HEN retrofit methods

Review of Heat Exchanger Network Retrotting Methodologies andTheir ApplicationsBhargava Krishna Sreepathi and G. P. Rangaiah*

Department of Chemical & Biomolecular Engineering, National University of Singapore, Singapore

*S Supporting Information

ABSTRACT: Heat exchanger network (HEN) retrotting improves heat recovery and thus reduces energy required in existingplants. This can be achieved by either increasing the heat transfer area and/or using heat transfer enhancements to increase heattransfer coecients. There is an increasing interest in HEN retrotting as can be seen from 20 journal papers since 2009 (about 5years) compared to 15 in the 10-year period 19992008. In total, there are about 60 journal papers on HEN retrotting since theyear 1985; however, in the past 20 years, there has been no review paper summarizing HEN retrotting methodologies and theirapplications. This provides the motivation for this review paper. HEN retrotting methods can be classied into three broadcategories, namely, mathematical programming based methods, pinch analysis based methods, and hybrid methods according totheir underlying approach. Further, some HEN retrotting methods include pressure drop considerations, and HEN retrottingcan be using heat transfer enhancements. This paper reviews all these methods and their applications in each of these categories.Finally, it discusses alternate solutions of ve application problems solved by several methods/researchers and/or for dierentobjectives. Review of HEN retrotting methods and their applications presented in this paper will be useful to both researchersand practitioners.

1. INTRODUCTION

Depleting energy resources, increasing environmental concerns,and energy prices provide the impetus to improve heatintegration in existing process plants. Recently, Klemes et al.1

provided an overview of recent developments in processintegration covering topics such as total site heat integration,mass integration, hydrogen pinch, and supply chain develop-ment. They discussed briey pinch analysis and mathematicalprogramming based methods applied to process integration. Inparticular, heat exchanger networks (HENs) play an importantrole in heat integration. See Grossmann et al.,2 Furman andSahinidis,3 and Morar and Agachi4 for reviews of papers onHEN synthesis for a new plant. In existing plants, HENs can beretrotted for higher heat recovery by adding heat transfer area,using heat transfer enhancements to increase heat transfercoecients, and/or reassigning existing exchangers. Retrottingtechniques can also be used to debottleneck the HEN forincreased throughput.In the past 5 years, there have been 20 journal papers

compared to 15 in the previous 10-year period 19992008.This fact shows the increasing interest and research in HENretrotting. In total, there are about 60 journal papers on HENretrotting since the year 1985; however, in the past 20 years,there has been no review paper summarizing HEN retrottingmethodologies and their applications. This provides themotivation for this review paper. In the past, Gundersen andNaess5 provided an evaluation of various HEN retrot methodsfrom an industrial perspective, and Jezowski6 provided a briefreview of the HEN retrot methods until 1993. Hence, thepresent review covers papers on HEN retrotting studies fromthe year 1993. A brief summary of these studies is presented inthe subsequent sections of this paper; it mostly followschronological order within each section. Figure 1 shows

many HEN retrotting topics studied over the years. Itindicates increasing research on graphical tools in pinch analysisbased methods, and application of stochastic global optimiza-tion in mathematical programming based methods.Methods for retrotting HENs can be broadly classied into

three groups: (a) pinch analysis based methods, (b)mathematical programming based methods, and (c) hybridmethods. Pinch analysis based methods, as the name suggests,uses pinch analysis to solve retrot problems. They employcomposite curves, grand composite curves, and/or griddiagrams to retrot HENs. Heuristics play a major role insolving problems by pinch analysis.7 Pinch analysis includingenergy targeting, network design, and evolution are describedin detail in both Kemp8 and Shenoy;9 these books include asection/chapter on retrotting of HEN. Pinch analysis methodsfor retrotting and their applications reported from 1993 to2013 are reviewed mostly in section 2.Mathematical programming based methods involve formula-

tion of a mathematical model followed by its solution usingoptimization methods, and so they are also referred to asoptimization based methods. They can be subdivided into twosubgroups based on the optimization methods used: thoseusing deterministic optimization methods and those usingstochastic optimization methods. Compared to the formermethods, stochastic methods are more likely to nd the globaloptimum for the HEN retrot problems.10 Recently,Bagajewicz et al.11 applied a mathematical programmingmethod and a pinch based method to a large retrot problem

Received: September 16, 2013Revised: June 12, 2014Accepted: June 17, 2014Published: June 17, 2014

Review

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and noted the diculties in achieving better solutions using thelatter. On the other hand, mathematical programming basedmethods are popular in academia but much less so in industrialpractice due to the diculty of setting up the problem models,particularly for practitioners. Mathematical programming basedmethods for HEN retrotting are discussed in section 3.Hybrid methods are the methods that make use of both

pinch analysis and mathematical programming, in an eort tocombine the strengths of both. They allow user interaction andcan also be applied to large problems. These methods arediscussed in section 4. Pressure drop considerations play animportant role in retrotting of HEN. Reported studies onretrotting considering pressure drop constraints are reviewedin section 5. Section 6 discusses retrotting HENs using heattransfer enhancements, which are receiving increasing attention.Five application problems used in many HEN retrottingstudies are presented and discussed in section 7. Finally,conclusions of this review are summarized in section 8.

2. PINCH ANALYSIS BASED METHODS

In this section, HEN retrot studies based on pinch analysismethods are reviewed in three subsections, namely, studies onmethodology, visualization techniques, and applications,depending on the focus of the study. In these subsections,method/technique and/or results reported in each of thesestudies are briey discussed, mostly in chronological sequence.To understand the basic steps of pinch analysis, readers arereferred to Shenoy,9 Kemp,8 and Gundersen.12 In 1986, Tjoeand Linnho7 studied HEN retrotting based on physicalinsights by setting targets. Retrotting was performed byfollowing the three basic rules of pinch analysis: no cold utilityabove the pinch, no hot utility below the pinch, and no processheat exchange across the pinch. The approach allows for userinteraction. This work7 has served as the basis for manysubsequent studies on HEN retrotting.2.1. Studies on Methodology. Carlsson et al.13 proposed

a retrot approach to nd the cost-optimal solution of an HENretrot problem taking into account various parameters such asheat exchanger type, space requirements, pressure drop costs,fouling, and maintenance costs. Instead of area targeting

assuming vertical heat exchange, criss-cross heat exchange wasallowed in this work after the vertical heat exchange was used toget a good approximation of area requirement. Carlsson et al.13

proposed a computer based model for nding near optimumHENs, which includes user interface to set practical constraints(based on experience), taking relevant parameters into account,and an option to conduct sensitivity analysis. To achieve theobjective, some relaxations are introduced to the networkdesign rules, the most notable of which is allowing thetemperature dierence to go below the minimum approachtemperature in individual matches. Also, the networks involvingheat transfer across the pinch point are considered only if theamount of heat transferred from below to above the pinchpoint is the same as that from above to below, thus allowingcriss-cross heat exchange. Carlsson et al.13 used their approachto solve a typical HEN application in the pulp and paperindustry. The results reported are for two scenarios: one with a7-month payback period and another with a 9-month paybackperiod. Both scenarios had the same objective function (ofincrease in annual savings) but a dierent Tmin of 18 and 10C respectively. This problem is solved in subsequent studies; acomparison of results in these studies is provided in Table 5,and discussed later in section 5.As the HEN retrot problems are complicated, many

researchers attempted to reduce their complexities beforesolving. One such approach is prescreening to identify apriorisolutions having certain heat recovery levels, which is chosenbased on various investment costs. van Reisen et al.14 proposeda method for decomposition and prescreening of the HENcalled path analysis. This method selects and evaluates parts ofthe existing HEN (potential to be improved), called subnet-works, while the remaining network is unchanged. Path analysisconsists of three stages, each dealing with an aspect of the HENretrot problem. In the rst stage, subnetworks are identiedbased on energy savings. The second stage compares all theidentied subnetworks based on savings, complexity, andpracticality of the network. In the last stage, the retrotnetwork is built for the selected subnetwork and compared withthe targets. As path analysis deals with subnetworks instead ofthe whole network, it simplies the problem signicantly. van

Figure 1. Contributions to HEN retrotting over the past 30 years; refer to acronyms and text for further details.

