化工过程设计的多目标不确定优化研究

In many circumstances, chemical process design can be formulated as a multi-objective optimization （MOO） problem. Examples include bi-objective optimization problems, where the economic objective is maximized and environmental impact is minimized simultaneously. Moreover, the random behavior in the process,property, market fluctuation, errors in model prediction and so on would affect the performance of a process. Therefore, it is essential to develop a MOO methodology under uncertainty. In this article, the authors propose a generic and systematic optimization methodology for chemical process design under uncertainty. It aims at identifying the optimal design from a number of candidates. The utility of this methodology is demonstrated by a case study based on the design of a condensate treatment unit in an ammonia plant.     

Multiobjective particles swarm optimization and multicriteria decision making of improved cumene production process including economic,environmental, and safety criteria

Cumene is one of the five chemicals with the highest production in the world. In this work, the design by Flegiel was improved to increase the production rate of the cumene process by adding a trans-alkylation reactor, then multi-objective optimization (MOO) using the particles swarm optimization (PSO) algorithm is used to improve the process design. Furthermore, seven multicriteria decision-making (MCDM) methods for selecting an optimal solution from the Pareto-optimal front related to two MOO problems were performed. In this optimization, conflicting objectives such as total capital cost (TCC), energy cost, wastage rate, and safety target are simultaneously minimized in the format of trade-offs. Finally, the results of this work were compared with those reported designs. The optimal solution chosen by MCDM methods is at TCC = 5589, damage index (DI) = 0.044, and material loss = 0.0005.     

Water integration in eco-industrial parks using a multi-leader-follower approach

The design and optimization of industrial water networks in eco-industrial parks are studied by formulating and solving multi-leader-follower game problems. The methodology is explained by demonstrating its advantages against multi-objective optimization approaches. Several formulations and solution methods for MLFG are discussed in detail. The approach is validated on a case study of water integration in EIP without and with regeneration units. In the latter, multi-leader-single-follower and single-leader-multi-follower games are studied. Each enterprise's objective is to minimize the total annualized cost, while the EIP authority objective is to minimize the consumption of freshwater within the ecopark. The MLFG is transformed into a MOPEC and solved using GAMS^® as an NLP. Obtained results are compared against the MOO approach and between different MLFG formulations. The methodology proposed is proved to be very reliable in multi-criteria scenarios compared to MOO approaches, providing numerical Nash equilibrium solutions and specifically in EIP design and optimization.     

Enhancing the ϵ-constraint method through the use of objective reduction and random sequences: Application to environmental problems

The ϵ-constraint method is an algorithm widely used to solve multi-objective optimization (MOO) problems. In this work, we improve this algorithm through its integration with rigorous dimensionality reduction methods and pseudo/quasi-random sequences. Numerical examples show that the enhanced algorithm outperforms the standard ϵ-constraint method in terms of quantity and quality of the Pareto points produced by the algorithm. Our approach, which is particularly suited for environmental problems that tend to contain several redundant objectives, allows dealing with complex MOO models with many objectives.     

On the use of Principal Component Analysis for reducing the number of environmental objectives in multi-objective optimization: Application to the design of chemical supply chains

Multi-objective optimization (MOO) has recently attracted an increasing interest in environmental engineering. One major limitation of the existing solution methods for MOO is that their computational burden tends to grow rapidly in size with the number of environmental objectives. In this paper, we study the use of Principal Component Analysis (PCA) to identify redundant environmental metrics in MOO that can be omitted without disturbing the main features of the problem, thereby reducing the associated complexity. We show that, besides its numerical usefulness, the use of PCA coupled with MOO provides valuable insights on the relationships between environmental indicators of concern for decision-makers. The capabilities of the proposed approach are illustrated through its application to the design of environmentally conscious chemical supply chains (SCs).     

On the use of filters to facilitate the post-optimal analysis of the Pareto solutions in multi-objective optimization

Multi-objective optimization (MOO) has emerged recently as a useful technique in the design and planning of engineering systems because it allows identifying alternatives leading to significant environmental savings. MOO models typically contain an infinite number of Pareto solutions, from which decision-makers should choose the best one according to their preferences. An approach is here presented that identifies and retains for further inspection a reduced set of Pareto solutions showing better overall performance. The capabilities of our approach are illustrated through its application to the design of reverse osmosis desalination plants considering simultaneously the unitary production cost and a set of environmental impacts in several damage categories. Our method reduces significantly the number of Pareto points, thereby facilitating the decision-making process in MOO.     

