Analysis and optimization of cross-flow reactors with distributed reactant feed and product removal

A systematic and general model was proposed for the simulation of cross-flow reactors with product removal and reactant feed policies. Six types of cross-flow reactors were analyzed for reversible series-parallel reaction systems and their optimal feed distributions were determined by maximizing the desired product yield at the outlet of the reactor. The performances of reactors with different types of feed policies were compared at their optimal operating conditions. For irreversible reaction systems with lower order in distributed reactant for the desired reaction than those for undesired reactions, a higher yield and selectivity of the desired product could be achieved with the reactors with staged feed than with conventional co-feed reactors and a sufficiently high residence time was required by staged feed reactors to significantly improve the desired product yields and selectivities over those obtained by a co-feed reactor. However, for reversible reaction systems, the desired product yield always reached a maximum value, and then dropped down as the residence time increased. In addition to the kinetic order and residence time requirements, the rate constants of the reactions involved have to fall within certain ranges for the distributed feed reactor to obtain a higher maximum yield than one-stage co-feed reactors. Optimally distributed feed reactors always give higher maximum product yields than evenly distributed reactors with the same number of feed points. However, the improvement of yields is not as great as that between co-feed reactors and evenly distributed reactors. On the other hand, for reaction systems with higher order with respect to the distributed reactant in the desired reaction than the undesired reactions, co-feed reactors always give higher yield than staged feed reactors.     

Systematic staging in chemical reactor design

The foundation and implementation of a method for systematic reactor design is described. The reactor path is sectioned into stages where each stage is designed so as to optimize an overall objective. This is a further development of a previously proposed method for designing chemical reactors (Hillestad, 2004, Hillestad, 2005). Reactants pass through a series basic operations or functions to form the desired products. The basic operations are represented by design functions on the path volume. The design functions are fluid mixing (dispersion), distribution of extra feed points, distribution of heat transfer area and coolant temperature, catalyst dilution distribution and more. The conceptual reactor design problem is solved as an optimal control problem. A direct method is applied where both the design functions and the state variables are discretized. The realization of the optimization is a staged process string of multi-functional units. A kinetic model of the gas phase methanol synthesis is used as an example. By applying the method on the model, a staged reactor design with less heat transfer area and higher production is possible.     

An input/output approach to the optimal transition control of a class of distributed chemical reactors

An input/output approach to the optimal concentration transition control problem of a certain type of distributed chemical reactors is proposed based on the concept of residence time distribution, which can be determined in practice by using data from experimental measurements or computer simulations. The main assumptions for the proposed control method to apply are that the thermal and fluid flow fields in the reactor are at pseudo-steady-state during transition and that the component whose concentration is to be controlled participates only in first-order reactions. Using the concept of cumulative residence time distribution, the output variable is expressed as the weighted sum of discretized inputs or input gradients in order to construct an input/output model, on the basis of which a constrained optimal control problem, penalizing a quadratic control energy functional in the presence of input constraints, is formulated and solved as a standard least squares problem with inequality constraints. The effectiveness of the proposed optimal control scheme is demonstrated through a continuous-stirred-tank-reactor (CSTR) network and a tubular reactor with axial dispersion and a first-order reaction. It is demonstrated through computer simulations that the proposed control method is advantageous over linear quadratic regulator (LQR) and proportional-integral (PI) control in terms of control cost minimization and input constraint satisfaction.     

Design and optimisation of batch and semi-batch reactors

This paper addresses a systematic methodology for batch and semi-batch reactor design and optimisation for both ideal and non-ideal mixing. It can be applied to non-isothermal and multiphase systems. The method starts from a general representation in the form of a temporal superstructure based on the similarity of between plug flow reactors and ideal batch reactors. The temporal superstructure of a batch reactor exists in both the space and time dimensions. For non-ideal mixing, this paper addresses a mixing compartment network model to represent mixing inside reactors. The mixing compartment network is then included into the temporal superstructure to model non-ideally mixed batch reactors and the mixing pattern optimised with the other variables. Besides the operation variables for batch reactors, this method can also suggest the optimum mixing pattern and promising reactor configurations for mechanical design. A profile-based approach is proposed to make a search of the profiles for temperature, pressure and feed addition. This approach starts from a set of initial profiles of temperature, pressure and feed addition. Then the performance of the batch reactor is evaluated against the objective function under different profiles. An optimal set of profiles is then found by this profile searching process. A stochastic optimisation technique based on simulated annealing is employed to obtain optimal solutions. This method is also extended to multiphase reaction systems based on the concept of shadow reactor compartments. A number of case studies are presented to illustrate the use of the proposed methodology.     