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Reisen et al.14 used their method to solve one problem fromTjoe and Linnho.7 An incremental area eciency targetingwas utilized in solving this problem. Two solutions wereobtained: one was identical (in terms of additional area andpayback period) to that in Tjoe and Linnho,7 and the secondsolution has a lower payback period of 1.4 years compared to1.6 years for the rst solution. The ranking of subnetworks inthe method of van Reisen et al.14 is not completely based onsavings and investment but also considers the complexity andpractical problems. Hence, one of the disadvantages of thismethod is the diculty to quantify the ranking of subnetworksand implement it in software.In a subsequent work, van Reisen et al.15 presented an

extension to the path analysis procedure presented earlier,14 byconsidering structural interconnections while solving theretrot problem. This is known as structural targeting. Usingpath analysis, the network is divided into many subnetworks bycombination of structural units. These unities, called zones,must be as self-contained as possible, similar to the approachused in grassroot problems. Paths help to classify the zones thatare better suitable to include structural modications. Thesepath based zones are further rened to get a practical set ofrened zones. These renements are based on plant layout,functionality of plant sections, temperature range of processstreams, operational aspects, etc. The extended path analysismethod was tested on two cases: an aromatic case study7 andthe C3/C4 separation section of an industrial ethylene plant.The results were generated very quickly, and the energy savingswere from 20% to 80% of the maximum possible according topinch analysis target.Asante and Zhu16 have introduced the concept of network

pinch, which reveals the bottleneck of the existing HEN. In thispaper, the network pinch is relaxed using process changes likeow rate, heat duty, and temperature changes. The overallmodel included the process model and a linear HEN model andconsiders all possible options for the retrot using both HENmodications and process changes similar to Zhang and Zhu.17

This model was then used to retrot a crude distillation columnwith preheat train. The model developed for solving this casestudy incorporated parameter changes in pump-aroundtemperatures and cut-points only. The results obtainedrequired less additional area with fewer new matches andlower cost. Note that process changes may sometimes givepositive eects, but there may be negative eects on thedownstream processes, which are not accounted for in thismodel.Varbanov and Klemes18 presented a systematic approach

based on network pinch and simple heuristics. It considers twoscenarios, where the direct application of network pinchapproach is not possible; they are retrot initialization andtopology modication. In certain HENs, network pinch cannotbe identied as there is no path despite poor heat recovery.Varbanov and Klemes18 tried to improve the handling ofretrot initialization in cases of no network pinch and alsoprovided a set of topology alterations to enable retrotting.This approach was then implemented on two exampleproblems (three hot and four cold streams, and two hot andnine cold streams). The results suggested addition of new heatexchangers to increase the energy recovery.Nordman and Berntsson19 developed a design method for

HEN retrot problems using pinch technology and modifyingthe grand composite curve (GCC). The original GCC has a fewdrawbacks for retrotting; one of them is that there is no

information about the existing HEN, thus giving no indicationof changes that can be made to the network to reach optimallevels. To resolve these problems, eight dierent curves (fourabove pinch and four below pinch) have been drawn fordierent measures. The four curves above the pinch are hotutility curve (HUC), actual heat load curve (AHLC),theoretical heat load curve (THLC), and extreme heat loadcurve (EHLC). Similarly, four more curves are drawn below thepinch, namely, cold utility curve (CUC), actual cooling loadcurve (ACLC), theoretical cooling load curve (TCLC), andextreme cooling load curve (ECLC). With the help of thesecurves, complexity of changes in heating and cooling can beidentied and evaluated. Nordman and Berntsson19 showedthat the investment cost depends on where the AHLC curve islocated between the THLC and EHLC curves. The matrixmethod was used to design the network, and the obtainedresults were compared to and shown to agree with the generalconclusions that could be drawn from the above new curves(i.e., for a certain energy saving, the total cost is higher whenheaters (coolers) are placed at high (low) temperature).In another study, Nordman and Berntsson20 presented a

graphical method to solve HEN retrot problems; the methodprovides insights into various scenarios (like criss-cross heatexchange, cooling above pinch, and heating below pinch) in theretrot, as well as various retrot alternatives. Nordman andBerntsson20 used advanced composite curves proposed ear-lier.19 In the new study,20 networks which reduce the problemsize (for certain level of heat recovery) are identied andchecked for economic feasibility before the detailed design. Theexternal energy consumption is decreased by improving heatexchange among process streams, avoiding criss-cross heatexchange, and correcting pinch violations (like heat transferacross pinch, cooling above pinch, and heating below pinch).All these issues are covered in the graphical tool presented inNordman and Berntsson.20 The cost functions used in thisgraphical tool are comprehensive including cost of newexchangers, cost of area added and cost of piping, valves, andpumps. So, the graphical tool provides a very good view of thefeasible solutions. However, there are cases that require specialattention such as streams with dierent heat transfercoecients (i.e., appropriate matching of streams based onheat transfer coecients), available pressure drops (i.e., pumpsshould be installed if a stream has insucient pressure),forbidden matches, preferred matches, etc. These cases are nothandled by the graphical tool, and so the user should take careof them. The advanced composite curves17 act more like aqualitative answer than a quantitative one, thus helping toscreen the solutions. The graphical tool was tested on twoapplications: a petrochemical plant and a pulp and paper mill.13

A variety of solutions have been obtained for each of them. Forthe pulp and paper mill application, payback period forrecovering the rst 34 MW is less than 6 months, to recover15 MW the payback period is about one year, and to recover allthe heat (i.e., 18 MW) the payback period turned out to be twoyears, showing a 4-fold dierence in payback periods betweenthe least expensive and the most expensive solutions. Thesevarious solutions with dierent savings and investments providemany options to choose from.Li and Chang21 developed a pinch based retrot method,

which identies the cross-pinch heat exchange and theneliminates, shifts, or reassigns them to above or below thepinch based on general design guidelines. When the cross-pinchheat transfer is eliminated, this heat load is divided and



transferred to various process streams. To minimize thenumber of exchangers, the conventional tick-o method withfew changes is used. The changes in heat duty of the matchabove pinch is to be maximized so as to exhaust heat load onthe hot stream; if this is not possible, then the heat duty shouldequal the heat load of a cold stream. This is also done formatches below the pinch. Li and Chang21 used their newmethod to solve two application problems, one each fromLinnho and Hindmarsh,22 and Tjoe and Linnho.7 Thenetworks were retrotted by eliminating the cross-pinch heatloads at a reasonably low capital cost.2.2. Visualization Techniques. Lakshmanan and Banares-

Alcantara23 discussed relative merits of mathematical program-ming based methods and pinch analysis based methods.Generally, the former methods for solving retrot problemsare black-box type (dened as an approach where therelationship between the inputs and outputs are known but theinternal structure is either unknown or not well understood.)This hinders them from providing a reasonable explanation tothe design choices provided by the program; also, the user hasto decide the number of heat exchangers to be used in thenetwork prior to the optimization, which may not be alwaysobvious, and no general guidelines are present. On the otherhand, pinch analysis based methods applied to grassrootproblems might not be applicable to HEN retrot problems.There is no theoretical foundation for the use of minimumapproach temperature for retrot. Also, pinch targeting is basedon area eciency assumptions (where area eciency is taken tobe constant after retrot, which need not be the case always),and so it may lead to suboptimal solutions.Also, Lakshmanan and BanaresAlcantara23 proposed a

visualization tool, namely, retrot thermodynamic diagram(RTD), which is a modication of the conventional griddiagram24 to provide a concise graphical description of both theloads and the driving forces in the existing HEN. This toolhelps to consider various possible retrot scenarios and tochoose the optimal one. Once RTD is developed, guidelineshave been provided to get to the retrot solution by inspection.These guidelines include load shifting, stream splitting, andexchanger relocation, thus combining the engineering intuitionwith heuristics. The RTD was used to solve two case studies,one each from Tjoe and Linnho,7 and Yee and Grossmann.25

It provided good retrot solutions within 10 min (compared to13 h25). It is claimed that the RTD will gain greater industrialacceptance than the black-box approach.23

Lakshmanan and Banares-Alcantara26 continued their pre-vious work23 and developed a prototype software program forrapid drawing and modication of the RTD. This also providesoptions for ne-tuning designs based on continuousoptimization (of areas) via a spreadsheet interface. The RTDwas then used to obtain 86% more energy recovery for the casestudy in Tjoe and Linnho.7 Note that the repiping expenseswere not considered in the objective function, and so thesuperiority of the solution depends on these costs. Using RTDfor the example problem from Briones and Kokossis,27 $6000(4.3%) reduction in capital cost was obtained by eliminating thecriss-cross heat transfer. However, for the case study fromAsante and Zhu,28 the additional area required in Lakshmananand Banares-Alcantara26 is higher by nearly 40%, but theretrot solution has no stream splits (compared to one in thesolution of Asante and Zhu28). For the application problemfrom Ciric and Floudas,29 the study of Lakshmanan andBanares-Alcantara26 provides the same energy savings as themixed integer nonlinear programming (MINLP) solution but at30% less investment cost and also a less complex solution.The Grid diagram table (GDT) was introduced by Abbood

et al.30 as an alternative tool to determine pinch points andutility targets. It is a single diagram which combines bothnumerical and visualization advantages (Figure 2). The existingHEN can be shown on the GDT, which enhances thevisualization of pinch rule violations. This was illustrated toimprove the heat recovery in a palm oil renery having four hotstreams and three cold streams.2.3. Applications. Bengtsson et al.31 used tools based on

pinch technology to study the eects of pre-evaporation ofchemothermomechanical pulp euent and heat pumping inan integrated pulp and paper mill. The new tool employsadvanced pinch curves and the matrix method. The advancedcurves present the heat load information at the actualtemperature instead of the shifted one and also provideinformation about the conguration of the existing HEN. Thematrix method tries to nd the cost optimal solution taking intoaccount parameters such as distance between streams, type ofheat exchangers, heat transfer coecients, pressure drop, andfouling. The HEN in the Skoghall Mill (with capacity of550,000 tons of board per year) was studied by Bengtsson etal.,31 to evaluate the tool. An investment cost of $500,000 isrequired for the process changes which yield 4.5 MW of heatabove 120 C. This heat is used for both pre-evaporation ofeuents and heat pumping to save fresh steam. The payback

Figure 2. Grid diagram table of two hot and two cold stream problems, adapted from Abbood et al.30 Copyright 2012 Elsevier.



period is 1.57 and 1.44 years in the case of thermal andmechanical vapor recompression, respectively. Finally, it wasclaimed that the proposed tool is more advantageous in thecase of complex problems.31

Matijaseviae and Otmaeiae32 used pinch technology methodsto retrot a nitric acid production plant in a petrochemical site.The process under retrot has 17 heat exchangers, 2 turbines(steam and gas), and 2 compressors. In this case study, Tmin ischanged from 38 to 10 C, to increase heat recovery and thusdecrease the utilities. The retrotted network required one lessheat exchanger and redesigning of three existing exchangers.This increased energy savings, and the HEN retrot solutionhas a payback time of 14.5 months.It can be observed from the above review that many pinch

analysis based methods try to eliminate the cross-pinch heattransfer to retrot the HEN and that the GCC needs to beimproved for a better usage (including structure of existingHEN). Also, visualization tools are used to aid in the HENretrot. Methods developed by Bengtsson et al.31 and Nordmanand Berntsson20 are promising, as they are able to deal with acomplex industrial problem (18 hot and 19 cold streams) withrelative ease. As will be seen in section 7, the optimal solutionobtained can involve dierent numbers of reassignments ormodications in the existing HEN.