Global optimization of large‐scale mixed‐integer linear fractional programming problems: A reformulation‐linearization method and process scheduling applications

Mixed‐integer linear fractional program (MILFP) is a class of mixed‐integer nonlinear programs (MINLP) where the objective function is the ratio of two linear functions and all constraints are linear. Global optimization of large‐scale MILFPs can be computationally intractable due to the presence of discrete variables and the pseudoconvex/pseudoconcave objective function. We propose a novel and efficient reformulation–linearization method, which integrates Charnes–Cooper transformation and Glover's linearization scheme, to transform general MILFPs into their equivalent mixed‐integer linear programs (MILP), allowing MILFPs to be globally optimized effectively with MILP methods. Extensive computational studies are performed to demonstrate the efficiency of this method. To illustrate its applications, we consider two batch scheduling problems, which are modeled as MILFPs based on the continuous‐time formulations. Computational results show that the proposed approach requires significantly shorter CPU times than various general‐purpose MINLP methods and shows similar performance than the tailored parametric algorithm for solving large‐scale MILFP problems. Specifically, it performs with respect to the CPU time roughly a half of the parametric algorithm for the scheduling applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4255–4272, 2013     

The optimal flow-pattern of multiple effect evaporator systems

The optimization of the flow-pattern for a multiple effect evaporator system is discussed as a vector minimum problem. First a new program to solve the design problem for various flow-patterns with no stream mixing or splitting and an arbitrary number of effects is described. Second the set of noninferior flow-patterns is generated by enumerating one-by-one for all flow-patterns. This method works well in synthesizing multiple effect evaporator configuration.     

Anwendung von Rechenprogrammen bei der Simulation und Optimierung von Rektifizieranlagen in der fettchemischen Industrie

Application of Computer Programs on the Simulation and Optimization of Rectification Plants in Fatty Chemicals Industry Three calculation programs (Bubble point, Tomich, Newton Raphson) were used for the simulation of rectification plants and for the optimization of the plate to plate method. The application of these programs is explained with an example, each, from the practical problems: 1. Fractionation of fatty acids in a production column. The results of optimization calculations are compared with five different fatty acid fractions and the possibilities of increasing the capacity are shown. 2. Recovery of methanol from a mixture of KPK-methyl ester, glycerol and water. Three alternatives for the reduction of recovery costs are discussed with the aid of simulation programs. An essential part of the calculation is the determination of thermodynamic vapour-liquid equilibria. In this context, the material data program is briefly described together with the means for data collection.     

Bilevel optimization formulation for parameter estimation in liquid-liquid phase equilibrium problems

Excess Gibbs free energy models contain parameters which for a given mixture are estimated from measurements of phase-splits. Local composition models are very flexible and can accurately predict complex phase behavior. However, in many cases it has been reported that use of local composition models leads to prediction of more phase splits or more phases than measured, modeling homogeneous azeotropes as heterogeneous, etc. Here, a formulation is proposed that addresses these limitations of current parameter estimation methods. The formulation is based on a bilevel program, i.e., an optimization problem embedded in another one. Minimizing the error between model predictions and measurements gives the upper-level program. The lower-level programs are given by the minimization of the Gibbs free energy, or equivalently the satisfaction of the Gibbs tangent plane criterion. Each of the experiments is cast as a separate lower-level program. Additional requirements on the phase behavior of the system, such as enforcing the correct number of phase splits and the correct number of phases in each phase split, are similarly formulated as additional lower-level programs. Global optimization techniques are necessary even to obtain a feasible point since the lower-level programs are nonconvex. The proposed formulation is applied to problems from the literature, in which inappropriate fitting of the parameters of the non-random two-liquid (NRTL) model to experimental data has been reported to result in significant model errors, such as the prediction of an additional spurious phase split. The discussion is restricted to binary mixtures, however, the formulation can in principle be applied also to multicomponent mixtures.     

Improved film evaporator for mechanistic understanding of microwave-induced separation process

Microwave-induced film evaporation separation process has been reported recently to separate the polar/nonpolar mixture. However, the efficiency of the separation is still too low for practical applications, which requires further enhancement via different strategies such as optimization design of evaporator structure. In addition the depth understanding of the separation mechanisms is great importance for better utilization of the microwave-induced separation process. To carry out these investigations, a novel microwave-induced falling film evaporation instrument was developed in this paper. The improvement of the enhancement effect of microwave-induced separation was observed based on the improved film evaporator. The systematic experiments on microwave-induced separation with different binary azeotropic mixtures (ethanol-ethyl acetate system and dimethyl carbonate (DMC)-H₂O system) were conducted based on the new evaporator. For the ethanol-ethyl acetate system, microwave irradiation shifted the direction of evaporation separation at higher ethanol content in the starting liquid mixture. Moreover, for DMC-H₂O system microwave-induced separation process broke through the limitations of the traditional distillation process. The results clearly demonstrated the microwave-induced evaporation separation process could be commendably applied to the separation of binary azeotrope with different dielectric properties. Effects of operating parameters are also investigated to trigger further mechanism understanding on the microwave-induced separation process.     

