Multiobjective dynamic optimization of a nonvaporizing nylon 6 batch reactor

Multiobjective dynamic optimization has been carried out on a nonvaporizing nylon 6 batch reactor. Three objective functions have been identified, viz., minimization of the concentration of unreacted monomer in the product, minimization of the dimer concentration, and minimization of the reaction time, for producing polymer having a specified value, μ_{n, d}, of the number average chain length. Two problems have been studied in this paper, each consisting of two objective functions taken from the above set. Pareto solutions have been generated using an algorithm based on Pontryagin's minimum principle and the method of Lagrangian multipliers. The effects of various physical and computational parameters have been studied, and methods have been developed to overcome the numerical difficulties that arise during the solution. The Pareto sets so generated can be coupled with the surrogate worth trade-off (SWT) method, which facilitates interaction with a decision maker (DM). The optimal temperature histories obtained for the two problems studied are quite different and suggest that one must solve the three-dimensional problem in which the vector objective function incorporates all three objective functions. Results from the present study could be used as starting guesses to converge rapidly on the solution of the three-dimensional problem.     

Optimization for the minimum reaction time of pet esterification

We have investigated the direct esterification reaction between terephthalic acid (TPA) and ethylene glycol (EG) in semi-batch reactors, the first stage process for making polyethylene terephthalate (PET), to get optimum conditions for the minimum reaction time. An independent-variable-minimization problem, i.e., a free-end-time/fixed-end-point problem, has been formulated for the system, and then converted to a dependent-variable-minimization (fixed-end-time/ free-end-point) problem by a coordinate transformation, for the latter problem readily yields to established solution methods. We have solved this reformulated problem to obtain the optimal temperature profiles in the reactor required for the minimum reaction time, by iteratively improving the temperature (manipulating variable) profile using the Pontryagin’s minimum principle. The results prove that the method employed here successfully finds an optimal solution for the PET esterification process. The reduction of the reaction time realized following this optimal temperature profile in the reactor was, however, found to be smaller than expected, due to the approximating assumptions of neglecting the solubility equation of TPA in the model. The results obtained using a more improved model of the system will be reported in the future.     

热泵供暖系统动态操作节能优化

采用系统工程的方法优化热泵供暖系统操作, 实现节能运行具有重要意义。在建立热泵供暖系统基本动态方程的基础上, 给出了考虑室温控制精度和能耗节省的优化操控目标, 通过联立求解方法将原微分代数方程优化问题(DAOPs)转化为非线性规划问题, 然后对不同目标侧重下的动态操作优化问题进行了分析, 并提出了动态调整目标函数权重的优化策略。优化计算结果表明:在室温跟踪误差最大为0.85℃的情况下系统可实现16%以上的节能效果;环境温度和电价对系统操作优化具有重要影响, 根据两者的变化特征而动态调整目标函数权重可以进一步降低系统能耗4.7%左右。本研究对热泵供暖系统优化节能控制具有一定的现实意义。     

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 grade transition and selection of closed-loop controllers in a gas-phase olefin polymerization fluidized bed reactor

To satisfy the diverse product quality specifications required by the broad range of polyolefin applications, polymerization plants are forced to operate under frequent grade transition policies. Commonly, the optimal solution to this problem is based on the minimization of a suitable objective function defined in terms of the changeover time, product quality specifications, process safety constraints and the amount of off-spec polymer, using dynamic optimization methods. However, considering the great impact that a given control structure configuration can have on the process operability and product quality optimization, the time optimal grade transition problem needs to be solved in parallel with the optimal selection of the closed-loop control pairings between the controlled and manipulated variables. In the present study, a mixed integer dynamic optimization approach is applied to a catalytic gas-phase ethylene-1-butene copolymerization fluidized bed reactor (FBR) to calculate both the “best” closed-loop control configuration and the time optimal grade transition policies. The gPROMS/gOPT computational tools for modelling and dynamic optimization, and the GAMS/CPLEX MILP solver are employed for the solution of the combined optimization problem. Simulation results are presented showing the significant quality and economic benefits that can be achieved through the application of the proposed integrated approach to the optimal grade transition problem for a gas-phase polyolefin FBR.     

