Prosyn—an MINLP process synthesizer

This paper reports the development of the program PROSYN, an automated implementation of the modelling/decomposition (M/D) strategy by Kocis and Grossmann (Computers chem. Engng 13, 797–819, 1989) for the MINLP optimization of process flowsheets. A systematic procedure is first presented for the decomposition of general superstructures of process flowsheets that avoids the optimization of units with zero flow. A model for simultaneous optimization and heat integration is also proposed that can account for area and energy considerations. Finally, a computer implementation is described that is suitable for the complex logic involved in the M/D strategy for the synthesis and heat integration of process flowsheets. Examples are presented to illustrate each of these points, as well as the performance of PROSYN.     

Exergy as a tool for measuring process intensification in chemical engineering

Exergy is defined as the maximum shaft work that can be done in a process to bring the system into equilibrium with the environment. Thus, exergy analyses are the first step to understand where the weak points of processes are. It considers intrinsically the quality of energy: when energy loses its quality, exergy is destroyed. In addition, optimization of processes aiming at the minimization of exergy destruction can be done as a function of the topology and physical characteristics of the system, such as finite dimensions, shapes, materials, finite speeds, and finite‐time intervals of operation, establishing a direct relationship between exergy and process intensification. However, the emphasis on exergy in chemical engineering is still very poor compared with other fields, in spite of being one of the areas in which more exergy is destroyed due to reaction and separation . This paper gives an overview of the current application of exergy analyses in chemical engineering, showing the main fields in which exergy studies are performed and focusing the attention on two critical points of action: separation technologies (distillation and membrane technology) and CO₂ capture. New research trends in chemical engineering using exergy as a tool for process intensification are highlighted. © 2013 Society of Chemical Industry     

基于目标函数瞬时值的反应器网络综合方法

反应器网络综合是化工过程集成的关键问题之一,但求解过程十分复杂。提出了目标函数瞬时值的概念,并研究了利用目标函数瞬时值曲线所对应的面积进行反应器网络综合的方法。以两个复杂反应为例说明了该方法的应用并和国内外文献进行了对比。从案例研究可以看出,本方法能够得到最优反应器网络,也避免了求解大规模的非线形最优化问题,也克服了可得区法维数的限制,具有几何直观的特点。     

MINLP synthesis of reactor networks in overall process schemes based on a concept of time-dependent economic regions

The design and optimization of reactor networks using the conventional concept of attainable region is based on technological (conversion, selectivity, etc.), rather than, economical criteria (cost, profit, etc.). The solution from the economical point of view when the operating and investment costs cannot be neglected may not be optimal, not even in regard to the structure. In order to circumvent this deficiency, the conventional Concentration Attainable Region (CAR) is transformed into an Economic Region (ER) using economic optimization criteria. A novel concept for ER construction is proposed for multi-D problems. One-parametric NLP or MINLP optimizations with reactor volume as a varying parameter are performed to construct trajectories in the ER. In this way the ER is aided by mathematical programming for 3D or more D problems in order to handle dimensions higher than 2 as degrees of freedom for the economic objective function. ER is attainable (EAR) only when the economic objective function is linear. The more the objective function is discontinuous, discrete, nonlinear and non-convex and the more its cost coefficients vary with time, the less the principles of AR can be applied to ER. However, economically optimal reactor systems always lie at the borders of ERs. Two important insights have been gained during the construction of different time-dependent ERs, which have been used in upgrading the MINLP approach to the synthesis of reactor networks in overall process schemes: (i) A reactor network superstructure has been reestablished based on economical optimization criteria and the principles of ER. (ii) Over a longer period, the performing of a stochastic multi-period MINLP synthesis is recommended, in order to consider the time variability and uncertainties of economic parameters. A special multi-period strategy is proposed to upgrade the efficiency of the MINLP synthesis.     

