Shell and tube heat exchanger design using mixed‐integer linear programming

The design of heat exchangers, especially shell and tube heat exchangers was originally proposed as a trial and error procedure where guesses of the heat transfer coefficient were made and then verified after the design was finished. This traditional approach is highly dependent of the experience of a skilled engineer and it usually results in oversizing. Later, optimization techniques were proposed for the automatic generation of the best design alternative. Among these methods, there are heuristic and stochastic approaches as well as mathematical programming. In all cases, the models are mixed integer non‐linear and non‐convex. In the case of mathematical programming solution procedures, all the solution approaches were likely to be trapped in a local optimum solution, unless global optimization is used. In addition, it is very well‐known that local solvers need good initial values or sometimes they do not even find a feasible solution. In this article, we propose to use a robust mixed integer global optimization procedure to obtain the optimal design. Our model is linear thanks to the use of standardized and discrete geometric values of the heat exchanger main mechanical components and a reformulation of integer nonlinear expressions without losing any rigor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1907–1922, 2017     

Design of shell and tube heat exchangers considering the interaction of fouling and hydraulics

We extend a formulation of the heat exchanger design optimization with fouling modeling to consider the effect of fouling on hydraulics. A shell-side fouling model was added so the optimization can consider cases with fouling in the tube and shell sides. The focus is the design of heat exchangers with fouling behavior associated with a threshold model, like in crude preheat trains. We solve the optimization problem by using a newly proposed Set Trimming technique. We compare our results with the traditional approach of using fixed fouling factors and the previous approach of not considering the hydraulic impact of fouling. We conclude that considering the deposit thickness leads to more realistic results that are different than the ones obtained using the previous approaches. Moreover, we show that previous approaches can render designs with larger pressure drops than the maximum imposed by the constraints, as well as exchangers with higher areas.     

Heat exchanger network synthesis with detailed exchanger designs—2. Hybrid optimization strategy for synthesis of heat exchanger networks

We propose a new strategy to synthesize heat exchanger networks with detailed designs of individual heat exchangers. The proposed strategy uses a multistep approach by first obtaining a heat exchanger network topology through solving a modified version of the mixed integer nonlinear programming (MINLP) stage-wise superstructure of Yee and Grossmann, which includes a smoothed LMTD approximation and pressure drops. In a second nonlinear programming (NLP) suboptimization step, we allow for nonisothermal mixing to solve problems with or without exchanger bypasses. The selected heat exchangers along with the mass and energy balances obtained are then used to design the network with detailed exchanger designs through solving a sequence of NLPs for individual heat exchanger designs. The NLPs are based on the detailed discretized optimization models of Kazi et al., which solve quickly and reliably to obtain heat exchangers based on rigorous, first-principles derived coupled differential equations. These models solve a differential algebraic equation system and do not rely on usual assumptions associated with other heuristic-based exchanger design methods, such as log mean temperature difference and F_T correction factors. These detailed exchanger designs are then used to update the network optimization model through sets of correction factors on heat exchanger area, number of shells, heat transfer coefficients, and pressure drops of each exchanger design, in a method based on that of Short et al. The method solves reliably, guaranteeing feasible exchangers for every potential network generated by the shortcut models, through validation with rigorous heat exchanger models at every iteration. In addition, the method does not increase the nonlinearity of the MINLP model, nor does it require any manual intervention or initialization from the user. Three examples are solved and the results are compared to those obtained in the literature.     

Constrained thermohydraulic optimization of the flow rate distribution in crude preheat trains

Crude preheat trains are heat exchanger networks which heat the crude oil stream in the petroleum distillation using hot product streams and pumparounds. The final heating step is executed in a furnace. The thermal efficiency of this process is strongly dependent on the crude preheat train performance, and, during the refinery operation, the heat load of the exchangers may decrease due to fouling. Associated to the reduction of the thermal effectiveness of the heat exchangers, fouling also causes an increase of the flow resistances along the thermal equipment. A potential approach to mitigate this problem is based on the optimization of the distribution of the flow rates in the crude preheat train for maximizing the final crude temperature. In this context, this paper presents a constrained nonlinear programming formulation for this task. The equality constraints encompass mass, energy and mechanical energy balances and heat exchanger equations for describing the thermal and hydraulic behavior of the system. The performance of the proposed approach is explored using two examples, a simple network and a crude preheat train based on a real Brazilian refinery.     