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.     

基于模拟分析技术和随机搜索算法的化工过程能量集成方法研究

夹点和模拟分析技术已在化工能量集成中广泛应用.今以夹点技术为基础,对化工过程系统用能进行诊断,根据"过程用能一致性"原则提出能量集成改造方案,通过改变塔压实现塔顶冷凝器与塔底再沸器的热集成多效蒸馏.夹点技术实现的优化目标仅是热回收最大或公用工程能耗最小,不能实现包括设备整体费用最小的过程全局最优化.研究基于模拟技术,通过灵敏度分析,得到精馏塔各操作参数的样本映射数据,通过多项式拟合得到参数关联方程,并在遗传算法及模式搜索中设计过程费用函数,提出了将模拟分析技术与随机搜索算法相结合的,以过程费用函数最小化为优化目标的能量集成方法.工业实例的成功设计应用证明了其有效性和可行性.     

基于等效电法的钢铁企业蒸汽系统多目标运行优化策略

针对钢铁企业蒸汽系统汽源设备多、能源品种多的特点,以某大型钢铁企业实际运行的蒸汽系统为背景,运用等效电方法对蒸汽系统的能量转换作出科学分析,采用数学规划方法,建立多目标的混合整数非线性规划模型（MINLP）。采用分步优化方法,先以蒸汽系统小时能源总成本最低为目标,将得到的结果乘以松弛系数建立成本约束并以(火用)效率最高为目标,利用LINGO软件求得多目标-约束优化模型的全局最优解,再通过改变松弛系数得到一组Pareto前沿。最后与单目标优化和多目标遗传算法结果相比较,证明分步优化方法所得的结果是可行的综合最优结果,能够实现低成本和高(火用)效率的双目标,并为生产调度提供依据。     

Sequential methodology for integrated optimization of energy and water use during batch process scheduling

Though commonly encountered in practice, energy and water minimization simultaneously during batch process scheduling has been largely neglected in literature. In this paper, we present a novel framework for incorporating simultaneous energy and water minimization in batch process scheduling. The overall problem is decomposed into three parts - scheduling, heat integration, and water reuse optimization - and solved sequentially. Our approach is based on the precept that in any production plant, utilities (energy and water) consumption is subordinate to the production target. Hence, batch scheduling is solved first to meet an economic objective function. Next, alternate schedules are generated through a stochastic search-based integer cut procedure. For each resulting schedule, minimum energy and water reuse targets are established and networks identified. As illustrated using two well-known case studies, a key feature of this approach is its ability to handle problems that are too complex to be solved using simultaneous methods.     

一种改进的热泵供暖系统动态实时优化策略

基于经济性目标的热泵供暖动态优化操作具有重要意义，但在操作区间内环境温度和模型参数变化的不确定性会对实际优化操控带来很大挑战。在完善热泵供暖系统模型的基础上，提出了一种改进的动态实时优化控制策略以改善系统的实际节能效果。该方法首先建立以压缩机和送水泵运行频率为控制变量的热泵供暖系统的非线性动态关系模型，并得到以24 h为周期、以综合性能指标最低为目标的动态实时优化命题。然后，在给定24 h环境温度预测情况下通过求解该优化命题得到热泵压缩机和送水泵的最优运行频率轨线，并以当前时间点的最优控制量对热泵供暖系统进行控制；接着，基于天气逐时预测和模型参数最新校验结果对环境温度轨线或者模型参数进行更新，不断地求解原优化命题以更新最优控制轨线，并不断地采用当前点的最优控制量对热泵供暖系统进行控制，直到当前时间点达到第24 h。实例计算结果表明：采用本文提出的方法可以进一步改善热泵供暖系统的动态优化操控效果，并能够很好地满足给定终端约束要求。本方法对于具有周期性和不确定参数的动态实时优化问题求解具有一定的借鉴意义。     

半连续脂肪酸甲酯化过程的研究(Ⅱ)——操作优化

对半连续脂肪酸甲酯化的操作优化问题进行了研究.定义生产费用为操作优化的目标泛函,选择甲醇进料速率为控制变量、反应压力为控制参数,分别应用动态规划法和Powell法对上述操作优化问题求解.两种方法求解的结果是一致的,采用优化的操作将使生产费用降低5%～15%,特别对有催化的快速甲酯化过程,优化操作的效果更明显.文中还讨论了价格等因素对优化操作策略的影响和求解计算量问题.实验表明,由理论计算得到的优化操作策略和目标是可以实现的.     

