Analysis of the particle swarm algorithm in the optimization of a three-phase slurry catalytic reactor

The Particle Swarm Optimization (PSO) method was employed to optimize an industrial chemical process characterized by being difficult to be optimized by conventional deterministic methods. The chemical process is a three phase catalytic slurry reactor (tubular geometry) in which the reaction of the hydrogenation of o-cresol producing 2-methyl-cyclohexanol is carried out. The optimization problem was formulated considering as input variables the operating conditions of the reactor and as objective function the maximization of productivity, subject to the environmental constraint of conversion. The process was represented by a multivariable non-linear rigorous mathematical model and in order to solve the optimization problem, the performance of the PSO algorithm was evaluated considering four sets of parameters values suggested by the literature. PSO demonstrated to be efficient and robust to solve the constrained optimization problem, independently of the values of the PSO parameters. The solution of the rigorous mathematical model of the reactor was associated with a high computational burden, and although the PSO algorithm presented high rate of convergence, the attempt to make possible the optimization in a timeframe suitable to real time applications failed because the algorithm lost robustness (fraction of the number of runs the algorithm reached the optimization goal) when run with a reduced number of function evaluations. Therefore, if this type of application is desired, simplified mathematical models with fast and simple numerical methods must be preferred.     

Process modeling and optimization of industrial ethylene oxide reactor by integrating support vector regression and genetic algorithm

This article presents an artificial intelligence‐based process modeling and optimization strategies, namely support vector regression–genetic algorithm (SVR‐GA) for modeling and optimization of catalytic industrial ethylene oxide (EO) reactor. In the SVR‐GA approach, an SVR model is constructed for correlating process data comprising values of operating and performance variables. Next, model inputs describing process operating variables are optimized using Genetic Algorithm (GAs) with a view to maximize the process performance. The GA possesses certain unique advantages over the commonly used gradient‐based deterministic optimization algorithms The SVR‐GA is a new strategy for chemical process modeling and optimization. The major advantage of the strategies is that modeling and optimization can be conducted exclusively from the historic process data wherein the detailed knowledge of process phenomenology (reaction mechanism, kinetics, etc.) is not required. Using SVR‐GA strategy, a number of sets of optimized operating conditions leading to maximized EO production and catalyst selectivity were obtained. The optimized solutions when verified in actual plant resulted in a significant improvement in the EO production rate and catalyst selectivity.     

Optimization of a Reverse Osmosis System Using Genetic Algorithm

Abstract

Reverse Osmosis (RO) has found extensive application in industry as a highly efficient separation process. In most cases, it is required to select the optimum set of operating variables such that the performance of the system is maximized. In this work, an attempt has been made to optimize the performance of RO system with a cellulose acetate membrane to separate NaCl‐Water system using Genetic Algorithm (GA). The GAs are faster and more efficient than conventional gradient based optimization techniques. The optimization problem was to maximize the observed rejection of the solute by varying the feed flowrate and overall permeate flux across the membrane for a constant feed concentration. To model the system, a well‐established transport model for RO system, the Spiegler‐Kedem model was used. It was found that the GA converged rapidly to the optimal solution at the 8th generation. The effect of varying GA parameters like size of population, crossover probability, and mutation probability on the result was also studied. The algorithm converged to the optimum solution set at the 8th generation. It was also seen that varying the computational parameters significantly affected the results.     

基于神经网络的丙烯腈流化床反应器的模拟与离线优化

利用人工神经网络的方法建立了工业合成丙烯腈流化反应器的数学模型。采用遗传算法与梯度下降法相结合的方法训练神经网络的权值和阀值。经过训练和可靠性检验的人工神经网络能够满足工业生产的模拟要求。利用单纯型算法与遗传算法相结合的优化方法合成丙烯腈工业流化反应器进行了操作系统优化，为在线实时优化控制奠定了基础。     

Hierarchical multiscale model-based design of experiments, catalysts, and reactors for fuel processing

