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

Keywords:Heat exchanger network Multi-period operation Retro fit Matching of heat transfer areas

ABSTRACT Multi-period heat exchanger network(HEN)retro fit is usually performed by targeting and matching heat transfer areas.In this paper,based on the reverse order matching method we proposed previously,three strategies of matching heat transfer areas are proposed to minimize the investment cost for the retrofit of HEN in multiperiod,in which replacement of heat exchangers,addition of heat exchangers and addition of heat transfer areas are performed.We demonstrate the procedures through three scenarios,including maximum number of substituted heat exchangers after retrofit,minimum additional heat transfer areas in the retrofitted HEN,and minimum investment cost for retrofit.The strategies are extended to a single period HEN retrofit problem.The results of multi-period and single period HEN retrofit problems indicate the effectiveness of the strategies.Moreover,these results are better than those reported in literature.The strategies are simple and easy to implement,which are of great benefit to large-scale HEN retrofit in practice.

1.Introduction

It is not unusual to retrofit heat exchanger network(HEN)for reducing energy consumption and improving economic performance to meet requirements in variation of operational conditions[1].Significant contributions have been made on HEN retrofit to attain energy-saving and economic goals[2].However,HEN retrofit under variable operation conditions is rarely reported[3].

For HEN retrofit to reduce the energy consumption,pinch analysis based methods are usually adopted[4].The procedure of HEN retrofit is divided into targeting step and retrofitting step.Tjoe and Linnhoff[5]initiated the pinch analysis to HEN retrofit.In their study,the retrofit target was first identified by assuming unchanged heat transfer area efficiencies before and after retrofit,then the retrofit schemes were empirically realized on the basis of pinch design principles.Nevertheless,this method could not assign additional heat transfer areas in HEN.Nordman and Berntsson[6]determined the retrofit target through improved composite curves and found that the closer the existing heaters and coolers are approaching to the pinch of the HEN,the higher the potential of cost-effective retrofit schemes are.To facilitate the retrofit process,Van Reisen et al.[7]presented a structural targeting retrofit method to find the critical parts of the network to modify.Li and Chang[8]developed a simple pinch-based method for HEN retrofit,in which the retrofit target of cross-pinch energy was first determined and the revamped network was then established by an improved pinch analysis method.In their method,only the cross-pinch matches were modified and existing heat exchangers(HEs)were sufficiently utilized.Then the investment cost for the retrofit was minimized.Bahador and Serge[9]modified and extended the pinch analysis method for HEN retrofit.The maximum heat recovery was reached in the structure modification stage and the optimal use of additional heat transfer areas was attained in the cost optimization stage.However,the quality of results with pinch-based methods relies on the experience and preference of engineers.The trade-off between energy cost and capital cost in the targeting step has not been taken into account.

The stage-wise model based methods for HEN retrofit can reach cost-effective retrofit schemes by taking the trade-off between energy and capitalcosts.Yee and Grossmann[10]proposed a systematic procedure for HEN retrofit based on a stage-wise superstructure model.In their method,the economic feasibility of the retrofit project was analyzed and then a mixed integer nonlinear programming(MINLP)model was solved to minimize the total costs for retrofit.

Much research has been done to improve Yee and Grossmann's model[10],and relevant algorithms have been developed.Ma et al.[11]proposed a two-step method for HEN retrofit.They first used a constant approach temperature model to optimize the HEN structure and then a MINLP model with actual approach temperature was adopted to finalize the retrofit.Sor?ak and Kravanja[12]took the types of HEs into account.Ponce-Ortega et al.[13]presented a HEN retrofit model with process modification.The plantlayoutand the piping arrangement were also included in their model.To make full use of the existing HEs,Sreepathi and Rangaiah[14]proposed a two-step procedure for HEN retrofit.In the first step,the retrofit target was determined by previous methods and then the heat exchanger reassignment strategy was used to finalize the retrofit scheme.Kova? Kralj[15]proposed a one-step model for HEN retrofit by embedding the existing structure and area parameters.To facilitate the calculation,the stream splitting was neglected and the number of HEs on each stream was restricted.Liu et al.[16]removed these restrictions and solved the improved model by using a hybrid genetic algorithm.The existing network structure and HEs were utilized as much as possible.Bj?rk and Nordman[17]combined the genetic algorithm with a deterministic algorithm to solve the large-scale model of HEN retrofit problem.Rezaei and Shafiei[18]presented a three-step method for HEN retrofit.The network structure was optimized by the genetic algorithm and the maximum heatrecovery was determined by solving a nonlinear programming model.Finally,the lowest investment cost for retrofit was reached by solving an integer linear programming model.To improve the solution quality,Zhang and Rangaiah[19]solved the model of HEN retrofit using an integrated differential evolutionary algorithm.