Casson流体层流反应器中连串反应的产品分布

引　言目前化工流体力学涉及的范围已由传统的牛顿流体发展到非牛顿流体 .常见的非牛顿流体包括幂律流体、Bingham流体和Casson流体 .有许多高聚物反应物系和生化反应物系属于非牛顿流体 .特别是某些生化反应系统 ,所处理的物系常由各种天然物质组成 ,因而表现出典型的非牛顿流     

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.     

树脂法合成双酚A反应器的优化设计

建立了树脂催化合成反应器的数学模型,通过约束优化的罚函数法得出了双酚A合成反应器进料中苯酚对丙酮的最佳配比M_α,反应料液的最佳进料温度T_α和适宜的单程转化率α。据此设计的绝热反应器经生产实践证实反应操作平稳。     

乙炔加氢反应过程混合建模与优化

针对传统单一建模方法所构建的乙炔加氢反应器数学模型存在预测性能无法满足工业实际应用需求的问题,提出了一种机理与神经网络嵌套的建模方法,充分利用机理模型包含的能质约束信息降低神经网络模型的约束违反度,得到了能够良好描述实际工业乙炔加氢反应过程特性的混合模型。基于反应器混合模型,研究了以运行效益为目标函数的优化问题。主要决策变量包括：一段反应器进料中氢气与乙炔的摩尔比（R _H/A）、进料温度和反应器运行周期等几个关键参数。针对反应器长期运行后,催化剂活性降低造成的处理能力下降的问题,提出了反应温度补偿机制和R _H/A并行调节的运行优化策略,并采用序列法对反应器运行周期进行离散化处理。通过引入差异化变异策略、潜在解替代策略对两阶段差分算法进行改进,采用增量式编码法结合改进两阶段差分算法,对优化问题进行求解。结果证实了优化策略与改进算法的有效性,并据此确定了反应器最佳运行方案。     

Modeling and simulation of an industrial slurry phase ethylene polymerization reactor: effect of reactor operating variables

A hierarchical and computationally efficient mathematical model was developed to explain the polymerization of high-density polyethylene (HDPE) in an isothermal, industrial, continuous stirred tank slurry reactor (CSTR). A modified polymeric multi-grain model (PMGM) was used. Steady-state macroscopic mass balance equations were derived for all species (namely, monomer, solvent, catalyst and polymer) to obtain the final particle size and the required monomer and solvent input rates for a given catalyst input and the reactor residence time. The interphase mass transfer coefficients were calculated for the industrial CSTR using the operating data on the reactor. The present model was tuned with some data on an isothermal industrial reactor and the simulation results were compared with data on another set of industrial reactor. The comparison revealed that the present tuned model is capable of predicting the productivity and the polymer yield at various catalyst feed rates and the mean residence times. The effects of variation of two operating variables (catalyst feed rate and mean residence time) on the productivity, the polymer yield, the polydispersity index (PDI) and the operational safety were analyzed. The present study indicated that an optimal value of the reactor residence time (for maximum productivity per catalyst particle) exists at any catalyst feed rate.

     

Open-loop control of particle size distribution in semi-batch emulsion copolymerization using a genetic algorithm

The open-loop generation of an optimal feed profile to attain a target particle size distribution (PSD) in the semi-batch emulsion co-polymerization of vinyl acetate and butyl acrylate is described. A nominal model of the process based on population balancing is utilized for this purpose. A Genetic Algorithm is employed as the optimization strategy. The optimal recipes generated in these studies are implemented on an experimental emulsion polymerization reactor. The end-point PSD obtained in these experiments closely matches the target in spite of the model uncertainties and process disturbances. Examination of the evolution of the PSD up to the end point provides useful information for feedback control strategies.     