Framework for work‐heat exchange network synthesis (WHENS)

Work and heat are the two predominant forms of energy in the process industry. Considerable savings can be achieved by synergizing the work and heat requirements of process streams. A generalized framework for integrating heat and work simultaneously is proposed based on a mixed‐integer nonlinear programing model for work‐heat exchange network synthesis. Starting with a set of streams with known flows, temperatures, and pressures, a network of single‐shaft‐turbine‐compressors with motors/generators, valves, heat exchangers, and utility heaters/coolers is synthesized for minimized total annualized cost. In contrast to existing works, (1) streams are not preclassified as hot/cold or high/low pressure, (2) pressure changes are allowed for streams with no net pressure change, (3) liquid‐vapor phase changes are allowed, and (4) phase‐based property correlations are used. Successful application of our approach to C3 splitting yields a nonintuitive configuration. Another application of an offshore natural gas liquefaction process is also studied. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2472–2485, 2018     

模拟退火方法用于带有中间换热器精馏塔的优化综合

This article presents a simulated annealing-based approach to the optimal synthesis of distillation column considering intermediate heat exchangers arrangements. T-he number of intermediate condensers and/or intermediate reboilers, the placement locations, the.operating pressure of column, and the heat duties of intermediate heat exchangers are treated as optimization variables. A novel coding procedure making use of an integer number series is proposed to represent and manipulate the structure of system and a stage-to-stage method is used for column design and cost calculation. With the representation procedure, the synthesis problem is formulated as a mixed integer nonlinear programming （MINLP） problem, which can then be solved with an improved simulated annealing algorithm. Two examples are illustrated to show the effectiveness of the suggested approach.     

Effects of fouling on performance of retrofitted heat exchanger networks: A thermo-hydraulic based analysis

The energy recovery performance of crude pre-heat trains (PHTs) in oil refineries is typically impaired by deposition over time of fouling on the thermal surfaces. Such time varying effects are normally not considered in the design or retrofit of heat exchangers networks. In this paper, the importance of taking into account such effects is demonstrated, by means of a case study. An existing industrial PHT network is simulated using a dynamic, distributed mathematical model for shell-and-tube heat exchangers undergoing crude oil fouling. To systematically assess the impact of fouling at the network level, several key performance indicators are proposed and used to analyse three retrofit options aimed at maximising overall heat recovery. Simulation results show that network designs that maximise energy recovery at steady state are not the best when fouling occurs. It is concluded that a proper retrofit design must include consideration of time varying fouling effects.     

Operational modeling of multistream heat exchangers with phase changes

Multistream heat exchangers (MSHE) enable the simultaneous exchange of heat among multiple streams, and are preferred in cryogenic processes such as air separation and LNG. Most MSHEs are complex; proprietary and involve phase changes of mixtures. Although modeling MSHE is crucial for process optimization, no such work exists to our knowledge. We present a novel approach for deriving an approximate operational (vs. design) model from historic data for an MSHE. Using a superstructure of simple 2‐stream exchangers, we propose a mixed‐integer nonlinear programming (MINLP) formulation to obtain a HE network that best represents the MSHE operation. We also develop an iterative algorithm to solve the large and nonconvex MINLP model in reasonable time, as existing commercial solvers fail to do so. Finally, we demonstrate the application of our work on an MSHE from an existing LNG plant, and successfully predict its performance over a variety of seasons and feed conditions. © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Heat Exchanger Network synthesis with Detailed Heat Exchanger Design

Pressure drop and fouling are important issues in heat exchanger network synthesis, which are usually neglected. Heat exchangers were designed in detail during the heat exchanger network synthesis, and pressure drop and fouling effects were taken into account. Pinch analysis combined with exergoeconomic analysis was used for determining optimal minimum approach temperature (ΔT_min) for heat exchanger network synthesis. Exergy consumption of heat transfer in HENs was calculated using a subsection integral on balanced composite curves. The heat transfer coefficients of all heat exchangers in the network were calculated iteratively to meet the requirements of optimal area and allowable pressure drops. The proposed method was applied to an industrial case. Numerical results indicate the importance of the detailed design of heat exchangers in HENs synthesis.     