For HEN retrofit in variable operation conditions,Zhang and Zhu[20]explored the interaction effects between process modification and HEN retrofit.Kang and Liu[3]proposed a two-step method to solve the HEN retrofit in multi-period operation.In their method,a retrofit target was first determined by solving the multi-period HEN design model,and then the retrofitted HEN was attained by matching the existing heat transfer areas with the required heat transfer areas in reverse order.Results presented the simplicity and effectiveness of the method.However,in this method,the minimal investment cost was reached on the basis of the greatest number of substituted HEs.If the requirements and constraints of HEN retrofit change,the strategies of heat transfer area matching should be changed accordingly.

In this paper,on the basis of the reverse order matching method[3],we propose a series of novel strategies for matching heat transfer areas to meet different requirements of multi-period HEN retrofit,in which all possible investment costs in HEN retrofit are considered,including maximum number of substituted HEs,minimum additional heat transfer areas and minimum investment cost for retrofit.The procedures of the proposed strategies are illustrated by retrofitting a multi-period HEN.The method is extended to solve a single period HEN retrofit problem.The effectiveness of the method is confirmed and the difference between results of single period and multi-period cases is analyzed.

2.Problem Statement

Given(1)parameters in the existing heat exchanger network,such as network structure,heat transfer areas and locations of existing HEs,(2)operation parameters in the multi-period HEN,such as inlet and outlet temperatures,heat capacity flow rates,and heat transfer coefficients in each period,and(3)cost parameters of HEs and utilities,different methods of matching heat transfer areas are adopted under certain retrofit target,including replacement and removal of HEs,addition of HEs and addition of heat transfer areas.The objective is to obtain the optimal matching strategies and the minimum investment cost in three scenarios:(1)maximum number of substituted HEs after retrofit,(2)minimum additional heat transfer areas after retrofit,and(3)minimum investment cost for retrofit.The investment cost for retrofit contains the cost of additional heat transfer areas,re-piping and rearrangement costs of existing HEs and investment and construction costs of newly added HEs.

3.Strategies of Matching Heat Transfer Areas to Minimize Investment Cost

There are N HEs in the existing HEN.The existing heat transfer area of each HE is. Let the number of HEs in the retrofitted HEN be M,and the required heat transfer area of each HE be.Subscript h,c,k represents the location of the heat exchanger in HEN.We sortandin a descending order separately,expressed as(i=1,2,…,N)and(j=1,2,…,M),respectively.If M≠N,the elements of the shorter sequence are supplemented by zero.For example,if M＞N,we let==…==0.Thus,there are M pairs of HEs after matching.

In this section,three matching strategies associated with three retrofit targets are presented in three scenarios.

3.1.Scenario 1:Maximum number of substituted HEs after retrofit

The reverse order matching method(ROMM)proposed by Kang and Liu[3]attains the lowest investment cost on the premise of maximum number of substituted HEs.Thus,matching the heat transfer areas in reverse order can realize the requirement of maximum number of substituted HEs in the retrofitted HEN.In this work,however,we improve ROMM by changing the matching procedure.The improved matching procedure is as follows.

Step 1 Sorting of heat transfer areas

Step 2 Matching and replacement of heat transfer areas

Step 3 Matching of heat transfer areas in reverse order

Step 4 Re-matching of the replaced heat transfer areas

The replaced matches in Step 2 are re-matched according to their locations in HEN.Re-matching ensures that the number of substituted HEs remains unchanged and the number of rearranged HEs reduces to its minimum.

It should be noted that the rearrangement cost of HEs obtained by re-matching can be further reduced.Therefore,the investment cost for retrofit obtained in this work is less than that obtained by ROMM proposed by Kang and Liu[3].

3.2.Scenario 2:Minimum additional heat transfer areas after retrofit

As mentioned above,there are M pairs of HEs after matching of heat transfer areas.The additional heat transfer area for each pair of heat exchanger is ΔAm,andsatis fies.It is obvious that if and only if ΔA1= ΔA2= … =gets the minimum M·ΔAm.This means that the closer the values of additional areas,the greater possibility for total additional heat transfer areas reaching its minimum.Therefore,the minimum additional heat transfer areas can be reached by matching heat transfer areas in the serial order.Details are as follows.