A multi-criteria optimisation approach for the design of sustainable utility systems

Large amounts of gaseous emissions are generated by combustion processes associated with the utility systems. The emissions include SO_x, CO₂, CO, NO_x, CH₄, and N₂O. Such emissions can result in significant impact on the surrounding environment. As a result of serious concerns about environmental problems in recent years, the design criteria for a modern utility system should include both environmental and economic requirements. This work proposes a multi-objective optimisation (MOO) strategy to identify the sustainable design of utility systems that satisfies both economic and environmental goals. A MOO mixed integer linear programming (MILP) model is developed to combine the minimisation of costs with the minimisation of environmental impact that is assessed in terms of life cycle environmental burdens. Most of the gaseous emissions are addressed in the model. The resulting MOO problem is solved using lexicographic goal programming (LGP) techniques. The new strategy has been applied to a case study for the design of a utility system with specific utility demands.     

Multi-objective optimization of reverse osmosis networks by lexicographic optimization and augmented epsilon constraint method

This study proposes a multi-objective optimization (MOO) of reverse osmosis (RO) networks for seawater desalination. The membrane transport model takes into consideration of the longitudinal variation of the velocity, the pressure, and the concentration in the membrane modules. The RO network with three type energy recovery device options (pressure exchanger (PX), Hydraulic Turbocharger, and turbine) is introduced. Lexicographic optimization (for calculation of a more effective payoff table) and augmented ε-constraint method (to avoid inefficient Pareto solutions) are proposed to solve the MOO problem. A fuzzy decision maker is introduced to derive the most efficient solution among Pareto-optimal solutions. Firstly, different energy recovery option studies show that using PX is seen to be the most profitable option. Exergy analysis is used to evaluate the contribution of the equipments in energy degradation. Secondly, the proposed multi-objective framework simultaneously optimizes the total annualized cost (TAC) and energy consumption. With the increases of weighting for the main objective function: TAC, the most efficient solution moves to lower TAC direction. Finally, system recovery rate is added as the third objective function. It is reasonable to stay at the appropriate system recovery rather than to increase up to its limit and generating high energetic losses.     

高分子中空纤维蒸发器传热过程分析

蒸发器广泛应用于化工、食品等行业,传统的金属管蒸发器由于其耐酸碱腐蚀性差、表面易结垢等弱点,一定程度上限制了其应用范围,而具有优良性能的高分子中空纤维管可有效解决这些问题,具有很好的应用前景。采用自制的高分子改性中空纤维管,制备出非金属换热器,并进行了蒸发传热实验。结果表明,高分子中空纤维蒸发器的性能与料液温度有密切关系,沸腾进料时蒸发器的传热系数、产水量和热量利用率均高于低温进料;传热热阻主要集中在管外蒸汽加热侧和管壁的导热性能,当沸腾进料时管壁热阻占总传热热阻的66%以上,而管内蒸发侧传热热阻所占比重较低,均低于15.3%,且随着料液流速的增大而降低到5%以下;随着料液温度的降低,蒸发过程的传热系数、能量利用效率以及产水量均显著下降。     

PGS-COM: A hybrid method for constrained non-smooth black-box optimization problems: Brief review,novel algorithm and comparative evaluation

In the areas of chemical processes and energy systems, the relevance of black-box optimization problems is growing because they arise not only in the optimization of processes with modular/sequential simulation codes but also when decomposing complex optimization problems into bilevel programs. The objective function is typically discontinuous, non-differentiable, not defined in some points, noisy, and subject to linear and nonlinear relaxable and unrelaxable constraints. In this work, after briefly reviewing the main available direct-search methods applicable to this class of problems, we propose a new hybrid algorithm, referred to as PGS-COM, which combines the positive features of Constrained Particle Swarm, Generating Set Search, and Complex. The remarkable performance and reliability of PGS-COM are assessed and compared with those of eleven main alternative methods on twenty five test problems as well as two challenging process engineering applications related to the optimization of a heat recovery steam cycle and a styrene production process.     