Thermo-hydraulic channelling in parallel heat exchangers subject to fouling

The thermal and hydraulic impacts of fouling by crude oil on the tube side of shell-and-tube heat exchangers is analysed for cases where a centrifugal pump and control valve determine the throughput. For co- and counter-current heat exchangers where the fouling layer thickness does not vary markedly over the tube length a new method of calculating the mean fouling rate was derived based on (i) a ‘threshold’ fouling rate model and (ii) an estimated linear profile in film temperature along the tubes. Over-design of exchangers, using guidelines such as those provided by TEMA, is shown to be capable of exacerbating fouling problems. The new mean is also used to evaluate the operation of parallel heat exchangers, such as are often employed at the hot end of a preheat train; a phenomenon that we call ‘thermo-hydraulic channelling’ is identified. It is shown that this may substantially impair network performance but that its effect may be countered by introducing a simple retrofit option of flow measurement and control.     

换热器网络设备面积与清洗时序同步优化

表面结垢会严重影响换热器的传热效率,定期清洗是解决该问题的主要方式.针对以往换热器网络清洗时序优化方法中用于决策的整型变量较多而难以求解的问题,提出以换热器清洗的最大允许污垢热阻为优化变量,取代表示换热器是否清洗的二进制变量,将混合整数非线性规划问题转化成非线性规划问题,能够有效地减小问题规模,降低求解难度.优化过程中兼顾换热器网络的设计型与操作型问题,采用遗传/模拟退火算法同步优化换热器的面积与清洗时序.将该方法用于一个实例,所得年度总费用与文献基本一致,验证了该方法的有效性.     

考虑关键换热器备用的原油预热系统清垢周期优化

原油结垢是原油预热过程面临的一个严峻问题,它使换热器的传热系数降低,影响正常的生产过程。应对原油预热过程的结垢问题最普遍的方法就是对换热器进行周期清洁,并优化清洁周期。许多结垢严重的行业都采用换热器备用的方式来减少因换热器离线造成的热回收减小,但原油预热系统尚未考虑,因而进一步考虑了关键换热器的备用来进行原油预热系统清垢周期优化。首先选取关键换热器,再通过模拟退火算法进行清洁周期优化。应用所提出的方法对简化的原油预热系统进行了清垢周期优化,结果显示,考虑换热器备用时所得到的清垢周期经济效益更好。     

Dynamic crude oil fouling prediction in industrial preheaters using optimized ANN based moving window technique

The objective of this paper is to develop and validate a reliable, efficient and robust artificial neural network (ANN) model for online monitoring and prediction of crude oil fouling behavior for industrial shell and tube heat exchangers. To explore the complex dynamics of fouling, a new modeling strategy based on moving-window neural network approach is proposed. The essential character of this modeling approach is online updating of the ANN model whenever a new data block is available, so that it can effectively capture the slowly changing of process dynamics. The results of these models have been compared with appropriate sets of experimental data. The mean relative errors (MRE) of training and prediction subsets were about 6.61% and 8.06%, respectively. Since the data extraction in the refinery was performed every 2 h, the modeling approach led to an MRE of about 8% for fouling rate prediction of the next 50 h.     

Thermo‐hydraulic analysis of refinery heat exchangers undergoing fouling

A complete, systematic approach is presented for the analysis and characterization of fouling and cleaning in refinery heat exchangers. Bringing together advanced thermo‐hydraulic dynamic models, some new formulations, and a method for dynamic analysis of plant data, it allows: extracting significant information from the data; evaluating the fouling state of the units based on thermal measurements and pressure drops, if available; identifying the range of deposit conductivity leading to realistic pressure drops, if pressure measurements are unavailable; estimating key fouling and ageing parameters; estimating the effectiveness of cleaning and surface conditions after a clean; and predicting thermal and hydraulic performance with good accuracy for other periods/exchangers operating in similar conditions. An industrial case study demonstrates the performance prediction in seamless simulations that include partial and total cleanings for over 1000 days operation. The risks of using thermal effects alone and the significant advantages of including pressure drop measurements are highlighted. © 2016 American Institute of Chemical Engineers AIChE J, 63: 984–1001, 2017     

A decomposition algorithm for simultaneous scheduling and control of CSP systems

We present a decomposition algorithm to perform simultaneous scheduling and control decisions in concentrated solar power (CSP) systems. Our algorithm is motivated by the need to determine optimal market participation strategies at multiple timescales. The decomposition scheme uses physical insights to create surrogate linear models that are embedded within a mixed‐integer linear scheduling layer to perform discrete (operational mode) decisions. The schedules are then validated for physical feasibility in a dynamic optimization layer that uses a continuous full‐resolution CSP model. The dynamic optimization layer updates the physical variables of the surrogate models to refine schedules. We demonstrate that performing this procedure recursively provides high‐quality solutions of the simultaneous scheduling and control problem. We exploit these capabilities to analyze different market participation strategies and to explore the influence of key design variables on revenue. Our results also indicate that using scheduling algorithms that neglect detailed dynamics significantly decreases market revenues. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2408–2417, 2018     