3. MATHEMATICAL PROGRAMMING BASEDMETHODS

In this section, mathematical programming based HENretrotting methods are briey described in chronologicalorder. It is divided into two subsections based on theoptimization methods: retrotting using deterministic methods(such as nonlinear programming (NLP) and MINLP) orstochastic methods (such as genetic algorithm (GA) andsimulated annealing (SA)), employed in the study. Many suchstudies use superstructure (Figure 3), which encompasses allpotential exchangers and all retrot designs possible. Fromthese designs, the optimization method searches for the bestnetwork satisfying the given constraints.

3.1. Retrotting Using Deterministic Methods. Ciricand Floudas29 proposed a two-stage, ve-step strategy for theredesign of the existing HENs. The objective function in thisstudy is to minimize investment cost (of new heat exchangers,additional area, and piping cost) for a xed heat recovery. Thelevel of heat recovery is selected in a way to reduce the amountof utilities required by the network. In the rst step of the ve-step strategy, a heat recovery approach temperature (HRAT) isselected either randomly or by using a targeting procedure. Inthe second step, utility cost is minimized which helps inlocating the pinch points. In the third step, all potential matchesof exchangers are considered. A retrot model including thedecisions about reassigning heat exchangers, purchasing newexchangers, and repiping is setup. The solution of this modelgives the minimum modication cost. In the fourth step, asuperstructure is generated containing all the alternativenetwork structures, and each network is solved as an NLPproblem to minimize investment cost for the specied heatrecovery. The exchanger minimum approach temperature isrelaxed for each match, and the temperature approach is treatedas a variable greater than a specied lower bound. In the laststep, the total prot is calculated, and this loop is repeated untilthe stopping criterion is reached. The rst three steps of thisstrategy form the rst stage, a mixed integer linearprogramming (MILP) stage. The fourth and fth steps formthe second stage. The rst stage provides the information aboutthe structural aspects (reassignment and addition of area); thesecond stage uses this to formulate an NLP problem and solveseach feasible structure to minimize modication cost. Thismethod was tested on the example problems from Yee andGrossmann33 and Tjoe and Linnho.7 The resulting HENshave higher prots and lower additional area requirements.In another study, Ciric and Floudas34 proposed an MINLP

model, which incorporates all possible network congurationsincluding the reassignment of heat exchangers and area additionto existing exchangers into a single formulation to solve andsimultaneously optimize the network structure of the retrotproblem. The formulation can also be expanded to incorporate

Figure 3. Superstructure for one hot and two cold streams, adapted from Yee and Grossmann.25 Copyright 1991 American Chemical Society.



piping costs, heat exchanger rating equations, dierent type ofheat exchangers, variable heat transfer coecients, and pressuredrop considerations. The MINLP model was solved byapplying the generalized Bender decomposition algorithm.35

The objective function consists of modication costs forreassignment, new exchangers ,and repiping. Ciric andFloudas34 used a simultaneous approach for solving retrotproblems instead of the sequential approach in their earlierstudy.29 The simultaneous approach was tested on exampleproblems from Yee and Grossmann33 and Tjoe and Linnho.7

The results obtained show signicant energy savings with apayback period of around 1.5 years.Yee and Grossmann25 presented a systematic procedure

involving prescreening and optimization stages, for HENretrot. The prescreening stage is used to determine theeconomic feasibility of the retrot. Lower bounds for totalannual cost (of utilities, additional area, and repiping) areestimated for various levels of energy recovery (HRAT). Thesebounds are compared with the existing costs to evaluatepotential savings. For a xed payback period (if specied),feasible solutions can be selected from a plot of total annualcost versus HRAT. Note that the HRAT value is not xed inthe prescreening stage but is optimized in the optimizationstage. If the prescreening stage shows signs of desirability, thenthe structural modication information is passed to theoptimization stage. This information is used to formulate asuperstructure, which in turn is optimized using an MINLPmodel to minimize the total annual cost. In the MINLP model,heat loads, minimum approach temperature, and streammatching are optimized to account for the trade-o betweencapital and energy costs. Due to the presence of bilinear termsin energy balance and exchanger design equations, the MINLPmight not converge to the global optimal solution. So,simplications were suggested to decrease the complexitysuch as arithmetic mean temperature dierence (AMTD)instead of log-mean temperature dierence (LMTD). Themethod was then applied to dierent examples and was shownto give optimal retrot designs which may not bestraightforward to identify.25

Abbas et al.36 used a set of heuristics to develop a novelapproach to solve the retrot problem using constraint logicprogramming (CLP). These heuristics were derived from theinteractive retrot method described in Lakshmanan andBanares-Alcantara.23 The following steps were consideredwhile developing heuristics: load shifting which transfersheat load from utilities to process exchangers by adding anothershell to the existing unit, criss-cross, and addition of a newexchanger where a new match could create a load path betweenutilities. The CLP implementation performs load shiftingboth before and after each modication, and it also includesstream splitting. This algorithm has a few assumptions such asisothermal mixing of split streams and a priori xed stream splitratios. The method was tested on the example from Ciric andFloudas,29 and it found a solution that had total cost 70% lessthan that of the MINLP approach.29

Briones and Kokossis37 proposed a design procedure,consisting of screening and optimization stages, for solvingHEN retrot problems. The screening stage is divided into twosub stages, namely, auditing and unit development stages, for aparticular energy recovery level. The auditing stage is carriedout with a heat exchanger auditing target (HEAT) model. Thisis a conceptual MILP model that uses integer variables forstructural changes and continuous variables for heat loads and

area calculations. The design objective of this model is exiblefor a variety of retrot priorities such as minimum heat transferarea and zero investment projects (emphasis on low investmentcost). The unit development stage uses targets for area andmodications of an existing network model, an MILP model, todecide on purchase of new units, area addition, andmodications to the existing units. The results from thesemodels are used in the optimization stage, to develop retrothypertargets and retrotted network. Retrot hypertargets aresimilar to the targets provided by energy-area or investment-savings plot provided by conventional methods, but instead ofcurves, they employ solution streams similar to the method ofhypertargets in grassroot designs which does not assume areaeciency and also includes process constraints. The hyper-targets can embed capital and operating costs as well as costsfor repiping, pumping, instrumentation, and auxiliary equip-ment. The two-stage design procedure was tested on fourproblems,13,29,38,39 and it was found to reduce the area(needed) and also the cost involved compared to the solutionsgiven by the previous methods.Ma et al.40 proposed a two-step approach for solving HEN

retrot problems. In the rst step, a constant approachtemperature (CAT) model is used to optimize the structureof the HEN. The main advantage of CAT over other models isthat the area calculations are linearized by xing T as aconstant for all heat exchangers, and so it can be easily solved asan MILP problem. Thus, the solution is obtained in a smallercomputational time, and also the possibility of solution beingtrapped in the local optimum is avoided. CAT adopts the stage-wise superstructure from Yee and Grossmann.25 The exchangerareas are not explicitly considered in this model, whichtherefore requires further optimization for the network. TheCAT model, due to linearization of area calculations, does notalways give feasible solutions, but it gives a good networkstructure and drives the solution close to the global optimum.Taking this network structure as the initial guess, the secondstep implements an MINLP model, which includes additionalvariables for exchanger areas. This model explicitly accounts fornetwork modications, energy consumption and heat transferareas simultaneously. Introduction of nonlinear terms into themodel makes it dicult to nd the global solution. This isovercome by providing a good initial guess based on CATmodel. To demonstrate the capability, the two-step approachwas used to solve problems from earlier studies.29,33,34,37 Goodresults (like better annualized cost for the same amount ofutilities and better utility cost for same investment cost) wereobtained in less computational time.Sorsak and Kravanja41 developed a simultaneous MINLP

model for solving HEN retrot problems, comprising dierentexchanger types. It is an extension of the model developed forHEN synthesis.42 The superstructure comprises dierentoptions for heat exchangers such as double pipe heatexchangers, shell and tube heat exchangers, plate and frameheat exchangers, and by-passes. For retrotting, the super-structure is updated with details of heat transfer area, type andposition of heat exchanger in the existing network. One of thenotable dierences of the new superstructure compared to theoriginal superstructure43 is the inclusion of an option for theexchanger type. So, within the same network, more than onetype of heat exchanger can be used. This method was applied tothree example problems and compared with the case of using asingle type (double pipe exchanger) model for HEN retrot.Though the latter (single type model) was simpler and



computationally less exhaustive, it produced suboptimalsolutions in a few cases. Thus, the proposed methodology41

(dierent exchanger types) was advantageous for the exampleproblems tested.Ponce-Ortega et al.44 proposed an MINLP model for solving