In this paper a hierarchical multiscale simulation framework is outlined and experimental data injection into this framework is discussed. Specifically, we discuss multiscale model-based design of experiments to optimize the chemical information content of a detailed reaction mechanism in order to improve the fidelity and accuracy of reaction models. Extension of this framework to product (catalyst) design is briefly touched upon. Furthermore, we illustrate the use of such detailed and reduced kinetic models in reactor optimization as an example toward more conventional process design. It is proposed that hierarchical multiscale modeling offers a systematic framework for identification of the important scale(s) and model(s) where one should focus research efforts on. The ammonia decomposition on ruthenium to produce hydrogen and the water–gas shift reactions on platinum for converting syngas to hydrogen serve as illustrative fuel processing examples of various topics. The former is used to illustrate hierarchical multiscale model development and model-based parameter estimation as well as product engineering. The latter is employed to demonstrate model reduction and process optimization. Finally, opportunities for process design and control in portable microchemical devices (lab-on-a chip) for power generation are discussed.     

Batch reactor optimization under liquid swelling safety constraint

This article presents the modeling and optimization of an industrial batch reactor operation with regard to production safety constraint which is represented by the reactor content swelling. Swelling occurs due to the evacuation of a coupled product which passes through the liquid in order to reach the reaction mass surface. In order to model the reaction system a chemical model linked to a hydrodynamic model is developed. The goal of the optimization is to calculate the temperature and pressure profiles which maximize conversion rates, without exceeding the maximum reactor level. The optimal temperature profile is calculated using the optimal control optimization method and the results show that a productivity increase of up to 36% can be achieved as compared to the industrial process.     

Dynamic Simulation and Optimization of a Dual‐Type Methanol Reactor Using Genetic Algorithms

In this investigation, a dynamic simulation and optimization for an auto‐thermal dual‐type methanol synthesis reactor was developed in the presence of catalyst deactivation. Theoretical investigation was performed in order to evaluate the performance, optimal operating conditions, and enhancement of methanol production in an auto‐thermal dual‐type methanol reactor. The proposed reactor model was used to simulate, optimize, and compare the performance of a dual‐type methanol reactor with a conventional methanol reactor. An auto‐thermal dual‐type methanol reactor is a shell‐and‐tube heat exchanger reactor in which the first reactor is cooled with cooling water and the second one is cooled with synthesis gas. The proposed model was validated against daily process data measured of a methanol plant recorded for a period of 4 years. Good agreement was achieved. The optimization was achieve by use of genetic algorithms in two steps and the results show there is a favorable profile of methanol production rate along the dual‐type reactor relative to the conventional‐type reactor. Initially, the optimal ratio of reactor lengths and temperature profiles along the reactor were obtained. Then, the approach was followed to get an optimal temperature profile at three periods of operation to maximize production rate. These optimization approaches increased by 4.7 % and 5.8 % additional yield, respectively, throughout 4 years, as catalyst lifetime. Therefore, the performance of the methanol reactor system improves using optimized dual‐type methanol reactor.     

A robust technique for process flowsheet optimization using simplified model approximations

Recently, embedded simplified process models have been shown to be very efficient for process simulation. When compared to the direct use of rigorous models, this approach has the potential to reduce the computational effort of process simulation by up to an order of magnitude or more. Application of this approach to process optimization should therefore lead to similar savings in computational effort as well as substantial improvement of the process.

However, current simplified model embedding schemes applied to process optimization cannot, in general, converge to the optimum defined by the more rigorous process models. Consequently, they require an expensive rigorous model optimization starting from the solution of the simplified model optimum to guarantee convergence.

In this paper we develop a framework that incorporates simplified models into an optimization algorithm and guarantees convergence to the rigorous model optimum. Here rigorous process models are evaluated only when necessary to insure progress toward the optimal solution. A theoretical justification of the algorithm is presented and several process examples are solved to demonstrate the effectiveness of this approach.     