A pinch‐like targeting framework for systematic thermal process intensification

The design of intensified systems remains an “Edisonian” effort, whereby new intensification schemes are the product of creativity rather than the result of applying systematic procedures. Under this motivation, this article presents a novel and systematic approach for identifying targets for thermal process intensification, defined as combining two or more heat sources and sinks present in a process flowsheet, possibly along with a thermal utility stream, in a single intensified device where heat exchange takes place. The targeting problem is formulated as a mixed‐integer linear program. An extensive case study illustrating its application is presented. © 2017 American Institute of Chemical Engineers AIChE J, 64: 877–885, 2018     

A computerized and integrated approach for heat exchanger network design in multipurpose batch plants

Significant savings in the utility cost of batch plants can be obtained by heat integration. In this study, an integrated mathematical programming approach is developed for the determination of the cost optimal heat exchanger network for multipurpose batch chemical plants. A single step, interactive computer program (BatcHEN) which is developed for the determination of the campaigns (i.e. the set of products which can be produced simultaneously), the heat exchange areas of all possible heat exchangers in the campaigns and finally the heat exchanger network are all discussed. A matrix search algorithm is used for the determination of the campaigns. Heat exchange areas for the possible heat exchangers are found by solving a nonlinear optimization model with a grid search algorithm. Finally the heat exchanger network optimization is modeled as a mixed integer linear programming problem and then solved by the modeling and optimization software GAMS/XA.     

Multistream heat exchangers: Equation‐oriented modeling and flowsheet optimization

Multistream heat exchangers (MHEXs), typically of the plate‐fin or spiral‐wound type, are a key enabler of heat integration in cryogenic processes. Equation‐oriented modeling of MHEXs for flowsheet optimization purposes is challenging, especially when streams undergo phase transformations. Boolean variables are typically used to capture the effect of phase changes, adding considerable difficulty to solving the flowsheet optimization problem. A novel optimization‐oriented MHEX modeling approach that uses a pseudo‐transient approach to rapidly compute stream temperatures without requiring Boolean variables is presented. The model also computes an approximate required heat exchange area to determine the optimal tradeoff between operating and capital expenses. Subsequently, this model is seamlessly integrated in a previously‐introduced pseudo‐transient process modeling and flowsheet optimization framework. Our developments are illustrated with two optimal design case studies, an MHEX representative of air separation operation and a natural gas liquefaction process. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1856–1866, 2015     

Impact of deposit ageing on thermal fouling: Lumped parameter model

The thermal and hydraulic performance of heat exchangers can be seriously impaired by the formation of fouling deposits on the heat transfer surfaces. The thermal effect of fouling can be complicated when the deposit is subject to ageing, represented here as a change in deposit thermal conductivity (but not thickness) over time. In this article, we revisit the ageing concept for crude oil fouling proposed by Nelson (Refiner Nat Gas Manufacturer. 1934;13:271–276, 292–298), using a numerical model incorporating first order kinetics to generate quantitative comparisons of different ageing rates. Results are reported for lumped parameter systems (which also simulate point measurement methods commonly used in laboratory testing) that demonstrate that ageing can have a substantial influence on the rate of heat transfer and hence on the surface temperature and rate of fouling. Rapid ageing (compared with the rate of deposition) does not pose problems, but slow ageing, or the use of constant heat fluxes in experiments, can lead to modified thermal fouling behavior. It is concluded that deposit ageing dynamics should be considered alongside deposition rate dynamics when interpreting experimental fouling data and when modeling fouling behavior in support of heat exchanger design or operation. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Integrated Scheduling and Dynamic Optimization of Sequential Batch Processes with Online Implementation

An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed‐integer dynamic optimization problem or a large‐scale mixed‐integer nonlinear programming (MINLP) problem by discretizing the dynamic models. To reduce the computational complexity, we first decompose all dynamic models from the integrated problem, which is then approximated by a scheduling problem based on the flexible recipe. The recipe candidates are expressed by Pareto frontiers, which are determined offline by using multiobjective dynamic optimization to minimize the processing cost and processing time. The operational recipe is then optimized simultaneously with the scheduling decisions online. Because the dynamic models are encapsulated by the Pareto frontiers, the online problem is a mixed‐integer programming problem which is much more computationally efficient than the original MINLP problem, and allows the online implementation to deal with uncertainties. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2379–2406, 2013