Design of heat exchanger network based on entransy theory☆

Li Xia,Yuanli Feng,Xiaoyan Sun,Shuguang Xiang*

Institute of Process System Engineering,Qingdao University of Science and Technology,Qingdao 266042,China

Keywords:Process systems Heat exchanger network synthesis Heat transfer Entransy Energy target Pinch

ABSTRACT The heat exchanger network(HEN)synthesis problem based on entransy theory is analyzed.According to the characteristics of entransy representation of thermal potential energy,the entransy dissipation represents the irreversibility of the heat transfer process,the temperature difference determines the entransy dissipation,and four HEN design steps based on entransy theory are put forward.The present study shows how it is possible to set energy targets based on entransy and achieve them with a network of heat exchangers by an example of heat exchanger network design for four streams.In order to verify the correctness of the heat exchanger networks design method based on entransy theory,the synthesis of the HEN for the diesel hydrogenation unit is studied.Using the heatexchange networks design method based on entransy theory,the HEN obtained is consistent with energy targets.The entransy transfer efficiency of HEN based on entransy theory is 92.29%,higher than the entransy transfer efficiency of the maximum heat recovery network based on pinch technology.

1.Introduction

HEN is an important part of energy recovery in petrochemical industry.It is of great significance to save energy and improve energy efficiency in the process industry with high energy consumption.Pinch technology is a well-established method for heat exchanger network synthesis.It not only gets the optimal design for heat exchanger network,but also obtains ideal HEN revamping for old unit.At present,the pinch design method is widely used in computer software[1,2],chemical production equipment[3,4],energy transportation system[5,6],safety and environmental management[7,8],etc.

In the HEN,the heat exchange process between the cold and hot streams is irreversible.The ratio of effective use of heat and total heat input in the system is defined as the thermal efficiency of the system,which further describes the extent of the effective utilization of heat.The pinch design method can calculate the heat conservation in the heat transfer process.But it cannot calculate the thermal efficiency of the HEN.Therefore,other physical quantities are needed to define for calculating the efficiency of the heat transfer process.Guo et al.[9]introduced a new physical quantity,entransy,based on the analogy between heat and electrical conduction.Hu and Guo[10]compared the efficiency of the heat transfer process based on entransy theory and exergy respectively.The result shows that the efficiency of the heat transfer process based on entransy was unaffected by the choice of base States.In order to analyze the performance of heat transfer processes intuitively,the temperature-heat flow diagram is proposed by Chen et al.[11]to describe the change rule of entransy in the process of heat transfer.Wu et al.analyze simple chemical processes by using the temperature-heat flow diagram based on entransy theory.The result shows that the heat recovery system has obvious characteristics of enhancing heat transfer performance.Xia et al.[12,13]proposed an energy target approach of HEN based on the concept of entransy.The entransy transfer efficiency is used to evaluate the entransy transfer of the HEN[14].Therefore,the entransy transfer efficiency can compensate for the weaknesses of pinch design method which cannot calculate the thermal efficiency of the HEN.The reasonable utilization of heat in heat exchange network is analyzed by calculating the quantity of entransy.

Based on “the law of conversation of energy”and “entransy dissipation extremum principle”,the matching principles of HEN are proposed in this work.Moreover,the design method of HEN based on entransy theory will be proposed.

2.Design of HEN Based on Entransy Theory

The entransy of cold and hot streams in the HEN can be used to analyze the heat transfer capability of the streams.Because of the entransy dissipation in heat transfer process,the calculated entransy transfer efficiency can be used to analyze the efficient utilization of entransy in the HEN.With the aim of maximum entransy transfer efficiency,a reasonable HEN structure based on entransy theory is obtained by setting the energy target of the HEN[12].Taking the four-stream HEN as an example,the data of streams are shown in Table 1.The composite curves of cold and hot streams are shown in Fig.1.

According to Fig.1,the cold and hot composite curves are respectively integrated to the Q-axis.As a result,the entransy of hot streams is 1.934×105kW·K,the entransy of cold streams is 1.725×105kW·K,the entransy of hotutility is 2.038×104kW·K,the entransy of cold utility is 2.952×104kW·K,so the entransy recovery is 1.521×105kW·K,the entransy dissipation is 1.176×104kW·K,and the entransy transfer efficiency is 78.65%.