Reactor modeling and recipe optimization of polyether polyol processes: Polypropylene glycol

The reactor modeling and recipe optimization of conventional semibatch polyether polyol processes, in particular for the polymerization of propylene oxide to make polypropylene glycol, is addressed. A rigorous mathematical reactor model is first developed to describe the dynamic behavior of the polymerization process based on first‐principles including the mass and population balances, reaction kinetics, and vapor‐liquid equilibria. Next, the obtained differential algebraic model is reformulated by applying a nullspace projection method that results in an equivalent dynamic system with better computational performance. The reactor model is validated against plant data by adjusting model parameters. A dynamic optimization problem is then formulated to optimize the process recipe, where the batch processing time is minimized, given a target product molecular weight as well as other requirements on product quality and process safety. The dynamic optimization problem is translated into a nonlinear program using the simultaneous collocation strategy and further solved with the interior point method to obtain the optimal control profiles. The case study result shows a good match between the model prediction and real plant data, and the optimization approach is able to significantly reduce the batch time by 47%, which indicates great potential for industrial applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2515–2529, 2013     

乙炔加氢串联反应器全周期乙炔转化率最优分配研究

在乙炔加氢反应器的实际生产运行过程中,乙炔加氢反应大部分在第一床层,加氢反应放出的大量热量使得床层内温度高于最佳反应温度范围,致使乙烯选择性降低,乙烯产量下降,而在进行全周期操作优化时并未考虑到此问题。因此,首先考虑温度对绿油累积的影响,修正了催化剂失活动力学方程;其次,为保证反应器各床层内温度都在最佳反应温度范围,从化学反应工程理论和实际生产过程中的安全性两个角度出发,给出两种反应器各床层乙炔转化率分配方案;最后,在常规全周期操作优化模型中添加乙炔转化率约束,建立全周期乙炔转化率分配操作优化模型,并对两种乙炔转化率分配方案进行全周期操作优化。优化结果表明,两种乙炔转化率分配方案操作优化的乙烯产量要远远高于常规操作优化,且乙炔转化率方案为33∶33∶33时,乙烯产量最高,而考虑实际生产过程中的安全性,乙炔转化率分配方案为43∶47∶10时具有更好的效果。     

乙炔加氢串联反应器全周期乙炔转化率最优分配研究

在乙炔加氢反应器的实际生产运行过程中,乙炔加氢反应大部分在第一床层,加氢反应放出的大量热量使得床层内温度高于最佳反应温度范围,致使乙烯选择性降低,乙烯产量下降,而在进行全周期操作优化时并未考虑到此问题。因此,首先考虑温度对绿油累积的影响,修正了催化剂失活动力学方程;其次,为保证反应器各床层内温度都在最佳反应温度范围,从化学反应工程理论和实际生产过程中的安全性两个角度出发,给出两种反应器各床层乙炔转化率分配方案;最后,在常规全周期操作优化模型中添加乙炔转化率约束,建立全周期乙炔转化率分配操作优化模型,并对两种乙炔转化率分配方案进行全周期操作优化。优化结果表明,两种乙炔转化率分配方案操作优化的乙烯产量要远远高于常规操作优化,且乙炔转化率方案为33∶33∶33时,乙烯产量最高,而考虑实际生产过程中的安全性,乙炔转化率分配方案为43∶47∶10时具有更好的效果。     

Optimization of Petlyuk sequences using a multi objective genetic algorithm with constraints

In this work we use genetic algorithms to optimize Petlyuk sequences using a rigorous design model. A multi objective genetic algorithm (GA) with constraints was formulated and interconnected with the Aspen Plus process simulator to obtain each data point during the search process. In addition to providing more energy-efficient designs than some reported structures, two relevant trends were observed from the results of the case studies; one had to do with the feed location to the prefractionator as a function of the mixture properties, and the other one with optimal structures requiring four interconnecting stages instead of the two normally used for Petlyuk sequences. An application for the separation of azeotropic mixtures is also included. The optimal placement of vapor-liquid interconnections is again shown to be different for each interconnecting stream. The GA showed a robust performance, and was practically independent on the initial values for the search variables.     

