Lixia Kang ,Yongzhong Liu ,2,*

1 Department of Chemical Engineering,Xi'an Jiaotong University,Xi'an 710049,China

2 Key Laboratory of Thermo-Fluid Science and Engineering,Ministry of Education,Xi'an 710049,China

1.Introduction

Heat exchanger network(HEN)is one of the most important energy utilization sub-systems in process industries,such as oil refining,petrochemical processes,steel,pharmacy and food[1].A well-designed HEN benefits both the economic and environmental sustainability[2,3].However,the variation of production plan and ambient conditions may cause the existing HEN,designed at fixed operation condition,becomes insufficient to the variable or multi-period operations[4].Moreover,the existing HEN,designed years ago,may fail to meet the economic and emission requirements due to increasing energy cost and tighter environmental regulations[5].Thus,a favorable retro fit of the HEN should not only satisfy the multi-period operations,but also meet the economic and emission requirements through proper retro fit actions.This problem can thus be formulated as a multi-objective optimization problem of multi-period HENs.However,the presentresearch on this topic is mainly focused on the single objective optimization of HENretro fitat fixed operating conditions,aiming to maximizing energy consumption reduction(emission reduction)or minimizing the cost for retro fit[6].

For energy consumption reduction purpose,pinch technology based methods and their variants are commonly adopted,where the retro fit target is determinedviathe graphic tools before the retro fit is performed according to simple heuristic rules[7].Examples of these methods include the modified pinch approaches[8,9],path analysis method[10]and various improved graphic tools,such as retro fit thermodynamic diagram[11]and the extended grid diagram[12].These methods,to some extent are helpful to reduce the CO2emissions in HENs because energy consumption is the main source of the CO2emissions in HENs.In spite of the successful applications of these methods in CO2emission reduction in HENs,other strategies,such as fuel switching[13]and heat pump installation[14]are also developed for retro fit of HENs where the existing structure and energy utilization have been optimal.

To consider the economic efficiency of HEN retro fit,a mixed-integer nonlinear programming(MINLP)model is involved[15].Extensive research activity has been focused on the development of the solving strategies for this MINLP model which can be solved by either onestep method where the topology modification,HE assignment and cost optimization are carried out simultaneously[16–18],or multistep method where the HEN retro fit model is solved in a step-wised manner[19,20].Besides,there are also some multi-objective optimization models for HEN retro fit,considering both economic efficiency and CO2emissions of HENs[14].However,these methods are based on the assumption thatthe operation parameters ofthe HENs keep unchanged,which is not the case in practice.

To address this problem,Zhang and Zhu[21]studied the interactions between process changes and HEN retro fit.For the HEN with variable heat capacity flow rates,Sreepathi and Rangaiah[5]formulated the heat capacity flow rates of streams as a function of temperaturesviapolynomial fitting.The HE assignment strategies[22]were then adopted to complete the retro fit.Unlike this continuous approach,Smithet al.[23]solved this HEN retro fit problem by using an interval approach,where the temperature range of the stream was divided into several intervals of constant specific heat capacity for calculations.This problem was then considered a multi-period HEN retro fit problem[24].A reverse order matching method[25]and a graph-theoretic approach[26]were proposed to solve this kind of problem.In these two methods,the retro fit target of multi-period HEN was determined by solving a HEN model involving multi-period operation[27],the existing HEs and the required HEs were then matched to finalize the retro fit through a series of retro fit actions.It is worth noting that the graph-theoretic method defined the HEs matching problem as a bipartite graph matching problem,where the existing HEs and required HEs are matched to meet differentobjectives under various restrictions.The main advantage of this method is that the computational effort in solving the HEN retro fit problem can be significantly reduced through the application of well-established graph algorithms.

However,the research on HEN retro fit in multi-period operation is still premature.Although the practical restrictions should be reinforced during HEN retro fit,as mentioned by some researchers[22,26,28],the restrictions on physical size and operating pressures of the existing HEs during the reassignment of HEs and heat transfer areas are often neglected in most of the cases.This,to some extent,may underestimate the capital cost for HEN retro fit.In addition,some strategies for CO2emission reduction in single period HENs take the assumption that the existing structure and energy utilization have been optimal.However,it is not the case in retro fit of multi-period HENs where the existing HEN has failed to meet the current operation conditions and energy and/or emission limitations.Thus,a trade-off between cost and emission of the multi-period HEN during the retro fitviaprocess integration turns out to be necessary.