HEN retrot problems which considers HEN structure andprocess modications simultaneously. Most of the studies priorto this paper assumed that the process conditions for an HENretrot problem are xed and did not consider any adjustmentsto the operating conditions which may provide more cost-eective heat integration. In addition, this model includesconstant temperature streams which may appear in the processas suggested by Ponce-Ortega et al.45 The formulation of thismodel uses the superstructure model proposed by Yee andGrossmann25 along with modications to explicitly includepiping layout, which gives the option for repiping to dierentheat exchangers to maximize use of existing area. This methodwas tested on example problems from Duran and Grossmann,46

Yee and Grossmann,25 and two simple problems. As expected,the results obtained for simultaneous retrot of HEN andprocess were better than those obtained for retrot with noprocess changes.Nguyen et al.47 proposed a one-step rigorous MILP model,

based on the formulation developed by Barbaro andBagajewicz,48 to solve HEN retrot problems. In this method,the temperature span of each stream is divided into severalsmall temperature intervals, which are considered for heatexchange between hot and cold streams. The model then uses aone-step strategy to optimize the network structure and heattransfer areas simultaneously. Two scenarios were solved inNguyen et al.:47 one disallows the relocation of exchangers andanother allows such relocation. This method was tested on anexample problem from Ciric and Floudas49 and the preheattrain of a crude distillation unit (having 18 streams and 18exchangers). It was able to nd a near optimal solution inreasonable time (2 h), but to get to the optimal solution it takesa very long time (34 h). A step by step strategy was proposed toreduce the computational time. It was also observed that themodel can result in suboptimal solutions due to prematuretermination of the algorithm (once an acceptable gap betweensolutions is obtained). These suboptimal solutions are simplerthan the optimal solution and allow the user to choose the bestamong them based on other factors such as implementationissues, benet, and marginal return of investment. The step bystep strategy can be made completely automatic by using binarydecision variables and has the option for user interface, wherethe user can enforce constraints and force the solution toexclude certain matches.3.2. Retrotting Using Stochastic Methods. Continuing

their previous work on HEN grassroot problems,50 Athier etal.51 proposed a new automatic approach for the retrot designof HEN; it is a two-level procedure. In the upper level (masterproblem), structural optimization of the network is carried outby SA; i.e., an HEN topology is generated and iterativelymodied by SA under the feasibility constraints. The upperlevel also calculates the investment cost due to new heatexchangers, reassignment of existing exchangers, and repiping.In the lower level (slave problem), the topological informationfrom the upper level is used, and an NLP tool is used tooptimize required area (= total of additional area in existingexchangers and area in new heat exchangers). This method wastested on two examples: one is an existing network integratingone cold and six hot process streams,34 and another involves

integration of two cold and two hot process streams.25 Theresults obtained by this method show 4% higher prot thancongurations obtained by Ciric and Floudas34 and Yee andGrossmann.25

Bochenek and Jezowski52 proposed a new method to solveHEN retrot problems; it uses GA instead of deterministicsolvers. Sorsak and Kravanja41 noted that existing mathematicalsolvers are not able to cope with the combinatorial complexitiesinvolved in HEN retrot problems. In the proposed method,instead of the classical superstructure, the structural optimiza-tion problem is formulated as a single multivariable problem forGA optimization using a structural matrix, which encapsulatesall the topological features of an HEN. This method is dividedinto two levels. The rst level is for structural optimization,where the topology of heat exchangers and location of splittersare optimized using GA. In the second level, the structuregenerated in the rst level is used to nd the split ratio and heatexchanger areas. The developed method was tested onproblems from Yee and Grossmann33 and Ciric and Floudas.34

It was able to nd a better solution (in terms of investmentcost) in both cases despite using standard heat exchangers.The method proposed by Bochenek and Jezowski52 required

high computational times (10 h) even for small networks. Itwas also seen that GA was not quite eective in dealing withcontinuous variables. To overcome these problems, GAcoupled with NLP and integer linear programming (ILP)methods was introduced by Rezaei and Shaei.53 The NLPformulation used in this method is similar to that for maximumenergy recovery for HEN synthesis used in Lewin54 and Lewinet al.55 In the method of Rezaei and Shaei,53 the GA choosesstructural modications to the HEN using node representationfor exchanger locations. The NLP is used to optimize thecontinuous variables (such as heat loads, temperature, splitratios) for maximum energy recovery. After this step, the ILPproblem is formulated and solved to minimize investment cost.The NLP problem is replaced by a search loop to ndminimum approach temperature and split ratios, thusconverting it to a linear programming (LP) problem. Thismethod was tested on three example problems taken fromShenoy,9 Ciric and Floudas,34 Briones and Kokossis.37 Forthese problems, it gave better results in utility savings comparedto the previous methods.Zhang and Rangaiah56 employed a one-step approach for

solving HEN retrot problems using integrated dierentialevolution (IDE) along with HEN structural representation viamatrices from Bochenek and others.57,58 This structuralrepresentation has both discrete and continuous variables tobe optimized. In previous works, these variables were handledin two steps; in Zhang and Rangaiah,56 both discrete andcontinuous variables are handled by IDE in one-step. The IDEalgorithm developed by Zhang et al.59 has been modied andimplemented to solve the HEN retrot problems. After theoptimal solution using IDE is found, it is then fed to a localoptimizer to obtain a more rened solution by optimizingcontinuous variables. The one-step approach was tested on casestudies from earlier studies,10,37,40,53 and the results obtainedshow a lower total annual cost (utility cost + annualizedinvestment cost) than the results reported in the previouspapers.10,37,40,53

From the review of mathematical programming basedmethods, it is observed that simultaneous (one-step) methodsprovide the optimal solution but require a high amount ofcomputational times. If suboptimal solutions are acceptable,



then it is suggested to use sequential (two-step) methods asthey provide improved solutions in less computational time.

4. HYBRID METHODSBriones and Kokossis,27 Asante and Zhu,28 and Smith et al.10

used both pinch analysis and mathematical programmingmethods for solving the HEN retrot problem. Pinch analysisis used to conceptualize the decomposition and to separatedierent design tasks. The conventional pinch analysis has afew limitations such as assumptions on area eciency anddiculties in handling design constraints. Area eciency isdened as the ratio between the target surface area to meet theexisting energy requirement and the actual surface area beingused. The assumption often made is that the area eciency ofthe existing network and that of the retrot network are thesame. These limitations lead to the use of mathematicalprogramming tools along with pinch analysis to search theoptions eectively.The integration of pinch analysis and mathematical

programming methods was achieved in three design stages inBriones and Kokossis,27 wherein several promising solutions aregenerated for dierent levels of energy recovery. In the rststage, solutions are screened by considering area targeting andminimizing modications simultaneously. This means classify-ing the existent and nonexistent matches and nding their areassimultaneously. In the second stage, the topology from theprevious stage is used to set up an MILP model to optimizemodications to the existing network and heat transfer areassimultaneously. Briones and Kokossis27 used area targeting,which helped in improving the area predictions over theprevious study.29 In the third stage, the network structureobtained from the second stage is used to formulate and solvean NLP model. Note that all promising networks are optimizedin the three stages. Briones and Kokossis27 applied the newapproach to an example problem from the pulp and paperindustry13 and provided three dierent designs each havingcertain advantages. The rst design featured low energy savingsbut had less investment involved, the second design had highenergy savings but required large investment, and the thirddesign is in between the two designs. Thus, the approach ofBriones and Kokossis27 provides several solutions for theengineer to choose from based on his/her expertise. Althoughthis procedure is fully automated, it can accommodate designerinteractions at various stages of decision making.Asante and Zhu28 proposed a two-stage procedure for

solving HEN retrot problems and continued their work alongsimilar lines.16 They too used both pinch and mathematicalprogramming techniques to develop an eective method. Theprocedure aims to minimize the number of modications madeto the existing HEN topology and to achieve a desired heatrecovery target. A term network pinch was introduced todene the recovery limit of a particular HEN topology withinthe given process. The major dierence between network pinchand process pinch is that the former is a property of bothprocess streams and HEN topology, whereas the process pinchis dependent on process streams alone. So, process pinch of anHEN cannot be changed (unless the streams are changed),whereas the network pinch can be changed by modications tothe HEN topology such as relocation of exchangers,introduction of new heat exchangers, and creating stream splits.In the rst (diagnosis) stage of the procedure of Asante and

Zhu,16 which is also covered in their other papers,28,60 a singletopology change is identied by network pinch rules so as to

overcome the network pinch. With the modied topology fromthe diagnosis stage, in the second (optimization) stage,exchanger areas are varied to obtain an optimal solution.Though this selection may provide a nonoptimal solutioncompared to simultaneous methods (where all topologychanges are optimized in one step), this procedure providesmuch welcomed user interaction. Asante and Zhu16 used thetwo-step procedure to debottleneck the crude oil unit39 to copewith a % increase in the throughput. The retrot designobtained by them, compared to that reported by Ahmad andPetela,39 involves fewer modications and smaller additionalarea (1265 m2 versus 1990 m2). This problem is furtherdiscussed in Table 4 of section 7.Smith et al.10 presented a methodology to solve HEN retrot

problems by modifying the network pinch concept.28 It canhandle temperature-dependent thermal properties of streams.The modied network pinch approach combines the diagnosisstage and the cost optimization stage into one to avoid missingpotentially cost-eective designs in the diagnosis stage. Theformulated NLP problem is then solved by employing SA alongwith a feasibility solver. This methodology was used to solve acrude preheat train problem (nine hot and three cold streams)with varying heat capacities; however, heat capacities areassumed to be constant in a temperature interval. The resultsshowed around 23% reduction in energy consumption with theaddition of one new heat exchanger. The methodology in Smithet al.10 looks promising for HEN retrot problems involvingstreams with varying heat capacities.

