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.     

Conceptual design of distillation processes for mixtures with distillation boundaries. II. Optimization of recycle policies

Geometric design methods for the conceptual design of azeotropic distillation processes are fast and efficient tools for the economic screening of different process alternatives. The second article of this two‐part series presents a novel optimization‐based conceptual design framework for azeotropic distillation processes, which allows a rapid screening of the different process alternatives with respect to feasibility and economic incentive. The design framework is based on the economic assessment of distillation columns by the rectification body method. The feasibility limits imposed by the azeotropes are incorporated using the split feasibility test introduced in the first part of this series. The application of the framework is highlighted with several ternary and quaternary process alternatives for the production of high‐purity alcohols. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Conceptual design of distillation processes for mixtures with distillation boundaries: I. Computational assessment of split feasibility

Geometric design methods for the conceptual design of azeotropic distillation processes are fast and efficient tools for the economic screening of different process alternatives. This two‐part series presents a fully automated conceptual design method for finding an optimal recycle policy for the separation of mixtures with distillation boundaries. It does not require visualization and graphical inspection of residue curve or pinch maps and is, hence, not limited to ternary mixtures. The first part introduces a fully computational geometric split feasibility test based on bifurcation analysis. This bifurcation‐based feasibility test can be used as a valuable stand‐alone tool for the assessment of different separation options. It is also one of the core elements of the recycle optimization discussed in the second part of this series. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Feed distribution in distillation: Assessing benefits and limits with column profile maps and rigorous process simulation

This contribution describes the column profile map (CPM) methodology for designing distributed feed distillation columns. For non‐sharp product distributions, a case study shows that energy savings of approximately 35% can be obtained if the feed stage(s) are designed optimally. Feed distribution allows capital cost savings, expands operating leaves, and can obtain greater separation feasibility. However, this column only has benefits in ternary and higer‐order systems and when product distributions are non‐sharp. To validate these counter‐intuitive claims, a real Benzene, p‐Xylene, Toluene system is modeled using CPMs, and the resulting design parameters are transported to Aspen Plus^®. Using a sum of squared errors objective function to quantify savings, a cost saving trend very similar to the one predicted by the CPM method is obtained. This article therefore describes a complete design methodology for distributed feed systems and provides convincing evidence of benefits of such a system. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1668–1683, 2013     

基于在线Kriging模型的隔板塔优化方法

隔板塔是一种新型的精馏节能技术,但其优化设计属于混合整数非线性规划问题,优化求解困难。本文提出在线Kriging代理模型优化方法,将其应用于隔板塔年度总费用优化。与传统离线代理模型相比,本文方法采用少量的隔板塔严格模拟数据点,即可得到优化问题的最优解。计算表明,较传统离线代理模型,本文提出的在线代理模型显示了更高的准确性和有效性,可以克服传统离线代理模型优化耗时、计算量大的缺点。     

甲醇精馏工艺及其塔器优化设计

对四塔甲醇精馏节能流程提出了四项优化措施,利用PRO/Ⅱ工艺模拟软件,进行了工况研究.结果表明,采用优化后的工艺流程,甲醇回收率可提高约0.3%,预精馏塔能耗降低约7%;并根据工况研究结果和生产数据,提出了各塔合适的理论级数和操作参数,推荐了各塔结构形式、参考塔径、填料高度或塔盘层数.     

Learning surrogate models for simulation‐based optimization

A central problem in modeling, namely that of learning an algebraic model from data obtained from simulations or experiments is addressed. A methodology that uses a small number of simulations or experiments to learn models that are as accurate and as simple as possible is proposed. The approach begins by building a low‐complexity surrogate model. The model is built using a best subset technique that leverages an integer programming formulation to allow for the efficient consideration of a large number of possible functional components in the model. The model is then improved systematically through the use of derivative‐free optimization solvers to adaptively sample new simulation or experimental points. Automated learning of algebraic models for optimization (ALAMO), the computational implementation of the proposed methodology, along with examples and extensive computational comparisons between ALAMO and a variety of machine learning techniques, including Latin hypercube sampling, simple least‐squares regression, and the lasso is described. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2211–2227, 2014     

基于Kriging代理模型的稳健优化设计

稳健优化设计需要进行不确定性分析,优化过程比较费时。为提高计算效率,提出了基于Kriging代理模型的稳健优化设计方法。该方法结合双重Kriging代理模型和多点加点准则进行稳健优化设计。双重Kriging代理模型的建立,减小了不确定性分析的计算量,提高了计算效率。多点加点准则实现了序列的迭代优化,在保证计算效率的同时提高了对全局最优解的逼近程度。数学函数测试结果表明,与一般模拟基稳健优化方法相比,本文所提出的序列稳健优化方法在效率上有很大的提高。最后,考虑注塑工艺的不稳定性,对一盒式注塑制件的壁厚和工艺进行稳健优化,结果表明该稳健优化设计方法是有效的。     