A Multi-Criteria Study of Optimal Working Fluids for High Temperature Heat Pumps

A bi-objective optimization with respect to coefficient of performance (COP) and volumetric heating capacity (VHC) is performed for a high temperature heat pump. For fixed temperature levels of the heat source and sink, the values for temperature in the evaporator and condenser as well as the degree of vapor super-heating and condensate sub-cooling are optimized. Constraints are placed on the minimal pressure in the evaporator, the maximal pressure in the condenser and the compressor discharge temperature. Results are presented for a one-stage and a two-stage heat pump cycle. Cyclobutane and several butene isomers are identified as working fluids with a good compromise between COP and VHC from a CoMT-CAMD approach based on PC-SAFT and a realistic model for the ideal gas heat capacity.     

基于(火用)的管式降膜蒸发器液位优化设定

在降膜蒸发器中,物料液位直接影响蒸发器分离室压力和出料温度从而影响加热蒸汽消耗,对蒸发器的优化操作十分重要。但实际生产中液位的设定值通常是一个较大的范围,难以优化运用。针对此问题提出了一种基于(火用)分析的管式降膜蒸发器液位优化设定方法。深入分析了液位高度对蒸发过程各参数的影响,基于实际生产数据,拟合得到了液位与其他参数间的关系模型。结合蒸发器物料平衡关系以及(火用)分析方法,建立了最大化(火用)效率的能耗优化模型。对优化模型求解得到了蒸发器(火用)效率随液位高度变化的关系曲线,最后计算了不同工况条件下的最优液位,为优化实际生产操作提供了参考。     

GAMS supported optimization and predictability study of a multi-objective adsorption process with conflicting regions of optimal operating conditions

In process systems engineering, it is critical to design an effective and optimized process in a short period with minimum experimental trials. However, improvement of some process variables may deteriorate some other criteria due to conflicting regions of factor interests for optimal solution in multi-objective optimization (MOO) processes. Here, the global optimization of an adsorption case study with conflicting optimal solutions based on multi-objective Response Surface Methodology (RSM) design is facilitated with the implementation of BARON solver based on General Algebraic Modeling System (GAMS) with identical factor variables, levels, and model equations. RSM suggested fifteen different optimum settings of which the validation is quite expensive and onerous, whereas GAMS suggested a single optimum setting which makes it more economically viable especially for large scale systems. In addition, the GAMS-based optimization provided more accurate and reliable results when experimentally validated as compared to the RSM-based solution.     

A Tubeless Evaporator

The first author of this paper has invented a process, which incorporates direct contact evaporation, for saline water conversion, and waste concentration, which can include by-products recovery.The process has several potential advantages: Simplicity - major components are four vessels without internals, pumps, and a fan (unneeded in one version of the process); wide application - seawater, waste water, and membrane plant effluents; produces distilled water, co-produces brine, or concentrated brine, or moist solid, or by-products; no pretreatment in the ordinary case (on some applications, trash removal and chlorination is required); no scaling problem in the evaporator; minimum corrosion (no acid addition) ; can be powered by electricity of heat, including waste heat; low energy consumption in the single stage version of the process, extremely low energy consumption in the multistage version of the process.The process uses a working substance (WS), such as a high melting organic compound, at its freezing point, to effect the direct contact evaporation. An acceptable WS must be insoluble in water, inert, and easily separated by specific gravity difference from brine, product water, and any solids produced. It is also desirable that they be non-toxic, non-flammable, cheap, and have a high heat of fusion. Several WSs were identified that had the potential to be used in a commercial plant.At this point, the Office of Water Research and Technology (OWRT) sponsored a research project to investigate the operating characteristics of various WSs in the laboratory and a bench scale plant (BSP). A WS screening program tested melting range, solubility, tendency to entrain or emulsify, and stability, in the laboratory program. The BSP program simulated the operation of major pieces of equipment with WSs that passed the screening program, and seawater and other saline waters.A total of eight WS candidates were subjected to the WS screening program. Of these, two proved to be unsatisfactory. It was believed that these substances could have been made to work, but with other satisfactory materials available, there was little incentive to pursue this effort. The other six were found to be satisfactory for use in the BSP. Three of these were selected for testing in the BSP.Prior to the above effort, there was no data with which to design a pilot plant. Any such attempt would have had to be based on engineering judgement. Now one set of data (feed rates, operating conditions, etcetera) has been taken. These data could be far from optimum. Additional WSs, particularly those with melting points above 100°C are needed for multistage operation. Finally, the direct contact concept should be extended to the preheaters as well as the evaporator in order to make the process completely tubeless. Such a program, sponsored by OWRT, has just commenced.This paper describes the process and its potential advantages in more detail, reports on the results of the laboratory and bench scale programs referred to above, and outlines the program for the future development of the process.