MINLP optimization of a heterogeneous azeotropic distillation process: Separation of ethanol and water with cyclohexane as an entrainer

Heterogeneous distillation processes are widely used in industry for the separation of azeotropic and close-boiling mixtures. This paper addresses the optimization of a heterogeneous distillation process for the separation of an azeotropic ethanol/water mixture using cyclohexane as an entrainer. Starting from a given process superstructure a MINLP problem is set up to consider continuous as well as discrete decision variables such as the feed locations and the number of stages of the distillation columns. A modified Generalized Benders Decomposition algorithm to account for non-convexities of the model equations solves the MINLP problem. The algorithm can be attached via Visual Basic for Applications (VBA) to any commercial process simulator with NLP and VBA capabilities. Various optimization runs show that the algorithm is easily applicable and returns solutions independent of the initial values.     

Using redundancy to strengthen the relaxation for the global optimization of MINLP problems

In this paper we present a strategy to improve the relaxation for the global optimization of non-convex MINLPs. The main idea consists in recognizing that each constraint or set of constraints has a meaning that comes from the physical interpretation of the problem. When these constraints are relaxed part of this meaning is lost. Adding redundant constraints that recover that physical meaning strengthens the relaxation. We propose a methodology to find such redundant constraints based on engineering knowledge and physical insight.     

Novel bound contraction procedure for global optimization of bilinear MINLP problems with applications to water management problems

We propose a new method to obtain the global optimum of MINLP problems containing bilinearities. Our special method that contracts the bounds of one variable at a time allows reducing the gap between a linear lower bound and an upper bound obtained solving the original problem. Unlike some methods based on variable partitioning, our bound contraction procedure does not introduce new integers or intervals. We illustrate the method by applying it to water management problems.     

MINLP formulations for solving strip packing problems in LCD mother glass production

Mother glass production for liquid crystal displays involves the cutting of small rectangles from a large rectangle (strip) to minimize the length of the strip used. This is called the strip packing problem. The main concept for formulating this problem is to generate cutting patterns that can be used to produce items from the strip. This problem is a non-convex mixed integer nonlinear programming (MINLP) problem due to the bilinear terms in the demand and objective function. To obtain global optimal solutions, this problem should be transformed into several linear forms. Numerical examples based on the strip packing problem in LCD mother glass production are provided. Different objective functions for two problems are presented and compared.     

Synthesis of reactor networks in overall process flowsheets within the multilevel MINLP approach

This paper presents the superstructure-based mixed-integer non-linear programming approach to the synthesis of reactor networks in an equation-oriented environment. The model comprises a general superstructure in which the exact formulation of the recycle reactor (RR) and a continuous stirring tank reactor (CSTR) are embedded so as to enable a different feeding (cross flow, side stream), recycling and bypassing. The reactor arrangement is capable of representing several reactor systems such as a pure CSTR, a pure plug flow reactor, pure RR, their combinations and also a cross flow reactor. The superstructure is suitable either for an isothermal or non-isothermal, simple or complex reactor network. With the multilevel-hierarchical strategy, it is possible to postulate the superstructure at different levels of representation of flowsheet alternatives. Therefore, the superstructure is optimized more effectively and reliably. The approach has been applied to a complex non-isothermal reaction problem — an industrial example of the production of allyl chloride.     

A new approach for global optimization of a class of MINLP problems with applications to water management and pooling problems

One of the biggest challenges in solving optimization engineering problems is rooted in the nonlinearities and nonconvexities, which arise from bilinear terms corresponding to component material balances and/or concave functions used to estimate capital cost of equipments. The procedure proposed uses an MILP lower bound constructed using partitioning of certain variables, similar to the one used by other approaches. The core of the method is to bound contract a set of variables that are not necessarily the ones being partitioned. The procedure for bound contraction consists of a novel interval elimination procedure that has several variants. Once bound contraction is exhausted the method increases the number of intervals or resorts to a branch and bound strategy where bound contraction takes place at each node. The procedure is illustrated with examples of water management and pooling problems. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2320–2335, 2012     

Sustainable decision making for chemical process systems via dimensionality reduction of many objective problems

Recent global events and the rise of sustainable investing have made clear that the chemical and energy industry must consider sustainability goals beyond profit maximization to remain competitive. Multiobjective optimization provides an ideal framework for analyzing sustainability tradeoffs, but when four or more objectives are considered, the ability to rigorously solve problems and interpret results is lost. This necessitates an approach to systematically reduce the dimensionality of many objective problems to three or fewer objectives. In this work, an algorithm to group objectives based on their correlating nature a priori to solving the full space problem is proposed. It utilizes community detection on a novel weighted objective correlation graph to identify two or three groups of correlated objectives. Results from three representative case studies demonstrate that objective groupings obtained from this algorithm minimize the amount of tradeoff information lost and outperform intuitive groupings by economics or the environment.     

