Numerical modelling of heat transfer processes with supplementary data

Mathematical models of heat transfer processes are usually studied using formulation that is unique in the mathematical sense. For example, in solving initial-boundary value problems in conduction heat transfer, the mathematical model consists of the governing equation and initial and boundary conditions. An extension of such an approach by introducing the supplementary information (or data) concerning the process has been proposed here as a method for verifying the accuracy of the model equations. This means that the mathematical model consists of more equations than unknowns which leads in consequence to a finite set of probable solutions. A criterion for choosing the most probable solution has been proposed. Special attention has been paid to numerical formulation. Computational methods have been derived using the Lagrange multipliers. Theoretical considerations have been illustrated by computing the temperature distribution inside a laboratory combustion chamber.     

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.     

无分流换热网络合成和控制的集成研究

提出了无分流换热网络合成和控制集成的策略和方法、步骤,建立了合成和控制同步优化的数学模型,使得换热网络的合成和控制的集成研究从试探法向数学规划方法发展,从理论研究向实用性方向发展,实现了同时考虑控制要求的换热网络的自动合成。通过示例说明了本文所提方法的有效性和实用前景。     

换热网络的同步综合设计

提出了换热网络的一种新的转运模型,以并串模式和非等温混合过程描述换热网络的热力学和经济性的总要求,不使用挟点分离、最小单元数等启发式规则,并允许交叉换热和不同物流间的膜传热系数与温差合理匹配.这一模型与优化模型相结合,自动产生换热网络,确定相应的最优公用工程费用、换热面积、换热器台数与冷热流间的匹配,其可行域由一集线性约束确定,鲁棒性很好,易于求解.该方法克服了换热网络的各种分步骤综合方法的缺陷(包括挟点技术、双温差法及相关数学规划方法).与文献上其它同步优化方法比较,具有模型简单、规模小、可算性强、初始化简易、计算结果可靠的优点.通过对文献中广泛使用的例题的检验,结果优于现有的其它方法.     

基于Kalman滤波的换热器非线性状态参数校正

炼化工艺系统中换热网络数据的准确提取将直接影响到集成优化方案和优化控制的性能。针对换热器非线性状态参数的数据校正,构建了换热器分段线性集总参数传热过程模型,有效地解决了换热器流股物性非线性变化所引起的非线性状态空间方程求解的问题;提出了分段线性的Kalman滤波状态空间方程建立和换热器状态参数校正方法,并通过蜡油加氢装置反应流出物高压换热器工业实例阐述了所提出方法的实现过程和效果。研究表明：换热器分段线性集总参数模型中分段数对Kalman滤波的计算收敛性具有重要影响,随着分段数的增大,换热器状态参数收敛于固定值,分段数需根据计算精度通过试差确定。本文方法可对换热器非线性状态参数实施有效的数据校正,对流股物性进行分段线性化处理具有较高的计算精度,可用于大温差或物性变化较剧烈情况下换热器非线性状态参数的数据校正。     

Improved area—energy targeting for fired heater integrated heat exchanger networks

Effective integration of various subsystems into the overall process, results in an energy efficient and economic plant design. In this paper, issues related to the area-energy targeting for fired heater integrated heat exchanger networks are studied. Performance of a fired heater is affected by the variables such as fuel fired and air-preheat temperature. These variables along with the minimum approach temperature difference for the heat recovery of the background process, affect the performance of the overall system. A methodology is proposed for the area-energy targeting for fired heater integrated processes. In the proposed methodology, the fired heater heat duty split between the radiation and the convection section is determined using the one gas zone furnace model.     

Optimal water purification using low grade waste heat in an absorption heat transformer

A proposal for rational energy saving using wasted heat is showed in the present paper. Thermodynamicmathematical model is presented like an effort for water purification from waste heat. This paper describes computing results of heat transformer operation for water purification using low grade waste heat. Equations, parameters and simplifications used in the model are briefly described. The main parameter of the carried out study is the coefficient of performance (COP) defined for reversed heat pumps and the second main parameter is absorber temperature, both parameters has been showed and correlated between them. Main objective of this work is to show the optimal operating condition for different process which deliver low grade waste heat and requires water purification. Assisted computing simulation was used for obtain these results. The main conclusion is an ecological proposal for optimal recover of low grade waste heat. Many operating conditions are showed in graphical form and discussed for different environment conditions.     

Synthesis of cost-optimal heat exchanger networks using differential evolution

Heat exchanger network synthesis (HENS) has been one of the most-studied problems in process synthesis. Nevertheless, the complexity of the HENS problem provides enough scope for the development of novel algorithms involving the application of specialized optimization techniques. Evolutionary algorithms (EA) have emerged as viable alternatives to traditional methods for optimizing functions of both continuous and discrete variables. Differential evolution (DE) is one such evolutionary algorithm that promises simple, fast and robust optimization. The present study illustrates the application of this novel technique for the synthesis of heat exchanger networks. The HENS model proposed here considers stream splitting, does away with the simplifying assumption of isothermal mixing of the split streams and has the capability to handle compulsory and forbidden matching of streams. The DE-based model (DEM) does not rely on the decomposition of the problem into subproblems but employs a simultaneous method of approach to optimize the structure of the network of heat exchangers, the heat loads of these exchangers, the split stream heat flows and the minimum approach temperature. The proposed model has been applied to some case studies available in the literature and the results of these studies are very encouraging. The present work represents thus a step forward in the search for robust and efficient global optimization algorithms for the solution of the HENS problem.     