In this direction,the major objective of this work is to develop a systematic strategy for retro fit of the multi-period HEN on the basis of the multi-objective optimization,aiming at minimizing the cost for retro fit and CO2emissions.In the proposed procedure,a simplified multi-objective optimization(MOO)model of the multi-period HEN is constructed and solved to target the retro fit,and the required HEs and the existing ones are then matched to selectthe proper retro fitschemes under the constraints ofphysicalsizes and operating pressures of HEs.A multi-period HEN retro fit in a vacuum gas oil hydro-treating unit is employed to illustrate the application of the proposed procedure.

2.Retro fit Strategy of the Multiperiod HENs

This section introduces the procedure for retro fit of the multi-period HEN considering emission limitation and practical retro fit restrictions,which includes the following three phases:

(1)Establishing a simplified multi-period HEN model through single period optimization;

(2)Targeting the multi-period HEN retro fit based on the multiobjective optimization;

(3)Selecting the retro fit schemesviamatching the required and existing HEs.

2.2.Targeting the multi-period HEN retrofi t

To obtain a retro fitted HEN that meets both the multi-period operations and the emission requirement,a CO2emission objective is appended to the model of multi-period HEN.ε-Constraint method is then adopted to solve this multi-objective optimization model so that a Pareto front of the economic and emission objectives is generated for selection of the retro fit target.

2.2.1.Economic objective

The TAC of the multi-period HEN is the sum of the capital cost and the operating cost.The capital cost is mainly the cost of HEs and the operating cost includes the costs of heating utility,cooling utility and electricity that consumed by compressors and pumps.

whereAfis the annual factor;Cfis the fixed cost of the HE;Caand β are the coefficient and exponent of area cost.fpis a cost correction factor caused by the pressure.zis a binary variable denoting the existence of a heat transfer unit.Ais the heat transfer area andqis the heat load of the utility.DOP and NOP are the duration of a subperiod and the duration of operation.Yis the annual operating time of the plant.NcompandNpumpare the power of compressor and pumps which can be calculated as[31]

wherePinandPoutare the pressures at the inlet and outlet of the compressor.Vinis the volume flow rate of gas at the inlet of the compressor.nis the ratio of the heat capacity at constant pressure and that at constant volume,n=CP/Cv.ηcompis the isentropic efficiency of the compressor[31].

where ΔPand ηpumpare the pressure difference and efficiency of the pump;andVis the volume flow rate of pumping fluid with the unit of m3·h-1.For process pumps,the volume flow rate of the streams can be calculated as

2.1.Establishing a simplifi ed multi-period HEN model

To reduce the subsequent computations,a simplified multi-period HEN model is constructed according to the procedure in our previous work[29].In this way,the number of binary variables reduces and introducing of commonly shared matches helps to improve the solution generation[30].Note that if the operation pressures are considered,a cost correction factorfpwill be introduced to distinguish the cost difference between a high-pressure HE and a low-pressure HE.In this work,a high-pressure HE is the one through which at least one of these high-pressure streams flows;otherwise,the HE is considered as a low-pressure one.

whereFis the mass flow rate of the process stream.ρ andcpare the density and specific heat capacity of the cooling utility;and Tcuinand Tcuoutare the inlet and outlet temperatures of the cooling utility.

2.2.2.CO2 emission objective

According to the previous investigations,the recessive CO2emissions in the construction stage of the HEN can be eliminated when CO2emitted by utility and electricity are involved.Thus,in this work,only the CO2emissions in operating stage of the HEN are considered as the total CO2emission(TCE)of the HEN.

where ωhuand ωeleare the emission coefficients of heating utility and electricity and can be calculated according to our previous work[33].