基于链式循环二氧化碳重整的甲烷制甲醇过程火用分析

二氧化碳重整制甲醇过程对碳源高效利用和环境保护具有重要意义,可作为替代传统高能耗、高排放水蒸气重整过程的途径。用Aspen Plus软件模拟链式循环二氧化碳重整的甲烷制甲醇过程。结果表明,该过程的?损失主要集中在化学过程,占总?损的76.47%,其中燃烧反应与重整反应分别占41.62%和27.69%,而甲醇合成反应与水汽变换反应分别占3.55%与3.61%。与传统水蒸气重整制甲醇过程相比,在原料甲烷输入量一定情况下,二氧化碳重整制甲醇系统的重整过程比水蒸气重整过程?损失减少21.44%,水蒸气消耗量减少77.02%,整体系统二氧化碳排放量降低了25.89%,甲醇的产量提高了12.03%。随着重整反应温度的提高,?效率和甲醇产量均出现先升高、后平稳的趋势,并在980℃达到最大值。此外,较低的重整反应压力有利于提高甲醇产量。     

携带流反应器中稻壳气化过程的火用分析

引言生物质能作为一种可再生的清洁能源,可以减少CO2、NOx、SOx及颗粒物的排放[1],其开发利用受到世界各国的极大关注[2]。生物质气化被认为是生物质利用的最有前途的能源转化方式之一[3],已经成为能源研发与利用的一大研究热点。研究结果表明,气化器或者锅炉是能源转化和利用过程中效率最低的一个操作单元[4],因此,气化器效率的提高能在很大程度上改善整个能源转化过程[5]。在忽略热量损失时,一个绝热良好的气化器的     

Economic model predictive control with time‐varying objective function for nonlinear process systems

Economic model predictive control (EMPC) is a control scheme that combines real‐time dynamic economic process optimization with the feedback properties of model predictive control (MPC) by replacing the quadratic cost function with a general economic cost function. Almost all the recent work on EMPC involves cost functions that are time invariant (do not explicitly account for time‐varying process economics). In the present work, we focus on the development of a Lyapunov‐based EMPC (LEMPC) scheme that is formulated with an explicitly time‐varying economic cost function. First, the formulation of the proposed two‐mode LEMPC is given. Second, closed‐loop stability is proven through a theoretical treatment. Last, we demonstrate through extensive closed‐loop simulations of a chemical process that the proposed LEMPC can achieve stability with time‐varying economic cost as well as improve economic performance of the process over a conventional MPC scheme. © 2013 American Institute of Chemical Engineers AIChE J 60: 507–519, 2014     

Multi‐objective optimization superimposed model‐based process design of an enzymatic hydrolysis process

The concepts of green process engineering and rigorous model‐based approaches have proven to be highly beneficial in process engineering. Although a combination of these two principles thus appears extremely promising, it is not found very commonly in literature. The very high complexity resulting from this combination poses great challenges for the process design and design engineers. Therefore, this work presents an innovative methodology for the model‐based process design with superimposed multi‐objective optimization for an exemplary process. This process for the enzymatic hydrolysis of fatty acid methyl ester combines several aspects of green process engineering and represents an exemplary process with an enzymatic liquid‐liquid‐solid reaction system. The optimization results based on operating and investment costs reveal important insights on the exemplary process and highlight the great advantages of the developed methodology as a profound basis for academic and industrial process design purposes. © 2017 American Institute of Chemical Engineers AIChE J, 63: 1974–1988, 2017     

Derivative‐free optimization for expensive constrained problems using a novel expected improvement objective function