A brown coal-based sorbent for water treatment for removal of humic substances: Optimization of the sorbent manufacturing process

A two-factor mathematical model has been proposed for the preparation of a lignite sorbent designed for the removal of humic substances from water purification. It has been shown that this model adequately describes the dependence of the sorption capacity of the sorbent on the preparation conditions, the temperature and time of the heat treatment process. Based on the proposed model, optimal conditions for the manufacture of the lignite sorbent that ensures the maximum extraction of humic substances from water. By means of the experimental-statistical analysis method, the dependence of the sorption capacity of the polydisperse sorbent on the particle size was found. It has been shown that these models can effectively predict the properties of a brown coal sorbent.     

多目标灰色局势决策在加热炉动态操作中的应用

对加热炉动态过程进行数学模型研究,针对不同待轧时间,采用多目标灰色局势决策方法,得出了相应合理的待轧优化控制策略,并给出了待轧时间变动时的动态修正方法.模拟结果表明,该方法具有良好的动态性能,适合于在线控制.     

Simultaneous synthesis of distillation trains and heat exchanger networks

A new mathematical formulation for the optimal synthesis of heat-integrated distillation systems that accounts for constrained heat matches between columns and the rest of the process is presented. The definition of temperature intervals commonly used by heat exchanger network synthesis procedures is embedded in the proposed formulation that can be regarded as a generalization of the network flow model of Cerdá and Westerberg (1983, Chem. Engng Sci.38, 1723) under conditions of variable stream temperatures. The minimization of the total flow-sheet utility cost has been chosen as the design target.The problem has been represented through a mixed-integer linear program. By performing the search with a standard branch-and-bound technique the global optimality of the solution found is guaranteed. Three case studies involving the separation of a ternary mixture by distillation have been solved. The consideration of the rest of the process produces in two of them new distillation train designs costing less overall.     

Synthesis of indirect work exchange networks considering both isothermal and adiabatic process together with exergy analysis

In this paper, an efficient methodology for synthesizing the indirect work exchange networks (WEN) considering isothermal process and adiabatic process respectively based on transshipment model is first proposed. In contrast with superstructure method, the transshipment model is easier to obtain the minimum utility consumption taken as the objective function and more convenient for us to attain the optimal network configuration for further minimizing the number of units. Different from division of temperature intervals in heat exchange networks, different pressure intervals are gained according to the maximum compression/expansion ratio in consideration of operating principles of indirect work exchangers and the characteristics of no pressure constraints for stream matches. The presented approach for WEN synthesis is a linear programming model applied to the isothermal process, but for indirect work exchange networks with adiabatic process, a nonlinear programming model needs establishing. Additionally, temperatures should be regarded as decision variables limited to the range between inlet and outlet temperatures in each sub-network. The constructed transshipment model can be solved first to get the minimum utility consumption and further to determine the minimum number of units by merging the adjacent pressure intervals on the basis of the proposed merging methods, which is proved to be effective through exergy analysis at the level of units structures. Finally, two cases are calculated to confirm it is dramatically feasible and effective that the optimal WEN configuration can be gained by the proposed method.     

Optimal operation of a catalytic tubular reactor with fouling catalyst by coke deposition

The dehydrogenation of isopentane over chromia-alumina catalyst has been carried out at three isothermal levels. The catalyst fouling and the deposited coke profiles were observed in a catalytic tubular reactor. A kinetic model is proposed and the kinetic parameters have been estimated by non linear regression methods.For the dehydrogenation with catalyst fouling, the problem of finding the isothermal optimal control was formulated by a distributed maximum principle and a computational algorithm using a quasi-steady state assumption was presented. The dehydrogenation of isopentane was carried out experimentally at the evaluated isothermal optimal temperature. The observed conversion, yields and coke content profiles agreed with the evaluated ones fairly well, which suggests that the kinetic model may be useful for optimal controls.     

Temperature Control of a Bench‐Scale Batch Polymerization Reactor for Polystyrene Production

Batch polymerization reactors commonly use optimal temperature control as the strategic operation parameter. This strategy allows for better operability and a more economic process. The main objective of the batch polymerization reactor control is to obtain acceptable product quality. Direct measurement of polymer quality is rarely achievable, which makes the online control of the reactor difficult. Temperature is the most controllable operational variable in the polymer reactor, which is seen to have a direct effect on the polymer properties. Temperature is chosen as the set point by using either the isothermal temperature or optimal temperature trajectory. Online control of the optimal temperature profile of a bench‐scale batch polymerization reactor was experimentally investigated in this study. The temperature trajectory was used as the target for controllers to follow. The time‐profile temperature was obtained with the objective of obtaining the desired conversion and number‐average chain length within the minimum time. Two advanced controls of fuzzy logic control and generic model control were applied to the polymer reactor. A comparison of the controllers reveals that both performed better than conventional controllers.     