2.3.Selecting the retrofi t scheme by matching of heat exchangers

In this section,a heuristic method and a graph-theoretic method that are proposed in our previous work[26]are introduced and extended to match the HEs.Four retro fit objectives are considered as follows:

·O1:Minimal modification of the existing HEN structure;·O2:Maximum number of substituted HEs after retro fit;

·O3:Minimum additional heat transfer areas after retro fit;

·O4:Minimal capital cost for retro fit for a given retro fit target.

To reach the first objective(O1),the retro fit target is determined by solving the multi-period HEN model with fixed structure,such that the existing HEN structure is maintained and only the heat transfer areas are modified to meet the multi-period operations.The rest of these objectives(O2–O4)are achieved based on the retro fit target obtained by solving the simplified multi-objective optimization model of the multi-period HEN.In this case,both the existing structure and the heat transfer areas are adjusted during the retro fit.

Following two practical restrictions will be considered during the matching of HEs:

·The restriction of physical size of the existing HE;If additional heat transfer area of an existing HE exceeds 15%of its original heat transfer area,a new HE should be considered.

·The restriction of operating pressures of HE;The required HEs at high operation pressures can only match with the existing HEs at high operation pressures,and the required HEs at low operation pressures can match with the existing HEs at low or high operation pressures.

2.3.1.Heuristic matching strategy

The main advantage of the heuristic method is that it is easy to implement and no mathematical formulations or complex algorithms are required.For each objective,the heuristic procedures for matching of the HEs are as follows.

2.3.1.1.O1:minimalmodification ofthe existing HENstructure.In this case,the retro fit target is first obtained by solving the multi-period HEN model with fixed structure.The following rules are then adopted to minimize the structural modification.

For an existing HE and a required HE with the same stream match,

·If the area of the existing HE is greater than that of the required HE,a dotted arrow is drawn from an existing HE to a required HE,implying that this required HE can be directly substituted by the existing HE.

·If the required area is greater than the existing area and the additional area is less than 15%of the existing area,a dotted arrow is drawn from a required HE to an existing HE;otherwise,there is no line linked between a required HE and an existing HE,implying that the existing HE is deleted and the required HE needs to be newly added.

Note that the operating pressures of HEs are automatically satis fied because the operating pressures of a required HE and an existing HE with the same stream match will be the same.In addition,by following these matching rules,the existing HEs will not be rearranged and the existing HEN structure will be less modified.

2.3.1.2.O2:maximum number of substituted HEs after retrofit.For a given retro fit target,when the number of substituted HEs is maximized,the number of newly added HEs and HEs that need to increase the areas is minimized,implying that the existing HEs are fully utilized.In this direction,the reverse order matching method can be adopted,which is developed on the basis of the convex–noconvex property of the area costfunction with respectto the additionalareas.However,this method is only applicable to matching HEs without considering practical restrictions.The procedure of the reverse order matching method is as follows:

Initially,we check the number of the required HEs and that of the existing HEs,and add the HEs of zero area to make them consistent.Then,all the required and existing HEs are ranked in descending order by their heat transfer areas.

·If an existing HE is adjacent to and located above a required HE,a dotted arrow is drawn from an existing HE to a required HE.Once matched,they are removed from the ranks.This step will be continued until all the required HEs are located below the existing HEs.

·When the remaining required HEs are matched with the existing HEs in reverse order and their heat transfer areas are not zero,a solid arrow is drawn from a required HE to an existing HE.

·If one of them has a zero area after reverse order matching,there is no line linked between a required HE and an existing HE.In such case,the required HE needs to be newly added,and the corresponding existing HE is deleted.

2.3.1.3.O3:minimum additional heat transfer areas after retrofit.The minimum additional heat transfer areas after retro fit can be achieved by matching the HEs in serial order.The matching procedure is inferred from the convex–noconvex property of total additional area function.Similar to the reverse order matching method,this procedure is only suitable to matching HEs without any restrictions.

In this procedure,the numbers of the required HEs and the existing HEsarefirstmatched by adding auxiliary HEs ofzero areas.The required HEs and the existing HEs are individually ranked in descending order by theirheattransferareas.Two HEs with same orders are correspondingly matched.