径向基函数神经网络在精馏塔软测量中的应用

精馏塔是化工过程中最常用的操作单元 ,具有很强的非线性和时变性 ,故很难进行机理建模分析或常规在线实时控制 ,因而提出一种基于径向基函数神经网络的优化控制方案。通过利用径向基函数神经网络建立精馏塔产品质量的软测量模型 ,将软测量结果与现场数据比较 ,表明本模型具有比较准确的跟踪显示效果 ,并将软测量模型进一步应用到精馏塔的回流量和釜液排放量的优化控制中     

Experimental validation of a flexible modeling approach for distillation columns with packings

The two main concepts for the modeling of distillation columns are the equilibrium‐stage (EQ) and the nonequilibrium‐stage (NEQ). A model is presented which combines decisive features of both conventional concepts. Based on the idea of a reduced nonequilibrium‐stage (RNEQ), this model can be used for the simulation of distillation columns with packings. In contrast to the conventional NEQ approach, this model neglects the influence of liquid side mass‐transfer coefficients, which ultimately allows to come up with only one empirical equation describing the overall mass transfer. Thus, a considerable reduction in model complexity is reached, which allows for an efficient consideration of new experimental distillation results. Fitted to experimental data, the model is able to predict, how different pressures and chemical systems might affect the separation efficiency. By comparing calculation results with experimentally determined separation efficiencies for three different packing types, these valuable RNEQ qualities are illustrated. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3833–3847, 2014     

A globally convergent method for finding all steady‐state solutions of distillation columns

A globally convergent method is proposed that either returns all solutions to steady‐state models of distillation columns or proves their infeasibility. Initial estimates are not required. The method requires a specific but fairly general block‐sparsity pattern; in return, the computational efforts grow linearly with the number of stages in the column. The well‐known stage‐by‐stage (and the sequential modular) approach also reduces the task of solving high‐dimensional steady‐state models to that of solving a sequence of low‐dimensional ones. Unfortunately, these low‐dimensional systems are extremely sensitive to the initial estimates, so that solving them can be notoriously difficult or even impossible. The proposed algorithm overcomes these numerical difficulties by a new reparameterization technique. The successful solution of a numerically challenging reactive distillation column with seven steady‐states shows the robustness of the method. No published software known to the authors could compute all solutions to this difficult model without expert tuning. © 2013 American Institute of Chemical Engineers AIChE J 60: 410–414, 2014     

三组元全热耦合精馏过程的模拟计算

本文利用Aspen软件对三组分进料全热耦合精馏的分离流程进行设计和模拟,建立了相应的具体计算步骤。首先利用三塔模型把热耦合精馏过程简化为3个单独的简单清晰分割塔,通过简捷法设计和模拟得到塔板数和回流比等初值后进行严格法模拟,得到热耦合精馏的数据和操作条件。然后采用Aspen软件中的RadFrac模型,将三塔模型的模拟初值代入全热耦合模块进行严格模拟。结果表明,采用全热耦合精馏分离C4三组分比传统精馏的直接序列和间接序列节能约为20%。     

基于粒子群算法的隔离壁精馏塔的综合与设计

隔离壁精馏塔（dividing-wall distillation column,DWDC）是提高两个或者多个传统精馏塔热力学效率的有效手段。由于隔离壁精馏塔内部结构复杂、相互作用强,传统的序贯优化方法计算时间长,很难达到全局最优解。标准粒子群算法应用广泛、易于实现,但易于早熟、易于陷入局部极值点。因此,本工作采用改进的元胞粒子群算法对Kaibel隔离壁精馏塔进行综合与设计研究。元胞粒子群算法通过改进粒子的学习策略,采用元胞邻域的方法可有效地将粒子分散在多个子空间。对比标准粒子群优化和元胞粒子群优化两种方法的50次优化效果,结果表明,两种粒子群算法能够对内部结构复杂、相互作用强的四组分Kaibel隔离壁精馏塔这一复杂分离系统进行优化,优化效果显著。     

A disjunctive programming approach for the optimal design of reactive distillation columns

A generalized disjunctive programming formulation is presented for the optimal design of reactive distillation columns using tray-by-tray, phase equilibrium and kinetic based models. The proposed formulation uses disjunctions for conditional trays to apply the MESH and reaction kinetics equations for only the selected trays in order to reduce the size of the nonlinear programming subproblems. Solution of the model yields the optimal feed tray locations, number of trays, reaction zones, and operating and design parameters. The disjunctive program is solved using a logic-based outer-approximation algorithm where the MILP master problem is based on the big-M formulation of disjunctions, and where a special initialization scheme is used to reduce the number of initial NLP subproblems that need to be solved. Two examples are presented that include reactive distillation for the metathesis reaction of 2-pentene and for the production of ethylene glycol. The results show that the proposed method can effectively handle these difficult nonlinear optimization problems.     