5. PRESSURE DROP CONSIDERATIONSMany retrot studies do not consider pressure drops in theHEN, which may mislead targeting, give incorrect capital-energy trade , and result in suboptimal solutions. It is alsoassumed that the addition of area to the existing heatexchangers does not aect the heat transfer coecient of theexchanger, and that the heat transfer coecient of the newexchanger is similar to that of the existing exchangers, whichmay not be valid. The dierence in the heat transfer coecientsof retrotted and new exchangers should not be neglected asthis may lead to suboptimal solutions.Polley et al.61 were the rst to consider pressure drops and

lm coecients in the retrot procedure. Silva and Zemp62

combined the pressure drop approach of Polley et al.61 and thearea matrix method63 into a method which solves for dierentheat transfer coecients for existing and new exchangers underpressure drop constraints. The combined method is targeted toachieve the minimum utilities under constraints. It was testedon a two hot and three cold streams example to decrease theenergy requirement, and it predicted the nal area (includingpressure constraints) within 7%, ahead of the design stage(during targeting including pressure constraints).Panjeshahi and Tahouni64 studied dierent bottlenecks

present in the existing HENs and tried to debottleneck themby considering optimal pressure drops. As the turbulence of thestream increases, both stream pressure drop and lm heattransfer coecient increase; the latter results in higher heattransfer and consequently requires smaller area. In the case oflarger pressure drops, new pumps/compressors may need to beinstalled. So, there is a trade-o between the capital cost of heatexchangers and the additional power and possibly capital costassociated with compressors/pumps. A targeting algorithm fordebottlenecking was proposed by Panjeshahi and Tahouni,64

and it was tested on a crude preheat train case study. The



throughput of the HEN was increased by 20%, and theresulting scenarios were debottlenecked. The results suggestedthe replacement of the existing pumps to improve heat transferas the most cost-eective way.Nie and Zhu65 successfully developed a method to solve

HEN retrot problems including pressure drop constraints,which were not considered in most design methods developedearlier. The major reason for not considering pressure drop inmost of the design methods is the use of the exchanger unit asthe basis for retrot, and not the eects of shell conguration ordistribution of area in the shell within one unit. For example,introduction of tube inserts, baes, and other enhancementtechniques improves the heat transfer area. This also increasesthe pressure drop in the exchanger, which was not an issue inthe previous studies since the exchanger conguration is notchanged except for the addition of new area, thus not changingthe pressure drop by a signicant amount. Nie and Zhu65

showed that change in the shell conguration has a signicantimpact on the pressure drops and lm coecients. If thepressure drop constraints are not met, expensive pumps orcompressors are required to meet the additional pressure drop.This will decrease the prot obtained by the modications ofthe HEN topology.To integrate pressure drop constraints into the model, a

decomposition strategy was proposed by Nie and Zhu.65 Thisstrategy has two stages. In the rst stage, a unit based model isused to deduce which units require additional area and whichunits do not. These two groups (based on area requirement)are used to formulate a combined model in the second stage,where shell and unit based models are utilized for dierentgroups. The shell based model is used to optimize the unitswhich require additional area. It calculates the additional areaand also pressure drops. The shell based model considers theshell arrangements in the units which require additional area.The additional area can be placed in a single new shell or couldbe installed in series or parallel. All these arrangements areembedded in the superstructure in the shell based model. Theunit based model is used for the units which do not needadditional area. The two groups of units interact amongthemselves during the combined optimization, and thus bothgroups are continuously updated. This is carried out untilconvergence among the groups. Nie and Zhu65 also exploredthe potential of heat transfer enhancement techniques to meetthe additional area requirement. The correlation for pressuredrop caused by the enhancement techniques was adopted fromPolley et al.66 Both the conventional method and the methoddiscussed in Nie and Zhu65 were used to retrot the preheattrain of a crude unit. The results show an investment of $1million for the new unit and enhancements compared to $1.64million for the plain tube design for the same energy recoveryin the HEN.Soltani and Shaei67 proposed a method, coupling GA with

LP and ILP, to address the HEN revamp considering pressuredrop costs. This method consists of three (GA, LP, and ILP)sections. The GA section provides networks for LP and ILPsections and then analyzes the tness of the population. In theLP section, each network is evaluated and the pressure dropcosts are calculated. This section nds the best minimumapproach temperature and split ratios within the network. Inthe ILP section, modication cost is minimized. For a givenmatch in the network, the ILP determines if a new exchangershould be purchased or an existing exchanger should bereassigned. It is also used to calculate the prot from HEN

during the structure optimization. Soltani and Shaei67 appliedtheir method to example problems from Shenoy,9 Silva andZemp,62 and Panjeshahi and Tahouni.64 The results show thatthe method proposed gives increased savings in utilitiescompared to the methods in the previous studies.Pressure drop considerations, if included in HEN retrotting,

will provide realistic solutions acceptable in industry. These aremore signicant when heat transfer enhancements are used forHEN retrotting. Increased pressure drop may requireretrotting existing pumps, and so the appropriate cost forthis will have to be included along with costs of area,enhancements, reassignments, and piping.

6. HEAT TRANSFER ENHANCEMENTSHEN retrotting using heat transfer enhancements is gainingpopularity. Gough et al.68 described hiTRAN technologies,which are used in a number of industrial projects. Also, theynoted that the intensied heat transfer technologies forenhanced heat recovery (INTHEAT) consortium is doingsubstantial research with many public and private collaboratorsto improve the enhancement technologies. This section reviewsHEN retrotting techniques, which specically consider heattransfer enhancements. For a detailed description of enhance-ment techniques in HENs, readers are referred to Smith et al.69

Zhu et al.70 studied the implementation of heat transferenhancements for HEN retrotting. First, the retrottingproblem is solved using the network pinch method, and thestructural changes to the network are identied; then, variousoptions of enhancements are tested. This involves identifyingthe controlling side (shell or tube side) for heat transfer andscope of enhancement and determining and analyzing theimpact of enhancements on the network. Enhancement choiceswith lower pressure drop index (PDI) meaning less pressurepenalty are selected. Cost factor is also taken into considerationwhile choosing the enhancement option. This approach wasthen applied to a crude oil distillation unit,71 where crude oilthroughput needs to be increased; it decreased the amount ofadditional area required by 16% from 2122.2 to 1782.6 m2.HEN retrotting using heat transfer intensication techni-

ques was studied in four papers by Pan et al.7275 Heat transfercoecients of heat exchangers can either be increased byimplementing these techniques or decreased by using streambypasses. In Pan et al.,72 an MINLP model was formulated forHEN retrotting via heat transfer intensication, and then anMILP method was employed to solve this MINLP model toreduce computational diculties. This method was tested on anexample problem in Li and Chang,21 and was shown to nd thebetter solutions (in terms of utilities) for HEN without majortopology modications. In another paper,73 Pan et al. proposedMILP optimization, which considers the option of tube-sideheat transfer enhancement. They showed that the computa-tional diculties faced due to nonlinear terms such as LMTDand LMTD correction factor (FT) were eciently handled inthis approach. This method was also tested on the problem inLi and Chang.21 The solutions obtained had very few topologymodications.Pan et al.74 studied HEN retrotting via intensied heat

transfer technique with a simple MILP model, and two iterationloops were proposed for obtaining the solution. The rstiteration loop is solved repeatedly to get optimal solutions forHEN retrot with either certain energy savings or retrot protas objective. The second loop then seeks to nd the maximumof retrot prot or energy savings, respectively. The algorithm



was tested on case studies from Li and Chang21 and Wang etal.76 From the studies, it was found that the new approach isable to achieve considerable energy savings with much lowercapital investment. As the MINLP problem is converted to asequential iterative MILP problem, the computational eciency(e.g., 40 s for an 11 hot and 3 cold stream problem) has beensignicantly improved. Pan et al.75 considered fouling eect inHEN retrotting, which provides realistic solutions, and alsotube inserts to improve the heat transfer coecient ofexchangers. An MILP model was developed with theseconsiderations and applied to an example problem having 11hot and 3 cold streams. The results obtained showed betterenergy savings and longer operating times compared to theoriginal HEN.Recently, Wang et al.77 developed a design approach for

HEN retrot based on heat transfer enhancement and areaaddition. It uses SA to nd the appropriate heat exchangerswhich are to be enhanced. Heat transfer enhancement can beused as a good alternative in cases where addition of extra areato a heat exchanger is not feasible because of topology, safetyand downtime constraints. To assess the eectiveness of heattransfer enhancements, ve dierent retrot scenarios werecompared. They are retrot with only enhancement, retrotwith only additional area, retrot with both enhancement andadditional area, retrot with only topology modications andretrot with both topology modications and enhancement.The design approach was applied to an existing preheat trainfor a crude distillation column,76 and the results show that, forcertain energy savings, the retrot strategies using enhancementtechniques had less investment costs than those without them.Recent studies show that heat transfer enhancements provide

a promising solution for HEN retrotting. These are of interestas they do not involve structural modications thus simplifyingthe retrot problem formulation. The downside is that theyinvolve additional equations to satisfy the increased pressuredrops in the system, which may require installation of pumps orretrotting the existing pumps. Hence, the investment termshould now include the cost of the pump(s) as well. On top ofthat, heat transfer enhancements can also be partial, thusbringing in another decision variable into optimization.