半连续脂肪酸甲酯化过程的研究(Ⅱ)——操作优化

对半连续脂肪酸甲酯化的操作优化问题进行了研究.定义生产费用为操作优化的目标泛函,选择甲醇进料速率为控制变量、反应压力为控制参数,分别应用动态规划法和Powell法对上述操作优化问题求解.两种方法求解的结果是一致的,采用优化的操作将使生产费用降低5%～15%,特别对有催化的快速甲酯化过程,优化操作的效果更明显.文中还讨论了价格等因素对优化操作策略的影响和求解计算量问题.实验表明,由理论计算得到的优化操作策略和目标是可以实现的.     

全流程卷式反渗透海水淡化系统操作优化

在对反渗透海水淡化系统流程和实际应用分析的基础上,提出了一种旨在降低总体操作费用的全流程反渗透海水淡化系统优化方法。首先根据系统变参数特点并充分利用蓄水池的缓冲能力,建立了反渗透过程机理模型、蓄水池动态过程模型以及变参数方程模型,实现了整个流程的方程描述。然后根据工艺流程和操作过程费用组成情况建立了总的操作费用模型,得到了全流程单位产水费用指标。在此基础上建立了以总体操作费用最低为目标、以开放方程描述的各模型方程为约束、以设备和产品质量限制为边界的优化命题,采用联立求解技术将该微分代数方程组成的优化（DAOP）问题转化为NLP问题后进行求解。最后对某海水淡化系统进行了实例研究。优化求解结果不仅表明本优化方法可以大幅降低实际操作费用,而且通过求解还可得到各种变参数条件下最优操作费用组成,以及实现费用最低的最优操作压力和流量变化曲线。本研究对优化海水淡化系统操作、降低总体操作费用具有重要意义。     

Exergy as an objective function to MINLP problems in process synthesis

The optimal layout of a chemical plant is determined by both economic and environmental aspects. The mathematical approach to this problem is given by representing the process through a superstructure, including any foreseeable process topology. It is described by integer variables, whereas real variables arise from the unit models and the thermodynamic calculations. By including process constraints and an objective function, a Mixed Integer Nonlinear Programming (MINLP) optimization problem is postulated. In this paper MINLP algorithms are combined with a technique for the exergy analysis of chemical processes for the preliminary screening of process alternatives. The exergy analysis as a screening technique is advantageous due to a significantly smaller amount of required data and computing time, compared with true optimization, including cost estimation at an earlier stage of process synthesis and analysis. Thus, a broader solution space can be examined. The subsequent cost analysis has then only to be focused on a reduced set of parameters.     

Impact of Fuel Cell Power Plants on Multi‐objective Optimal Operation Management of Distribution Network

This paper presents an interactive fuzzy satisfying method based on hybrid modified honey bee mating optimization and differential evolution (MHBMO‐DE) to solve the multi‐objective optimal operation management (MOOM) problem, which can be affected by fuel cell power plants (FCPPs). The objective functions are to minimize total electrical energy losses, total electrical energy cost, total pollutant emission produced by sources, and deviation of bus voltages. A new interactive fuzzy satisfying method is presented to solve the multi‐objective problem by assuming that the decision‐maker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions. Then, by considering the current solution, the DM acts on this solution by updating the reference membership values until the satisfying solution for the DM can be obtained. The MOOM problem is modeled as a mixed integer nonlinear programming problem. Evolutionary methods are used to solve this problem because of their independence from type of the objective function and constraints. Recently researchers have presented a new evolutionary method called honey bee mating optimization (HBMO) algorithm. Original HBMO often converges to local optima, in order to overcome this shortcoming, we propose a new method that improves the mating process and also, combines the modified HBMO with DE algorithm. Numerical results for a distribution test system have been presented to illustrate the performance and applicability of the proposed method.     