基于主曲线的软测量方法及其在精馏塔上的应用

为解决工业过程软测量中的变量维数高、数据相互耦合、非线性强等问题,提出了基于主曲线的软测量方法。其中的基于主曲线的非线性回归模型借鉴了PLS的基本思想,采用主曲线提取隐变量信息的同时考虑了自变量与因变量的相关性;在隐变量空间中,采用多项式函数拟合隐变量之间的非线性关系。在实例研究中,分别采用纯函数数据和氯乙烯精馏塔实时运行数据对该模型进行了验证。仿真结果表明,该模型所需要的隐变量数目比传统的PLS模型更少,并且能够实现更为精确的预测,可较好地处理工业过程中存在的数据高耦合度以及强非线性问题。     

基于有效能分析的复杂精馏塔优化设计

提出了以有效能消耗最小为目标的复杂精馏塔优化设计新方法。给出了精馏塔优化设计模型及最佳进料位置、适宜理论板数NT、塔内换热器简约的确定方法,并以两组分正庚烷和乙苯的混合物为例进行设计与讨论。优化后的精馏塔含有中间换热器,与传统的简单塔有本质的区别,平衡线和操作线均处于相对平均的位置,更节能。     

Multi-objective optimisation using surrogate models for the design of VPSA systems

Vacuum/pressure swing adsorption is an attractive and often energy efficient separation process for some applications. However, there is often a trade-off between the different objectives: purity, recovery and power consumption. Identifying those trade-offs is possible through use of multi-objective optimisation methods but this is computationally challenging due to the size of the search space and the need for high fidelity simulations due to the inherently dynamic nature of the process. This paper presents the use of surrogate modelling to address the computational requirements of high fidelity simulations needed to evaluate alternative designs. We present SbNSGA-II ALM, surrogate based NSGA-II, a robust and fast multi-objective optimisation method based on kriging surrogate models and NSGA-II with the Active Learning MacKay (ALM) design criterion. The method is evaluated by application to an industrially relevant case study: a two column six step system for CO₂/N₂ separation. A 5 times reduction in computational effort is observed.     

A new technique for recovering energy in thermally coupled distillation using vapor recompression cycles

Even though it has been proved that a fully thermally coupled distillation (TCD) system minimizes the energy used by a sequence of columns, it is well‐known that vapor/liquid transfers between different sections produce an unavoidable excess of vapor (liquid) in some of them, increasing both the investment and operating costs. It is proposed here to take advantage of this situation by extracting the extra vapor/liquid and subjecting it to a direct/reverse vapor compression cycle. This new arrangement restores the optimal operating conditions of some of the affected sections with energy savings of around 20–30% compared with conventional TCD columns. Various examples, including the direct and reverse vapor recompression cycles, are presented. Furthermore, in each example, all possible modes of distillation (direct, indirect and Petlyuk distillation) with and without vapor recompression cycles (VRC) are compared to ensure that this approach delivers the best results. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3767–3781, 2013     

Conceptual design of single-feed kinetically controlled reactive distillation columns

Reactive distillation, simultaneous reaction and separation within a single unit, represents an exciting alternative to conventional processes, leading to significantly reduced in capital and operating costs. Process design for reactive distillation is facilitated by fast and effective methods for synthesis and conceptual design that take into account reactions that do not instantaneously reach equilibrium. This work presents a new methodology for synthesis and design of single-feed kinetically controlled reactive distillation columns. The design method allows rapid and relatively simple screening of different reactive distillation column configurations. Feasibility is assessed and operating conditions are determined using an extension of boundary-value methods. The approach is limited to systems with four or fewer chemical species. Both fully reactive and hybrid columns are considered. The methodology is illustrated for a metathesis reaction and for MTBE production.     

基于Kriging代理模型的气辅注射成型工艺优化

针对气辅成型工艺设定及控制的复杂性,使用Kriging代理模型近似拟合气辅成型工艺参数与气体穿透长度之间的非线性函数关系,建立起Kriging代理模型与APSO算法相结合的优化策略。应用所建立的优化方案,以气体的穿透深度为优化的目标,模拟了某汽车后视镜的气辅成型工艺优化过程。算例表明,基于Kriging代理模型与APSO算法耦合的优化策略可以在小样本情况下获取较高的求解精度和较快的收敛速度。