Step 1 Sorting of heat transfer areas

Step 2 Matching and replacement of heat transfer areas

Step 3 Group-based matching of heat transfer areas in reverse order

The pairs of heat exchanger requiring additional heat transfer area in Step 2 are selected.If the group of two or more pairs of HEs satisfies,the heat transfer areas in this group are matched in the reverse order.Otherwise,the rest groups of matches in Step 2 remain unchanged.

Step 4 Re-matching of replaced heat transfer areas

The replaced matches in Step 2 are re-matched according to their locations in HEN.Re-matching ensures that the number of substituted HEs remains unchanged and the number of rearranged HEs reduces to its minimum.

3.3.Scenario 3:Minimum investment cost for retrofit

To reach the minimum investment cost for retrofit,a MINLP model for the minimum investment cost after retrofit is established to optimize the matching of heat transfer areas.

The additional heat transfer area after matching is defined as

The largest heat transfer area in each match is defined as

To ensure the connections between the existing heat transfer area and required heat transfer area,the following constraints should be imposed.

To distinguish the ways for matching of heat transfer areas,including re-piped existing HEs,newly added exchangers and rearranged HEs,the binary parameters,andare defined according to the heat transfer areas and locations of the required and existing HEs.The ways of rearrangement of HEs include changing the location of existing HEs,adding new HEs and removing the existing HEs.

The objective is to minimize the investment cost after retrofit,which is the sum of the cost of additional heat transfer areas,repiping cost of the existing HEs,rearrangement costs of HEs,and investment and construction costs of newly added HEs.The objective function is formulated as

where cfis the fixed investment cost for a new heat exchanger;caand β are the coefficient and exponent of heat transfer area cost;fpipis the correction factor of re-piping cost for an existing heat exchanger,fconis the correction factor of construction cost for a new heat exchanger,feris the correction factor of rearrangement cost of the heat exchanger,and zi,jis a binary variable to judge the match betweenand.If the match exists,zi,j=1.Otherwise,zi,j=0.

It is worthy of noting that these objectives mentioned above are the most commonly used ones in optimization and retrofit of HEN.The substitution of HEs and the addition of heat transfer areas are two major measures in the retrofit of HEN.More HEs substituted and less additional heat transfer are as lead to a higher utilization efficiency of the existing HEs,and hence reach a less modification of HEN retrofit.Moreover,once the required and existing heat transfer areas are known,the objectives of the maximum number of substituted HEs and the minimum additional heat transfer areas usually present an opposite trend,and both of the solutions for these two objectives are locally optimal in HEN retrofit.However,when the economy of HEN retrofit becomes a major consideration,a trade-off between these two objectives should be made to minimize the investment cost for HEN retrofit.

4.Retro fit of HEN in multi-period operations

The procedure of solving multi-period HEN retrofit problem contains mainly two steps,targeting and matching.In the targeting step,the retrofit target is determined.In the matching step,the retrofit target is realized by matching heat transfer areas.To confirm the effectiveness of the proposed three strategies,a multi-period HEN retrofit problem for a diesel hydrogenation unit[21]is solved.In the following sections,the procedures are exemplified to illustrate the matching strategies with the minimum investment cost for retrofit.

The existing heat exchanger network in the single period operation is shown in Fig.1,with 11 heat exchangers.The existing heat transfer areas are marked.Table 1 presents the operation conditions in three periods[21].The investment cost of the heat exchanger is formulated as 8333.3+641.7A0.7EUR,and the costs of heating and cooling utilities are Chu=115.2 EUR·kW-1·a-1and Ccu=1.3 EUR·kW-1·a-1,respectively.

4.1.Determination of retrofit target for multi-period HEN

The retrofit target obtained by solving the multi-period HEN design model is listed in Table 2.There are 14 heat exchangers in the retrofitted HEN.The required heat transfer areasare also listed in the table.

4.2.Matching heat transfer areas with different requirements

According to the retrofit targets given in Section 4.1,the existing heat transfer areas and required heat transfer areas are matched separately to meet three requirements described by Scenarios 1,2 and 3.The matching of heat transfer areas in the three scenarios is presented in Fig.2.The dotted arrow,from the existing heat transfer area to the required heat transfer area,denotes that the required heat exchanger can be replaced by the existing heat exchanger directly,while the solid arrow,from the required heat transfer area to the existing heat transfer area,denotes that the required heat transfer area cannot be directly replaced because the existing areaneeds to be increased first.In addition,there exists no connection between the required heat transfer areas and the existing heat transfer areas,which require additional HEs and removal of existing HEs.