·If the area of the existing HE is greater than that of the required HE,a dotted arrow is drawn from an existing HE to a required HE.In this case,the required HE is directly replaced by the existing HE.

·If the area of the existing HE is smaller than that of the required HE,a solid arrow is drawn from a required HE to an existing HE,which indicates that the area of the existing HE needs to be increased.

·If one of them has a zero area,there is no line linked between a required HE and an existing HE.It implies that the existing HE is deleted and the required HE should be newly added.

2.3.2.Graph-theoretic matching strategy

Unlike matching HEsviaheuristic rules,the graph-theoretic approach enables the consideration of practical matching restrictions,extra retro fit objectives and various investment costs simultaneously.In this method,the matching of HEs is defined as a bipartite graph matching problem,which is accessible to take the advantage of the well-established graph algorithms to solve the problems.The corresponding relationships between the matching of HEs with different objectives and the matching of bipartite graph are given in Table 1.

Table 1Relationships between the matching of HEs and the matching of bipartite graph

Table 1 shows that the objective of the maximum number of substituted heat transfer units after retro fit can be achieved by solving a maximum matching of the bipartite graph,taking the matrix of the substituted HEs as the weight matrix.The classic algorithm for this problem is theaugmenting path algorithm.The objectives of the minimum additional heat transfer areas and the minimum cost for retro fit equals to solve the corresponding minimum weighted matching of the bipartite graph,taking the additional heat transfer area and retro fit investment cost as an edge weight,respectively.TheHungarian algorithmcan be used to find the desired matching.

The key to this method is to construct weight matrices whose elements are calculated by considering the practical restrictions and retro fit objectives.The definition and construction of weight matrices can be found in our previous work[26].

3.Case Study

3.1.Fundamentals of the HEN in a VGO hydrotreating unit

In this section,a HEN of vacuum gas oil(VGO)hydro-treating unitin a refinery in China is employed.The annual processing capacity of the unit is 2.6 million tons[33].For the VGO process,the reaction is carried out under high temperature and high pressure.A well-designed HEN of such system leads to both economic and environmental benefits.The existing HEN structure is shown in Fig.1,in which six hot streams and four cold streams are involved,and the minimum temperature difference is 20°C.In this unit,the existing operating parameters under nominal operating conditions are presented in Table 1.We can see that the reactor ef fluent(H1),gas from high pressure separator(H5 and H6),mixture feed(C1)and mixture hydrogen(C4),with pressures of about 10 MPa are the high-pressure streams in this unit.The rest of the streams are low-pressure streams with pressures less than 2 MPa.

In this unit,only the power consumed by the water pumps changes during the HEN retro fit.Thus,the CO2emissions of heating utility and electricity consumed by water pumps are considered in this example.The total annual CO2emission of the existing HEN is 50 kt.

Consider a variation of the production demands,three additional operating periods are introduced,corresponding to the 80%,90%and 110%of the existing processing capacity.The operating conditions of these additional periods are listed in Table 2,which are obtainedviasimulation performed on the software package ASPEN Plus.

Table 2Fundamental data under the nominal operating condition of the HEN

The capital cost of the HE is calculated by 10000+324A(Ais heat transfer area,m2).The annual costs of the heating utility,cooling utility and electricity are 70 USD·kW-1,7 USD·kW-1and 0.1604 USD·(kW·h)-1.When considering the HEN retro fit,we adopt the Smith's method[31]to calculate the potential costs for retrofit,including construction cost of the newly added HEs,repiping cost of HEs requiring additional heat transfer areas and rearrangement cost of the HE when the stream matches change.

3.2.Retrofi t of the multi-period HEN without any restrictions

In this section,neither the emission limitation nor the restrictions on HE matching are imposed.Initially,we obtain the optimal HEN matches in each sub-period by solving the single period HEN models.The commonly shared matches in four subperiods are selected and used to construct the simplified multi-period HEN model.This simplified model is then solved to determine the retro fit target of the multi-period HEN,aiming at minimizing the TAC.For comparison purpose,the retro fit targets under the fixed structure,referred as Scenario 1(S1),and without fixing the structure,referred as Scenario 2(S2)are separately obtained.Both the heuristic method and graph-theoretic method are further adopted to finalize the retro fit scheme.

