases

In this work, we obtain and compare the control properties of thermally coupled reactive distillation sequences and thermally coupled extractive distillation sequences with those of conventional reactive and extractive distillation configurations. All sequences have been designed using a multiobjective genetic algorithm with restrictions. The theoretical control properties of those schemes were obtained using the singular value decomposition technique in all frequency domain. In order to complete the control study, the distillation options were subjected to closed-loop dynamic simulations. The effects of total stages, reactive stages, and extractant/feed ratio on the energy consumption and control properties are obtained for the intensified distillation options. The results show that there are cases in which integrated reactive and extractive sequences do not only provide significant energy savings with respect to the conventional reactive and extractive arrangements, but also may offer dynamic advantages in high energy consumption conditions.     

Gravitational Search,Monkey, and Krill Herd Swarm Algorithms for Phase Stability,Phase Equilibrium,and Chemical Equilibrium Problems

Phase equilibrium calculations (PECs) and phase stability (PS) analysis of reactive and nonreactive systems problems are important for the simulation and design of chemical engineering processes. These problems, which are challenging, multi-variable, and non-convex, require optimization techniques that are both efficient and effective in finding the solution. Stochastic global optimization algorithms, especially swarm algorithms, are promising tools for such problems. In this study, monkey algorithm (MA), gravitational search algorithm (GSA), and Krill Herd algorithm (KHA) were used to solve PS, phase equilibrium, and chemical equilibrium problems. We have also studied the effect of adding a local optimizer at the end of the stochastic optimizer run. The results were compared to determine the strengths and weaknesses of each algorithm. When a local optimizer was used, MA was found to be a reliable algorithm in solving the problems. GSA had relatively the least numerical effort for all problems among the three algorithms but with low reliability. KHA was more reliable than other two algorithms without the use of a local optimizer. The performance of GSA, MA, and KHA was compared with firefly algorithm and cuckoo search (CS). In summary, this study found that CS algorithm was more reliable than the newly tested algorithms. Nevertheless, MA and GSA algorithms, when combined with a local optimizer, solve the thermodynamic problems as reliably and efficiently as CS.     

Enhancing mass and energy integration by external recycle in reactive distillation columns

The synthesis and design of reactive distillation columns separating reacting mixtures with the most unfavorable relative volatilities (i.e., the reactants are the heaviest and lightest components with the products being the intermediate ones) are described. The unfavorable thermodynamics poses great difficulties in combining the reaction operation and the separation operation involved and limits severely the potential of reactive distillation columns in the reduction of capital investment (CI) and operating cost. To remove the limitation, we propose two strategies for facilitating the synthesis and design of this kind of reactive distillation columns in this article. One is to arrange prudentially the reactive section so as to strengthen internal energy integration between the reaction operation and the separation operation involved; that is, while the reactive section should be placed at the bottom of the reactive distillation columns separating exothermic reactions, it should be at the top of the reactive distillation columns separating endothermic reactions. The other is to introduce an external recycle flow between the two ends of the reactive distillation columns to reinforce internal mass integration and internal energy integration between the reaction operation and the separation operation involved; that is, whereas the external recycle flow should be directed from the top to bottom of the reactive distillation columns separating exothermic reactions, it should be from the bottom to top of the reactive distillation columns separating endothermic reactions. Separation of four hypothetical ideal (i.e., two quaternary and two ternary systems, respectively) and two real nonideal (i.e., two quaternary systems) reacting mixtures is chosen to evaluate the proposed strategies. The results show that they can considerably lower energy requirement besides a further reduction in CI. © 2012 American Institute of Chemical Engineers AIChE J, 59: 2015–2032, 2013     

Attainable regions of reactive distillation. Part II: Single reactant azeotropic systems

In reactive distillation (RD) one can conveniently manipulate the concentration profiles on the reactive stages by exploiting the difference in volatility of the various components. This property of RD can be advantageously used to improve the selectivity toward the desired product in case of series or series parallel reactions, and obtain a performance superior to the network of conventional reactors. In the previous work [Agarwal, V., et al., 2008. Attainable regions of reactive distillation—Part I. Single reactant non-azeotropic systems. Chemical Engineering Science, submitted for publication], we introduced representative unit models of RD to obtain the attainable regions of RD for non-azeotropic systems. In this work, we extend the approach to a system involving single binary azeotrope. Design guidelines have been formulated based on the residue curve maps, to obtain the improved attainable region with the help of these representative RD models either alone or in the form of their network.     