7. APPLICATION PROBLEMS

In the papers reviewed above, there are about 30 exampleproblems on HEN retrotting, but many of them have beenused in one, two, or three studies only. There are only ve

problems which have been used in four or more studies onHEN retrotting. They are, in chronological order of the rststudy: crude oil preheat train problem,78 two exampleproblems from Yee and Grossmann,79 crude preheat trainproblem,80 and pulp and paper industry problem.13 Theseapplication problems and their reported solutions are discussedin this section. The stream data for the ve applicationproblems are provided in the Supporting Information.Saboo et al.78 proposed a retrot solution, without stream

splits, for the crude oil preheat train of an oil renery unit. It isa medium scale problem with six hot and one cold streams. Theobjective is to decrease additional area (i.e., investment) forimproved energy recovery (i.e., using hot utility of 9500 kWand cold utility of 565 kW). From the hypertargetsdeveloped,37 it was found that the network could be improvedby simply relocating existing units. Briones and Kokossis37

solved the same problem with a slightly dierent objective ofminimizing total cost of modications and additional area, forthe same level of energy recovery. The solution obtainedinvolves higher additional area but has no reassignments. Theeect of reassignments can be seen when one compares thesolutions of Briones and Kokossis37 and Ma et al.40 summarizedin Table 1. Both these papers solved for the same amount ofutilities; the solution of Ma et al.40 involves ve reassignmentsand requires 18% less additional area less than that in Brionesand Kokossis.37

Rezaei and Shaei53 achieved a better solution in terms ofboth capital cost and the amount of utilities, but it involvedreassignment of all heat exchangers. Recently, Zhang andRangaiah56 obtained a solution dierent from that in Rezaeiand Shaei53 for the same objective; it has 5% lower totalannual cost and involved a dierent trade-o between capitaland the utility costs, which emphasizes the necessity of ndingmultiple retrot solutions to choose from based on engineersrequirements. In summary, the crude oil preheat trainproblem78 was solved by both pinch analysis and mathematicalprogramming based methods; some studies found the retrotsolution based on total annual cost,40,53,56 and few provided asolution based on minimizing the number of modications.37 Itcan be seen from Table 1 that all ve studies solved for similarlevel of utilities, but the obtained optimal solution varied in theamount of additional area and the required number ofmodications to the existing network.The rst of the two examples studied by Yee and

Grossmann79 is on retrotting an HEN to eliminate hot utility.

Table 1. Reported Retrot Solutions for the Crude Oil Preheat Train Problem with Six Hot and One Cold Streams78

reported results

reference (with basis ofthe method in brackets) total capital cost

total utilitycost remarks

Saboo et al.78

(pinch analysis)b$566,100a

(additional area1883 m2)

$572,825 objective is to minimize additional area for an improvement in energy recovery (with hot utility of 9500 kWand cold utility of 565 kW). Four reassignments are involved in the optimal solution.

Briones and Kokossis37

(mathematical)b$591,600a

(additional area1972 m2)

$571,005 objective is to minimize total cost of modications and additional area for similar energy recovery (hotutility 9472 kW and cold utility 537 kW). No reassignments involved in the optimal solution.

Ma et al.40

(mathematical)b$487,659 (additionalarea 1612.13 m2)

$571,005 Objective is to minimize total annual cost (= investment cost + utility cost) for same energy recovery asBriones and Kokossis.37 Five reassignments are involved in the optimal solution.

Rezaei and Shaei53


$556,625 All heat exchangers were reassigned.

Zhang and Rangaiah56


$574,400 Objective is to minimize total annual cost (= annualized investment + utility cost). All but two heatexchangers were reassigned.

aThis value, not available in the cited reference, was calculated using the data in the paper. bReassignment costs used in ref 40 are dierent from thecosts used in refs 53 and 56.



It involves three hot and three cold streams, and the initialnetwork required hot utility of 360 kW and cold utility of 800kW. Yee and Grossmann79 provided two solutions withdierent additional areas and amount of repiping; the solutionwith more repiping requires less additional area (Table 2). Ciricand Floudas29 proposed a solution with a lower additional area,but it involved a higher amount of repiping. Thus, retrot ofthis problem requires a trade-o between repiping cost and costof additional area. Ciric and Floudas34 used a single stepapproach in place of a two-step approach used in their earlierstudy29 and obtained a solution with much less additional areacompared to the two-step approach. As the investment costsinvolved in the two-step approach are not provided, it isdicult to compare the costs involved for repiping. However,comparing the additional areas, it can be said that the singlestep approach performed better (Table 2). Briones andKokossis37 solved the example problem to minimize thenumber of modications involved to achieve the amount ofutilities targeted. The solution obtained involved only twomodications to the system. Ma et al.40 provided a solutionwith less additional area and investment cost, but it involvedfour reassignments. The change in investment cost with the

number of modications involved (in various studies) can beseen from Table 2. It shows a trade-o between the number ofmodications and the amount of area added. This indicates theneed to include cost of topology modications in the objectivefunction and also the need for multiobjective optimization(MOO).The second example from Yee and Grossmann79 is to

minimize the total cost (for retrot) for a xed minimumapproach temperature dierence (Tmin). This is a small scaleproblem featuring two hot and two cold streams along withutilities (existing utility cost $158,000/year). Both Yee andGrossmann,79 and Ciric and Floudas34 solved the problem forthe same Tmin (10 K). The latter study included the costs forreassignment of heat exchangers and yet found a better solutionrequiring lower additional area and investment (Table 3);although it had higher piping cost, it was oset by a decrease inthe additional area. Subsequently, Yee and Grossmann,25 Athieret al.,51 Bochenek and Jezowski52 solved the problem for Tmin= 5 K. As can be seen in Table 3, solutions obtained in thesestudies show the trade-o between utility and investment costs.Ma et al.40 solved the retrot problem with a constraint onTmin to be more than 1 K; however, the nal network had a

Table 2. Reported Retrot Solutions for the Example Problem (with Three Hot and Three Cold Streams) from Yee andGrossmann79

results

reference (with basis of themethod in brackets) additional area

investmentcost ($)a remarks

Yee and Grossmann79

(mathematical)88.54 m2, 118.7 m2

(dierent piping)Two solutions (requiring cold utility of 440 kW and no hot utility) are reported. Bothinvolve six units but dierent reassignments and area additions.

Ciric and Floudas29

(mathematical)50.9 m2 Optimal solution for minimizing additional area to eliminate hot utility has seven units

(including heaters and coolers). Two-step approach was used.Ciric and Floudas34

(mathematical)27.53 m2 10800 Single step instead of two-step approach as in Ciric and Floudas29 was used. The solution

involved ve reassignments.Briones and Kokossis37

(mathematical)59.1 m2 10930 Minimize number of modications to achieve specied utilities target. Optimal solution has

only two reassignments.Ma et al.40 (mathematical) 23.05 m2 9732 Four reassignments were present in the nal solutionRezaei and Shaei53

(mathematical)not provided 11235 The retrotted HEN has six reassignments.

aUtility cost in all studies included in this table is $8,800/year.

Table 3. Reported Retrot Solutions for the Example Problem (with Two Hot and Two Cold Streams) from Yee andGrossmann79

results

reference (with basisof the method in

brackets) additional area utility cost ($/year) investment cost ($) remarks

Yee and Grossmann79

(mathematical)187.2 m2 (Tmin = 10 K) 28,000 37,486a Reassignment costs were neglected.

Ciric and Floudas34

(mathematical)169.9 m2 (Tmin = 10 K) 28,000 35,784 Included reassignment costs.

Yee and Grossmann25

(mathematical)195.3 m2 (Tmin = 5 K) 24,670 41,079b Decreased the approach temperature to 5 K.

Athier et al.51 (mathe-matical)

224 m2 (Tmin = 5 K) 16,950b 52,413 Payback period is about 4 months.

Bochenek and Jezow-ski52 (Mathemati-cal)

160 m2 (Tmin = 5 K) 28,850 32,216 Payback period is about 3 months

Ma et al.40 (mathe-matical)

167.05 m2 (Tmin = 7.3 K) 23,300 36,741 Payback period is 3 months

Rezaei and Shaei53

(mathematical)not provided 8,000 59,503 There is no limit on Tmin, and steam utility is completely

eliminated.

Pan et al.81 (mathe-matical)

Not applicable as retrottingis via heat transfer en-hancements

28,000, 8,000, and 8,000for Tmin = 10, 5, and2.7 K

34,800, 54,700, and 53,600for Tmin = 10, 5, and 2.7K

Retrot using stream splitting and heat transfer enhance-ments. Three optimal solutions for dierent Tmin arepresented.

aTaken from Ma et al.40 bCalculated using cost equations from Athier et al.51



Tmin of 7.3 K, and so they also obtained a similar trade-osolution. Rezaei and Shaei53 obtained a solution which doesnot require any hot utility but requires higher investment; intheir study, there was no limit assumed on Tmin. The nalnetwork has a Tmin of 2.7 K. Pan et al.