Table 1 The data of streams

Fig.1.The composite curve diagram of four-stream HEN.

When the minimum heat transfer temperature difference(ΔTmin)is 10 K,the T–Q diagram is shown in Fig.2.At this time,the entransy of hot utility is 8.210× 103kW·K,the entransy of cold utility is 1.933×104kW·K,so the entransy recovery is 1.643×105kW·K,the entransy dissipation is 9.725×103kW·K,and the entransy transfer efficiency is 84.98%.Therefore,the energy target of the four-stream HEN is obtained.

Fig.2.The composite curve diagram of four-stream HEN for setting energy target.

According to the irreversibility of heat transfer,the high thermal potential energy streams can only transfer the quantity of entransy into the low thermal potential energy stream.Therefore,the hot and cold composite curves in Fig.3 are divided into two thermodynamically distinct regions.The two regions are the high thermal potential energy region(in the region to the right)and the low thermal potential energy region(in the region to the left).

Fig.3.Dissecting a problem at the entransy point.

As is shown in Fig.3,in the high thermal potential energy region,all hot streams(hot composite curve)have transferred the amount of entransy into the cold streams(cold composite curve).For the cold streams that cannot be heated to the target temperature by the hot streams,additional hot utility requirements(Eh)should be added.Similarly,in the low thermal potential energy region,additional cold utility requirements(Ec)should be added.This gives three rules for the designer wishing to produce a design achieving maximum entransy transfer efficiency:

①The high thermal potential energy region cannot transfer the amount of entransy through the entransy pointinto the low thermal potential energy region.

②Don't use cold utility in the high thermal potential energy region.

③Don't use hot utility in the low thermal potential energy region.

The heat exchanger network(HEN)synthesis based on entransy theory is analyzed.The four matching principles of HEN were proposed,including entransy conservation principle,minimum entransy dissipation principle,minimum heat transfer temperature differences principle,and the thermal potential energy transfer irreversibility principle.

In order to obtain energy targets based on entransy and achieve them with a network of heat exchangers,the above four principles and these steps are as follows.

Step 1:In order to ensure the conservation of entransy of the HEN,the entransy of cold streams plus entransy dissipation in the high thermal potential energy region is equal to the entransy of hot streams minus entransy dissipation in the low thermal potential energy region.

Taking the four-stream HEN as an example,the HEN is divided into two parts from the entransy point temperature of 358 K,as illustrated in Fig.4.

The heat flow rate of hot stream is CP1and the heat flow rate of cold stream is CP2.In the matching process of the temperature range from T1to T2,the relation between hot stream entransy E1and cold stream entransy E2is,

In order to ensure the conservation of entransy of the HEN,the entransy of cold streams in the high thermal potential energy region should plus entransy dissipation.According to the relationship in Eq.(1),the amount of entransy dissipation can be assigned to each cold stream.According to Table 1,the entransy dissipation in the high thermal potential energy region is 6.525×103kW·K.The relationship between the entransy dissipation of cold stream 1 and cold stream 3 is as follows:

Fig.4.Partition of four-stream HEN.

Then,the entransy of cold streams plus entransy dissipation is shown in Table 2.Similarly,the entransy of hot streams in the low thermal potential energy region should minus entransy dissipation.According to Table 1,the entransy dissipation in the low thermal potential energy region is 3.20×103kW·K.The relationship between the entransy dissipation of hot stream 2 and hot stream 4 is as follows:

Then,the entransy of hot streams minus entransy dissipation is shown in Table 3.

Step 2:It is necessary to analyze whether the streams in the high and low thermal potential energy regions violate the irreversibility of thermal potential transfer,that is,whether the number of cold and hot streams meets the requirements.

Table 2 The data of streams of high thermal potential energy region

Table 3 The data of streams of low thermal potential energy region

The streams in the high thermal potential energy region can only transfer the amount of entransy into the low thermal potential energy region,as shown in Fig.3.In the high thermal potential energy region,there is a part of the cold streams which needs to be heated to the target temperature by using additional hot utility.Then the matching process of cold and hot streams that should be satisfied:

where Nhis the number of hot streams or branches in high thermal potential energy region,Ncis the number of cold streams or branches.If the above relationship is not satisfied,the cold stream is required to be split.