In this work, an algorithm for the optimization of costly constrained systems is introduced. The proposed method combines advantages of global‐ and local‐search algorithms with new concepts of feasibility space mapping, within a framework that aims to find global solutions with minimum sampling. A global search is initially performed, during which kriging surrogate models of the objective and the feasible region are developed. A novel search criterion for locating feasibility boundaries is introduced, which does not require any assumptions regarding the convexity and nonlinearity of the feasible space. Finally, local search is performed starting from multiple locations identified by clustering of previously obtained samples. The performance of the proposed approach is evaluated through both benchmark examples and a case study from the pharmaceutical industry. A comparison of the method with commercially available software reveals that the proposed method has a competitive performance in terms of sampling requirements and quality of solution. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2462–2474, 2014     

Process optimization at the design stage with an objective function linear in profit and investment

In the optimization of chemical processes at the design stage, it is suggested that the optimization of a linear function of profit and investment allows the economics of the process to be presented in a particularly simple way. All technical considerations have been taken into account and the final design choice can be made from a purely economic point of view. The results can be represented most conveniently by curves in the profit-investment plane. The approach is illustrated with simplified examples of cross-current extraction and a first-order reversible reaction carried out in a sequence of continuous stirred tank reactors.     

能量利用系统的能量流结构--能量、(火用)、(火无)新概念

认为火用是系统和环境构成的不平衡复合系统作功能力的衡量,重新表述了火用概念,论证了(火用)不是严格意义上系统的状态参数.指出环境能量在任何情况下都不能用于作功的传统观点是违背热力学第二定律的,能量利用的实质是利用系统和环境之间非平衡推动力引发的动态能量流, 它包含可转化能量的多少与能量流的方向无关,无论来自系统还是环境的能量都可被转化.文中给出的能量、(火用)、(火无)新概念严格遵守热力学第二定律,克服了Rant Z.定义的局限性,对进一步改进(火用)分析方法促进用能过程热力学的发展有积极意义.     

能量利用系统的能量流结构——能量、[火用]、[火无]赋新概念

认为[火用]是系统和环境构成的不平衡复合系统作功能力的衡量，重新表述了[火用]概念，论证了[火用]不是严格意义上系统的状态参数。指出环境能量在任何情况下都不能用于作功的传统观点是违背热力学第二定律的，能量利用的实质是利用系统和环境之间非平衡推动力引发的动态能量流，它包含可转化能量的多少与能量流的方向无关，无论来自系统还是环境的能量都可被转化。文中给出的能量、[火用]、[火无]新概念严格遵守热力学第二定律，克服了Rant Z．定义的局限性，对进一步改进[火用]分析方法促进用能过程热力学的发展有积极意义。     

Optimization of process synthesis and design problems: A modified differential evolution approach

A large number of process synthesis and design problems in chemical engineering can be modeled as mixed integer nonlinear programming (MINLP) problems. They involve continuous (floating point) and integer variables. A common feature of this class of mathematical problems is the potential existence of non-convexities due to the particular form of the objective function and/or the set of constraints. Due to their combinatorial nature, these problems are considered to be difficult. In recent years, evolutionary algorithms (EAs) are gaining popularity for finding the optimal solution of nonlinear multimodal problems encountered in many engineering disciplines. In the present study, a novel modified differential evolution [Angira, R., Babu, B.V., 2005a. Optimization of non-linear chemical processes using modified differential evolution (MDE). Proceedings of the Second Indian International Conference on Artificial Intelligence (IICAI-05), Pune, India, December 20-22, pp. 911-923. Also available at 〈http://discovery.bits-pilani.ac.in/discipline/chemical/bvb/publications.html〉], one of the evolutionary algorithms, is used for solving process synthesis and design problems. To illustrate the applicability and efficiency of modified differential evolution (MDE), seven test problems on process synthesis and design have been solved. These problems arise from the area of chemical engineering, and represent difficult nonconvex optimization problems, with continuous and discrete variables. The performance of MDE is compared with that of Genetic Algorithm, Evolution Strategy, and MINLP-Simplex Simulated Annealing (M-SIMPSA).