A new dual modifier-adaptation approach for iterative process optimization with inaccurate models

In order to deal with plant-model mismatch, iterative process optimization schemes use some adaptation strategy based on measurements. The modifier-adaptation approach consists in performing first-order corrections of the cost and constraint functions in the model-based optimization problem. The approach has the ability to converge to the true process optimum but the first-order corrections require the experimental estimation of the process gradients. Dual modifier-adaptation algorithms estimate the gradients by finite difference approximation based on the measurements obtained at the current and past operating points. In order to guarantee the accuracy of the estimated gradients a constraint is added to the optimization problem in order to position the next operating points with respect to the previous ones. This paper presents an alternative first-order correction, which provides an improved approximation of the cost and constraint functions, together with a new gradient error constraint for use in dual modifier adaptation. By means of the Williams–Otto reactor case study, the new dual modifier-adaptation approach is compared in simulation with a previous approach found in the literature showing faster convergence to a neighborhood of the plant optimum.     

A hybrid approach to global optimization using a clustering algorithm in a genetic search framework

The concern of this work is global optimization using genetic algorithms (GAs). In this work we propose a synergy between the cluster analysis technique, popular in classical stochastic global optimization, and the GA to accomplish global optimization. This synergy minimizes redundant searches around local optima and enhances the capability of the GA to explore new areas in the search space. The proposed methodology demonstrates superior performance when compared with the simple GA on benchmark cases. We also report our solution of the optimal pumps configuration synthesis problem.     

Use of genetic algorithms to optimize gate and vent locations for the resin transfer molding process

Resin infusion processes are finding increasing applications in the manufacture of composite parts that have geometric and material complexities. In such cases, the placement of gates and vents is non-intuitive and may require expensive repetitive experimentation. Finite element based resin flow simulation codes have been successfully used for modeling and analysis of the mold filling process. Such filling simulations, when coupled with a search algorithm, can also prove useful for optimal design of the filling process. Genetic algorithms (GAs) mimic natural selection and can efficiently “evolve” near-global optimal solutions from a large number of alternative solutions. In this paper, GAs are used to optimize gate and vent locations for the resin transfer molding process in order to minimize fill times and dry spot formation. A process performance index or cost function is defined that incorporates the fill time and dry spot formation as primary variables. A part having material and geometric complexities was chosen for a case study. A genetic algorithm and mold filling simulations were used interactively to search for optimal gate and vent locations to locate near optimal solutions. The GA was able to find good solutions using less than 1% of simulations of the possible permutations of gates and vents. The case study was also repeated in the presence of recetracking channels. Again, the optimal locations were found by the GA using less than 1% of all possible combinations. Thus, GAs can be efficiently used for minimization of fill time and dry spot formation through optimal location of gates and vents in RTM processes. However, the optimal location will be a function of the cost function, the choice of which depends on the trade-offs between different factors and the quality of the part desired.     

基于相对增益和优先级的化工过程协调优化裕量设计

化工过程设计裕量一般是通过设计经验或经济优化给出的,设计经验无法保证经济性能的优化,而经济优化需要求解大规模非线性优化问题,计算复杂,容易陷入局部极值点,设计结果有时与设计经验违背。本文用非方相对增益阵和非方相对能量增益阵描述化工过程设计的自变量和因变量的灵敏度关系,将自变量划分为操作变量和设计变量,将因变量划分为经济指标和约束变量。相对增益具有无量纲化和归一化的优点,因此可根据经济指标和约束变量的相对增益对操作变量和设计变量划分优先级,针对过程不确定性的大小按照优先级依次调整各个操作变量和设计变量,找到对过程经济性能影响最小并有效移动操作点、远离约束边界的裕量设计方案。以串联反应釜为例对该设计方法进行了验证,结果表明,与求解经济最优化问题的裕量设计方法相比,本设计方法得到了经济性能与之接近的设计结果,计算简单,无须求解最优化问题。     