Similarly,in the low thermal potential energy region,there is a part of the hot streams which needs to be cooled to the target temperature by using additional cold utility.Then the matching process of cold and hot streams that should be satisfied:

where Nhis the number of hot streams or branches,Ncis the number of cold streams or branches.If the above relationship is not satisfied,the hot stream is required to be split.

As shown in Fig.4,cold and hot streams do not need to be split.But in Fig.5,the cold streams need to be split into two streams.

Step 3:The entransy dissipation of cold and hot streams exists in the heat transfer process.In the matching process,the minimum entransy dissipation and the minimum temperature difference are taken into account.

Fig.5.The high thermal potential energy region matching.

The entransy dissipation during the heat transfer process from the temperature T1to the temperature T2is:

From Eq.(6),we find that the entransy dissipation is related to the heat flow rate CP and the temperature T.The smaller the difference in heat flow rate or temperature between the cold and hot streams,the smaller the entransy dissipation,the higher the entransy transfer efficiency.

In order to reduce the entransy dissipation in high thermal potential energy region,and to meet the irreversibility of entransy transfer,the cold and hot streams should meet:

Similarly,the cold and hot streams in the low thermal potential energy region should meet:

As is known to all,the high temperature of the streams has high quality of heat and high thermal potential.So the hot streams should be selected to match the cold streams whose temperature is as close as possible.According to Table 2,in order to meet Eq.(7)and the minimum temperature difference between the cold and hot streams,the hot stream 2 is matched with the cold stream3 by the heat exchanger1.Then,the remaining entransy of the hot stream 2 continues to match the cold stream 1.The hot stream 4 is matched with the cold stream 3 by the heat exchanger 3,and 8.21×103kW·K of hot utility entransy is added,as shown in Fig.6.

Fig.6.The high thermal potential energy region matching.

According to Table 3,in order to meet Eq.(8)and the minimum temperature difference between the cold and hot streams,the hot stream 2 is matched with the cold stream1 by the heat exchanger4.Then,the hot stream 4 is matched with the cold stream 1 by the heat exchanger5,and 1.933×104kW·K of cold utility entransy is added,as shown in Fig.7.

Fig.7.The low thermal potential energy region matching.

The two parts can be combined together in order to obtain a complete HEN,as shown in Fig.8.The above-mentioned HEN achieves energy targets,as shown in Table 4.

Step 4:In order to meet the requirements of the process,the internal structure of the HEN based on entransy theory can be adjusted.

Fig.8.Synthesis of a four-stream HEN based on entransy theory.

Table 4 Comparison between the synthetic HEN and the energy targets

Table 5 The data of streams for diesel hydrogenation unit

In summary,according to the four specific steps of the design method of HEN based on entransy theory,we can get the HEN structure which is consistent with the energy target.

3.Case Study

Fig.9.The composite curve of diesel hydrogenation unit(ΔT min=10 K).

Table 6 The entransy data of hot streams of high thermal potential energy region

Fig.10.The HEN of high thermal potential energy region.

Diesel hydrogenation technology can reduce the content of sulfur,nitrogen and other impurities in diesel oil.And it can also increase the sixteen alkane value of diesel oil.In order to improve the energy efficiency of the diesel hydrogenation unit and increase the economic efficiency of the enterprise,it is necessary to study the HEN of the diesel hydrogenation unit.The HEN of the unit includes 10 hot steams and 7 cold steams,and the data of streams is shown in Table 5[12].

3.1.Design of HEN based on entransy theory

When the minimum heat transfer temperature difference(ΔTmin)is 10 K,the T–Q diagram is shown in Fig.9.The energy targets of the HENis determined:The entransy of hot streams is 6.762× 107kW·K,the entransy of cold streams is 6.352×107kW·K,the minimum hot utility entransy is 8.543× 106kW·K,the minimum cold utility entransy is 7.428× 106kW·K,the entransy recovery is 5.498× 107kW·K,the entransy dissipation is 5.212×106kW·K,so the entransy transfer efficiency is 92.29%[12].