间歇反应精馏过程的模拟及其刚性问题

本文修正了Boston等人用于间歇精馏过程的数学模型,使之能适用于间歇反应精馏过程;提出了用解离法完成间歇反应精馏过程模拟的计算步骤;比较了SIRK,GEAR和EPISODE等软件在间歇精馏过程刚性微分方程数学模型积分中的有效性;并以醋酸丁酯用乙醇转移酯化反应精馏过程为例说明了方法的应用。     

An iteratively refined distillation line method

The focus of this article is distillation design feasibility. It is shown that existing methods for determining feasibility can give incorrect results or produce feasible designs that waste energy due to over‐specification and mass balance errors. An iterative refinement procedure based on direct substitution is proposed within the distillation line method of Lucia et al. that automatically adjusts one product composition to determine feasibility. Direct substitution equations are presented in detail and 14 literature examples are used to illustrate the efficacy of iterative refinement. Numerical results show that iterative refinement can find feasible designs that other methods cannot find, often resulting in significant reductions in energy requirements, and that it is all product compositions, not just trace compositions that affect most shortcut methods for distillation design. Iterative refinement can also find minimum energy requirements and identify sets of specifications that give infeasible designs. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Difference points in reactive and extractive cascades: IV—Feasible regions for multisection columns with kinetic reactions and side streams

The feasibility of three component distillation columns containing kinetically controlled chemical reactions and side streams is addressed through the use of difference points. We decompose complex columns into sections and identify feasible regions in composition space where each section operates. These regions enclose sectional profiles for the full range of operating parameters and are bounded by profiles constructed under extreme conditions. We efficiently determine the bounding profiles without computing interior compositions. We also develop a graphical feasibility test to connect sections and construct full columns using feasible regions. Finally, we present a technique to characterize the feasible regions and quantify how much reaction or side stream may be placed on any stage of a column section. The first three papers in this series [Hauan et al., 2000. Difference points in extractive and reactive cascades. I—Basic properties and analysis. Chemical Engineering Science 55 (16) 3145–3159; Lee et al., 2000. Difference points in extractive and reactive cascades. II—Generating design alternatives by the lever rule for reacting systems. Chemical Engineering Science 55 (16) 3161–3174; Hoffmaster and Hauan, 2004. Difference points in extractive and reactive cascades. III—Properties of column section profiles with arbitrary reaction distribution. Chemical Engineering Science 59 (17) 3671–3693] derive the fundamental properties of difference points, develop a lever rule to facilitate full column design, and analyze the properties of sectional profiles in reactive cascades. This fourth paper develops the necessary feasibility analysis tools for systematic identification of reactive distillation design alternatives.     

基于(火用)损失分析的反应精馏塔板上反应体积的优化设计

针对以选择性为主要目标的反应精馏塔设计中反应段塔板上反应体积或催化剂的分配问题,提出一种基于热力学(火用)损失分析和流程模拟计算相结合的优化设计策略。为了深层次分析反应精馏塔板上(火用)损失的原因并为制定调优方向提供理论依据,将塔板上的总(火用)损失区分为物理(火用)损失和化学(火用)损失两部分并分别进行计算。在此基础上,将建立的(火用)损失计算方法和流程模拟技术相结合,将反应段塔板上的反应体积的分配和对应的(火用)损失分布相关联,以再沸器热负荷最小为目标,通过建立的方法对反应体积的分配逐步调优,可实现反应精馏塔的优化设计。方法的有效性通过环氧乙烷水合制乙二醇反应精馏体系进行了验证。结果表明,与普遍采用的塔板上等反应体积分配的设计方法相比,通过本文建立的优化分配方法,可使系统的能耗降低18%以上,同时结果优于文献值。     

Optimal design of distillation systems with less than N − 1 columns for a class of four component mixtures

The optimal design of complex distillation systems is a highly non-linear and multivariable problem, with several local optimums and subject to different constraints. In addition, some attributes for the design of these separation schemes are often conflicting objectives, and the design problem should be represented from a multiple objective perspective. As a result, solving with traditional optimization methods is not reliable because they generally converge to local optimums, and often fail to capture the full Pareto optimal front. In this paper, a method for the multiobjective optimization of distillation systems, conventional and thermally coupled, with less than N − 1 columns is presented. We use a multiobjective genetic algorithm with restrictions coupled to AspenONE Aspen Plus; so, the complete MESH equations and rigorous phase equilibrium calculations are used. Results show some tendencies in the design of intensified sequences, according to the nature of the mixture and feed compositions.     

基于信赖域算法的精馏塔优化

从结构优化角度建立精馏塔优化的混合整数非线性规划(MINLP)模型,为了消除整数变量,引入绕流效率将MINLP问题转化为非线性规划(NLP)问题。针对得到的NLP问题提出一种优化方法,在该方法中采用结构优化中常用的信赖域优化算法进行求解,并应用虚拟瞬态连续性方程辅助优化中的稳态模拟。采用提出的优化方法对3个精馏系统进行设计优化,以不同初始值开始,均可得到令人满意的优化结果,表明所提优化方法具有良好的稳健性,对于较复杂的部分热耦合精馏过程仍然可以有效优化求解;信赖域算法在精馏塔优化中也表现出良好的收敛性。