Optimization of a Process Synthesis Superstructure Using an Ant Colony Algorithm

The optimization of chemical syntheses based on superstructure modeling is a perfect way for achieving the optimal plant design. However, the combinatorial optimization problem arising from this method is very difficult to solve, particularly for the entire plant. Relevant literature has focused on the use of mathematical programming approaches. Some research has also been conducted based on meta‐heuristic algorithms. In this paper, two approaches are presented to optimize process synthesis superstructure. Firstly, mathematical formulation of a superstructure model is presented. Then, an ant colony algorithm is proposed for solving this nonlinear combinatorial problem. In order to ensure that all the constraints are satisfied, an adaptive, feasible bound for each variable is defined to limit the search space. Adaptation of these bounds is executed by the suggested bound updating rule. Finally, the capability of the proposed algorithm is compared with the conventional Branch and Bound method by a case study.     

Dynamics and Control of a Biodiesel Transesterification Reactor

Biodiesel transesterification reactors resemble the heart of any biodiesel manufacturing plant. These reactors involve a highly complex set of chemical reactions and heat transfer characteristics. The high nonlinearity inherent in the dynamics of these reactors requires an efficient process control algorithm to handle the variation of operational process parameters and the effect of process disturbances efficiently. In this work, a multi‐model adaptive control strategy is considered for achieving the goal mentioned above. In order to implement the adaptive controller, a rigorous mechanistic model of the biodiesel transesterification reactor was developed and validated with published experimental results. The validated model was analyzed for stability and nonlinearity. The analysis revealed that the system is stable. However, its high nonlinearity necessitates an advanced control strategy to be considered. The input‐output relationship between the effective process variables was studied and the control system synthesis revealed a two‐by‐two control system. Two adaptive control loops were then designed and tuned to optimize the performance of the controller. Finally, a comparison with conventional controllers revealed the superiority of the new control system in terms of set‐point tracking and disturbance rejection. The results of this work prove that an adequately designed adaptive control system can be used to improve the performance of the transesterification reactor.     

Geometrical Optimization of the Overlap in Mixed Adhesive Lap Joints

The aim of this research is to optimize the geometry of the overlap in mixed adhesive single- and double-lap joints using a modified version of Bees and Genetic Algorithms (BA and GA). Accounting for adherends Poisson's ratio in the deduced equilibrium equations, the proposed shear lag model gives a more accurate approximation of joint failure load in comparison with Volkersen's solution. The objective functions used in this work are used separately to maximize the load bearing capacity f and the specific strength (f/w) of the joint. This procedure is applied to optimize aeronautical adhesively bonded assemblies, while taking manufacturing constraints into account. The employed constraints are the application of yield criterion on adherends as well as geometrical constraint on the overlap length. The proposed straightforward procedure provides 18 optimal configurations amid a wide range of changes for optimization variables, among which the designer can take a choice, depending on his/her goal. The efficiency of the two employed algorithms, BA and GA, in searching for the optimum geometrical design of the mixed adhesive joints have also been investigated. The results show the more robust and efficient performance of the modified version of BA over GA in such kinds of engineering problems.     

An integrated dimensionality reduction and surrogate optimization approach for plant-wide chemical process operation

With liquefied natural gas becoming increasingly prevalent as a flexible source of energy, the design and optimization of industrial refrigeration cycles becomes even more important. In this article, we propose an integrated surrogate modeling and optimization framework to model and optimize the complex CryoMan Cascade refrigeration cycle. Dimensionality reduction techniques are used to reduce the large number of process decision variables which are subsequently supplied to an array of Gaussian processes, modeling both the process objective as well as feasibility constraints. Through iterative resampling of the rigorous model, this data-driven surrogate is continually refined and subsequently optimized. This approach was not only able to improve on the results of directly optimizing the process flow sheet but also located the set of optimal operating conditions in only 2 h as opposed to the original 3 weeks, facilitating its use in the operational optimization and enhanced process design of large-scale industrial chemical systems.