81 considered heattransfer enhancements and stream splitting to get better resultsfor various Tmin.One can compare the solutions found by various researchers

(Table 3) and select one of them based on the particularrequirements. For example, for Tmin of 10 K, the best solutionis the one including heat transfer enhancements, which showsthe potential of enhancement techniques. On the other hand,for Tmin of 5 K, there is no clear choice as the optimalsolutions reported show a trade-o between the utility andinvestment costs. This indicates the need for MOO and forPareto-optimal solutions to choose from.Ahmad et al.80 proposed a solution for a crude oil preheat

unit to debottleneck the HEN for an increased throughput of10%. The crude unit (operating under winter conditions inEurope) has a ow rate of 700 tons/h, the cold stream is thecrude feed, and the hot streams are overheads, naphtha,kerosene, and three types of gasoil.82 Ahmad et al.80 used afurnace duty of 99.6 MW, and the subsequent studiesmaintained this value for fair comparison. They also split thecold stream into three substreams, but the subsequent studiesassumed that the cold stream is split into only two substreamsin their solution. Ahmad and Polley82 reported the samesolution as that of Ahmad et al.80 Shokoya and Kotjabasakis83

obtained a solution for the same amount of utilities but withfewer new exchangers. Asante and Zhu60 proposed a solutionwith slightly higher additional area but involving very minimalmodications to the existing HEN. The summary of results inTable 4 show that, as the number of reassignments orresequenced (change its position on a stream but the matchis between the same streams) heat exchangers decreases, the

additional area required increases to achieve the specied heatduty. This highlights the trade-o present in these objectives.A pulp and paper industry problem was rst used by

Carlsson et al.13 It involves nine hot and six cold streams, andexisting HEN requires hot and cold utilities of 11.9 MW and7.5 MW respectively, which correspond to Tmin of 27 C. Forretrotting, Tmin was changed to 18 C, and the reportedsolution included criss-cross heat exchange instead of justvertical heat exchange between composite curves. The objectivein Carlsson et al.13 was to minimize the investment cost toachieve the energy recovery target at Tmin = 18 C. In Brionesand Kokossis,27,37 the objective was decreasing the area costalong with costs related to reassignments and piping. In Zhuand Asante,60 the major objective was to decrease the topologychanges involved in the retrot along with cost minimization.Thus, the solution obtained has minimum topology changescompared to those by other methods. Results obtained for thepulp and paper industry problem by various researchers arecompiled in Table 5. From this table, it appears that thesolution provided by Briones and Kokosis37 is the globaloptimum, but the number of topology changes involved is high(although fewer units are present).From Tables 15, one can see that, over the years, the

solutions reported for similar conditions are better in objectivefunction value, number of modications, and/or paybackperiod. One can also see that, to obtain an optimal solution,the costs involved for the topology changes need to beaccounted. In the literature, costs for topology modicationsare around $300,34,78 which were provided in the early 90s.31,73

These values are still being used to solve the problems, perhapsfor fair comparison, but the costs involved in performing amodication have increased multifold in the past 20 years dueto increases in material, engineering, and manpower costs.Hence, there is a necessity for updating the topologymodication costs along with additional area and heatexchanger costs, used for solving HEN retrot problems.

Table 4. Reported Retrot Solutions for the Crude Preheat Train Problem with Seven Hot and One Cold Streams80

reference (with basis of themethod in brackets)

additional area (with furnaceduty in brackets) remarks

Ahmad et al.80 (pinch analysis) 2,248 m2 (99.6 MW) Involves three new exchangers, one repiped exchanger, one resequenced exchanger and twoexchangers with added area

Ahmad and Polley82 (pinchanalysis)

2,248 m2 (99.6 MW) Same amount of reassignments and resequencing as above80

Shokoya and Kotjabasakis83

(pinch analysis)1,257 m2 (99.6 MW)a Involves two new exchangers, two resequenced exchangers and four exchangers with added

areaAsante and Zhu16,60 (hybrid) 1,265 m2 (99.6 MW) Involves one new heat exchanger and one resequenced exchanger. Has the least number of

modications compared to earlier works.aThese values are from Asante and Zhu.60

Table 5. Reported Retrot Solutions for the Pulp and Paper Industry Problem with Nine Hot and Six Cold Streams13

results

reference (with basis of the method inbrackets) investment cost payback period remarks

Carlsson et al.13 (pinch analysis) $176,000 (Tmin =18 C)

7 months(approx)

Includes criss-cross heat exchange.

$385,000 (Tmin =10 C)

9 months(approx)

Briones and Kokossis27 (hybrid) $140,300 7 months(approx)

Tmin is not provided but it seems to be 18 C from the energy savingsobtained.

Briones and Kokossis37 (mathematical) $114,300 (Tmin =18 C)

6 months(approx)

Fewer units in HEN.

Zhu and Asante60 (hybrid) $139,000 (Tmin =18 C)

Minimum topology changes.



Also, the application problems in many HEN retrottingstudies are mainly small to medium scale problems. Theecacy of a retrotting method should be tested on largeproblems as their retrotting involves more complexities.Finally, MOO should be considered in HEN retrotting; it

provides many optimal solutions (known as Pareto-optimalsolutions or front) with dierent trade-o among theobjectives. These solutions are equally good with respect tothe objectives used in the MOO problem. It has been applied tonumerous applications in chemical engineering.84 The Pareto-optimal solutions generated by MOO can be reviewed, and oneof them can be chosen based on user preferences. For example,where investment cost is constrained, a suitable retrot solutionunder this constraint can be chosen. Recently, MOO wasapplied to three HEN retrot problems.85 Figure 4 shows the

Pareto-optimal front for the crude oil preheat train problem;there are numerous optimal solutions with dierent investmentand utility costs. It is desirable to know the quantitative trade-o among the objectives for deeper understanding and forselection of an optimal solution for implementation. Further,discontinuities in the Pareto-optimal front in Figure 4 maycorrespond to installation of a new exchanger or a change in theHEN structure. Knowing all these, the optimal solution,meeting the practical considerations not included in theMOO problem, can be chosen from among a few nearbysolutions.

8. CONCLUDING REMARKSIn this paper, a comprehensive review of papers on HENretrotting and a brief discussion of reported retrot solutionsfor selected application problems are provided. From thereview, several interesting issues were identied and discussed.The rst one is the reassignment of the existing heatexchangers. If the heat exchange between certain streamsrequires more area than that in the existing heat exchanger, it ismet by installing a new exchanger. Shokoya63 developed an areaassignment strategy, area matrix method, to assign the existingexchangers to the new requirements by decreasing the areadeviations. Many studies, both pinch analysis and mathematicalprogramming based studies, allow area addition to existing heatexchangers. It has been observed that these studies use dierentstrategies for reassigning the existing heat exchangers usingintuition and/or experience.47,53,56,67 Our recent study shows

that heat exchanger reassignment strategy plays a key role insolving the retrot problems.85 So, to improve retrotting ofHENs, it is important to choose and employ a suitableexchanger reassignment strategy, especially in medium to largescale problems.As suggested recently,86 it is of quintessential importance to

provide practical solutions. This applies to solutions of HENretrot problems too. For example, it is assumed that anyamount of area can be added to the existing heat exchanger inmany studies,29,37,40,47,53,56,67 but this may not be practical. Forexample, in Ma et al.,40 an existing exchanger having heattransfer area of 448 m2 was assigned to an exchanger requiredto have 845 m2, thus adding 397 m2 which is nearly 90%increase in the area. Hence, a limit on the area that can beadded to an existing heat exchanger needs to be set inretrotting, by considering the industrial practice and type ofheat exchanger.Many techniques have been developed in the past 25 years to

solve HEN retrot problems, considering constant heatcapacity of streams. Heat capacity may change a lot dependingon the temperature range. The recent study by Smith et al.10

used an interval approach (i.e., divide the temperature rangeinto intervals and assume constant heat capacity in each ofthese intervals) to tackle the varying heat capacity problems.Another method to handle this varying heat capacity problem isto express the thermal properties as functions of temperatureand use them in nding the retrot solution. This method maypose computational complexities. In general, further studies arerequired to improve the solution of HEN retrot problemsinvolving streams having variable heat capacities.Retrotting via heat transfer enhancement techniques needs

to be pursued further, as several studies showed it to bepromising. In solving industrial problems, a single optimalsolution may not always be sucient. The proposed retrotnetwork may not be satisfactory for the particular plant becauseof various reasons such as a slight decrease in operating costmay not justify the investment, the new retrot network maylead to process control issues, and a heat exchanger cannot berelocated because of spatial constraints. These issues, if knownin advance, can be handled to some extent by including them asconstraints in the problem formulation, but its solution may bechallenging. Instead, it is better to provide multiple optimalsolutions for the same problem, for example, through MOO, sothat experienced engineers can review and choose one of themusing practical considerations. It is foreseen that research onHEN retrotting will remain active to tackle the challenges andissues mentioned above.

ASSOCIATED CONTENT*S Supporting InformationTable S1: stream data of crude oil preheat train problem;Tables S2 and S3: stream data of two example problems fromYee and Grossmann; Table S4: stream data of crude preheattrain problem; Table S5: pulp and paper industry problem. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected]. Fax: (65) 67791936.NotesThe authors declare no competing nancial interest.

Figure 4. Pareto-optimal front for the crude oil preheat train problem,adapted from Sreepathi and Rangaiah.85



ACKNOWLEDGMENTSWe thank Prof. Simon Harvey of Chalmers University ofTechnology, Sweden, for providing valuable feedback in thepreparation of the original manuscript. The nancial supportprovided by the National University of Singapore for thedoctoral studies of the rst author is gratefully acknowledged.