Fig.1.The existing HEN structure of the VGO system.

3.2.1.Establishing the simplified multi-period HEN model

By solving the single period optimization model of the HEN,the optimal matches and corresponding heat transfer areas in each subperiod are obtained,which can be found in Supplementary materials.The optimal MTDs of the HENs in the four sub-periods are 20 °C,17 °C,21 °C and 19 °C.According to the optimal structures,seven HEs are commonly shared in the four sub-periods.By fixing the optimal MTD in each subperiod and introducing these commonly shared HEs,a simplified multi-period HEN optimization model is constructed.

3.2.2.Targeting the retrofit of the multi-period HENs through single objective optimization

The retro fit targets in two scenarios(i.e.S1 and S2)are listed in Supplementary materials.According to the results,the required matches in Scenario 1 are the same as the existing matches in Scenario 2,and few matches required are the same as those in the existing HEN.

3.2.3.Matching of heat exchangers

Based on the retro fit targets obtained above,the required HEs and the existing HEs are matched to meet the following objectives:

·Minimal modification of the existing structure(S1-O1);

·Maximum number of the substituted HEs after retro fit(S2-O2);

·Minimal additional heat transfer areas after retro fit(S2-O3).

Fig.2.The diagram of HE matching via heuristic-based method in the single objective optimization case with the(a)minimal modification of the existing structure(S1-O1)and the(b)maximum utilization of the existing heat transfer units(S2-O2)and areas(S2-O3).

By using the heuristic matching method,we obtain the diagrams of HE matching with three objectives,as shown in Fig.2.A comparison of results is presented in Table 3.Results show that by using the heuristic method,all objectives(O1–O3)can be well achieved.

Table 3Multi-period operation conditions of the HEN

In Fig.2(a),although there is only one existing HE requriring re-arrangement,the minimum modification among all retro fit cases,seven HEs require additional heat transfer areas.A main disadvantage of the method is that it assumes that the existing HEN structure is optimal or still suitable to the multi-period operations.However,the retro fit target in Scenario 2 shows that the optimal structure has different stream matches and number of HEs with the existing one.Moreover,Fig.3 presents the diagram ofHE matching corresponding to S1-O4 where the retro fit target is obtained by solving the multi-period HEN model with the fixed structure(S1)and the objective is to minimize the capital cost for retro fit.It can be seen that the capital cost of HEN retro fit without modification is higher than that with structure modifications,indicating the necessity of structure modification during retro fit.The payback period in Scenario 1 is in finite because the energy consumption increases after retro fit,which also shows the fact that the existing HEN structure may not be optimal,and the retro fit of the HEN with thefixed structure may lead to a worse performance on economy and energy utilization.

For the retro fit target without considering the fixed structure,the diagrams of HE matching in objectives O2 and O3 are given in Fig.2(b).It can be seen that the required HEs and the existing HEs are matched in the reverse order in objective O2,whereas they are matched in the serialorder to minimize the additional areas after retro fit.Results in Table 3 show that the maximum number of the substituted HEs and the minimal additional areas after retro fit are 13 and 3923 m2.Note that the payback periods in these two objectives are reasonable,implying that compared with the existing HEN,the retro fitted HEN is energy-efficient.

Table 3 also gives the results of graph-theoretic matching method in the three objectives,i.e.O2,O3 and O4.The corresponding diagrams of HE matching can be found in Supplementary materials online.These results show that the graph-theoretic method enables to meet all different retro fit objectives.For a given retro fit target in Scenario 2,the maximumnumberofthe substituted HEs is 13,and the heattransfer areas should be increased by at least 3923 m2after retro fit.The lowest capital cost for retro fit is 4.784×106USD,corresponding to a shortest payback period of 7.6 years.Although both two methods happen to reach the same results in objectives O2 and O3,the heuristic method cannot get a better solution in most cases.The major reason is that the matching problems in objectives O2 and O3 have multiple solutions and the graph-theoretic method can easily screen the optimal one with the lowest capital cost.In addition,the graph-theoretic method can guarantee the lowest capital cost for retro fit(O4),whereas the heuristic method cannot.