According to the four steps of the design method of HEN,the HEN of the diesel hydrogenation unit is divided into two parts which start with the entransy point temperature of 391 K.According to step 1,the entransy dissipation in the high thermal potential energy region is 4.953× 106kW·K,the changes of entransy values are shown in Table 6.

Table 7 The entransy data of streams in the low thermal potential energy region

Then,the HEN structure of the high thermal potential energy region in the diesel hydrogenation unit can be obtained,as shown in Fig.10.By matching the cold and hot streams through the data of Table 7,the HEN structure of the low thermal potential energy region can be obtained,as shown in Fig.11.The two parts can be combined together in order to obtain a HEN,as shown in Fig.12.The above-mentioned HEN achieves energy targets,as shown in Table 8.

3.2.Design of HEN based on pinch

Fig.11.The HEN of low thermal potential energy region.

Fig.12.Synthesis of diesel hydrogenation unit HEN based on entransy theory.

Table 8 Comparison between the synthesis HEN and the energy targets for diesel hydrogenation unit

When the minimum heat transfer temperature difference(ΔTmin)is 10 K,the minimum hot utility requirement is 1.421×104kW and the minimum cold utility requirement is 2.173×104kW.The hot utility requirement of the actual diesel hydrogenation unit HEN is 1.933×104kW,and the cold utility requirement is 3.754×104kW.Therefore,when achieving the energy targets,the hot utility requirement can save 26.48%and the cold utility requirement can save 42.13%.

According to the matching criterion of the pinch design method,the HEN of the diesel hydrogenation unit is divided into the two parts,as shown in Figs.13 and 14.Combining the design of above and below the pinch to obtain a maximum energy recovery(MER)network can achieve energy targets,as shown in Fig.15.

Fig.13.Design above the pinch for diesel hydrogenation unit.

Fig.14.Design below the pinch for diesel hydrogenation unit.

3.3.Comparison of the designed method of HEN based on entransy and pinch

The HEN of the diesel hydrogenation unit is respectively designed by the methods based on the entransy and pinch.The minimum heat transfer temperature difference(ΔTmin=10 K)is the same.The cold and hot composition curve is drawn(seen in Fig.9).The energy target of the HEN is obtained.Then the HEN is divided into two parts.The HEN designed by the two methods can achieve the energy targets,as shown in Figs.12 and 15.The cold stream C2 and hot stream H2 are matched in the structure of HEN based on entransy theory,which does not exist in the HEN based on pinch.In addition,the HEN structure obtained in the two methods has the same match between 1 and 6 of the hot streams and 1 to 7 of the cold streams.

The entransy transfer efficiency can be calculated by the ratio of the entransy of cold streams to the entransy of hot streams.The entransy transfer efficiency of the HEN obtained by the entransy design is 92.29%.But the transfer efficiency cannot be calculated if it is based on pinch.In order to further compare the two methods,the calculation methods based on entransy transfer efficiency are used in the MER network.The entransy transfer efficiency which is based on pinch is 91.18%in the MER network.So the energy in the design of HEN based on entransy theory can be better used.

4.Conclusions

Based on the amount of entransy transfer in hot and cold streams,the HEN matching principles based on entransy theory is put forward,and a design method of HEN based on entransy theory is established.The present study shows how it is possible to set energy targets based on entransy and achieve them with a network of heat exchangers by an example of heat exchanger network design for four-stream.For the diesel hydrogenation unit,the design method of HEN based on pinch and entransy is applied respectively.The main conclusions are as follows:

(1)The entransy dissipation exits in the heat transfer process,and the amount of entransy transfer in the HEN was evaluated by the entransy transfer efficiency.The effective utilization of heat in the HEN was further evaluated.Therefore,the concept of entransy can be used to analyze HEN.

Fig.15.MER network for diesel hydrogenation unit.

(2)The heat exchanger network based on entransy theory is consistent with the energy target.For the diesel hydrogenation unit,when the minimum heat transfer temperature difference ΔTminis 10 K,the entransy transfer efficiency is 92.29%.Compared with the MER network by pinch,it is higher for HEN based on entransy theory.

(3)The design method of HEN based on entransy theory not only gets the energy target but also the structure of HEN.Compared with HEN based on pinch,HEN based on entransy theory can directly obtain the entransy dissipation and the entransy transfer efficiency of the HEN.

Nomenclature

Subscripts