Fig.1.Original HEN structure for the single period operation.

Fig.2 shows that the matching strategies in the three scenarios are different.In Scenario 1,ten required heat exchangers can be replaced directly,as shown in Fig.2(a).The area of existing heat exchanger10 is increased to match the required heat transfer area of the heat exchanger located at(3,1,3).Three required HEs located at(1,1,1),(2,2,3)and(2,CU,4)are newly added.In Scenario 2,two required heat exchangers can be substituted by existing heat exchangers 3 and 10.Nine existing heat exchangers require additional heat transfer areas.These nine pairs of heat transfer areas are matched in reverse order by dividing into six groups,as shown in Fig.2(b).The areas of three newly added heat exchangers are the smallest among the required heat transfer areas.In Scenario 3,seven required heat exchangers can be replacedby the existing heat exchangers.Four pairs of heat exchangers requiring additional areas are matched in reverse order,as shown in Fig.2(c).The three newly added heat exchangers in this scenario are as the same as those in Scenario 2.

Table 1 Stream data in the multi-period HEN

Table 2 Retro fit for multi-period HEN(ΔT min=10 °C)

Fig.3 shows the retrofitted HEN corresponding to the minimum investment cost for retrofit.Three newly added heat exchangers are marked as N1,N2 and N3.Existing heat exchangers 5,6,8 and 9 require additional heat transfer areas.The values of additional heat transfer areas are marked with Δ.Existing heat exchangers 3,4,and 9 do not change their locations before and after retrofit.

4.3.Results and discussion

The results of the three scenarios are listed in Table 3.For the convenience of comparison,we also give the results obtained by the reverse order matching method in this table.It shows that the maximum number of substituted heat exchanger is ten,and the minimum additional heat transfer areas are 1219 m2.The minimum investment cost for retrofit is 577907 EUR,corresponding to the shortest payback period 0.67 years,which is bold-faced in Table 3.

Although the number of substituted heat exchangers in Scenario 1 is the largest,the additional heat transfer area is the largest.Scenario 2 attains the least additional heat transfer areas,which means that the utilization efficiency of the existing heat transfer areas is high,but the number of re-piped HEs is the largest.In contrast,Scenario 3 reaches the lowest investment cost for retrofit,in which the number of replaced heat exchangers and additional heat transfer areas are in the midst of Scenarios 1 and 2.Thus the results in Scenario 3 can be considered as a trader-off between Scenarios 1 and 2.

Fig.3.HEN structure corresponding to the minimum investment cost for HEN retrofit in multi-period operations.

Table 3 Comparison of results obtained in three scenarios

Scenario 3 attains the lowest investment cost,followed by Scenario 1.On the other hand,Scenario 2 achieves the highest investment cost for retrofit.It is possibly because Scenario 3 weighs the costs of investment simultaneously,whereas Scenarios 1 and 2 obtain the investment cost step by step.Investment cost for retrofit in Scenario 1 is lower than that in Scenario 2,probably because the proportions of repiping cost and construction cost are much larger than that of additional heat transfer areas in the investment cost for retrofit.Furthermore,the result in Scenario 1 attains the least number of re-piped heat exchangers and reaches a much lower investment cost than the result obtained by ROMM in literature,while Scenario 2 achieves the highest re-piping cost.

5.Extension to Single Period HEN Retro fit

To explore the extensive effects of the proposed methods,we further verify the effectiveness of the methods by solving a single period HEN retrofit case.The results obtained by this work are compared with those by the methods in literature.

The stream data and the existing structure of single period HEN are adopted from Ciric and Floudas'work[22],shown in Table 4 and Fig.4.Seven existing HEs are identified with numbers and the existing heat transfer areas are given.In this case,the cost of a new heat exchanger is calculated by 4000+1200A0.6USD and the costof an additional heat transfer area is 1200A0.6USD.The cost parameters of heating and cooling utilities are Chu=80 USD·kW-1·a-1and Ccu=20 USD·kW-1·a-1,respectively.The overall heat transfer coefficient for all streams is 0.8 kW·m-2·K-1.The plant time is 5 years and the rate of return is 20%.

Table 4 Stream data of single period case

The retrofit target for the single period HEN is first determined by solving a single period HEN design model.There are six required heat exchangers after retrofit.We find that the results obtained by the three strategies are identical.The matching of heat transfer areas is shown in Fig.5.Five required heat exchangers are replaced directly.The area of existing heat exchanger 3,which is the largest area,should be increased and matched with the required heat exchanger located at(1,1,1).Existing heat exchanger5,which is the smallest area,is removed after retrofit.