Synthesis of Rice Processing Plants. II. MINLP Optimization

A systematic design approach was applied to develop the optimal process flowsheet for a rice processing plant. The optimization problem was formulated as a Mixed-Integer NonLinear Programme, MINLP, consisting of vectors of binary and continuous variables. A superstructure flowsheet comprising all serial structures of drying, cooling, and tempering units in the process was postulated. The set of optimum decision variables including the number of drying, cooling, and tempering units, temperature and relative humidity of drying air, drying time, cooling time, and tempering time were determine as the solution of the corresponding MINLP. Six objective functions were investigated as possible performance criteria: production time, number of the operating units, energy consumption, total operating cost, head rice yield, and the profit. The choice of objective function was found to have a significant effect on the optimal solution. Comparison with typical design and operating conditions, the MINLP results showed that a 22% reduction in energy consumption was possible along with a 2.4% increase in head rice yield. These savings, if applied to the world-wide rice industry, translate into more than $3 billion dollars/year increase in profit.     

Optimal design for split-and-recombine-type flow distributors of microreactors based on blockage detection

In order to increase the productivity of microreactors, the parallelization of the microreactors is required. The performances of flowdistributors can affect the product yield and fault detection abilitywhen blockage happens. In this research, an optimal design method to calculate the channel diameters and to determine the flow sensor location is derived based on mass balance and pressure balancemodels of split-and-recombine-type flow distributors (SRFDs). The model accuracy is verified by experiment data. The proposed method is applied to optimal design of SRFDs under constant flowrate operation conditions. The maximumangle difference between normal and blockage conditions at one sensor to those at the other sensors is set to be the objective function and the uniformity of flow distribution in microreactors under normal condition is also required. The diameters of each pipe in SRFDs are selected as the design variables. Simulated annealing algorithmis used to solve the optimization problem. The effectiveness of the optimal design results is demonstrated by fluid dynamics simulations. The results show that using the optimal channel diameters of SRFDs, the pressure drop in SRFD section is lower than that of the microreactor section. Meanwhile, in the case studies, only a few sensors that are located inside the SRFDs can easily detect the blockage abnormal condition in the parallelized microreactor system.     

Optimal reaction conditions for pyridine synthesis in riser reactor

Pyridine has been generally synthesized by aldehydes and ammonia in a turbulent fluidized-bed reactor. In this paper, a novel riser reactor was proposed for pyridine synthesis. Experiment result showed that the yield of pyridine and 3-picoline decreased, but the selectivity of pyridine over 3-picoline increased compared to turbulent fluidized-bed reactor. Based on experimental data, a modified kinetic model was used for the determination of optimal operating condition for riser reactor. The optimal operating condition of riser reactor given by this modified model was as follows: The reaction temperature of 755 K, catalyst to feedstock ratio(CTFR) of 87, residence time of 3.8 s and initial acetaldehydes concentration of 0.0029 mol·L~(-1)(acetaldehydes to formaldehydes ratio by mole(ATFR) of 0.65 and ammonia to aldehydes ratio by mole(ATAR) of 0.9, water contention of 63 wt%(formaldehyde solution)).     

Synthesis of Rice Processing Plants. II. MINLP Optimization

Abstract

A systematic design approach was applied to develop the optimal process flowsheet for a rice processing plant. The optimization problem was formulated as a Mixed-Integer NonLinear Programme, MINLP, consisting of vectors of binary and continuous variables. A superstructure flowsheet comprising all serial structures of drying, cooling, and tempering units in the process was postulated. The set of optimum decision variables including the number of drying, cooling, and tempering units, temperature and relative humidity of drying air, drying time, cooling time, and tempering time were determine as the solution of the corresponding MINLP. Six objective functions were investigated as possible performance criteria: production time, number of the operating units, energy consumption, total operating cost, head rice yield, and the profit. The choice of objective function was found to have a significant effect on the optimal solution. Comparison with typical design and operating conditions, the MINLP results showed that a 22% reduction in energy consumption was possible along with a 2.4% increase in head rice yield. These savings, if applied to the world-wide rice industry, translate into more than $3 billion dollars/year increase in profit.     