ACRONYMSACLC = actual cooling load curveAHLC = actual heat load curveAMTD = arithmetic mean temperature dierenceCAT = constant approach temperatureCC = composite curveCLP = constraint logic programmingCUC = cold utility curveECLC = extreme cooling load curveEHLC = extreme heat load curveGA = genetic algorithmGCC = grand composite curveGDT = grid diagram tableHEN = heat exchanger networkHRAT = heat recovery approach temperatureHUC = hot utility curveIDE = integrated dierential evolutionILP = integer linear programmingLMTD = logarithmic mean temperature dierenceMILP = mixed integer linear programmingMINLP = mixed integer nonlinear programmingMOO = multi objective optimizationNLP = nonlinear programmingPTA = problem table algorithmsRTD = retrot thermodynamic diagramSA = simulated annealingSTEP = stream temperature versus enthalpy plotTCLC = theoretical cooling load curveTHLC = theoretical heat load curve

REFERENCES(1) Klemes, J. J.; Varbanov, P. S.; Kravanja, Z. Recent developmentsin Process Integration. Chem. Eng. Res. Des. 2013, 91 (10), 20372053.(2) Grossmann, I. E.; Caballero, J. A.; Yeomans, H. Advances inmathematical programming for the synthesis of process systems. Lat.Am. Appl. Res. 2000, 30 (4), 263284.(3) Furman, K. C.; Sahinidis, N. V. A critical review and annotatedbibliography for heat exchanger network synthesis in the 20th century.Ind. Eng. Chem. Res. 2002, 41 (10), 23352370.(4) Morar, M.; Agachi, P. S. Review: Important contributions indevelopment and improvement of the heat integration techniques.Comput. Chem. Eng. 2010, 34 (8), 11711179.(5) Gundersen, T.; Naess, L. The Synthesis of Cost Optimal Heat-Exchanger Networks - an Industrial Review of the State of the Art.Comput. Chem. Eng. 1988, 12 (6), 503530.(6) Jezowski, J. Heat-Exchanger Network Grassroot and RetrofitDesign - the Review of the State-of-the-Art 0.2. Heat-ExchangerNetwork Synthesis by Mathematical-Methods and Approaches forRetrofit Design. Hung J. Ind. Chem. 1994, 22 (4), 295308.(7) Tjoe, T. N.; Linnhoff, B. Using Pinch Technology for ProcessRetrofit. Chem. Eng. (New York) 1986, 93 (8), 4760.(8) Kemp, I. C. Pinch Analysis and Process Integration. A User Guide onProcess Integration for Ecient Use of Energy; Elsevier: Amsterdam, theNetherlands, 2007.(9) Shenoy, U. V. Heat Exchanger Network Synthesis: ProcessOptimization by Energy and Resource Analysis; Gulf PublishingCompany: Houston, TX, 1995.

(10) Smith, R.; Jobson, M.; Chen, L. Recent development in theretrofit of heat exchanger networks. Appl. Therm Eng. 2010, 30 (16),22812289.(11) Bagajewicz, M.; Valtinson, G.; Nguyen Thanh, D. Retrofit ofCrude Units Preheating Trains: Mathematical Programming versusPinch Technology. Ind. Eng. Chem. Res. 2013, 52 (42), 1491314926.(12) Gundersen, T., Heat integration: targets and heat exchangernetwork design. In Handbook of Process Integration (PI); Klemes, J. J.,Ed.; Woodhead Publishing: Cambridge, UK, 2013.(13) Carlsson, A.; Franck, P. A.; Berntsson, T. Design Better Heat-Exchanger Network Retrofits. Chem. Eng. Prog. 1993, 89 (3), 8796.(14) van Reisen, J. L. B.; Grievink, J.; Polley, G. T.; Verheijen, P. J. T.The placement of two-stream and multi-stream heat-exchangers in anexisting network through path analysis. Comput. Chem. Eng. 1995, 19(SUPPL. 1), 143148.(15) van Reisen, J. L. B.; Polley, G. T.; Verheijen, P. J. T. Structuraltargeting for heat integration retrofit. Appl. Therm Eng. 1998, 18 (5),283294.(16) Asante, N. D. K.; Zhu, X. X. An automated and interactiveapproach for heat exchanger network retrofit. Chem. Eng. Res. Des.1997, 75 (A3), 349360.(17) Zhang, J.; Zhu, X. X. Simultaneous optimization approach forheat exchanger network retrofit with process changes. Ind. Eng. Chem.Res. 2000, 39 (12), 49634973.(18) Varbanov, P. S.; Klemes, J. Rules for paths construction forHENs debottlenecking. Appl. Therm Eng. 2000, 20 (1516), 14091420.(19) Nordman, R.; Berntsson, T. New pinch technology based HENanalysis methodologies for cost-effective retrofitting. Can. J. Chem. Eng.2001, 79 (4), 655662.(20) Nordman, R.; Berntsson, T. Use of advanced composite curvesfor assessing cost-effective HEN retrofit I: Theory and concepts. Appl.Therm Eng. 2009, 29 (23), 275281.(21) Li, B. H.; Chang, C. T. Retrofitting Heat Exchanger NetworksBased on Simple Pinch Analysis. Ind. Eng. Chem. Res. 2010, 49 (8),39673971.(22) Linnhoff, B.; Hindmarsh, E. The Pinch Design Method forHeat-Exchanger Networks. Chem. Eng. Sci. 1983, 38 (5), 745763.(23) Lakshmanan, R.; Banares-Alcantara, R. A Novel VisualizationTool for Heat Exchanger Network Retrofit. Ind. Eng. Chem. Res. 1996,35 (12), 45074522.(24) Linnhoff, B.; Flower, J. R. Synthesis of heat exchanger networks- 1. Systematic generation of energy optimal networks. AIChE J. 1978,24 (4), 633642.(25) Yee, T. F.; Grossmann, I. E. A Screening and OptimizationApproach for the Retrofit of Heat-Exchanger Networks. Ind. Eng.Chem. Res. 1991, 30 (1), 146162.(26) Lakshmanan, R.; Banares-Alcantara, R. Retrofit by inspectionusing thermodynamic process visualisation. Comput. Chem. Eng. 1998,22 (Suppl. 1), S809S812.(27) Briones, V.; Kokossis, A. A new approach for the optimal retrofitof heat exchanger networks. Comput. Chem. Eng. 1996, 20, S43S48.(28) Asante, N. D. K.; Zhu, X. X. An automated approach for heatexchanger network retrofit featuring minimal topology modifications.Comput. Chem. Eng. 1996, 20 (Suppl. 1), S7S12.(29) Ciric, A. R.; Floudas, C. A. A retrofit approach for heatexchanger networks. Comput. Chem. Eng. 1989, 13 (6), 703715.(30) Abbood, N. K.; Manan, Z. A.; Wan Alwi, S. R. A combinednumerical and visualization tool for utility targeting and heat exchangernetwork retrofitting. J. Cleaner Prod. 2012, 23 (1), 17.(31) Bengtsson, C.; Nordman, R.; Berntsson, T. Utilization of excessheat in the pulp and paper industry - a case study of technical andeconomic opportunities. Appl. Therm. Eng. 2002, 22 (9), 10691081.(32) Matijaseviae, L.; Otmaeiae, H. Energy recovery by pinchtechnology. Appl. Therm. Eng. 2002, 22 (4), 477484.(33) Yee, T. F.; Grossmann, I. E. Optimization model for structuralmodications in the retrot of heat exchanger networksProceedings ofthe First International Conference on Foundations of Computer Aided



Process Operations, Park City, Utah, 1987; Elsevier Science Ltd:Amsterdam, Netherlands, pp 652663(34) Ciric, A. R.; Floudas, C. A. A mixed integer nonlinearprogramming model for retrofitting heat exchanger networks. Ind.Eng. Chem. Res. 1990, 29 (2), 239251.(35) Geoffrion, A. M. Generalized Benders decomposition. J. Opt.Theory Appl. 1972, 10 (4), 237260.(36) Abbas, H. A.; Wiggins, G. A.; Lakshmanan, R.; Morton, W. Heatexchanger network retrofit via constraint logic programming. Comput.Chem. Eng. 1999, 23 (Suppl. 1), S129S132.(37) Briones, V.; Kokossis, A. C. Hypertargets: a ConceptualProgramming approach for the optimization of industrial heatexchanger networks - II. Retrofit design. Chem. Eng. Sci. 1999, 54(4), 541561.(38) Saboo, A. K.; Morari, M.; Colberg, R. D. RESHEX - anInteractive Software Package for the Synthesis and Analysis ofResilient Heat-Exchanger Networks 0.2. Discussion of Area Targetingand Network Synthesis Algorithms. Comput. Chem. Eng. 1986, 10 (6),591599.(39) Ahmad, S.; Petela, E. A. SUPERTARGET: Application Softwarefor Oil Renery Retrot, AIChE Spring National Meeting, Houston,USA, 1987.(40) Ma, K. L.; Hui, C. W.; Yee, T. F. Constant approachtemperature model for HEN retrofit. Appl. Therm Eng. 2000, 20 (15),15051533.(41) Sorsak, A.; Kravanja, Z. MINLP retrofit of heat exchangernetworks comprising different exchanger types. Comput. Chem. Eng.2004, 28 (12), 235251.(42) Sorsak, A.; Kravanja, Z. Simultaneous MINLP synthesis of heatexchanger networks comprising different exchanger types. Comput.Chem. Eng. 2002, 26 (45), 599615.(43) Yee, T. F.; Grossmann,

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