Fig.6 presents the HEN structure after retrofit,corresponding to the minimum investment cost.The heat transfer areas for each heat exchanger in the retrofitted HEN are marked,and the additional heat transfer area of existing heat exchanger 3 is tagged with Δ.Locations of existing heat exchangers 1,2 and 3 remain unchanged before and after retrofit.

Fig.4.Original HEN structure of the single period case.

Fig.5.Diagram of heat transfer area match in single period case.

Fig.6.HEN structure corresponding to the minimum investment cost for HEN retrofit of single period case.

The results obtained in this work are compared with those reported in literature in Table 5.For different minimum approach temperatures,the costs of energy-saving are the same because of the nature of the HEN optimization problem.When the minimum approach temperature is less than 20°C,the problem reduces to a threshold problem,in which only cooling utilities are required in the HEN.Hence,the energy consumption and energy-saving cost remain unchanged as the minimum approach temperature increases.The number of newly added HEs and additional heat transfer areas obtained by the proposed strategies are less than those reported in literature.It indicates that the proposed strategies for HEN retrofit attain higher efficiency to utilize the existing heat exchangers and heat transfer areas,eventually with lower investment costs and the shortest payback periods.The major reason is that the results reported in literature are obtained by solving the mathematical programming models for the retrofit of HEN,in which the structure and operation parameters in the existing HEN are embedded.Although the existing HEN structure is adopted as possibly as they can,more possible structure modifications and heat transfer area matching strategies may be excluded.In contrast,in this work,the structure and operation parameters are not considered in the determination of the retrofit target.As a result,much more structure modifications and heat transfer area matching strategies are included.Subsequently,the possibility of reaching a better modification and a lower investment cost increases.The proposed strategies are simple and easy to implement,which are of great benefit to the solutions to large-scale HEN retrofit problems in practice.

In the single period HEN retrofit case,the results in the three scenarios are identical,whereas in the multi-period HEN retrofit case,the results in Scenario 3 are better than those in Scenarios 1 and 2.We can infer that the results in different retrofit requirements are relatively easy to unify in the single period HEN retrofit,in which the increased heat loads and heat transfer areas are restricted to fixed operation conditions.Thus the structure modifications and area matching strategies are limited.The results with different retrofit requirements are more likely to unify.On the contrary,in the multi-period HEN,the parameters,such as temperatures,heat capacity flow rates and heat transfer coefficients,vary with the operational periods.The increased heat loads and heat transfer areas are variable.More factors should be considered,and the structure modification and area matching strategies are diverse.Therefore,it is difficult to unify the results to meet different requirements.

6.Conclusions

The multi-period HEN retrofit problem is commonly solved step by step.The retrofit target is determined first and matching heat transfer areas finalizes the retrofit schemes.In this paper,on the basis of the reverse order matching method,three strategies of matching heat transfer areas are proposed to minimize the investment cost for the multiperiod HEN retrofit.The methods of matching heat transfer areas by replacement of heat exchangers,addition of heat exchangers and addition of heat transfer are a are considered.All possible investment costs are estimated to investigate the optimal matching strategies in three scenarios,including maximum number of substituted heat exchangers after retrofit,minimum additional heat transfer areas in the retrofitted HEN,and minimum investment cost for retrofit.

Two cases,a multi-period HEN retrofit and a single period HEN retrofit,are employed to demonstrate the effectiveness of the proposed strategies.Results indicate that lower investment costs and shorter payback periods can be reached.Moreover,the proposed strategies are simple and easy to implement,which are of great benefit to the solutions to large-scale HEN retrofit problems in practice.

Nomenclature

A heat transfer area,m2

cacoefficient of heat transfer area cost

cfinstallation cost of heat exchanger

fconcorrection factor of construction cost of newly added heat exchangers

Table 5 Comparison of results obtained by the proposed method and published in literature

fercorrection factor of re-erection cost of heat exchangers in HEN

fpipcorrection factor of re-piping cost of inner tubes in heat exchangers

ΔTminminimum approach temperature

z binary parameter

β exponent of heat transfer area cost

Superscripts

e expanded

ex existing

l location reassigned

n newly added

p period

req required

Subscripts

cu cooling utility

hu heating utility

i the i th existing heat transfer area in sequence

j the j th required heat transfer area in sequence

k tags of heat exchanger network

m number of required heat exchangers

max maximum

min minimum

n number of existing heat exchangers