Therefore,by fixing the existing HEN structure,we can meet the requirements of the multi-period operations through area increase and obtain a HEN with minimal modification along with lower capital cost for retro fit.However,when the existing HEN structure is not optimal for the multi-period operations,the retro fit target obtained by fixing the existing structure may increase the energy consumption,leading to an in finite payback period for retro fit.On the contrary,for a given retro fit target obtained without fixing the existing structure,although the capital cost for retro fit is higher,the extra energy saving is reached,which results in a relatively reasonable payback period for retro fit.According to the abovementioned results,both the heuristic method and graph-theoretic method can be used for different objectives during HEN retro fit.However,the graphtheoretic method can solely guarantee a retro fitted HEN with lowest capital cost.Moreover,the problem ofHENretro fitconsidering multiple practical restrictions can also be realized by the graph-theoretic method.

3.3.Retrofi t of the multi-period HEN based on the multi-objective optimization

In this section,the practical restrictions on CO2emission,physical sizes and operating pressures of HEs are imposed during the multiperiod HEN retro fit.In this section,the multi-objective optimization(MOO)is employed to target the retro fit,and the graph-theoretic method is used to match the required and existing HEs.Four distinct objectives for the multi-period HEN retro fit are discussed under different combinations of the scenario and the objective,e.g.S1-O1,S2-O2,S2-O3 and S2-O4.

3.3.1.Establishing the simplified multi-period HEN model

The optimal stream matches and the corresponding heat transfer areas in four subperiods are obtained through the solutions to the HEN optimization model for the single period operation.The optimal MTDs of the HENs in four subperiods are 18 °C,17 °C,16 °C and 19°C and ten commonly shared stream matches are selected and used to construct the simplified multi-period HEN model.More details of single period optimization can be found in Supplementary materials.

Note that,in this case,a cost correction factorfpis introduced in the HEN optimization models such thatfp=1 for a low-pressure HE andfp=1.3 for a high-pressure HE.In this example,as is shown in Table 1,the reactor ef fluent(H1),gas from high pressure separator(H5 and H6),mixture feed(C1)and mixture hydrogen(C4),with pressures of above 10 MPa are the high-pressure streams in this unit.The rest of the streams are low-pressure streams with pressures less than 2 MPa.

3.3.2.Targeting the retrofit of the multi-period HENs through multiobjective optimization

By solving the MOO model of the multi-period HEN,the retro fit targets under different total annual CO2emissions are obtained,as shown in Fig.4.

Taking the minimum total annual cost and minimum CO2emissions in Fig.4 as benchmarks,we can see that the range of the TAC is less than 0.3%when the TCE reduces from 38.4 kt to 18.2 kt(variation range＞110%).It suggests that a slight increase in TAC of the multi-period HEN will cause a significant decrease in total CO2emissions.Note that each point on Pareto front corresponds to a feasible retro fit target of the multi-period HEN,and decision-makers can choose a desirable one according to the practical economy and emission limitations.

Fig.4.The Pareto front of the multi-period HEN considering economic and emission objectives.

If the CO2emission of the existing HEN is reduced to its half,the TCE of the HEN after retro fit should be less than 24.9 kt·a-1,as marked as red solid circle in Fig.4.The corresponding operation parameters can be found in Supplementary materials.Table 4 gives a comparison of the retro fit targets obtained with and without emission restrictions.

It can be seen that for a given retro fit target,the number of HEs in HEN obtained with emission restriction is less than that in HEN without emission restriction;total areas and TAC of the HEN with emission restriction increase when compared with those of the HEN without emission restriction.When the CO2emission is restricted,the TCE of the HEN in Scenario 1 will be 65.7 kt·a-1,which is greater than that of the existing HEN.

3.3.3.Matching heat exchangers

By using the graph-theoretic approach,the diagrams ofHE matching corresponding to four objectives(O1–O4)are shown in Fig.5(a)–(c).The diagram of HE matching for the case of S1-O4 is also given in Fig.6.