Dynamics and stability of ethylene polymerization in multizone circulating reactors

Multizone circulating bed reactors (MZCR) have the exclusive characteristics of producing polymers of different molecular weights in a single particle. Traditional fluidized bed reactors, on the other hand, can produce only one kind of molecular weight with relatively narrow distribution. A dynamic model for the MZCR is used to illustrate the basic dynamic behavior of the new reactor design used for polyethylene production. The model is used to study the copolymerization of ethylene with butene. Several parameter sensitivity analyses are performed to show the computer-simulated time responses for reactor temperature, number-average molecular weight, weight-average molecular weight, catalyst feed rate and the monomer/comonomer concentration along the reactor length. At certain operating conditions dynamic instability is observed and the results for the effect of cooling water temperature, catalyst feed rate, monomer and comonomer initial feed concentration on the reactor temperature and polymer molecular weight reveal that the system is very sensitive to disturbances in the heat exchanger coolant temperature. Also, at some operating conditions, the reactor temperature oscillates above the polymer melting temperature. Temperature runaway above polymer softening point is a serious problem which may cause polymer melting and hence reactor shutdown. The oscillatory behavior of the reactor temperature necessitates a suitable temperature control scheme to be installed.     

Using Dynamic Optimization Technique to Study the Operation of Batch Reactors

How to apply the global optimization technique, simulated annealing, and to explore the operation of batch reactors is addressed in this study. Based on the operating purposes and the imposed constraints, the batch reactor operations are first formulated as two optimal control problems: the maximal yield (or conversion) problem and the minimal operating time problem. The problems are then converted into non‐linear programming problems by the concept of control vector parameterization. The converted problems are solved by the algorithm derived from simulated annealing to determine the optimal operating policy and the performance index. These results are useful in assessing design and operation of batch reactors. In this article, the CSTR model is used to demonstrate the convenience and robustness of the proposed algorithm. Two typical reaction models are used to discuss the operations based on the optimal solutions.     

A catalyst deposited over the external surface of the reactor tubes—A new solution for carrying out heterogeneous catalytic processes

A mathematical model of a new reactor design has been proposed. In the new reactor the catalyst is deposited over the external surface of the tubes, where the coolant flows. The widespread industrial process of oxidation of o‐xylene into phthalic anhydride was investigated. The results obtained show significant advantages of the new design in comparison with the conventional fixed bed reactor operating in the industry. They are: much higher productivity, easily controlled temperature regime, raised selectivity and decrease content of side products, as well as an opportunity for additional feed‐in of the reagent along the reactor height. The technological regime of the oxidation process was optimized.     

OPTIMAL DESIGN FOR THE RESIDUAL OIL HYDRODEMETALLATION IN A FIXED BED REACTOR

A restricted diffusion model was used to investigate the optimal design for the residual oil hydrodemetallation in a fixed bed reactor. Based on the total lifetime activity, the optimal catalyst pore sizes and their corresponding optimal division locations in the bed were determined. The results indicate that the total amount of demetallation could be significantly improved by using a multi-layers reactor and the nonuniform activity catalysts. In addition, the influence of the Thiele modulus on the optimal designs were illustrated.     

Modeling of key reaction pathways: Zeolite catalyzed alkylation processes

A six lump kinetic model that considers the key reactions for the zeolite catalyzed alkylation process is presented. The influence of different reactions and rate limiting steps on reactor performance is examined by coupling an appropriate reactor model that accounts for different back-mixing on reactor scale, with a zeolite particle model which accounts for the diffusion inside the zeolite pore, the alkylation reaction, and zeolite deactivation. Model predictions are compared with experimental results and lead to conclusions that hydride transfer and oligomerization reactions are the key kinetic steps affecting the overall performance of zeolite catalyzed alkylation processes. It is suggested that higher alkylate yield and longer zeolite activity are achieved by increasing the intrinsic hydride transfer rate and the ratio of feed isobutane to n-butene (P/O) concentration. For a given P/O feed ratio, achieving close to plug flow for isobutane and high back-mixing for n-butene further enhances local P/O ratio and yield. Furthermore, optimal zeolite catalyst design should consider the egg shell type of Brønsted acid site distribution and a lower silicon to alumina (Si/Al) ratio.