木材热解过程的热化学平衡分析

基于Gibbs自由能最小化法,利用HSC Chemistry软件对木材热解过程进行了热化学平衡计算。讨论了温度对热化学平衡产物组成和比例的影响,并把热解过程划分为4个阶段。首次根据自发反应的判据即反应的Gibbs自由能变与温度关系讨论了产物相互之间反应,由此确定热解各个阶段可能发生的反应。最后总结了文献中实验研究温度对木材热解产物影响情况,并与计算结果比较,结果表明,所预测的不同温度下木材热解产物分布特性与前人的实验结果相似。     

基于经济目标和分解协调策略的换热网络最优设计

分析了换热网络在过程系统中的功能 ,从火用分析和火用经济学的角度提出了换热网络最优合成设计的实用火用经济目标函数 ,它包含了网络的流动火用损费 ,且可分解为各个换热单元的总费用之和 .在换热网络目标函数可分解性的基础上 ,本文又进一步提出了换热网络分解协调优化的研究策略 ,它是在各个匹配单元 (子系统 )和整个换热网络结构 (复杂系统 )之间进行优化协调 ,并获得换热网络的最优结构和各匹配单元的最优操作参数 .最后 ,通过一换热网络的最优合成 ,说明了该方法的应用前景     

基于经济目标和分解协调策略的换热网络最优设计

分析了换热网络在过程系统中的功能 ,从火用分析和火用经济学的角度提出了换热网络最优合成设计的实用火用经济目标函数 ,它包含了网络的流动火用损费 ,且可分解为各个换热单元的总费用之和 .在换热网络目标函数可分解性的基础上 ,本文又进一步提出了换热网络分解协调优化的研究策略 ,它是在各个匹配单元 (子系统 )和整个换热网络结构 (复杂系统 )之间进行优化协调 ,并获得换热网络的最优结构和各匹配单元的最优操作参数 .最后 ,通过一换热网络的最优合成 ,说明了该方法的应用前景     

Multiscale optimization using hybrid PDE/kMC process systems with application to thin film growth

The problem of optimal time-constant and time-varying operation for transport-reaction processes is considered, when the cost functional and/or equality constraints necessitate the consideration of phenomena that occur over disparate length scales. Multiscale process models are initially developed, linking continuum conservation laws with microscopic scale simulators. Subsequently, order reduction techniques for dissipative partial-differential equations are combined with adaptive tabulation of microscopic simulation data to reduce the computational requirements of the optimization problem, which is then solved using standard search algorithms. The method is applied to a conceptual thin film deposition process to compute optimal substrate-surface temperature profiles that simultaneously maximize film-deposition-rate uniformity (macroscale objective) and minimize surface roughness (microscale objective) across the film surface for a steady-state process operation. Subsequently, optimal time-varying policies of substrate temperature and precursor inlet concentrations are computed under the assumption of quasi-steady-state process operation.     

Optimization of district heating systems based on the demand forecast in the capital region

A district heating system (DHS) consists of energy suppliers and consumers, heat generation and storage facilities and power transmission lines in the region. DHS has taken charge of an increasingly important role as the energy cost increases recently. In this work, a model for operational optimization of the DHS in the metropolitan area is presented by incorporating forecast for demand from customers. In the model, production and demand of heat in the region of Suseo near Seoul, Korea, are taken into account as well as forecast for demand using the artificial neural network. The optimization problem is formulated as a mixed integer linear programming (MILP) problem where the objective is to minimize the overall operating cost of DHS. The solution gives the optimal amount of network transmission and supply cost. The optimization system coupled with forecast capability can be effectively used as design and longterm operation guidelines for regional energy policies.