多管程换热器换热网络的合成

Many methods have been proposed for synthesis of heat exchanger networks in recent years, most of which consider single pass exchangers. In this study some evolutionary rules have been proposed for synthesis of multipass exchanger networks. The method is based on the heuristic that optimal networks should feature maximum energy recovery and have the minimum number of shells. The effectiveness of the developed evolutionary rules is demonstrated through some literature examples.     

考虑间接换热额外换热温差的间歇过程储热集成

间歇过程流股间换热有直接换热和间接换热两种方式,通过储热介质进行间接换热会产生额外的换热温差。现有的夹点分析方法考虑间接换热额外换热温差后,难以得到经济且可行的储热集成方案。本文在夹点分析的基础上,提出了一种考虑间接换热额外换热温差的间歇过程储热集成方法。该方法首先使用不同的直接换热和间接换热温差进行热级联分析,确定储热集成后的最小冷、热公用工程用量,识别储热位置和储热量,并依据热级联分析结果,建立时间段温焓图确定储热介质温度,得到储热方案。然后,将储热流股转化为放热时间段的冷流股和需热时间段的热流股,进行换热网络综合与优化,得到符合实际应用的储热集成方案。最后,通过经典实例证明了所提方法的可行性和有效性。     

Globally optimal design of Minimal WHEN systems using enumeration

The process synthesis problem referred to as work and heat exchange networks (WHENs) asks to determine the optimal heat exchanger network intertwined with compressors, expanders, and valves, all integrated into one single network, such that streams with certain initial temperature and pressure attain their temperature and pressure targets at minimum cost. This article presents a procedure that obtains the globally optimal solution of Minimal WHEN systems using an enumeration scheme, using only a few subproblems, each one solved using mathematical programming to global optimality. Minimal structures feature one compression/decompression task and one heat exchange task per stream. In addition, we depart from the ideal gas assumption and use a cubic equation of state for stream properties. Finally, the approach allows for the use of turboexpanders. Four examples are presented to show the effectiveness and accuracy of the proposed method.     

换热网络运行模拟优化

换热网络系统大多数是按给定工况,以投资费用和运行费用最优为目标设计的。但在实际运行过程中,确定和不确定性的影响因素往往导致换热网络的运行工况偏离设计值。偏离设计工况运行的换热网络性能变差,导致运行费用增加,甚至不能满足工艺物流换热要求。在换热网络结构给定条件下,将满足物流目标温度和运行费用最优作为目标函数,以单体模型和Yee et al.（1990）提出的多级超结构为基础,建立换热网络运行模拟优化模型,并进一步去除恒定膜传热系数假设使模型贴近实际问题。针对提出的非线性数学模型（NLP）问题,以标准粒子群算法为基础建立求解策略。在论文的最后,4个来源于已发表论文的实例研究证明了该优化方法的有效性。     

Design of resilient processing plants—II Design and control of energy management systems

The “standard heat exchanger network problem” has been surprisingly difficult to solve. It is only now that simple and reliable methods have evolved to synthesize the most efficient network of heat exchangers to heat and cool known process streams between stated temperature bounds. This has taken over a decade of research and scores of publications.The “resilient heat exchanger network problem” requires a solution that can cope with the uncertainties of industrial design. Fixed flow rates and temperature bounds rarely occur industrially. Rather, an industrial heat exchanger network problem necessarily involves ranges of flow rates and ranges of temperature bounds, and must include ease of operation and control.In this paper we make several fundamental advances in the design of resilient heat exchanger networks. (1) An efficient design procedure is developed to yield resilient designs which handle fluctuations within the condition of maximum energy efficiency. (2) A control structure and operating policy are developed to adjust flow distributions in the network to meet temperature constraints with minimum utility usage.These developments are based on several new theorems concerning resiliency in network design.     

Performance Optimization of a Brick Dryer Using Porous Simulation Approach

In the present study, an innovative method for an accurate simulation and design of a chamber dryer used in the brick/ceramic industry has been proposed. A thorough investigation of currently used dryers is conducted and optimization criteria are detected and discussed. Three-dimensional modeling of the chamber dryer has been performed. In the second step, from the result of 3D modeling, the critical values for heat transfer coefficient are obtained. The governing equations for a two-dimensional brick as a porous solid are derived by combining conservation laws and Fourier's law for heat conduction and Darcy's and Fick's laws for mass diffusion in porous material. The set of partial differential equations governing heat and mass transport in a single brick together with the respective temperature and humidity boundary conditions have been solved numerically based on finite difference method. Finally, an efficient scheme for the air circulation devices, inlet air temperature and humidity, burner characteristics, flow rates, and drying process control have been proposed for a typical industrial-scale brick dryer.