In Fig.5,when the restrictions of the physical sizes and operating pressures of the existing HEs are considered,the feasible matches between the required HEs and the existing HEs(i.e.the HE matches where the required HEs can be substituted or matched by increasing the area of the existing HE)reduce,and the number of newly added HEs increases after retro fit.The additional areas and the capital cost for the multi-period HEN retro fit thus increase.In addition,the matching relationships in objectives O2 and O3 will not be consistent with the reverse order matching or serial order matching rules becausethe corresponding HEs cannot be matched due to oversize of the HE or compatible operating pressures.

Table 4A comparison of results in SOO case

Fig.5.Diagrams of HE matching solved by graph-theoretic method in MOO case with the(a)minimal modification of the existing HEN(S1-O1),(b)maximum utilization of the existing heat transfer units and areas(S2-O2 and S2-O3)and the(c)minimal cost for retro fit(S2-O4).

Results in Table 5 show that differentobjectives can be well satis fied by using the graph-theoretic method under practical restrictions.Whenever the existing HEN structure is fixed or not,the number of utility exchangers in retro fit target with the emission limitation decreases.The payback periods for retro fit in different cases are finite,implying additional energy saving due to a limitation on CO2emission.Note that,for the retro fit target with fixed structure,the capital cost for retro fit is higher and the payback period is longer when comparing with those corresponding to the retro fit targets without fixing the existing structure.It is likely that the total heat transfer areas of the multi-period HEN will increase when the emission limitation is considered.Although by fixing the existing structure,the required stream matches will be the same with those in the existing HEN,they cannot match due to additional area restrictions.The number of newly added HEs thus increases,leading to a highercapitalcostfor retro fit.Moreover,fixing the existing structure may also hinder the energy saving of the multi-period HEN.However,when the existing structure is not fixed,the retro fit target can be achieved through a trade-off between the economic and emission objectives,and the multi-period operational conditions can be satis fied by adjusting the stream matches,increasing heat transfer areas and heat transfer units.A more favorable energy saving and payback period are accordingly reached,as listed in Table 6.

Fig.6.The diagram of HE matching in the case of S1-O4.

4.Conclusions

In this paper,a systematic strategy for retro fit of the multi-period HENs is developed.A simplified multi-objective optimization model is constructed and solved to target the retro fit of the multi-period HEN,aiming to minimizing the retro fit cost and CO2emissions.After the selection of a retro fit target according to the practical cost and emission limitations,the required and existing HEs are matched to finalize the retro fitviathe heuristic and graph-theoretic strategies considering distinct retro fit requirements and matching restrictions.A HEN of vacuum gas oil hydro-treating unit is used to illustrate the application of the procedure.

When the retro fit is targeted by minimizing the TAC and the matching restrictions are absent,both the heuristic and graphtheoretic methods can guarantee the specific objectives during retro fit.In particular,a retro fitted HEN with minimal modification and lower capital cost can be reached through determination of the retro fit target with fixed HEN structure.However,such practice may increase energy consumption and lead to an in finite payback period for retro fit.When the retro fit is targeted without fixing the existing HEN structure,additional energy saving and a desirable payback period for retro fit will be reached although the capital cost for retro fit of the multiperiod HEN is higher.

When multi-objective optimization is employed to targetthe retro fit ofthe multi-period HENs considering practicalrestrictions,the heuristic method becomes not applicable,and the graph-theoretic method is used for multi-period HEN retro fit.Compared with the results obtained without any restrictions,the number of feasible HE matches reducesand the number of newly added HEs increases,resulting in more additionalareas and higher capitalcostfor retro fit.However,the energy consumption and CO2emission are suppressed,and a reasonable payback period is attained.In addition,the retro fit targets of the multi-period HENdetermined through the multi-objective optimization method are usefulfor the decision-makers.According to these methods,one can readily select a desirable scheme according to the practical economic and emission restrictions.

Table 5A comparison of retro fit targets obtained with and without emission restriction

Table 6A comparison of results in MOO case

Supplementary Material

Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.cjche.2017.01.002.

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